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</div><h2>HL Paper 2</h2><div class="specification">
<p class="p1">The graph of \(y = \ln (5x + 10)\) is obtained from the graph of \(y = \ln x\) by a translation of \(a\) units in the direction of the \(x\)-axis followed by a translation of \(b\) units in the direction of the \(y\)-axis.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(a\) and the value of \(b\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The region bounded by the graph of \(y = \ln (5x + 10)\), the \(x\)-axis and the lines \(x = {\text{e}}\) and \(x = 2{\text{e}}\), is rotated through \(2\pi \) radians about the \(x\)-axis. Find the volume generated.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>\(y = \ln (x - a) + b = \ln (5x + 10)\) <strong><em>(M1)</em></strong></p>
<p>\(y = \ln (x - a) + \ln c = \ln (5x + 10)\)</p>
<p>\(y = \ln \left( {c(x - a)} \right) = \ln (5x + 10)\) <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p>\(y = \ln (5x + 10) = \ln \left( {5(x + 2)} \right)\) <strong><em>(M1)</em></strong></p>
<p>\(y = \ln (5) + \ln (x + 2)\) <strong><em>(M1)</em></strong></p>
<p><strong>THEN</strong></p>
<p>\(a = - 2,{\text{ }}b = \ln 5\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept graphical approaches.</p>
<p> </p>
<p><strong>Note:</strong> Accept \(a = 2,{\text{ }}b = 1.61\)</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(V = \pi {\int_e^{2e} {\left[ {\ln (5x + 10)} \right]} ^2}{\text{d}}x\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\( = 99.2\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>Total [6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">Consider \(p(x) = 3{x^3} + ax + 5a,\;\;\;a \in \mathbb{R}\).</p>
<p class="p1">The polynomial \(p(x)\) leaves a remainder of \( - 7\) when divided by \((x - a)\).</p>
<p class="p1">Show that only one value of \(a\) satisfies the above condition and state its value.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>using \(p(a) = - 7\) to obtain \(3{a^3} + {a^2} + 5a + 7 = 0\) <strong><em>M1A1</em></strong></p>
<p>\((a + 1)(3{a^3} - 2a + 7) = 0\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1</em></strong> for a cubic graph with correct shape and <strong><em>A1</em></strong> for clearly showing that the above cubic crosses the horizontal axis at \(( - 1,{\text{ }}0)\) only.</p>
<p> </p>
<p>\(a = - 1\) <strong><em>A1</em></strong></p>
<p><strong>EITHER</strong></p>
<p>showing that \(3{a^2} - 2a + 7 = 0\) has no real (two complex) solutions for \(a\) <strong><em>R1</em></strong></p>
<p><strong>OR</strong></p>
<p>showing that \(3{a^3} + {a^2} + 5a + 7 = 0\) has one real (and two complex) solutions for \(a\) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>R1</em></strong> for solutions that make specific reference to an appropriate graph.</p>
<p> </p>
<p><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>A large number of candidates, either by graphical (mostly) or algebraic or via use of a GDC solver, were able to readily obtain \(a = - 1\). Most candidates who were awarded full marks however, made specific reference to an appropriate graph. Only a small percentage of candidates used the discriminant to justify that only one value of \(a\) satisfied the required condition. A number of candidates erroneously obtained \(3{a^3} + {a^2} + 5a - 7 = 0\) or equivalent rather than \(3{a^3} + {a^2} + 5a + 7 = 0\).</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 \(\int {x{{\sec }^2}x{\text{d}}x} \).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine the value of <em>m</em> if \(\int_0^m {x{{\sec }^2}x{\text{d}}x = 0.5} \), where <em>m</em> > 0.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {x{{\sec }^2}x{\text{d}}x} = x\tan x - \int {1 \times \tan x{\text{d}}x} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = x\tan x + \ln \left| {\cos x} \right|( + c){\text{ }}\left( { = x\tan x - \ln \left| {\sec x} \right|( + c)} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to solve an appropriate equation <em>eg</em> \(m\tan m + \ln (\cos m) = 0.5\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>m</em> = 0.822 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> if </span><em style="font-family: 'times new roman', times; font-size: medium;">m</em><span style="font-family: 'times new roman', times; font-size: medium;"> = 0.822 is specified with other positive solutions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (a), a large number of candidates were able to use integration by parts correctly but were unable to use integration by substitution to then find the indefinite integral of tan <em>x</em>. In part (b), a large number of candidates attempted to solve the equation without direct use of a GDC’s numerical solve command. Some candidates stated more than one solution for <em>m </em>and some specified <em>m </em>correct to two significant figures only.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (a), a large number of candidates were able to use integration by parts correctly but were unable to use integration by substitution to then find the indefinite integral of tan <em>x</em>. In part (b), a large number of candidates attempted to solve the equation without direct use of a GDC’s numerical solve command. Some candidates stated more than one solution for <em>m </em>and some specified <em>m </em>correct to two significant figures only.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>It is given that \(f(x) = 3{x^4} + a{x^3} + b{x^2} - 7x - 4\) where \(a\) and \(b\) are positive integers.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that \({x^2} - 1\) is a factor of \(f(x)\) find the value of \(a\) and the value of \(b\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Factorize \(f(x)\) into a product of linear factors.</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>Sketch the graph of \(y = f(x)\), labelling the maximum and minimum points and the \(x\) and \(y\) intercepts.</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>Using your graph state the range of values of \(c\) for which \(f(x) = c\) has exactly two distinct real roots.</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>\(g(x) = 3{x^4} + a{x^3} + b{x^2} - 7x - 4\)</p>
<p>\(g(1) = 0 \Rightarrow a + b = 8\) <strong><em>M1A1</em></strong></p>
<p>\(g( - 1) = 0 \Rightarrow - a + b = - 6\) <strong><em>A1</em></strong></p>
<p>\( \Rightarrow a = 7,{\text{ }}b = 1\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(3{x^4} + 7{x^3} + {x^2} - 7x - 4 = ({x^2} - 1)(p{x^2} + qx + r)\)</p>
<p>attempt to equate coefficients <strong><em>(M1)</em></strong></p>
<p>\(p = 3,{\text{ }}q = 7,{\text{ }}r = 4\) <strong><em>(A1)</em></strong></p>
<p>\(3{x^4} + 7{x^3} + {x^2} - 7x - 4 = ({x^2} - 1)(3{x^2} + 7x + 4)\)</p>
<p>\( = (x - 1){(x + 1)^2}(3x + 4)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept any equivalent valid method.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-10_om_09.04.14.png" alt="M17/5/MATHL/HP2/ENG/TZ2/11.c/M"></p>
<p><strong><em>A1 </em></strong>for correct shape (<em>ie </em>with correct number of max/min points)</p>
<p><strong><em>A1 </em></strong>for correct \(x\) and \(y\) intercepts</p>
<p><strong><em>A1 </em></strong>for correct maximum and minimum points</p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(c > 0\) <strong><em>A1</em></strong></p>
<p>\( - 6.20 < c < - 0.0366\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for correct end points and <strong><em>A1 </em></strong>for correct inequalities.</p>
<p> </p>
<p><strong>Note:</strong> If the candidate has misdrawn the graph and omitted the first minimum point, the maximum mark that may be awarded is <strong><em>A1FTA0A0 </em></strong>for \(c > - 6.20\) seen.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function \(f(x) = 3\sin x + 4\cos x\) is defined for \(0 < x < 2\pi \) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the coordinates of the minimum point on the graph of <em>f </em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The points \({\text{P}}(p,{\text{ }}3)\) and \({\text{Q}}(q,{\text{ }}3){\text{, }}q > p\), lie on the graph of \(y = f(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find <em>p </em>and <em>q </em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the coordinates of the point, on \(y = f(x)\) , where the gradient of the graph is 3.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the coordinates of the point of intersection of the normals to the graph at the points P and Q.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\((3.79, - 5)\) <span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1 </em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark] </em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(p = 1.57{\text{ or }}\frac{\pi }{2},{\text{ }}q = 6.00\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = 3\cos x - 4\sin x\) <strong><em>(M1)(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(3\cos x - 4\sin x = 3 \Rightarrow x = 4.43...\) <strong><em>(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\((y = -4)\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">Coordinates are \((4.43, -4)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[4 marks]</span><br></em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\({m_{{\text{normal}}}} = \frac{1}{{{m_{{\text{tangent}}}}}}\) <strong><em>(M1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">gradient at P is \( - 4\) so gradient of normal at P is \(\frac{1}{4}\) </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>(A1)</em></strong></p>
<p><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">gradient at Q is 4 so gradient of normal at Q is \( - \frac{1}{4}\) </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>(A1)</em></strong></p>
<p><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">equation of normal at P is \(y - 3 = \frac{1}{4}(x - 1.570...){\text{ }}({\text{or }}y = 0.25x + 2.60...)\) </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>(M1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">equation of normal at Q is \(y - 3 = \frac{1}{4}(x - 5.999...){\text{ }}({\text{or }}y = -0.25x + \underbrace {4.499...}_{})\) <strong><em>(M1)</em></strong></span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">Award the previous two </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>M1 </em></strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">even if the gradients are incorrect in \(y - b = m(x - a)\) where \((a,b)\) are coordinates of P and Q (or in \(y = mx + c\) with </span><em style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">c </em><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">determined using coordinates of P and Q.</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">intersect at \((3.79,{\text{ }}3.55)\) <strong><em>A1A1</em></strong></span> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>N2 </em></strong>for 3.79 without other working.</span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]<br></em></strong></span></p>
<p> </p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates answered parts (a) and (b) of this question well and, although many were also successful in part (c), just a few candidates gave answers to the required level of accuracy. Part d) was rather challenging for many candidates. The most common errors among the candidates who attempted this question were the confusion between tangents and normals and incorrect final answers due to premature rounding.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates answered parts (a) and (b) of this question well and, although many were also successful in part (c), just a few candidates gave answers to the required level of accuracy. Part d) was rather challenging for many candidates. The most common errors among the candidates who attempted this question were the confusion between tangents and normals and incorrect final answers due to premature rounding.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates answered parts (a) and (b) of this question well and, although many were also successful in part (c), just a few candidates gave answers to the required level of accuracy. Part d) was rather challenging for many candidates. The most common errors among the candidates who attempted this question were the confusion between tangents and normals and incorrect final answers due to premature rounding.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates answered parts (a) and (b) of this question well and, although many were also successful in part (c), just a few candidates gave answers to the required level of accuracy. Part d) was rather challenging for many candidates. The most common errors among the candidates who attempted this question were the confusion between tangents and normals and incorrect final answers due to premature rounding.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that the quadratic equation \({x^2} - (5 - k)x - (k + 2) = 0\) has two distinct real roots for all real values of <em>k </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: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\Delta = {(5 - k)^2} + 4(k + 2)\) <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;">\( = {k^2} - 6k + 33\) <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;">\( = {(k - 3)^2} + 24\) which is positive for all <em>k </em> </span><span style="font-family: 'times new roman', times; font-size: medium;"><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;"><strong>Note: </strong>Accept analytical, graphical or other correct methods. In all cases only award <strong><em>R1 </em></strong>if a reason is given in words or graphically. Award <strong><em>M1A1A0R1 </em></strong>if mistakes </span><span style="font-family: 'times new roman', times; font-size: medium;">are made in the simplification but <span style="text-decoration: underline;">the argument given is correct.</span></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;"> </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>
<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;">Overall the question was pretty well answered but some candidates seemed to have mixed up the terms determinant with discriminant. In some cases a lack of quality mathematical reasoning and understanding of the discriminant was evident. Many worked with the quadratic formula rather than just the discriminant, conveying a lack of understanding of the strategy required. Errors in algebraic simplification (expanding terms involving negative signs) prevented many candidates from scoring well in this question. Many candidates were not able to give a clear reason why the quadratic has always two distinct real solutions; in some cases a vague explanation was given, often referring to a graph which was not sketched.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Express \({x^2} + 4x - 2\) <span class="s1">in the form \({(x + a)^2} + b\) </span>where \(a,{\text{ }}b \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">If \(f(x) = x + 2\) </span>and \((g \circ f)(x) = {x^2} + 4x - 2\) <span class="s1">write down \(g(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\({(x + 2)^2} - 6\) </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p2"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\((g \circ f)(x) = {(x + 2)^2} - 6\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\( \Rightarrow g(x) = {x^2} - 6\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><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">Well done by most candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Well done by most candidates. Those students who lost marks on this question tended to do so in part (b), seemingly through misinterpreting the question.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following graph represents a function \(y = f(x)\)<span class="s1">, where \( - 3 \le x \le 5\).</span></p>
<p class="p2">The function has a maximum at \((3,{\text{ }}1)\) and a minimum at \(( - 1,{\text{ }} - 1)\).</p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-29_om_14.45.13.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The functions \(u\) and \(v\) are defined as \(u(x) = x - 3,{\text{ }}v(x) = 2x\) where \(x \in \mathbb{R}\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>State the range of the function \(u \circ f\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>State the range of the function \(u \circ v \circ f\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Find the largest possible domain of the function \(f \circ v \circ u\).</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>Explain why \(f\) does not have an inverse.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>The domain of \(f\) is restricted to define a function \(g\) so that it has an inverse \({g^{ - 1}}\).</p>
<p class="p1">State the largest possible domain of \(g\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Sketch a graph of \(y = {g^{ - 1}}(x)\), showing clearly the <span class="s1">\(y\)</span>-intercept and stating the coordinates of the endpoints.</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>Consider the function defined by \(h(x) = \frac{{2x - 5}}{{x + d}}\), \(x \ne - d\) and \(d \in \mathbb{R}\).</p>
<p>(i) Find an expression for the inverse function \({h^{ - 1}}(x)\).</p>
<p>(ii) Find the value of \(d\) such that \(h\) is a self-inverse function.</p>
<p>For this value of \(d\), there is a function \(k\) such that \(h \circ k(x) = \frac{{2x}}{{x + 1}},{\text{ }}x \ne - 1\).</p>
<p>(iii) Find \(k(x)\).</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>Note: </strong>For Q12(a) (i) – (iii) and (b) (ii), award <strong><em>A1 </em></strong>for correct endpoints and, if correct, award <strong><em>A1 </em></strong>for a closed interval.</p>
<p>Further, award <strong><em>A1A0 </em></strong>for one correct endpoint and a closed interval.</p>
<p> </p>
<p>(i) \( - 4 \le y \le - 2\) <strong><em>A1A1</em></strong></p>
<p>(ii) \( - 5 \le y \le - 1\) <strong><em>A1A1</em></strong></p>
<p>(iii) \( - 3 \le 2x - 6 \le 5\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for \(f(2x - 6)\).</p>
<p> </p>
<p>\(3 \le 2x \le 11\)</p>
<p>\(\frac{3}{2} \le x \le \frac{{11}}{2}\) <strong><em>A1A1</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 class="p1">(i) <span class="Apple-converted-space"> </span>any valid argument <em>eg</em> \(f\) is not one to one, \(f\) is many to one, fails horizontal line test, not injective <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>largest domain for the function \(g(x)\) to have an inverse is \([ - 1,{\text{ }}3]\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1">(iii) <span class="Apple-converted-space"> <img src="images/Schermafbeelding_2016-01-29_om_15.23.38.png" alt></span></p>
<p class="p1"><span class="s1">\(y\)</span>-intercept indicated (coordinates not required) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">correct shape <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">coordinates of end points \((1,{\text{ }}3)\) and \(( - 1,{\text{ }} - 1)\) <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>Do not award any of the above marks for a graph that is not one to one.</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>(i) \(y = \frac{{2x - 5}}{{x + d}}\)</p>
<p>\((x + d)y = 2x - 5\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for attempting to rearrange \(x\) and \(y\) in a linear expression.</p>
<p> </p>
<p>\(x(y - 2) = - dy - 5\) <strong><em>(A1)</em></strong></p>
<p>\(x = \frac{{ - dy - 5}}{{y - 2}}\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> \(x\) and \(y\) can be interchanged at any stage</p>
<p> </p>
<p>\({h^{ - 1}}(x) = \frac{{ - dx - 5}}{{x - 2}}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A1 </em></strong>only if \({h^{ - 1}}(x)\) is seen.</p>
<p> </p>
<p>(ii) self Inverse \( \Rightarrow h(x) = {h^{ - 1}}(x)\)</p>
<p>\(\frac{{2x - 5}}{{x + d}} \equiv \frac{{ - dx - 5}}{{x - 2}}\) <strong><em>(M1)</em></strong></p>
<p>\(d = - 2\) <strong><em>A1</em></strong></p>
<p>(iii) <strong>METHOD 1</strong></p>
<p>\(\frac{{2k(x) - 5}}{{k(x) - 2}} = \frac{{2x}}{{x + 1}}\) <strong><em>(M1)</em></strong></p>
<p>\(k(x) = \frac{{x + 5}}{2}\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\({h^{ - 1}}\left( {\frac{{2x}}{{x + 1}}} \right) = \frac{{2\left( {\frac{{2x}}{{x + 1}}} \right) - 5}}{{\frac{{2x}}{{x + 1}} - 2}}\) <strong><em>(M1)</em></strong></p>
<p>\(k(x) = \frac{{x + 5}}{2}\) <strong><em>A1</em></strong></p>
<p><strong><em>[8 marks]</em></strong></p>
<p><strong><em>Total [21 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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> has inverse \({f^{ - 1}}\) and derivative \(f'(x)\) for all \(x \in \mathbb{R}\). For all functions with these properties you are given the result that for \(a \in \mathbb{R}\) with \(b = f(a)\) and \(f'(a) \ne 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[({f^{ - 1}})'(b) = \frac{1}{{f'(a)}}.\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Verify that this is true for \(f(x) = {x^3} + 1\) at <em>x</em> = 2.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(g(x) = x{{\text{e}}^{{x^2}}}\), show that \(g'(x) > 0\) for all values of <em>x</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the result given at the start of the question, find the value of the gradient function of \(y = {g^{ - 1}}(x)\) at <em>x</em> = 2.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) With <em>f</em> and <em>g</em> as defined in parts (a) and (b), solve \(g \circ f(x) = 2\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Let \(h(x) = {(g \circ f)^{ - 1}}(x)\). Find \(h'(2)\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(2) = 9\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}(x) = {(x - 1)^{\frac{1}{3}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(({f^{ - 1}})'(x) = \frac{1}{3}{(x - 1)^{ - \frac{2}{3}}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(({f^{ - 1}})'(9) = \frac{1}{{12}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = 3{x^2}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{{f'(2)}} = \frac{1}{{3 \times 4}} = \frac{1}{{12}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> The last </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> are independent of previous marks.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g'(x) = {{\text{e}}^{{x^2}}} + 2{x^2}{{\text{e}}^{{x^2}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g'(x) > 0\) as each part is positive <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">to find the <em>x</em>-coordinate on \(y = g(x)\) solve</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2 = x{{\text{e}}^{{x^2}}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 0.89605022078 \ldots \) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">gradient \( = ({g^{ - 1}})'(2) = \frac{1}{{g'(0.896 \ldots )}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{{{\text{e}}^{{{(0.896 \ldots )}^2}}}\left( {1 + 2 \times {{(0.896 \ldots )}^2}} \right)}} = 0.172\) to 3sf <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(using the \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) function on gdc \(g'(0.896 \ldots ) = 5.7716028 \ldots \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{{g'(0.896 \ldots )}} = 0.173\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(({x^3} + 1){{\text{e}}^{{{({x^3} + 1)}^2}}} = 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = - 0.470191 \ldots \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((g \circ f)'(x) = 3{x^2}{{\text{e}}^{{{({x^3} + 1)}^2}}}\left( {2{{({x^3} + 1)}^2} + 1} \right)\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((g \circ f)'( - 0.470191 \ldots ) = 3.85755 \ldots \) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(h'(2) = \frac{1}{{3.85755 \ldots }} = 0.259{\text{ }}(232 \ldots )\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> The solution can be found without the student obtaining the explicit form of the composite function.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 2</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(h(x) = ({f^{ - 1}} \circ {g^{ - 1}})(x)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(h'(x) = ({f^{ - 1}})'\left( {{g^{ - 1}}(x)} \right) \times ({g^{ - 1}})'(x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3}{\left( {{g^{ - 1}}(x) - 1} \right)^{ - \frac{2}{3}}} \times ({g^{ - 1}})'(x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(h'(2) = \frac{1}{3}{\left( {{g^{ - 1}}(2) - 1} \right)^{ - \frac{2}{3}}} \times ({g^{ - 1}})'(2)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3}{(0.89605 \ldots - 1)^{ - \frac{2}{3}}} \times 0.171933 \ldots \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.259{\text{ }}(232 \ldots )\) <strong><em>A1 N4</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There were many good attempts at parts (a) and (b), although in (b) many were unable to give a thorough justification.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There were many good attempts at parts (a) and (b), although in (b) many were unable to give a thorough justification.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Few good solutions to parts (c) and (d)(ii) were seen although many were able to answer (d)(i) correctly.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Few good solutions to parts (c) and (d)(ii) were seen although many were able to answer (d)(i) correctly.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = x{(x + 2)^6}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Solve the inequality \(f(x) > x\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(\int {f(x){\text{d}}x} \).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">sketch showing where the lines cross or zeros of \(y = x{(x + 2)^6} - x\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 0\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = - 1\) and \(x = - 3\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the solution is \( - 3 < x < - 1\) or \(x > 0\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award either final <strong><em>A1 </em></strong>mark if strict inequalities are not given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">separating into two cases \(x > 0\) and \(x < 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">if \(x > 0\) then \({(x + 2)^6} > 1 \Rightarrow \) always true <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">if \(x < 0\) then \({(x + 2)^6} < 1 \Rightarrow - 3 < x < - 1\) <em><strong>(M1)</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">so the solution is \( - 3 < x < - 1\) or \(x > 0\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award either final <strong><em>A1 </em></strong>mark if strict inequalities are not given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = {x^7} + 12{x^6} + 60{x^5} + 160{x^4} + 240{x^3} + 192{x^2} + 64x\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solutions to \({x^7} + 12{x^6} + 60{x^5} + 160{x^4} + 240{x^3} + 192{x^2} + 63x = 0\) are <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 0,{\text{ }}x = - 1\) and \(x = - 3\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so the solution is \( - 3 < x < - 1\) or \(x > 0\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award either final <strong><em>A1 </em></strong>mark if strict inequalities are not given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 4</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = x\) when \(x{(x + 2)^6} = x\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">either \(x = 0\) or \({(x + 2)^6} = 1\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">if \({(x + 2)^6} = 1\) then \(x + 2 = \pm 1\) so \(x = - 1\) or \(x = - 3\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the solution is \( - 3 < x < - 1\) or \(x > 0\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award either final <strong><em>A1 </em></strong>mark if strict inequalities are not given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1 </strong>(by substitution)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">substituting \(u = x + 2\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{d}}u = {\text{d}}x\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {(u - 2){u^6}{\text{d}}u} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{8}{u^8} - \frac{2}{7}{u^7}( + c)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{8}{(x + 2)^8} - \frac{2}{7}{(x + 2)^7}( + c)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2 </strong>(by parts)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(u = x \Rightarrow \frac{{{\text{d}}u}}{{{\text{d}}x}} = 1,{\text{ }}\frac{{{\text{d}}v}}{{{\text{d}}x}} = {(x + 2)^6} \Rightarrow v = \frac{1}{7}{(x + 2)^7}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {x{{(x + 2)}^6}{\text{d}}x = \frac{1}{7}x{{(x + 2)}^7} - \frac{1}{7}\int {{{(x + 2)}^7}{\text{d}}x} } \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{7}x{(x + 2)^7} - \frac{1}{{56}}{(x + 2)^8}( + c)\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3 </strong>(by expansion)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {f(x){\text{d}}x = \int {\left( {{x^7} + 12{x^6} + 60{x^5} + 160{x^4} + 240{x^3} + 192{x^2} + 64x} \right){\text{d}}x} } \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{8}{x^8} + \frac{{12}}{7}{x^7} + 10{x^6} + 32{x^5} + 60{x^4} + 64{x^3} + 32{x^2}( + c)\) <strong><em>M1A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1A1 </em></strong>if at least four terms are correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="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;">One root of the equation \({x^2} + ax + b = 0\) is \(2 + 3{\text{i}}\) where \(a,{\text{ }}b \in \mathbb{R}\). Find the value of \(a\) and the value of \(b\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">substituting</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;">\( - 5 + 12{\text{i}} + a(2 + 3{\text{i}}) + b = 0\) <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;">equating real or imaginary parts <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;">\(12 + 3a = 0 \Rightarrow a = - 4\) <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;">\( - 5 + 2a + b = 0 \Rightarrow b = 13\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">other root is \(2 - 3{\text{i}}\) <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;">considering either the sum or product of roots or multiplying factors <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;">\(4 = - a\) (sum of roots) so \(a = - 4\) <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;">\(13 = b\) (product of roots) <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">
[N/A]
</div>
<br><hr><br><div class="question">
<p>The polynomial \({x^4} + p{x^3} + q{x^2} + rx + 6\) is exactly divisible by each of \(\left( {x - 1} \right)\), \(\left( {x - 2} \right)\) and \(\left( {x - 3} \right)\).</p>
<p>Find the values of \(p\), \(q\) and \(r\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1</strong></p>
<p>substitute each of \(x\) = 1,2 and 3 into the quartic and equate to zero <em><strong>(M1)</strong></em></p>
<p>\(p + q + r = - 7\)</p>
<p>\(4p + 2q + r = - 11\) or equivalent <em><strong> (A2)</strong></em></p>
<p>\(9p + 3q + r = - 29\)</p>
<p><strong>Note:</strong> Award <em><strong>A2</strong> </em>for all three equations correct, <em><strong>A1</strong> </em>for two correct.</p>
<p>attempting to solve the system of equations <em><strong>(M1)</strong></em></p>
<p>\(p\) = −7, \(q\) = 17, \(r\) = −17 <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Only award <em><strong>M1</strong></em> when some numerical values are found when solving algebraically or using GDC.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempt to find fourth factor <em><strong> (M1)</strong></em></p>
<p>\(\left( {x - 1} \right)\) <em><strong>A1</strong></em></p>
<p>attempt to expand \({\left( {x - 1} \right)^2}\left( {x - 2} \right)\left( {x - 3} \right)\) <em><strong>M1</strong></em></p>
<p>\({x^4} - 7{x^3} + 17{x^2} - 17x + 6\) (\(p\) = −7, \(q\) = 17, \(r\) = −17) <em><strong>A2</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A2</strong> </em>for all three values correct, <em><strong>A1</strong> </em>for two correct.</p>
<p><strong>Note:</strong> Accept long / synthetic division.</p>
<p><em><strong>[5 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">
<p class="p1">A function \(f\) is defined by \(f(x) = {x^3} + {{\text{e}}^x} + 1,{\text{ }}x \in \mathbb{R}\). By considering \(f'(x)\) determine whether \(f\) is a one-to-one or a many-to-one function.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">\(f'(x) = 3{x^2} + {{\text{e}}^x}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Accept labelled diagram showing the graph \(y = f'(x)\) above the <span class="s2"><em>x</em></span>-axis;</p>
<p class="p3">do not accept unlabelled graphs nor graph of \(y = f(x)\).</p>
<p class="p2"> </p>
<p class="p3"><strong>EITHER</strong></p>
<p class="p1">this is always \( > 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>R1</em></strong></span></p>
<p class="p3">so the function is (strictly) increasing <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p3">and thus \(1 - 1\) <span class="Apple-converted-space"> </span><span class="s3"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">this is always \( > 0\;\;\;{\text{(accept }} \ne 0{\text{)}}\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">so there are no turning points <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p3"><span class="s3">and thus </span>\(1 - 1\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong> is dependent on the first <strong><em>R1</em></strong>.</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[4 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">The differentiation was normally completed correctly, but then a large number did not realise what was required to determine the type of the original function. Most candidates scored 1/4 and wrote explanations that showed little or no understanding of the relation between first derivative and the given function. For example, it was common to see comments about horizontal and vertical line tests but applied to the incorrect function.In term of mathematical language, it was noted that candidates used many terms incorrectly showing no knowledge of the meaning of terms like ‘parabola’, ‘even’ or ‘odd’ ( or no idea about these concepts).</p>
</div>
<br><hr><br><div class="specification">
<p>When carpet is manufactured, small faults occur at random. The number of faults in Premium carpets can be modelled by a Poisson distribution with mean 0.5 faults per 20\(\,\)m<sup>2</sup>. Mr Jones chooses Premium carpets to replace the carpets in his office building. The office building has 10 rooms, each with the area of 80\(\,\)m<sup>2</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the carpet laid in the first room has fewer than three faults.</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 probability that exactly seven rooms will have fewer than three faults in the carpet.</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>\(\lambda = 4 \times 0.5\) <strong><em>(M1)</em></strong></p>
<p>\(\lambda = 2\) <strong><em>(A1)</em></strong></p>
<p>\({\text{P}}(X \leqslant 2) = 0.677\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(Y \sim B(10,{\text{ }}0,677)\) <strong><em>(M1)(A1)</em></strong></p>
<p>\({\text{P}}(Y = 7) = 0.263\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1 </em></strong>for clear recognition of binomial distribution.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Sketch the graph of \(y = {(x - 5)^2} - 2\left| {x - 5} \right| - 9,{\text{ for }}0 \le x \le 10\).</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, or otherwise, solve the equation \({(x - 5)^2} - 2\left| {x - 5} \right| - 9 = 0\).</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"><img src="images/Schermafbeelding_2016-01-06_om_14.19.20.png" alt></p>
<p class="p2">general shape including <span class="s1">\[(\) </span>minimums, cusp <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2">correct domain and symmetrical about the middle \((x = 5)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(x = 9.16\;\;\;{\text{or}}\;\;\;x = 0.838\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>Total [5 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The probability density function of a continuous random variable \(X\) is given by</p>
<p>\[f(x) = \left\{ {\begin{array}{*{20}{c}} {0,{\text{ }}x < 0} \\ {\frac{{\sin x}}{4},{\text{ }}0 \le x \le \pi } \\ {a(x - \pi ),{\text{ }}\pi < x \le 2\pi } \\ {0,{\text{ }}2\pi < x} \end{array}.} \right.\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Sketch the graph \(y = f(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \({\text{P}}(X \le \pi )\).</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">Show that \(a = \frac{1}{{{\pi ^2}}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the median of \(X\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the mean of \(X\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the variance of \(X\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \({\text{P}}\left( {\frac{\pi }{2} \le X \le \frac{{3\pi }}{2}} \right)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that \(\frac{\pi }{2} \le X \le \frac{{3\pi }}{2}\) find the probability that \(\pi \le X \le 2\pi \).</p>
<div class="marks">[4]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="images/Schermafbeelding_2016-01-06_om_08.40.33.png" alt></p>
<p class="p2">Award <strong><em>A1</em></strong> for sine curve from \(0\) to \(\pi \), award <strong><em>A1</em></strong> for straight line from \(\pi \) to \(2\pi \) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\int_0^\pi {\frac{{\sin x}}{4}{\text{d}}x = \frac{1}{2}} \) <strong><em>(M1)A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>require \(\frac{1}{2} + \int_\pi ^{2\pi } {a(x - \pi ){\text{d}}x = 1} \) <strong><em>(M1)</em></strong></p>
<p>\( \Rightarrow \frac{1}{2} + a\left[ {\frac{{{{(x - \pi )}^2}}}{2}} \right]_\pi ^{2\pi } = 1\;\;\;\left( {{\text{or }}\frac{1}{2} + a\left[ {\frac{{{x^2}}}{2} - \pi x} \right]_\pi ^{2\pi } = 1} \right)\) <strong><em>A1</em></strong></p>
<p>\( \Rightarrow a\frac{{{\pi ^2}}}{2} = \frac{1}{2}\) <strong><em>A1</em></strong></p>
<p>\( \Rightarrow a = \frac{1}{{{\pi ^2}}}\) <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Must obtain the exact value. Do not accept answers obtained with calculator.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(0.5 + {\text{ area of triangle }} = 1\) <strong><em>R1</em></strong></p>
<p>area of triangle \( = \frac{1}{2}\pi \times a\pi = 0.5\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for correct use of area formula \( = 0.5\), <strong><em>A1</em></strong> for \(a\pi \).</p>
<p> </p>
<p>\(a = \frac{1}{{{\pi ^2}}}\) <strong><em>AG</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">median is \(\pi \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\mu = \int_0^\pi {x \cdot \frac{{\sin x}}{4}{\text{d}}x + \int_\pi ^{2\pi } {x \cdot \frac{{x - \pi }}{{{\pi ^2}}}{\text{d}}x} } \) <strong><em>(M1)(A1)</em></strong></p>
<p>\( = 3.40339 \ldots = 3.40\;\;\;\left( {{\text{or }}\frac{\pi }{4} + \frac{{5\pi }}{6} = \frac{{13}}{{12}}\pi } \right)\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<p> </p>
<p> </p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>For \(\mu = 3.40339 \ldots \)</p>
<p><strong>EITHER</strong></p>
<p>\({\sigma ^2} = \int_0^\pi {{x^2} \cdot \frac{{\sin x}}{4}{\text{d}}x + \int_\pi ^{2\pi } {{x^2} \cdot \frac{{x - \pi }}{{{\pi ^2}}}{\text{d}}x - {\mu ^2}} } \) <strong><em>(M1)(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>\({\sigma ^2} = \int_0^\pi {{{(x - \mu )}^2} \cdot \frac{{\sin x}}{4}{\text{d}}x + \int_\pi ^{2\pi } {{{(x - \mu )}^2} \cdot \frac{{x - \pi }}{{{\pi ^2}}}{\text{d}}x} } \) <strong><em>(M1)(A1)</em></strong></p>
<p><strong>THEN</strong></p>
<p>\( = 3.866277 \ldots = 3.87\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\int_{\frac{\pi }{2}}^\pi {\frac{{\sin x}}{4}{\text{d}}x + \int_\pi ^{\frac{{3\pi }}{2}} {\frac{{x - \pi }}{{{\pi ^2}}}{\text{d}}x = 0.375\;\;\;\left( {{\text{or }}\frac{1}{4} + \frac{1}{8} = \frac{3}{8}} \right)} } \) <strong><em>(M1)A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{P}}\left( {\pi \le X \le 2\pi \left| {\frac{\pi }{2} \le X \le \frac{{3\pi }}{2}} \right.} \right) = \frac{{{\text{P}}\left( {\pi \le X \le \frac{{3\pi }}{2}} \right)}}{{{\text{P}}\left( {\frac{\pi }{2} \le X \le \frac{{3\pi }}{2}} \right)}}\) <strong><em>(M1)(A1)</em></strong></p>
<p>\( = \frac{{\int_\pi ^{\frac{{3\pi }}{2}} {\frac{{(x - \pi )}}{{{\pi ^2}}}{\text{d}}x} }}{{0.375}} = \frac{{0.125}}{{0.375}}\;\;\;\left( {{\text{or }} = \frac{{\frac{1}{8}}}{{\frac{3}{8}}}{\text{ from diagram areas}}} \right)\) <strong><em>(M1)</em></strong></p>
<p>\( = \frac{1}{3}\;\;\;(0.333)\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<p><strong><em>Total [20 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates sketched the graph correctly. In a few cases candidates did not seem familiar with the shape of the graphs and ignored the fact that the graph represented a pdf. The correct sketch assisted greatly in the rest of the question.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates answered this question correctly.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">A few good proofs were seen but also many poor answers where the candidates assumed what you were trying to prove and verified numerically the result.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates stated the value correctly but many others showed no understanding of the concept.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates scored full marks in this question; many others could not apply the formula due to difficulties in dealing with the piecewise function. For example, a number of candidates divided the final answer by two.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many misconceptions were identified: use of incorrect formula (e.g. formula for discrete distributions), use of both expressions as integrand and division of the result by 2 at the end.</p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This part was fairly well done with many candidates achieving full marks.</p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates had difficulties with this part showing that the concept of conditional probability was poorly understood. The best candidates did it correctly from the sketch.</p>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The vertical cross-section of a container is shown in the following diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-10_om_11.45.14.png" alt></p>
<p class="p1">The curved sides of the cross-section are given by the equation \(y = 0.25{x^2} - 16\). The horizontal cross-sections are circular. The depth of the container is \(48\) cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">If the container is filled with water to a depth of \(h\,{\text{cm}}\), show that the volume, \(V\,{\text{c}}{{\text{m}}^3}\), of the water is given by \(V = 4\pi \left( {\frac{{{h^2}}}{2} + 16h} \right)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The container, initially full of water, begins leaking from a small hole at a rate given by \(\frac{{{\text{d}}V}}{{{\text{d}}t}} =<span class="Apple-converted-space"> </span>- \frac{{250\sqrt h }}{{\pi(h + 16)}}\) where <em>\(t\) </em>is measured in seconds.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Show that \(\frac{{{\text{d}}h}}{{{\text{d}}t}} =<span class="Apple-converted-space"> </span>- \frac{{250\sqrt h }}{{4{\pi ^2}{{(h + 16)}^2}}}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>State \(\frac{{{\text{d}}t}}{{{\text{d}}h}}\) and hence show that \(t = \frac{{ - 4{\pi ^2}}}{{250}}\int {\left( {{h^{\frac{3}{2}}} + 32{h^{\frac{1}{2}}} + 256{h^{ - \frac{1}{2}}}} \right){\text{d}}h} \).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Find, correct to the nearest minute, the time taken for the container to become empty. (\(60\) seconds = 1 minute)</p>
<div class="marks">[10]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Once empty, water is pumped back into the container at a rate of \(8.5\;{\text{c}}{{\text{m}}^3}{{\text{s}}^{ - 1}}\). At the same time, water continues leaking from the container at a rate of \(\frac{{250\sqrt h }}{{\pi (h + 16)}}{\text{c}}{{\text{m}}^3}{{\text{s}}^{ - 1}}\).</p>
<p class="p1">Using an appropriate sketch graph, determine the depth at which the water ultimately stabilizes in the container.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempting to use \(V = \pi \int_a^b {{x^2}{\text{d}}y} \) <span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">attempting to express \({x^2}\) in terms of <em>\(y\) ie</em> \({x^2} = 4(y + 16)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">for \(y = h,{\text{ }}V = 4\pi \int_0^h {y + 16{\text{d}}y} \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(V = 4\pi \left( {\frac{{{h^2}}}{2} + 16h} \right)\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <strong>METHOD 1</strong></p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{{{\text{d}}h}}{{{\text{d}}V}} \times \frac{{{\text{d}}V}}{{{\text{d}}t}}\) <strong><em>(M1)</em></strong></p>
<p>\(\frac{{{\text{d}}V}}{{{\text{d}}h}} = 4\pi (h + 16)\) <strong><em>(A1)</em></strong></p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{1}{{4\pi (h + 16)}} \times \frac{{ - 250\sqrt h }}{{\pi (h + 16)}}\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for substitution into \(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{{{\text{d}}h}}{{{\text{d}}V}} \times \frac{{{\text{d}}V}}{{{\text{d}}t}}\).</p>
<p> </p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{{250\sqrt h }}{{4{\pi ^2}{{(h + 16)}^2}}}\) <strong><em>AG</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 4\pi (h + 16)\frac{{{\text{d}}h}}{{{\text{d}}t}}\;\;\;\)(implicit differentiation)<strong><em>(M1)</em></strong></p>
<p>\(\frac{{ - 250\sqrt h }}{{\pi (h + 16)}} = 4\pi (h + 16)\frac{{{\text{d}}h}}{{{\text{d}}t}}\;\;\;\)(or equivalent) <strong><em>A1</em></strong></p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{1}{{4\pi (h + 16)}} \times \frac{{ - 250\sqrt h }}{{\pi (h + 16)}}\) <strong><em>M1A1</em></strong></p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{{250\sqrt h }}{{4{\pi ^2}{{(h + 16)}^2}}}\) <strong><em>AG</em></strong></p>
<p>(ii) \(\frac{{{\text{d}}t}}{{{\text{d}}h}} = - \frac{{4{\pi ^2}{{(h + 16)}^2}}}{{250\sqrt h }}\) <strong><em>A1</em></strong></p>
<p>\(t = \int { - \frac{{4{\pi ^2}{{(h + 16)}^2}}}{{250\sqrt h }}} {\text{d}}h\) <strong><em>(M1)</em></strong></p>
<p>\(t = \int { - \frac{{4{\pi ^2}({h^2} + 32h + 256)}}{{250\sqrt h }}} {\text{d}}h\) <strong><em>A1</em></strong></p>
<p>\(t = \frac{{ - 4{\pi ^2}}}{{250}}\int {\left( {{h^{\frac{3}{2}}} + 32{h^{\frac{1}{2}}} + 256{h^{ - \frac{1}{{2}}}}} \right){\text{d}}h} \) <strong><em>AG</em></strong></p>
<p>(iii) <strong>METHOD 1</strong></p>
<p>\(t = \frac{{ - 4{\pi ^2}}}{{250}}\int_{48}^0 {\left( {{h^{\frac{3}{2}}} + 32{h^{\frac{1}{2}}} + 256{h^{ - \frac{1}{2}}}} \right)} {\text{d}}h\) <strong><em>(M1)</em></strong></p>
<p>\(t = 2688.756 \ldots {\text{ (s)}}\) <strong><em>(A1)</em></strong></p>
<p>\(45\) minutes (correct to the nearest minute) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(t = \frac{{ - 4{\pi ^2}}}{{250}}\left( {\frac{2}{5}{h^{\frac{5}{2}}} + \frac{{64}}{3}{h^{\frac{3}{2}}} + 512{h^{\frac{1}{2}}}} \right) + c\)</p>
<p>when \(t = 0,{\text{ }}h = 48 \Rightarrow c = 2688.756 \ldots \left( {c = \frac{{4{\pi ^2}}}{{250}}\left( {\frac{2}{5} \times {{48}^{\frac{5}{2}}} + \frac{{64}}{3} \times {{48}^{\frac{3}{2}}} + 512 \times {{48}^{\frac{1}{2}}}} \right)} \right)\) <strong><em>(M1)</em></strong></p>
<p>when \(h = 0,{\text{ }}t = 2688.756 \ldots \left( {t = \frac{{4{\pi ^2}}}{{250}}\left( {\frac{2}{5} \times {{48}^{\frac{5}{2}}} + \frac{{64}}{3} \times {{48}^{\frac{3}{2}}} + 512 \times {{48}^{\frac{1}{2}}}} \right)} \right){\text{ (s)}}\) <strong><em>(A1)</em></strong></p>
<p>45 minutes (correct to the nearest minute) <strong><em>A1</em></strong></p>
<p><strong><em>[10 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p1">the depth stabilizes when \(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 0\;\;\;ie\;\;\;8.5 - \frac{{250\sqrt h }}{{\pi (h + 16)}} = 0\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">attempting to solve \(8.5 - \frac{{250\sqrt h }}{{\pi (h + 16)}} = 0\;\;\;{\text{for }}h\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">the depth stabilizes when \(\frac{{{\text{d}}h}}{{{\text{d}}t}} = 0\;\;\;ie\;\;\;\frac{1}{{4\pi (h + 16)}}\left( {8.5 - \frac{{250\sqrt h }}{{\pi (h + 16)}}} \right) = 0\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">attempting to solve \(\frac{1}{{4\pi (h + 16)}}\left( {8.5 - \frac{{250\sqrt h }}{{\pi (h + 16)}}} \right) = 0\;\;\;{\text{for }}h\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p1">\(h = 5.06{\text{ (cm)}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<p class="p1"><strong><em>Total [16 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was done reasonably well by a large proportion of candidates. Many candidates however were unable to show the required result in part (a). A number of candidates seemingly did not realize how the container was formed while other candidates attempted to fudge the result.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (b) was quite well done. In part (b) (i), most candidates were able to correctly calculate \(\frac{{{\text{d}}V}}{{{\text{d}}h}}\) and correctly apply a related rates expression to show the given result. Some candidates however made a sign error when stating \(\frac{{{\text{d}}V}}{{{\text{d}}t}}\). A large number of candidates successfully answered part (b) (ii). In part (b) (iii), successful candidates either set up and calculated an appropriate definite integral or antidifferentiated and found that \(t = C\) when \(h = 0\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (c), a pleasing number of candidates realized that the water depth stabilized when either \(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 0\) or \(\frac{{{\text{d}}h}}{{{\text{d}}t}} = 0\), sketched an appropriate graph and found the correct value of \(h\). Some candidates misinterpreted the situation and attempted to find the coordinates of the local minimum of their graph.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The seventh, third and first terms of an arithmetic sequence form the first three terms of a geometric sequence.</p>
<p class="p1">The arithmetic sequence has first term <em>\(a\) </em>and non-zero common difference <em>\(d\)</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(d = \frac{a}{2}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The seventh term of the arithmetic sequence is \(3\). The sum of the first \(n\) terms in the arithmetic sequence exceeds the sum of the first <em>\(n\) </em>terms in the geometric sequence by at least \(200\).</p>
<p class="p1">Find the least value of <em>\(n\) </em>for which this occurs.</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>using \(r = \frac{{{u_2}}}{{{u_1}}} = \frac{{{u_3}}}{{{u_2}}}\) to form \(\frac{{a + 2d}}{{a + 6d}} = \frac{a}{{a + 2d}}\) <strong><em>(M1)</em></strong></p>
<p>\(a(a + 6d) = {(a + 2d)^2}\) <strong><em>A1</em></strong></p>
<p>\(2d(2d - a) = 0\;\;\;\)(or equivalent) <strong><em>A1</em></strong></p>
<p>since \(d \ne 0 \Rightarrow d = \frac{a}{2}\) <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">substituting \(d = \frac{a}{2}\) into \(a + 6d = 3\) and solving for \(a\) and \(d\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\(a = \frac{3}{4}\) and \(d = \frac{3}{8}\) <span class="Apple-converted-space"> </span><span class="s1"><em>(</em><strong><em>A1)</em></strong></span></p>
<p class="p1">\(r = \frac{1}{2}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(\frac{n}{2}\left( {2 \times \frac{3}{4} + (n - 1)\frac{3}{8}} \right) - \frac{{3\left( {1 - {{\left( {\frac{1}{2}} \right)}^n}} \right)}}{{1 - \frac{1}{2}}} \ge 200\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1">attempting to solve for \(n\) <span class="Apple-converted-space"> </span><span class="s1">(<strong><em>M1)</em></strong></span></p>
<p class="p1">\(n \ge 31.68 \ldots \)</p>
<p class="p1">so the least value of \(n\) is 32 <strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<p class="p1"><strong><em>Total [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">Part (a) was reasonably well done. A number of candidates used \(r = \frac{{{u_1}}}{{{u_2}}} = \frac{{{u_2}}}{{{u_3}}}\) rather than \(r = \frac{{{u_2}}}{{{u_1}}} = \frac{{{u_3}}}{{{u_2}}}\). This invariably led to candidates obtaining \(r = 2\) in part (b).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (b), most candidates were able to correctly find the first term and the common difference for the arithmetic sequence. However a number of candidates either obtained \(r = 2\) via means described in part (a) or confused the two sequences and used \({u_1} = \frac{3}{4}\) for the geometric sequence.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(z = r(\cos \alpha + {\text{i}}\sin \alpha )\), where \(\alpha \) is measured in degrees, be the solution of \({z^5} - 1 = 0\) which has the smallest positive argument.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Use the binomial theorem to expand \({(\cos \theta + {\text{i}}\sin \theta )^5}\).</p>
<p>(ii) Hence use De Moivre’s theorem to prove</p>
<p>\[\sin 5\theta = 5{\cos ^4}\theta \sin \theta - 10{\cos ^2}\theta {\sin ^3}\theta + {\sin ^5}\theta .\]</p>
<p>(iii) State a similar expression for \(\cos 5\theta \) in terms of \(\cos \theta \) and \(\sin \theta \).</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(r\) and the value of \(\alpha \).</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>Using (a) (ii) and your answer from (b) show that \(16{\sin ^4}\alpha - 20{\sin ^2}\alpha + 5 = 0\).</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"><span class="s1">Hence express \(\sin 72^\circ \) </span>in the form \(\frac{{\sqrt {a + b\sqrt c } }}{d}\) where \(a,{\text{ }}b,{\text{ }}c,{\text{ }}d \in \mathbb{Z}\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) \({(\cos \theta + {\text{i}}\sin \theta )^5}\)</p>
<p>\( = {\cos ^5}\theta + 5{\text{i}}{\cos ^4}\theta \sin \theta + 10{{\text{i}}^2}{\cos ^3}\theta {\sin ^2}\theta + \)</p>
<p>\(10{{\text{i}}^3}{\cos ^2}\theta {\sin ^3}\theta + 5{{\text{i}}^4}\cos \theta {\sin ^4}\theta + {{\text{i}}^5}{\sin ^5}\theta \) <strong><em>A1A1</em></strong></p>
<p>\(( = {\cos ^5}\theta + 5{\text{i}}{\cos ^4}\theta \sin \theta - 10{\cos ^3}\theta {\sin ^2}\theta - \)</p>
<p>\(10{\text{i}}{\cos ^2}\theta {\sin ^3}\theta + 5\cos \theta {\sin ^4}\theta + {\text{i}}{\sin ^5}\theta )\)</p>
<p> </p>
<p><strong>Note:</strong> Award first <strong><em>A1</em></strong> for correct binomial coefficients.</p>
<p> </p>
<p>(ii) \({({\text{cis}}\theta )^5} = {\text{cis}}5\theta = \cos 5\theta + {\text{i}}\sin 5\theta \) <strong><em>M1</em></strong></p>
<p>\( = {\cos ^5}\theta + 5{\text{i}}{\cos ^4}\theta \sin \theta - 10{\cos ^3}\theta {\sin ^2}\theta - 10{\text{i}}{\cos ^2}\theta {\sin ^3}\theta + \)</p>
<p>\(5\cos \theta {\sin ^4}\theta + {\text{i}}{\sin ^5}\theta \) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Previous line may be seen in (i)</p>
<p> </p>
<p>equating imaginary terms <strong><em>M1</em></strong></p>
<p>\(\sin 5\theta = 5{\cos ^4}\theta \sin \theta - 10{\cos ^2}\theta {\sin ^3}\theta + {\sin ^5}\theta \) <strong><em>AG</em></strong></p>
<p>(iii) equating real terms</p>
<p>\(\cos 5\theta = {\cos ^5}\theta - 10{\cos ^3}\theta {\sin ^2}\theta + 5\cos \theta {\sin ^4}\theta \) <strong><em>A1</em></strong></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>\({(r{\text{cis}}\alpha )^5} = 1 \Rightarrow {r^5}{\text{cis}}5\alpha = 1{\text{cis}}0\) <strong><em>M1</em></strong></p>
<p>\({r^5} = 1 \Rightarrow r = 1\) <strong><em>A1</em></strong></p>
<p>\(5\alpha = 0 \pm 360k,{\text{ }}k \in \mathbb{Z} \Rightarrow a = 72k\) <strong><em>(M1)</em></strong></p>
<p>\(\alpha = 72^\circ \) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1A0</em></strong> if final answer is given in radians.</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>use of \(\sin (5 \times 72) = 0\) <strong>OR</strong> the imaginary part of \(1\) is \(0\) <strong><em>(M1)</em></strong></p>
<p>\(0 = 5{\cos ^4}\alpha \sin \alpha - 10{\cos ^2}\alpha {\sin ^3}\alpha + {\sin ^5}\alpha \) <strong><em>A1</em></strong></p>
<p>\(\sin \alpha \ne 0 \Rightarrow 0 = 5{(1 - {\sin ^2}\alpha )^2} - 10(1 - {\sin ^2}\alpha ){\sin ^2}\alpha + {\sin ^4}\alpha \) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1</em></strong> for replacing \({\cos ^2}\alpha \).</p>
<p> </p>
<p>\(0 = 5(1 - 2{\sin ^2}\alpha + {\sin ^4}\alpha ) - 10{\sin ^2}\alpha + 10{\sin ^4}\alpha + {\sin ^4}\alpha \) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1</em></strong> for any correct simplification.</p>
<p> </p>
<p>so \(16{\sin ^4}\alpha - 20{\sin ^2}\alpha + 5 = 0\) <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>\({\sin ^2}\alpha = \frac{{20 \pm \sqrt {400 - 320} }}{{32}}\) <strong><em>M1A1</em></strong></p>
<p>\(\sin \alpha = \pm \sqrt {\frac{{20 \pm \sqrt {80} }}{{32}}} \)</p>
<p>\(\sin \alpha = \frac{{ \pm \sqrt {10 \pm 2\sqrt 5 } }}{4}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1</em></strong> regardless of signs. Accept equivalent forms with integral denominator, simplification may be seen later.</p>
<p> </p>
<p>as \(72 > 60\), \(\sin 72 > \frac{{\sqrt 3 }}{2} = 0.866 \ldots \) we have to take both positive signs (or equivalent argument) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Allow verification of correct signs with calculator if clearly stated</p>
<p> </p>
<p>\(\sin 72 = \frac{{\sqrt {10 + 2\sqrt 5 } }}{4}\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<p><strong><em>Total [19 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (i) many candidates tried to multiply it out the binomials rather than using the binomial theorem. In parts (ii) and (iii) many candidates showed poor understanding of complex numbers and made no attempt to equate real and imaginary parts. In a some cases the correct answer to part (iii) was seen although it was unclear how it was obtained.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was poorly done. Very few candidates made a good attempt to apply De Moivre’s theorem and most of them could not even equate the moduli to obtain \(r\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was poorly done. From the few candidates that attempted it, many candidates started by writing down what they were trying to prove and made no progress.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Very few made a serious attempt to answer this question. Also very few realised that they could use the answers given in part (c) to attempt this part.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider \(f(x) = - 1 + \ln \left( {\sqrt {{x^2} - 1} } \right)\)</p>
</div>
<div class="specification">
<p>The function \(f\) is defined by \(f(x) = - 1 + \ln \left( {\sqrt {{x^2} - 1} } \right),{\text{ }}x \in D\)</p>
</div>
<div class="specification">
<p>The function \(g\) is defined by \(g(x) = - 1 + \ln \left( {\sqrt {{x^2} - 1} } \right),{\text{ }}x \in \left] {1,{\text{ }}\infty } \right[\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the largest possible domain \(D\) for \(f\) to be a function.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of \(y = f(x)\) showing clearly the equations of asymptotes and the coordinates of any intercepts with the axes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why \(f\) is an even function.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the inverse function \({f^{ - 1}}\) does not exist.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the inverse function \({g^{ - 1}}\) and state its domain.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(g'(x)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, show that there are no solutions to \(g'(x) = 0\);</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, show that there are no solutions to \(({g^{ - 1}})'(x) = 0\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\({x^2} - 1 > 0\) <strong><em>(M1)</em></strong></p>
<p>\(x < - 1\) or \(x > 1\) <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-09_om_15.40.09.png" alt="M17/5/MATHL/HP2/ENG/TZ1/12.b/M"></p>
<p>shape <strong><em>A1</em></strong></p>
<p>\(x = 1\) and \(x = - 1\) <strong><em>A1</em></strong></p>
<p>\(x\)-intercepts <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>\(f\) is symmetrical about the \(y\)-axis <strong><em>R1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(f( - x) = f(x)\) <strong><em>R1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>\(f\) is not one-to-one function <strong><em>R1</em></strong></p>
<p><strong>OR</strong></p>
<p>horizontal line cuts twice <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept any equivalent correct statement.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x = - 1 + \ln \left( {\sqrt {{y^2} - 1} } \right)\) <strong><em>M1</em></strong></p>
<p>\({{\text{e}}^{2x + 2}} = {y^2} - 1\) <strong><em>M1</em></strong></p>
<p>\({g^{ - 1}}(x) = \sqrt {{{\text{e}}^{2x + 2}} + 1} ,{\text{ }}x \in \mathbb{R}\) <strong><em>A1A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(g'(x) = \frac{1}{{\sqrt {{x^2} - 1} }} \times \frac{{2x}}{{2\sqrt {{x^2} - 1} }}\) <strong><em>M1A1</em></strong></p>
<p>\(g'(x) = \frac{x}{{{x^2} - 1}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(g'(x) = \frac{x}{{{x^2} - 1}} = 0 \Rightarrow x = 0\) <strong><em>M1</em></strong></p>
<p>which is not in the domain of \(g\) (hence no solutions to \(g'(x) = 0\)) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(({g^{ - 1}})'(x) = \frac{{{{\text{e}}^{2x + 2}}}}{{\sqrt {{{\text{e}}^{2x + 2}} + 1} }}\) <strong><em>M1</em></strong></p>
<p>as \({{\text{e}}^{2x + 2}} > 0 \Rightarrow ({g^{ - 1}})'(x) > 0\) so no solutions to \(({g^{ - 1}})'(x) = 0\) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept: equation \({{\text{e}}^{2x + 2}} = 0\) has no solutions.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.ii.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = {x^4} + 0.2{x^3} - 5.8{x^2} - x + 4,{\text{ }}x \in \mathbb{R}\).</p>
</div>
<div class="specification">
<p class="p1"><span class="s1">The domain of \(f\) </span>is now restricted to \([0,{\text{ }}a]\)<span class="s1">.</span></p>
</div>
<div class="specification">
<p class="p1">Let \(g(x) = 2\sin (x - 1) - 3,{\text{ }} - \frac{\pi }{2} + 1 \leqslant x \leqslant \frac{\pi }{2} + 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the solutions of \(f(x) > 0\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the curve \(y = f(x)\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the coordinates of both local minimum points.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the \(x\)-coordinates of the points of inflexion.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the largest value of \(a\) for which \(f\) <span class="s1">has an inverse. Give your answer correct to 3 </span>significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">For this value of <span class="s1"><em>a </em></span>sketch the graphs of \(y = f(x)\) and \(y = {f^{ - 1}}(x)\) on the same set of axes, showing clearly the coordinates of the end points of each curve.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Solve \({f^{ - 1}}(x) = 1\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \({g^{ - 1}}(x)\), stating the domain.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Solve \(({f^{ - 1}} \circ g)(x) < 1\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">valid method <em>eg</em>, sketch of curve or critical values found <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2">\(x < - 2.24,{\text{ }}x > 2.24,\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3">\( - 1 < x < 0.8\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p4"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1A1A0 </em></strong>for correct intervals but with inclusive inequalities.</p>
<p class="p4"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\((1.67,{\text{ }} - 5.14),{\text{ }}( - 1.74,{\text{ }} - 3.71)\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p3"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1A0 </em></strong></span>for any two correct terms.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(f'(x) = 4{x^3} + 0.6{x^2} - 11.6x - 1\)</p>
<p class="p1">\(f''(x) = 12{x^2} + 1.2x - 11.6 = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p5">\( - 1.03,{\text{ }}0.934\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span><em>M1 </em></strong>should be awarded if graphical method to find zeros of \(f''(x)\) or turning points of \(f'(x)\) is shown.</p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">1.67 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-01-26_om_12.42.21.png" alt="M16/5/MATHL/HP2/ENG/TZ1/11.c.ii/M"> <strong><em>M1A1A1</em></strong></p>
<p> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for reflection of their \(y = f(x)\) in the line \(y = x\) provided their \(f\) is one-one.</p>
<p class="p1"><strong><em>A1 </em></strong><span class="s1">for \((0,{\text{ }}4)\), \((4,{\text{ }}0)\) </span>(Accept axis intercept values) <strong><em>A1 </em></strong>for the other two sets of coordinates of other end points</p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(x = f(1)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2">\( = - 1.6\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(y = 2\sin (x - 1) - 3\)</p>
<p class="p1">\(x = 2\sin (y - 1) - 3\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2">\(\left( {{g^{ - 1}}(x) = } \right){\text{ }}\arcsin \left( {\frac{{x + 3}}{2}} \right) + 1\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3">\( - 5 \leqslant x \leqslant - 1\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong><span class="s2">for −5 and −1</span>, and <strong><em>A1 </em></strong>for correct inequalities if numbers are reasonable.</p>
<p class="p1"><strong><em>[8 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({f^{ - 1}}\left( {g(x)} \right) < 1\)</p>
<p class="p1">\(g(x) > - 1.6\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(x > {g^{ - 1}}( - 1.6) = 1.78\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p3"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Accept = in the above.</p>
<p class="p3">\(1.78 < x \leqslant \frac{\pi }{2} + 1\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p3"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span><em>A1 </em></strong>for \(x > 1.78\) </span>(allow ≥<span class="s1">) and <strong><em>A1 </em></strong></span>for \(x \leqslant \frac{\pi }{2} + 1\).</p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part d(i) was generally well done, but there were few correct answers for d(ii).</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part d(i) was generally well done, but there were few correct answers for d(ii).</p>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \left| x \right| - 1\).</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;">(a) The graph of \(y = g(x)\) is drawn below.</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_2014-09-12_om_11.31.12.png" alt></span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 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;"> (i) Find the value of \((f \circ g)(1)\).</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;"> (ii) Find the value of \((f \circ g \circ g)(1)\).</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;"> (iii) Sketch the graph of \(y = (f \circ g)(x)\).</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) 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;"> (ii) State the zeros of <em>f</em>.</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) (i) Sketch the graph of \(y = (f \circ f)(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) State the zeros of \(f \circ f\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) Given that we can denote \(\underbrace {f \circ f \circ f \circ \ldots \circ f}_{n{\text{ times}}}\) as \({f^n}\),</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;"> (i) find the zeros of \({f^3}\);</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) find the zeros of \({f^4}\);</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (iii) deduce the zeros of \({f^8}\).</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;">(e) The zeros of \({f^{2n}}\) are \({a_1},{\text{ }}{a_2},{\text{ }}{a_3},{\text{ }} \ldots {\text{, }}{a_N}\).</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;"> (i) State the relation between <em>n </em>and <em>N</em>;</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) Find, and simplify, an expression for \(\sum\limits_{r = 1}^N {\left| {{a_r}} \right|} \) in terms of <em>n</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) \(f(0) = - 1\) <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;"> (ii) \((f \circ g)(0) = f(4) = 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (iii)<br> <img src="images/maths_12_a_i_markscheme.png" alt> <strong><em>(M1)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> Award <strong><em>M1 </em></strong>for evidence that the lower part of the graph has been reflected and <strong><em>A1 </em></strong>correct shape with <em>y</em>-intercept below 4.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) (i)<br> <img src="images/maths_12_b_i_markscheme.png" alt> <strong><em>(M1)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> Award <strong><em>M1 </em></strong>for any translation of \(y = \left| x \right|\).</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) \( \pm 1\) <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> Do not award the <strong><em>A1 </em></strong>if coordinates given, but do not penalise in the rest of the question</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;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) (i)<br> <img src="images/maths_12_c_i_markscheme.png" alt> <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1 </em></strong>for evidence that lower part of (b) has been reflected in the <em>x</em>-axis and translated.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) \(0,{\text{ }} \pm 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) (i) \( \pm 1,{\text{ }} \pm 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) \(0,{\text{ }} \pm 2,{\text{ }} \pm 4\) <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;"> (iii) \(0,{\text{ }} \pm 2,{\text{ }} \pm 4,{\text{ }} \pm 6,{\text{ }} \pm 8\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) (i) \({\text{(1, 3), (2, 5), }} \ldots \) <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;"> \(N = 2n + 1\) <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;"> (ii) Using the formula of the sum of an arithmetic series <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: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \(4(1 + 2 + 3 + \ldots + n) = \frac{4}{2}n(n + 1)\)</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;"> \( = 2n(n + 1)\) <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> OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \(2(2 + 4 + 6 + \ldots + 2n) = \frac{2}{2}n(2n + 2)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \( = 2n(n + 1)\) <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;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [18 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The function \(f\) is given by \(f(x) = \frac{{3{x^2} + 10}}{{{x^{\text{2}}} - 4}},{\text{ }}x \in \mathbb{R},{\text{ }}x \ne 2,{\text{ }}x \ne - 2\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Prove that \(f\) is an even function.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Sketch the graph \(y = f(x)\).</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 class="p1">Write down the range of \(f\).</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 class="p1">\(f( - x) = \frac{{3{{( - x)}^2} + 10}}{{{{( - x)}^2} - 4}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">\( = \frac{{3{x^2} + 10}}{{{x^2} - 4}} = f(x)\)</p>
<p class="p2">\(f(x) = f( - x)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>R1</em></strong></span></p>
<p class="p1">hence this is an even function <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>A1R1 </em></strong>for the statement, all the powers are even hence \(f(x) = f( - x)\).</p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Just stating all the powers are even is <strong><em>A0R0</em></strong>.</p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Do not accept arguments based on the symmetry of the graph.</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"><img src="images/Schermafbeelding_2017-01-26_om_09.33.59.png" alt="M16/5/MATHL/HP2/ENG/TZ1/05.b.i/M"></p>
<p class="p1">correct shape in 3 parts which are asymptotic and symmetrical <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">correct vertical asymptotes clear at 2 and –2 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">correct horizontal asymptote clear at 3 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="s1"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(f(x) > 3\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(f(x) \leqslant - 2.5\) <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">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates were able to prove that a function was even, although many attempted to show special cases, rather than a general proof. Many lost marks through not showing the asymptotes on their sketch. Marks were commonly lost in incorrect use of inequalities for the range of the function.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates were able to prove that a function was even, although many attempted to show special cases, rather than a general proof. Many lost marks through not showing the asymptotes on their sketch. Marks were commonly lost in incorrect use of inequalities for the range of the function.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates were able to prove that a function was even, although many attempted to show special cases, rather than a general proof. Many lost marks through not showing the asymptotes on their sketch. Marks were commonly lost in incorrect use of inequalities for the range of the function.</p>
<div class="question_part_label">b.ii.</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;">Find the set of values of <em>x</em> for which \(\left| {0.1{x^2} - 2x + 3} \right| < {\log _{10}}x\) .</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Attempting to solve \(\left| {0.1{x^2} - 2x + 3} \right| = {\log _{10}}x\) numerically or graphically. <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>x</em> = 1.52, 1.79 <strong><em>(A1)(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;"><em>x</em> = 17.6, 19.1 <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;">\((1.52 < x < 1.79) \cup (17.6 < x < 19.1)\) <strong><em>A1A1 N2</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>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally not well done. A number of candidates attempted an ‘ill-fated’ algebraic approach. Most candidates who used their GDC were able to correctly locate one inequality. The few successful candidates were able to employ a suitable window or suitable window(s) to correctly locate both inequalities.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the functions \(f(x) = {x^3} + 1\) and \(g(x) = \frac{1}{{{x^3} + 1}}\). The graphs of \(y = f(x)\) and \(y = g(x)\) meet at the point (0, 1) and one other point, P.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the coordinates of P.</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Calculate the size of the acute angle between the tangents to the two graphs at the point P.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">\({x^3} + 1 = \frac{1}{{{x^3} + 1}}\)</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;">\(( - 1.26, - 1)\,\,\,\,\,\left( { = \left( { - \sqrt[3]{2}, - 1} \right)} \right)\) <strong><em>A1</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;"><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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'( - 1.259...) = 4.762…\) \((3 \times {2^{\frac{2}{3}}})\) <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;">\(g'( - 1.259...) = - 4.762…\) \(( - 3 \times {2^{\frac{2}{3}}})\) <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;">required angle \( = 2\arctan \left( {\frac{1}{{4.762...}}} \right)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 30px; line-height: normal; font-family: Helvetica; text-align: left;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.414\) (accept 23.7 ) <strong><em> A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept alternative methods including finding the obtuse angle first.</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>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">In part (a) almost all candidates obtained the correct answer, either in numerical form or in exact form. Although many candidates scored one mark in (b), for one gradient, few scored any more. Successful candidates almost always adopted a vector approach to finding the angle between the two tangents, rather than using trigonometry.</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;">In part (a) almost all candidates obtained the correct answer, either in numerical form or in exact form. Although many candidates scored one mark in (b), for one gradient, few scored any more. Successful candidates almost always adopted a vector approach to finding the angle between the two tangents, rather than using trigonometry.</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;">(a) Simplify the difference of binomial coefficients</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;">\[\left( {\begin{array}{*{20}{c}}<br> n \\ <br> 3 <br>\end{array}} \right) - \left( {\begin{array}{*{20}{c}}<br> {2n} \\ <br> 2 <br>\end{array}} \right),{\text{ where }}n \geqslant 3.\]</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) Hence, solve the inequality</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;">\[\left( {\begin{array}{*{20}{c}}<br> n \\ <br> 3 <br>\end{array}} \right) - \left( {\begin{array}{*{20}{c}}<br> {2n} \\ <br> 2 <br>\end{array}} \right) > 32n,{\text{ where }}n \geqslant 3.\]</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) the expression is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{n!}}{{(n - 3)!3!}} - \frac{{(2n)!}}{{(2n - 2)!2!}}\) <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;">\(\frac{{n(n - 1)(n - 2)}}{6} - \frac{{2n(2n - 1)}}{2}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{n({n^2} - 15n + 8)}}{6}{\text{ }}\left( { = \frac{{{n^3} - 15{n^2} + 8n}}{6}} \right)\) <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;"> </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) the inequality is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{n^3} - 15{n^2} + 8n}}{6} > 32n\)</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;">attempt to solve cubic inequality or equation <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;">\({n^3} - 15{n^2} - 184n > 0\,\,\,\,\,n(n - 23)(n + 8) > 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(n > 23\,\,\,\,\,(n \geqslant 24)\) <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>
<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;">Part(a) - Although most understood the notation, few knew how to simplify the binomial coefficients.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part(b) - Many were able to solve the cubic, but some failed to report their answer as an integer inequality.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The function \(f(x) = 4{x^3} + 2ax - 7a\) , \(a \in \mathbb{R}\), leaves a remainder of \(−10\) when divided by \(\left( {x - a} \right)\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of \(a\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that for this value of \(a\) there is a unique real solution to the equation \(f (x) = 0\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(a) = 4{a^3} + 2{a^2} - 7a = - 10\) <em><strong>M1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(4{a^3} + 2{a^2} - 7a + 10 = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\left( {a + 2} \right)\left( {4{a^2} - 6a + 5} \right) = 0\) or sketch or GDC <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(a = - 2\) <em><strong>A1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">substituting \(a = - 2\) into \(f (x)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = 4{x^3} - 4x + 14 = 0\) <em><strong>A1</strong></em></span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">EITHER</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">graph showing unique solution which is indicated (must include max and min) <em><strong>R1</strong></em></span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">OR</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">convincing argument that only one of the solutions is real <em><strong>R1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(−1.74, 0.868 ±1.12i)</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[5 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates found this question surprisingly challenging. The most straightforward approach was use of the Remainder Theorem but a significant number of candidates seemed unaware of this technique. This lack of knowledge led many candidates to attempt an algebraically laborious use of long division. In (b) a number of candidates did not seem to appreciate the significance of the word unique and hence found it difficult to provide sufficient detail to make a meaningful argument. However, most candidates did recognize that they needed a technological approach when attempting (b).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates found this question surprisingly challenging. The most straightforward approach was use of the Remainder Theorem but a significant number of candidates seemed unaware of this technique. This lack of knowledge led many candidates to attempt an algebraically laborious use of long division. In (b) a number of candidates did not seem to appreciate the significance of the word unique and hence found it difficult to provide sufficient detail to make a meaningful argument. However, most candidates did recognize that they needed a technological approach when attempting (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the quadratic expression \(2{x^2} + x - 3\) as the product of two linear factors.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Hence, or otherwise, find the coefficient of \(x\) in the expansion of \({\left( {2{x^2} + x - 3} \right)^8}\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(2{x^2} + x - 3 = \left( {2x + 3} \right)\left( {x - 1} \right)\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Accept \(2\left( {x + \frac{3}{2}} \right)\left( {x - 1} \right)\)</span><span style="font-family: times new roman,times; font-size: medium;">.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Either of these may be seen in (b) and if so <em><strong>A1</strong></em> should be awarded.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">EITHER</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\left( {2{x^2} + x - 3} \right)^8} = {\left( {2x + 3} \right)^8}{\left( {x - 1} \right)^8}\) <em><strong>M1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = \left( {{3^8} + 8\left( {{3^7}} \right)\left( {2x} \right) + ...} \right)\left( {{{\left( { - 1} \right)}^8} + 8{{\left( { - 1} \right)}^7}\left( x \right) + ...} \right)\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">coefficient of \(x = {3^8} \times 8 \times {\left( { - 1} \right)^7} + {3^7} \times 8 \times 2 \times {\left( { - 1} \right)^8}\) <em><strong>M1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">= −17 496 <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Under ft, final <em><strong>A1</strong></em> can only be achieved for an integer answer.</span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">OR</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\left( {2{x^2} + x - 3} \right)^8} = {\left( {3 - \left( {x - 2{x^2}} \right)} \right)^8}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1</span></strong></em></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = {3^8} + 8\left( { - \left( {x - 2{x^2}} \right)\left( {{3^7}} \right) + ...} \right)\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">coefficient of \(x = 8 \times \left( { - 1} \right) \times {3^7}\) <em><strong>M1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">= −17 496 <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Under ft, final <em><strong>A1</strong></em> can only be achieved for an integer answer.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">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 struggled to find an efficient approach to this problem by applying the Binomial Theorem. A disappointing number of candidates attempted the whole expansion which was clearly an unrealistic approach when it is noted that the expansion is to the 8<sup>th</sup> power. The fact that some candidates wrote down Pascal’s Triangle suggested that they had not studied the Binomial Theorem in enough depth or in a sufficient variety of contexts.</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 struggled to find an efficient approach to this problem by applying the Binomial Theorem. A disappointing number of candidates attempted the whole expansion which was clearly an unrealistic approach when it is noted that the expansion is to the 8<sup>th</sup> power. The fact that some candidates wrote down Pascal’s Triangle suggested that they had not studied the Binomial Theorem in enough depth or in a sufficient variety of contexts.</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 \(f(x) = \ln x - {{\text{e}}^{\cos x}},{\text{ }}0 < x \leqslant 10\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(y = f(x)\), stating the coordinates of any maximum and minimum points and points of intersection with the <em>x</em>-axis.</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;">Solve the inequality \(\ln x \leqslant {{\text{e}}^{\cos x}},{\text{ }}0 < x \leqslant 10\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/maths_3a_markscheme.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A correct graph shape for \(0 < x \leqslant 10\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">maxima (3.78, 0.882) and (9.70, 1.89) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">minimum (6.22, –0.885) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>x</em>-axis intercepts (1.97, 0), (5.24, 0) and (7.11, 0) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1 </em></strong>if two <em>x</em>-axis intercepts are correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 < x \leqslant 1.97\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(5.24 \leqslant x \leqslant 7.11\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was reasonably well done although more care was required when showing correct endpoint behaviour. A number of sketch graphs suggested the existence of either a vertical axis intercept or displayed an open circle on the vertical axis. A large number of candidates did not state the coordinates of the various key features correct to three significant figures. A large number of candidates did not locate the maximum near \(x = 10\). Most candidates were able to locate the <em>x</em>-axis intercepts and the minimum. A few candidates unfortunately sketched a graph from a GDC set in degrees.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b), a number of candidates identified the correct critical values but used incorrect inequality signs. Some candidates attempted to solve the inequality algebraically.</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 as \(f(x) = - 3 + \frac{1}{{x - 2}},{\text{ }}x \ne 2\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Sketch the graph of \(y = f(x)\), clearly indicating any asymptotes and axes intercepts.</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 the equations of any asymptotes and the coordinates of any axes intercepts.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 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 inverse function \({f^{ - 1}}\), stating its domain.</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: 21.0px Helvetica;"><br><span style="font-family: 'times new roman', times;"><img src="images/Schermafbeelding_2014-09-15_om_12.42.13.png" alt><span style="font-size: medium;"> <strong><em>A1A1A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1 </em></strong>for correct shape, <strong><em>A1 </em></strong>for \(x = 2\) clearly stated and <strong><em>A1 </em></strong>for \(y = - 3\) clearly stated.</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: 21.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font: 21.0px 'Times New Roman';"><em>x</em> </span>intercept (2.33, 0) <span style="font: 21.0px 'Times New Roman';">and <em>y</em> </span>intercept (0, –3.5) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept –3.5 and 2.33 (7/3) marked on the correct axes.</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>[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: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = - 3 + \frac{1}{{y - 2}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica; min-height: 26.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1 </em></strong>for interchanging <em>x </em>and <em>y </em>(can be done at a later stage).</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;">\(x + 3 = \frac{1}{{y - 2}}\)</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;">\(y - 2 = \frac{1}{{x + 3}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1 </em></strong>for attempting to make <em>y </em>the subject.</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;">\({f^{ - 1}}(x) = 2 + \frac{1}{{x + 3}}\left( { = \frac{{2x + 7}}{{x + 3}}} \right),{\text{ }}x \ne - 3\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1 </em></strong>only if \({f^{ - 1}}(x)\) is seen. Award <strong><em>A1 </em></strong>for the domain.</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>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A Chocolate Shop advertises free gifts to customers that collect three vouchers. The vouchers are placed at random into 10% of all chocolate bars sold at this shop. Kati buys some of these bars and she opens them one at a time to see if they contain a voucher. Let \({\text{P}}(X = n)\) be the probability that Kati obtains her third voucher on the \(n{\text{th}}\) <span class="s1">bar opened.</span></p>
<p class="p1">(It is assumed that the probability that a chocolate bar contains a voucher stays at 10% throughout the question.)</p>
</div>
<div class="specification">
<p class="p1">It is given that \({\text{P}}(X = n) = \frac{{{n^2} + an + b}}{{2000}} \times {0.9^{n - 3}}\) for \(n \geqslant 3,{\text{ }}n \in \mathbb{N}\).</p>
</div>
<div class="specification">
<p class="p1">Kati’s mother goes to the shop and buys \(x\) chocolate bars. She takes the bars home for Kati to open.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({\text{P}}(X = 3) = 0.001\) and \({\text{P}}(X = 4) = 0.0027\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the values of the constants \(a\) <span class="s1">and \(b\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce that \(\frac{{{\text{P}}(X = n)}}{{{\text{P}}(X = n - 1)}} = \frac{{0.9(n - 1)}}{{n - 3}}\) for \(n > 3\).</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>Hence show that \(X\) has two modes \({m_1}\) and \({m_2}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>State the values of \({m_1}\) and \({m_2}\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Determine the minimum value of \(x\) </span>such that the probability Kati receives at least one free gift is greater than <span class="s2">0.5.</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 class="p1"><span class="Apple-converted-space">\({\text{P}}(X = 3) = {(0.1)^3}\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = 0.001\) </span><strong><em>AG</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(X = 4) = {\text{P}}(VV\bar VV) + {\text{P}}(V\bar VVV) + {\text{P}}(\bar VVVV)\) </span><strong><em>(M1)</em></strong></p>
<p class="p1">\( = 3 \times {(0.1)^3} \times 0.9\) (or equivalent) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = 0.0027\) </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 class="p1"><strong>METHOD 1</strong></p>
<p class="p1">attempting to form equations in \(a\) and \(b\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{9 + 3a + b}}{{2000}} = \frac{1}{{1000}}{\text{ }}(3a + b = - 7)\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{16 + 4a + b}}{{2000}} \times \frac{9}{{10}} = \frac{{27}}{{10\,000}}{\text{ }}(4a + b = - 10)\) </span><strong><em>A1</em></strong></p>
<p class="p1">attempting to solve simultaneously <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(a = - 3,{\text{ }}b = 2\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(X = n) = \left( {\begin{array}{*{20}{c}} {n - 1} \\ 2 \end{array}} \right) \times {0.1^3} \times {0.9^{n - 3}}\) </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{(n - 1)(n - 2)}}{{2000}} \times {0.9^{n - 3}}\) </span><strong><em>(M1)A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{{n^2} - 3n + 2}}{{2000}} \times {0.9^{n - 3}}\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(a = - 3,b = 2\) </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Condone the absence of \({0.9^{n - 3}}\) in the determination of the values of \(a\) and \(b\).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1"><strong>EITHER</strong></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(X = n) = \frac{{{n^2} - 3n + 2}}{{2000}} \times {0.9^{n - 3}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(X = n) = \left( {\begin{array}{*{20}{c}} {n - 1} \\ 2 \end{array}} \right) \times {0.1^3} \times {0.9^{n - 3}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{(n - 1)(n - 2)}}{{2000}} \times {0.9^{n - 3}}\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(X = n - 1) = \frac{{(n - 2)(n - 3)}}{{2000}} \times {0.9^{n - 4}}\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{P}}(X = n)}}{{{\text{P}}(X = n - 1)}} = \frac{{(n - 1)(n - 2)}}{{(n - 2)(n - 3)}} \times 0.9\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{0.9(n - 1)}}{{n - 3}}\) </span><strong><em>AG</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{P}}(X = n)}}{{{\text{P}}(X = n - 1)}} = \frac{{\frac{{{n^2} - 3n + 2}}{{2000}} \times {{0.9}^{n - 3}}}}{{\frac{{{{(n - 1)}^2} - 3(n - 1) + 2}}{{2000}} \times {{0.9}^{n - 4}}}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{0.9({n^2} - 3n + 2)}}{{({n^2} - 5n + 6)}}\) </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for a correct numerator and <strong><em>A1 </em></strong>for a correct denominator.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{0.9(n - 1)(n - 2)}}{{(n - 2)(n - 3)}}\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{0.9(n - 1)}}{{n - 3}}\) </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></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>attempting to solve \(\frac{{0.9(n - 1)}}{{n - 3}} = 1\) for \(n\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(n = 21\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{0.9(n - 1)}}{{n - 3}} < 1 \Rightarrow n > 21\) </span><strong><em>R1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{0.9(n - 1)}}{{n - 3}} > 1 \Rightarrow n < 21\) </span><strong><em>R1</em></strong></p>
<p class="p1">\(X\) has two modes <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>R1R1 </em></strong>for a clearly labelled graphical representation of the two inequalities (using \(\frac{{{\text{P}}(X = n)}}{{{\text{P}}(X = n - 1)}}\)).</p>
<p class="p2"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the modes are <span class="s1">20 </span>and <span class="s1">21 <span class="Apple-converted-space"> </span></span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1"><span class="Apple-converted-space">\(Y \sim {\text{B}}(x,{\text{ }}0.1)\) </span><strong><em>(A1)</em></strong></p>
<p class="p1">attempting to solve \({\text{P}}(Y \geqslant 3) > 0.5\) (or equivalent <em>eg</em> \(1 - {\text{P}}(Y \leqslant 2) > 0.5\)) for \(x\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for attempting to solve an equality (obtaining \(x = 26.4\)).</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\(x = 27\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1"><span class="Apple-converted-space">\(\sum\limits_{n = 0}^x {{\text{P}}(X = n) > 0.5} \) </span><strong><em>(A1)</em></strong></p>
<p class="p1">attempting to solve for \(x\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(x = 27\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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 class="p1">A function \(f\) is defined by \(f(x) = (x + 1)(x-1)(x-5),{\text{ }}x \in \mathbb{R}\).</p>
<p class="p1">Find the values of \(x\) for which \(f(x) < \left| {f(x)} \right|\).</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">A function \(g\) is defined by \(g(x) = {x^2} + x - 6,{\text{ }}x \in \mathbb{R}\).</p>
<p class="p1">Find the values of \(x\) for which \(g(x) < \frac{1}{{g(x)}}\).</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 class="p1"><img src="images/Schermafbeelding_2016-01-06_om_07.51.39.png" alt></p>
<p>as roots of \(f(x) = 0\) are \( - 1,{\text{ }}1,{\text{ }}5\) <strong><em>(M1)</em></strong></p>
<p>solution is \(\left] { - \infty ,{\text{ }} - 1} \right[ \cup \left] {1,{\text{ }}5} \right[\;\;\;(x < - 1\;\;\;{\text{or}}\;\;\;1 < x < 5)\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1A0</em></strong> for closed intervals.</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"><strong>METHOD 1</strong></p>
<p class="p1">\(\left( {{\text{graphs of }}g(x){\text{ and }}\frac{1}{{g(x)}}} \right)\)</p>
<p class="p2"><img src="images/Schermafbeelding_2016-01-06_om_08.02.41.png" alt></p>
<p>roots of \(g(x) = 0\) are \( - 3\) and 2 <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>M1</em></strong> if quadratic graph is drawn or two roots obtained.</p>
<p>Roots may be indicated anywhere eg asymptotes on graph or in inequalities below.</p>
<p> </p>
<p>the intersections of the graphs \(g(x)\) and of \(1/g(x)\)</p>
<p>are \( - 3.19,{\text{ }} - 2.79,{\text{ }}1.79,{\text{ 2.19}}\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1</em></strong> for at least one of the values above seen anywhere.</p>
<p> </p>
<p>solution is \(\left] { - 3.19,{\text{ }} - 3} \right[ \cup \left] { - 2.79,{\text{ }}1.79} \right[ \cup \left] {2,{\text{ }}2.19} \right[\)</p>
<p>\(( - 3.19 < x < - 3\;\;\;{\text{or}}\;\;\; - 2.79 < x < 1.79\;\;\;{\text{or}}\;\;\;2 < x < 2.19)\) <strong><em>A1A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1A1A0</em></strong> for closed intervals.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(\left( {{\text{graph of }}g(x) - \frac{1}{{g(x)}}} \right)\)</p>
<p class="p2"><img src="images/Schermafbeelding_2016-01-06_om_08.20.21.png" alt></p>
<p>asymptotes at \(x = - 3\) and \(x = 2\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> May be indicated on the graph.</p>
<p> </p>
<p>roots of graph are \( - 3.19,{\text{ }} - 2.79,{\text{ }}1.79,{\text{ }}2.19\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for at least one of the values above seen anywhere.</p>
<p> </p>
<p>solution is (when graph is negative)</p>
<p>\(\left] { - 3.19,{\text{ }} - 3} \right[ \cup \left] { - 2.79,{\text{ }}1.79} \right[ \cup \left] {2,{\text{ }}2.19} \right[\)</p>
<p>\(( - 3.19 < x < - 3\;\;\;{\text{or}}\;\;\; - 2.79 < x < 1.79\;\;\;{\text{or}}\;\;\;2 < x < 2.19)\) <strong><em>A1A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1A1A0</em></strong> for closed intervals.</p>
<p><em><strong>[7 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;">
<p class="p1">In general part (a) was performed correctly, with the vast majority of candidates stating the correct open intervals as required.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (b) many candidates scored a few marks by just finding intersection points and equations of asymptotes; many other candidates showed difficulties in manipulating inequalities and ignored the fact that the quantities could be negative. Candidates that used the graph well managed to achieve full marks. Unfortunately many sketches were very crudely drawn hence they were of limited value for assessment purposes.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function \(f(x) = \frac{{\sqrt x }}{{\sin x}},{\text{ }}0 < x < \pi \).</p>
</div>
<div class="specification">
<p>Consider the region bounded by the curve \(y = f(x)\), the \(x\)-axis and the lines \(x = \frac{\pi }{6},{\text{ }}x = \frac{\pi }{3}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the \(x\)-coordinate of the minimum point on the curve \(y = f(x)\) satisfies the equation \(\tan x = 2x\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the values of \(x\) for which \(f(x)\) is a decreasing function.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of \(y = f(x)\) showing clearly the minimum point and any asymptotic behaviour.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of the point on the graph of \(f\) where the normal to the graph is parallel to the line \(y = - x\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>This region is now rotated through \(2\pi \) radians about the \(x\)-axis. Find the volume of revolution.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to use quotient rule or product rule <strong><em>M1</em></strong></p>
<p>\(f’(x) = \frac{{\sin x\left( {\frac{1}{2}{x^{ - \frac{1}{2}}}} \right) - \sqrt x \cos x}}{{{{\sin }^2}x}}{\text{ }}\left( { = \frac{1}{{2\sqrt x \sin x}} - \frac{{\sqrt x \cos x}}{{{{\sin }^2}x}}} \right)\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for \(\frac{1}{{2\sqrt x \sin x}}\) or equivalent and <strong><em>A1 </em></strong>for \( - \frac{{\sqrt x \cos x}}{{{{\sin }^2}x}}\) or equivalent.</p>
<p> </p>
<p>setting \(f’(x) = 0\) <strong><em>M1</em></strong></p>
<p>\(\frac{{\sin x}}{{2\sqrt x }} - \sqrt x \cos x = 0\)</p>
<p>\(\frac{{\sin x}}{{2\sqrt x }} = \sqrt x \cos x\) or equivalent <strong><em>A1</em></strong></p>
<p>\(\tan x = 2x\) <strong><em>AG</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x = 1.17\)</p>
<p>\(0 < x \leqslant 1.17\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for \(0 < x\) and <strong><em>A1 </em></strong>for \(x \leqslant 1.17\). Accept \(x < 1.17\).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-08_om_16.19.25.png" alt="N17/5/MATHL/HP2/ENG/TZ0/10.b/M"></p>
<p>concave up curve over correct domain with one minimum point above the \(x\)-axis. <strong><em>A1</em></strong></p>
<p>approaches \(x = 0\) asymptotically <strong><em>A1</em></strong></p>
<p>approaches \(x = \pi \) asymptotically <strong><em>A1</em></strong></p>
<p> </p>
<p>Note: For the final <strong><em>A1 </em></strong>an asymptote must be seen, and \(\pi \) must be seen on the \(x\)-axis or in an equation.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(f’(x){\text{ }}\left( { = \frac{{\sin x\left( {\frac{1}{2}{x^{ - \frac{1}{2}}}} \right) - \sqrt x \cos x}}{{{{\sin }^2}x}}} \right) = 1\) <strong><em>(A1)</em></strong></p>
<p>attempt to solve for \(x\) <strong><em>(M1)</em></strong></p>
<p>\(x = 1.96\) <strong><em>A1</em></strong></p>
<p>\(y = f(1.96 \ldots )\)</p>
<p>\( = 1.51\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(V = \pi \int_{\frac{\pi }{6}}^{\frac{\pi }{3}} {\frac{{x{\text{d}}x}}{{{{\sin }^2}x}}} \) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> <strong><em>M1 </em></strong>is for an integral of the correct squared function (with or without limits and/or \(\pi \)).</p>
<p> </p>
<p>\( = 2.68{\text{ }}( = 0.852\pi )\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Particle <em>A </em>moves such that its velocity \(v{\text{ m}}{{\text{s}}^{ - 1}}\), at time <em>t </em>seconds, is given by \(v(t) = \frac{t}{{12 + {t^4}}},{\text{ }}t \geqslant 0\).</span></p>
</div>
<div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Particle <em>B </em>moves such that its velocity \(v{\text{ m}}{{\text{s}}^{ - 1}}\) is related to its displacement \(s{\text{ m}}\), by the equation \(v(s) = \arcsin \left( {\sqrt s } \right)\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(y = v(t)\). Indicate clearly the local maximum and write down its coordinates.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Use the substitution \(u = {t^2}\) to find \(\int {\frac{t}{{12 + {t^4}}}{\text{d}}t} \).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times;"><span style="font-size: medium; line-height: normal; background-color: #f7f7f7;">Find the exact distance travelled by particle </span>\(A\) <span style="font-size: medium; line-height: normal; background-color: #f7f7f7;">between \(t = 0\) and \(t = 6\) seconds.</span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Give your answer in the form \(k\arctan (b),{\text{ }}k,{\text{ }}b \in \mathbb{R}\).</span></p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of particle B when \(s = 0.1{\text{ m}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a)<br><img src="images/maths_14a_markscheme_1.png" alt> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>A1</strong> for</span><span style="font-family: 'times new roman', times; font-size: medium;"> correct shape and correct domain</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\((1.41,{\text{ }}0.0884){\text{ }}\left( {\sqrt 2 ,{\text{ }}\frac{{\sqrt 2 }}{{16}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(u = {t^2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}u}}{{{\text{d}}t}} = 2t\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t = {u^{\frac{1}{2}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}t}}{{{\text{d}}u}} = \frac{1}{2}{u^{ - \frac{1}{2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{t}{{12 + {t^4}}}{\text{d}}t = \frac{1}{2}\int {\frac{{{\text{d}}u}}{{12 + {u^2}}}} } \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{2\sqrt {12} }}\arctan \left( {\frac{u}{{\sqrt {12} }}} \right)( + c)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{4\sqrt 3 }}\arctan \left( {\frac{{{t^2}}}{{2\sqrt 3 }}} \right)( + c)\) or equivalent <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^6 {\frac{t}{{12 + {t^4}}}{\text{d}}t} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left[ {\frac{1}{{4\sqrt 3 }}\arctan \left( {\frac{{{t^2}}}{{2\sqrt 3 }}} \right)} \right]_0^6\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{4\sqrt 3 }}\left( {\arctan \left( {\frac{{36}}{{2\sqrt 3 }}} \right)} \right){\text{ }}\left( { = \frac{1}{{4\sqrt 3 }}\left( {\arctan \left( {\frac{{18}}{{\sqrt 3 }}} \right)} \right)} \right){\text{ (m)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept \(\frac{{\sqrt 3 }}{{12}}\arctan \left( {6\sqrt 3 } \right)\) or equivalent.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica; min-height: 26.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}v}}{{{\text{d}}s}} = \frac{1}{{2\sqrt {s(1 - s)} }}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = v\frac{{{\text{d}}v}}{{{\text{d}}s}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = \arcsin \left( {\sqrt s } \right) \times \frac{1}{{2\sqrt {s(1 - s)} }}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = \arcsin \left( {\sqrt {0.1} } \right) \times \frac{1}{{2\sqrt {0.1 \times 0.9} }}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = 0.536{\text{ (m}}{{\text{s}}^{ - 2}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the values of \(k\) such that the equation \({x^3} + {x^2} - x + 2 = k\) has three distinct real solutions.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">from GDC, sketch a relevant graph <em><strong> A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">maximum: \(y = 3\) or (–1, 3) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">minimum: \(y = 1.81\) or (0.333, 1.81) \(\left( {{\text{or }}y = \frac{{49}}{{27}}{\text{ or }}\left( {\frac{1}{3},\frac{{49}}{{27}}} \right)} \right)\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">hence, \(1.81 < k < 3\) <em><strong>A1A1 N3</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for \(1.81 \leqslant k \leqslant 3\) .</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[5 marks]</span></strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Responses to this question were surprisingly poor. Few candidates recognised that the easier way to answer the question was to use a graph on the GDC. Many candidates embarked on fruitless algebraic manipulation which led nowhere.</span></p>
</div>
<br><hr><br><div class="question">
<p class="p1">When \({x^2} + 4x - b\) is divided by \(x - a\) <span class="s1">the remainder is 2</span>.</p>
<p class="p1">Given that \(a,{\text{ }}b \in \mathbb{R}\), find the smallest possible value for \(b\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">\({a^2} + 4a - b = 2\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"><strong>EITHER</strong></p>
<p class="p1">\({a^2} + 4a - (b + 2) = 0\)</p>
<p class="p2">as \(a\) is real \( \Rightarrow 16 + 4(b + 2) \geqslant 0\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p2"><strong>OR</strong></p>
<p class="p1">\(b = {a^2} + 4a - 2\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1">\( = {(a + 2)^2} - 6\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"><strong>THEN</strong></p>
<p class="p3">\(b \geqslant - 6\)</p>
<p class="p2">hence smallest possible value for \(b\) <span class="s2">is \( - 6\) <span class="Apple-converted-space"> </span></span><strong><em>A1</em></strong></p>
<p class="p2"><strong><em>[5 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">For quite a difficult question, there were many good solutions for this, including many different methods. It was disturbing to see how many students did not seem to be aware of the remainder theorem, instead choosing to divide the polynomial.</p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the set of values of \(k\) that satisfy the inequality \({k^2} - k - 12 < 0\).</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>The triangle ABC is shown in the following diagram. Given that \(\cos B < \frac{1}{4}\), find the range of possible values for AB.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-09_om_18.13.24.png" alt="M17/5/MATHL/HP2/ENG/TZ2/04.b"></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\({k^2} - k - 12 < 0\)</p>
<p>\((k - 4)(k + 3) < 0\) <strong><em>(M1)</em></strong></p>
<p>\( - 3 < k < 4\) <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\cos B = \frac{{{2^2} + {c^2} - {4^2}}}{{4c}}{\text{ }}({\text{or }}16 = {2^2} + {c^2} - 4c\cos B)\) <strong><em>M1</em></strong></p>
<p>\( \Rightarrow \frac{{{c^2} - 12}}{{4c}} < \frac{1}{4}\) <strong><em>A1</em></strong></p>
<p>\( \Rightarrow {c^2} - c - 12 < 0\)</p>
<p>from result in (a)</p>
<p>\(0 < {\text{AB}} < 4\) or \( - 3 < {\text{AB}} < 4\) <strong><em>(A1)</em></strong></p>
<p>but AB must be at least 2</p>
<p>\( \Rightarrow 2 < {\text{AB}} < 4\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Allow \( \leqslant {\text{AB}}\) for either of the final two <strong><em>A </em></strong>marks.</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="question">
<p>The equation \({x^2} - 5x - 7 = 0\) has roots \(\alpha \) and \(\beta \). The equation \({x^2} + px + q = 0\) has roots \(\alpha + 1\) and \(\beta + 1\). Find the value of \(p\) and the value of \(q\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1</strong></p>
<p>\(\alpha + \beta = 5,\,\,\alpha \beta = - 7\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1A0</strong></em> if only one equation obtained.</p>
<p>\(\left( {\alpha + 1} \right) + \left( {\beta + 1} \right) = 5 + 2 = 7\) <em> <strong>A1</strong></em></p>
<p>\(\left( {\alpha + 1} \right)\left( {\beta + 1} \right) = \alpha \beta + \left( {\alpha + \beta } \right) + 1\) <em><strong>(M1)</strong></em></p>
<p>\( = - 7 + 5 + 1 = - 1\)</p>
<p>\(p = - 7,\,\,q = - 1\) <em><strong> A1A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(\alpha = \frac{{5 + \sqrt {53} }}{2} = 6.1 \ldots {\text{;}}\,\,\beta = \frac{{5 - \sqrt {53} }}{2} = - 1.1 \ldots \) <em><strong>(M1)(A1)</strong></em></p>
<p>\(\alpha + 1 = \frac{{7 + \sqrt {53} }}{2} = 7.1 \ldots {\text{;}}\,\,\beta + 1 = \frac{{7 - \sqrt {53} }}{2} = - 0.1 \ldots \) <em> <strong>A1</strong></em></p>
<p>\(\left( {x - 7.14 \ldots } \right)\left( {x + 0.14 \ldots } \right) = {x^2} - 7x - 1\) <em><strong>(M1)</strong></em></p>
<p>\(p = - 7,\,\,q = - 1\) <em><strong> A1A1</strong></em></p>
<p><strong>Note:</strong> Exact answers only.</p>
<p><em><strong>[6 marks]</strong></em></p>
<p> </p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the function \(f\) defined by \(f(x) = 3x\arccos (x)\) where \( - 1 \leqslant x \leqslant 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Sketch the graph of \(f\) </span>indicating clearly any intercepts with the axes and the coordinates of any local maximum or minimum points.</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">State the range of \(f\).</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">Solve the inequality \(\left| {3x\arccos (x)} \right| > 1\).</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"><img src="images/Schermafbeelding_2017-03-01_om_06.12.12.png" alt="N16/5/MATHL/HP2/ENG/TZ0/05.a/M"></p>
<p class="p2">correct shape passing through the origin and correct domain <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3"> </p>
<p class="p2"><strong>Note: </strong>Endpoint coordinates are not required. The domain can be indicated by \( - 1\) and 1 marked on the axis.</p>
<p class="p2"><span class="Apple-converted-space">\((0.652,{\text{ }}1.68)\) </span><strong><em>A1</em></strong></p>
<p class="p2">two correct intercepts (coordinates not required) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3"> </p>
<p class="p2"><strong>Note: </strong>A graph passing through the origin is sufficient for \((0,{\text{ }}0)\).</p>
<p class="p3"> </p>
<p class="p2"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\([-9.42,{\text{ }}1.68]{\text{ }}({\text{or }} - 3\pi ,{\text{ }}1.68])\) </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>A1A0 </em></strong>for open or semi-open intervals with correct endpoints. Award <strong><em>A1A0 </em></strong>for closed intervals with one correct endpoint.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempting to solve either \(\left| {3x\arccos (x)} \right| > 1\) (or equivalent) or \(\left| {3x\arccos (x)} \right| = 1\) (or equivalent) (<em>eg</em>. graphically) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><img src="images/Schermafbeelding_2017-03-01_om_06.22.47.png" alt="N16/5/MATHL/HP2/ENG/TZ0/05.c/M"></p>
<p class="p1"><span class="Apple-converted-space">\(x = - 0.189,{\text{ }}0.254,{\text{ }}0.937\) </span><strong><em>(A1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( - 1 \leqslant x < - 0.189{\text{ or }}0.254 < x < 0.937\) </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>A0 </em></strong>for \(x < - 0.189\).</p>
<p class="p2"> </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;">
[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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A polynomial \(p(x)\) with real coefficients is of degree five. The equation \(p(x) = 0\) has a complex root 2 + i. The graph of \(y = p(x)\) has the <em>x</em>-axis as a tangent at (2, 0) and intersects the coordinate axes at (−1, 0) and (0, 4).</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;">Find \(p(x)\) in factorised form with real coefficients.</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;">other root is 2 – <em>i</em> <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;">a quadratic factor is therefore \((x - 2 + i)(x - 2 - i)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {x^2} - 4x + 5\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>x</em> + 1 is a factor <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(x - 2)^2}\) is a factor <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;">\(p(x) = a(x + 1){(x - 2)^2}({x^2} - 4x + 5)\) <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;">\(p(0) = 4 \Rightarrow a = \frac{1}{5}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(p(x) = \frac{1}{5}(x + 1){(x - 2)^2}({x^2} - 4x + 5)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Whilst most candidates knew that another root was \(2 - {\text{i}}\) , much fewer were able to find the quadratic factor. Surprisingly few candidates knew that \(\left( {x - 2} \right)\) must be a repeated factor and less surprisingly many did not recognise that the whole expression needed to be multiplied by \(\frac{1}{5}\).</span></p>
</div>
<br><hr><br><div class="question">
<p>In the quadratic equation \(7{x^2} - 8x + p = 0,{\text{ }}(p \in \mathbb{Q})\), one root is three times the other root.<br>Find the value of \(p\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1</strong></p>
<p>let roots be \(\alpha \) and \(3\alpha \) <strong><em>(M1)</em></strong></p>
<p>sum of roots \((4\alpha ) = \frac{8}{7}\) <strong><em>M1</em></strong></p>
<p>\( \Rightarrow \alpha = \frac{2}{7}\) <strong><em>A1</em></strong></p>
<p><strong>EITHER</strong></p>
<p>product of roots \((3{\alpha ^2}) = \frac{p}{7}\) <strong><em>M1</em></strong></p>
<p>\(p = 21{\alpha ^2} = 21 \times \frac{4}{{49}}\)</p>
<p><strong>OR</strong></p>
<p>\(7{\left( {\frac{2}{7}} \right)^2} - 8\left( {\frac{2}{7}} \right) + p = 0\) <strong><em>M1</em></strong></p>
<p>\(\frac{4}{7} - \frac{{16}}{7} + p = 0\)</p>
<p><strong>THEN</strong></p>
<p>\( \Rightarrow p = \frac{{12}}{7}{\text{ }}( = 1.71)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(x = \frac{{8 \pm \sqrt {64 - 28p} }}{{14}}\) <strong><em>(M1)</em></strong></p>
<p>\(\frac{{8 + \sqrt {64 - 28p} }}{{14}} = 3\left( {\frac{{8 - \sqrt {64 - 28p} }}{{14}}} \right)\) <strong><em>M1A1</em></strong></p>
<p>\(8 + \sqrt {64 - 28p} = 24 - 3\sqrt {64 - 28p} \Rightarrow \sqrt {64 - 28p} = 4\) <strong><em>(M1)</em></strong></p>
<p>\(p = \frac{{12}}{7}{\text{ }}( = 1.71)\) <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="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that the graph of \(y = {x^3} - 6{x^2} + kx - 4\) has exactly one point at which the gradient is zero, find the value of <em>k </em>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 3{x^2} - 12x + k\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">For use of discriminant \({b^2} - 4ac = 0\) or completing the square \(3{(x - 2)^2} + k - 12\) (<strong><em>M1)</em></strong></span></p>
<p> <span style="font-family: 'times new roman', times; font-size: medium;">\(144 - 12k = 0\) </span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Accept trial and error, sketches of parabolas with vertex (2,0) or use of second derivative.</span></p>
<p> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(k = 12\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks] </em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Generally candidates answer this question well using a diversity of methods. Surprisingly, a small number of candidates were successful in answering this question using the discriminant of the quadratic and in many cases reverted to trial and error to obtain the correct answer.</span></p>
</div>
<br><hr><br><div class="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 vectors <strong><em>a</em></strong> and <strong><em>b</em></strong> are such that <strong><em>a</em></strong> \( = (3\cos \theta + 6)\)<strong><em>i</em></strong> \( + 7\) <strong><em>j</em></strong> and <strong><em>b</em></strong> \( = (\cos \theta - 2)\)<strong><em>i</em></strong> \( + (1 + \sin \theta )\)<strong><em>j</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;">Given that <strong><em>a</em></strong> and <strong><em>b</em></strong> are perpendicular,</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">show that \(3{\sin ^2}\theta - 7\sin \theta + 2 = 0\);</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">find the smallest possible positive value of \(\theta \).</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: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to form \((3\cos \theta + 6)(\cos \theta - 2) + 7(1 + \sin \theta ) = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(3{\cos ^2}\theta - 12 + 7\sin \theta + 7 = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(3\left( {1 - {{\sin }^2}\theta } \right) + 7\sin \theta - 5 = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(3{\sin ^2}\theta - 7\sin \theta + 2 = 0\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><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: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to solve algebraically (including substitution) or graphically for \(\sin \theta \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sin \theta = \frac{1}{3}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = 0.340{\text{ }}( = 19.5^\circ )\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[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: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was very well done. Most candidates were able to use the scalar product and \({\cos ^2}\theta = 1 - {\sin ^2}\theta \) to show the required result.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) was reasonably well done. A few candidates confused ‘smallest possible positive value’ with a minimum function value. Some candidates gave \(\theta = 0.34\) as their final 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;">The function <em>f</em> is of the form \(f(x) = \frac{{x + a}}{{bx + c}}\), \(x \ne - \frac{c}{b}\). Given that the graph of <em>f</em> has asymptotes <em>x</em> = −4 and <em>y</em> = −2 , and that the point \(\left( {\frac{2}{3},{\text{ }}1} \right)\) lies on the graph, find the values of <em>a</em> , <em>b</em> and <em>c</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">vertical asymptote \(x = - 4 \Rightarrow - 4b + c = 0\) <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;">horizontal asymptote \(y = - 2 \Rightarrow \frac{1}{b} = - 2\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(b = - \frac{1}{2}{\text{ and }}c = - 2\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1 = \frac{{\frac{2}{3} + a}}{{ - \frac{1}{2} \times \frac{2}{3} - 2}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = - 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of \(y = \ln (x)\) is transformed into the graph of \(y = \ln \left( {2x + 1} \right)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Describe two transformations that are required to do this.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Solve \(\ln \left( {2x + 1} \right) > 3\cos (x)\), \(x \in [0,10]\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">EITHER</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">translation of \( - \frac{1}{2}\)</span><span style="font-family: times new roman,times; font-size: medium;"> parallel to the \(x\)-axis</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">stretch of a scale factor of \(\frac{1}{2}\) </span><span style="font-family: times new roman,times; font-size: medium;">parallel to the \(x\)-axis <em><strong> A1A1</strong></em></span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">OR</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">stretch of a scale factor of \(\frac{1}{2}\) </span><span style="font-family: times new roman,times; font-size: medium;">parallel to the \(x\)-axis</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">translation of \( - 1\) parallel to the \(x\)-axis <em><strong>A1A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Accept clear alternative terminologies for either transformation.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">EITHER</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(1.16 < x < 5.71 \cup 6.75 < x \leqslant 10\) <em><strong>A1A1A1A1</strong></em></span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">OR</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">]\(1.16\), \(5.71\)[ </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"> \(\cup\) </span> ]\(6.75\), \(10\)] <em><strong>A1A1A1A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for 1 intersection value, <em><strong>A1</strong></em> for the other 2, <em><strong>A1A1</strong></em> for the intervals.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[6 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well done by many candidates. It would appear, however, that few candidates were aware of the standard terminology – <em>Stretch</em> and <em>Translation</em> - used to describe the relevant graph transformations. Most made good use of a GDC to find the critical points and to help in deciding on the correct intervals. A significant minority failed to note \(x = 10\)</span><span style="font-family: times new roman,times; font-size: medium;"> as an endpoint.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well done by many candidates. It would appear, however, that few candidates were aware of the standard terminology – <em>Stretch</em> and <em>Translation</em> - used to describe the relevant graph transformations. Most made good use of a GDC to find the critical points and to help in deciding on the correct intervals. A significant minority failed to note \(x = 10\)</span><span style="font-family: times new roman,times; font-size: medium;"> as an endpoint.</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The arithmetic sequence \(\{ {u_n}:n \in {\mathbb{Z}^ + }\} \) has first term \({u_1} = 1.6\) and common difference <em>d</em> = 1.5. The geometric sequence \(\{ {v_n}:n \in {\mathbb{Z}^ + }\} \) has first term \({v_1} = 3\) and common ratio <em>r</em> = 1.2.</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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for \({u_n} - {v_n}\) in terms of <em>n</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 the set of values of <em>n</em> for which \({u_n} > {v_n}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine the greatest value of \({u_n} - {v_n}\). Give your answer correct to four significant figures.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">\({u_n} - {v_n} = 1.6 + (n - 1) \times 1.5 - 3 \times {1.2^{n - 1}}{\text{ }}( = 1.5n + 0.1 - 3 \times {1.2^{n - 1}})\) <strong><em>A1A1</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;">attempting to solve \({u_n} > {v_n}\) numerically or graphically. <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;">\(n = 2.621 \ldots ,9.695 \ldots \) <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;">So \(3 \leqslant n \leqslant 9\) <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>[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: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The greatest value of \({u_n} - {v_n}\) is 1.642. <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;"> Do not accept 1.64.</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;"><em> </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;"><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (a), most candidates were able to express \({u_n}\) and \({v_n}\) correctly and hence obtain a correct expression for \({u_n} - {v_n}\). Some candidates made careless algebraic errors when unnecessarily simplifying \({u_n}\) while other candidates incorrectly stated \({v_n}\) as \(3{(1.2)^n}\).</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 parts (b) and (c), most candidates treated <em>n</em> as a continuous variable rather than as a discrete variable. Candidates should be aware that a GDC’s table feature can be extremely useful when attempting such question types.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In parts (b) and (c), most candidates treated <em>n</em> as a continuous variable rather than as a discrete variable. Candidates should be aware that a GDC’s table feature can be extremely useful when attempting such question types. In part (c), a number of candidates attempted to find the maximum value of <em>n </em>rather than attempting to find the maximum value of \({u_n} - {v_n}\).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A particle moves in a straight line, its velocity \(v{\text{ m}}{{\text{s}}^{ - 1}}\) at time \(t\) seconds is given by \(v = 9t - 3{t^2},{\text{ }}0 \le t \le 5\).</p>
<p class="p1">At time \(t = 0\), the displacement \(s\) of the particle from an origin \(O\) is 3 m.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the displacement of the particle when \(t = 4\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Sketch a displacement/time graph for the particle, \(0 \le t \le 5\), showing clearly where the curve meets the axes and the coordinates of the points where the displacement takes greatest and least values.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">For \(t > 5\)</span>, the displacement of the particle is given by \(s = a + b\cos \frac{{2\pi t}}{5}\) <span class="s1">such that \(s\) is continuous for all \(t \ge 0\).</span></p>
<p class="p2">Given further that \(s = 16.5\) when \(t = 7.5\), find the values of \(a\) and \(b\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">For \(t > 5\)</span>, the displacement of the particle is given by \(s = a + b\cos \frac{{2\pi t}}{5}\) <span class="s1">such that \(s\) is continuous for all \(t \ge 0\).</span></p>
<p class="p1">Find the times \({t_1}\) and \({t_2}(0 < {t_1} < {t_2} < 8)\) when the particle returns to its starting point.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p2">\(s = \int {(9t - 3{t^2}){\text{d}}t = \frac{9}{2}{t^2} - {t^3}( + c)} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2">\(t = 0,{\text{ }}s = 3 \Rightarrow c = 3\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2">\(t = 4 \Rightarrow s = 11\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p2">\(s = 3 + \int_0^4 {(9t - 3{t^2}){\text{d}}t} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)(A1)</em></strong></span></p>
<p class="p2">\(s = 11\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="s1"><strong><em>[3 marks]</em></strong></span></p>
<p class="p2"><span class="s1"> </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="images/Schermafbeelding_2016-01-07_om_07.29.21.png" alt></p>
<p class="p2">correct shape over correct domain <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">maximum at \((3,{\text{ }}16.5)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">\(t\) intercept at \(4.64\), \(s\) intercept at \(3\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">minimum at \((5,{\text{ }} - 9.5)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\( - 9.5 = a + b\cos 2\pi \)</p>
<p>\(16.5 = a + b\cos 3\pi \) <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Only award <strong><em>M1</em></strong> if two simultaneous equations are formed over the correct domain.</p>
<p> \(a = \frac{7}{2}\) <strong><em>A1</em></strong></p>
<p>\(b = - 13\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">at \({t_1}\):</p>
<p class="p1">\(3 + \frac{9}{2}{t^2} - {t^3} = 3\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\({t^2}\left( {\frac{9}{2} - t} \right) = 0\)</p>
<p class="p1">\({t_1} = \frac{9}{2}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">solving \(\frac{7}{2} - 13\cos \frac{{2\pi t}}{5} = 3\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\({\text{GDC}} \Rightarrow {t_2} = 6.22\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Accept graphical approaches.</p>
<p class="p3"><em><strong>[4 marks]</strong></em></p>
<p class="p3"><em><strong>Total [15 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Prove that the equation \(3{x^2} + 2kx + k - 1 = 0\) has two distinct real roots for all values of \(k \in \mathbb{R}\).</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>k</em> for which the two roots of the equation are closest together.</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: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\Delta = {b^2} - 4ac = 4{k^2} - 4 \times 3 \times (k - 1) = 4{k^2} - 12k + 12\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 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>M1A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> if expression seen within quadratic formula.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica; min-height: 22.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(144 - 4 \times 4 \times 12 < 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\Delta \) always positive, therefore the equation always has two distinct real roots <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(and cannot be always negative as \(a > 0\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">sketch of \(y = 4{k^2} - 12k + 12\) or \(y = {k^2} - 3k + 3\) not crossing the <em>x</em>-axis <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\Delta \) always positive, therefore the equation always has two distinct real roots <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">write \(\Delta \) as \(4{(k - 1.5)^2} + 3\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\Delta \) always positive, therefore the equation always has two distinct real roots <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">closest together when \(\Delta \) is least <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;">minimum value occurs when <em>k</em> = 1.5 <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><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;">Most candidates were able to find the discriminant (sometimes only as part of the quadratic formula) but fewer were able to explain satisfactorily why there were two distinct roots.</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;">Most candidates were able to find the discriminant (sometimes only as part of the quadratic formula) but fewer were able to explain satisfactorily why there were two distinct roots. Only the better candidates were able to give good answers to part (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Farmer Bill owns a rectangular field, 10 m by 4 m. Bill attaches a rope to a wooden post at one corner of his field, and attaches the other end to his goat Gruff.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that the rope is 5 m long, calculate the percentage of Bill’s field that Gruff is able to graze. Give your answer correct to the nearest integer.</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>Bill replaces Gruff’s rope with another, this time of length \(a,{\text{ }}4 < a < 10\), so that Gruff can now graze exactly one half of Bill’s field.</p>
<p>Show that \(a\) satisfies the equation</p>
<p>\[{a^2}\arcsin \left( {\frac{4}{a}} \right) + 4\sqrt {{a^2} - 16} = 40.\]</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(a\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="images/Schermafbeelding_2016-01-06_om_16.06.57.png" alt></p>
<p class="p2"><strong>EITHER</strong></p>
<p class="p1">area of triangle \( = \frac{1}{2} \times 3 \times 4\;\;\;( = 6)\) <span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">area of sector \( = \frac{1}{2}\arcsin \left( {\frac{4}{5}} \right) \times {5^2}\;\;\;( = 11.5911 \ldots )\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><strong>OR</strong></p>
<p class="p1">\(\int_0^4 {\sqrt {25 - {x^2}} {\text{d}}x} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"><strong>THEN</strong></p>
<p class="p1">total area \( = 17.5911 \ldots {\text{ }}{{\text{m}}^2}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1">percentage \( = \frac{{17.5911 \ldots }}{{40}} \times 100 = 44\% \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[4 marks]</em></strong></span></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"><img src="images/Schermafbeelding_2016-01-06_om_16.38.28.png" alt></p>
<p>area of triangle \( = \frac{1}{2} \times 4 \times \sqrt {{a^2} - 16} \) <strong><em>A1</em></strong></p>
<p>\(\theta = \arcsin \left( {\frac{4}{a}} \right)\) <strong><em>(A1)</em></strong></p>
<p>area of sector \( = \frac{1}{2}{r^2}\theta = \frac{1}{2}{a^2}\arcsin \left( {\frac{4}{a}} \right)\) <strong><em>A1</em></strong></p>
<p>therefore total area \( = 2\sqrt {{a^2} - 16} + \frac{1}{2}{a^2}\arcsin \left( {\frac{4}{a}} \right) = 20\) <strong><em>A1</em></strong></p>
<p>rearrange to give: \({a^2}\arcsin \left( {\frac{4}{a}} \right) + 4\sqrt {{a^2} - 16} = 40\) <strong><em>AG</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(\int_0^4 {\sqrt {{a^2} - {x^2}} {\text{d}}x = 20} \) <strong><em>M1</em></strong></p>
<p>use substitution \(x = a\sin \theta ,{\text{ }}\frac{{{\text{d}}x}}{{{\text{d}}\theta }} = a\cos \theta \)</p>
<p>\(\int_0^{\arcsin \left( {\frac{4}{a}} \right)} {{a^2}{{\cos }^2}\theta {\text{d}}\theta = 20} \)</p>
<p>\(\frac{{{a^2}}}{2}\int_0^{\arcsin \left( {\frac{4}{a}} \right)} {(\cos 2\theta + 1){\text{d}}\theta = 20} \) <strong><em>M1</em></strong></p>
<p>\({a^2}\left[ {\left( {\frac{{\sin 2\theta }}{2} + \theta } \right)} \right]_0^{\arcsin \left( {\frac{4}{a}} \right)} = 40\) <strong><em>A1</em></strong></p>
<p>\({a^2}\left[ {(\sin \theta \cos \theta + \theta } \right]_0^{\arcsin \left( {\frac{4}{a}} \right)} = 40\)</p>
<p>\({a^2}\arcsin \left( {\frac{4}{a}} \right) + {a^2}\left( {\frac{4}{a}} \right)\sqrt {\left( {1 - {{\left( {\frac{4}{a}} \right)}^2}} \right)} = 40\) <strong><em>A1</em></strong></p>
<p>\({a^2}\arcsin \left( {\frac{4}{a}} \right) + 4\sqrt {{a^2} - 16} = 40\) <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">solving using \({\text{GDC}} \Rightarrow a = 5.53{\text{ cm}}\) <em><strong>A2</strong></em></p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<p class="p1"><em><strong>Total [10 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The functions \(f\) and \(g\) are defined by</p>
<p class="p1">\[f(x) = \frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2},{\text{ }}x \in \mathbb{R}\]</p>
<p class="p1">\[g(x) = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2},{\text{ }}x \in \mathbb{R}\]</p>
</div>
<div class="specification">
<p class="p1">Let \(h(x) = nf(x) + g(x)\) where \(n \in \mathbb{R},{\text{ }}n > 1\).</p>
</div>
<div class="specification">
<p class="p1">Let \(t(x) = \frac{{g(x)}}{{f(x)}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Show that \(\frac{1}{{4f(x) - 2g(x)}} = \frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}\).</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Use the substitution \(u = {{\text{e}}^x}\) to find \(\int_0^{\ln 3} {\frac{1}{{4f(x) - 2g(x)}}} {\text{d}}x\). Give your answer in the form \(\frac{{\pi \sqrt a }}{b}\) where \(a,{\text{ }}b \in {\mathbb{Z}^ + }\).</p>
<div class="marks">[9]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>By forming a quadratic equation in \({{\text{e}}^x}\)<span class="s1">, solve the equation \(h(x) = k\), where \(k \in {\mathbb{R}^ + }\).</span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Hence or otherwise show that the equation \(h(x) = k\) has two real solutions provided that \(k > \sqrt {{n^2} - 1} \) and \(k \in {\mathbb{R}^ + }\).</p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Show that \(t'(x) = \frac{{{{[f(x)]}^2} - {{[g(x)]}^2}}}{{{{[f(x)]}^2}}}\) <span class="s1">for \(x \in \mathbb{R}\).</span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Hence show that \(t'(x) > 0\) for \(x \in \mathbb{R}\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) \(\frac{1}{{4\left( {\frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}} \right) - 2\left( {\frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}} \right)}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{1}{{2({{\text{e}}^x} + {{\text{e}}^{ - x}}) - ({{\text{e}}^x} - {{\text{e}}^{ - x}})}}\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{1}{{{{\text{e}}^x} + 3{{\text{e}}^{ - x}}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> \(u = {{\text{e}}^x} \Rightarrow {\text{d}}u = {{\text{e}}^x}{\text{d}}x\)</span> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\int {\frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}{\text{d}}x = \int {\frac{1}{{{u^2} + 3}}{\text{d}}u} } \) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2">(when \(x = 0,{\text{ }}u = 1\) and when \(x = \ln 3,{\text{ }}u = 3\))</p>
<p class="p1"><span class="Apple-converted-space">\(\int_1^3 {\frac{1}{{{u^2} + 3}}{\text{d}}u\left[ {\frac{1}{{\sqrt 3 }}\arctan \left( {\frac{u}{{\sqrt 3 }}} \right)} \right]_1^3} \) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">\(\left( { = \left[ {\frac{1}{{\sqrt 3 }}\arctan \left( {\frac{{{{\text{e}}^x}}}{{\sqrt 3 }}} \right)} \right]_0^{\ln 3}} \right)\)</p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{\pi \sqrt 3 }}{9} - \frac{{\pi \sqrt 3 }}{{18}}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{\pi \sqrt 3 }}{{18}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><strong><em>[9 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \((n + 1){{\text{e}}^{2x}} - 2k{{\text{e}}^x} + (n - 1) = 0\)</span> <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\({{\text{e}}^x} = \frac{{2k \pm \sqrt {4{k^2} - 4({n^2} - 1)} }}{{2(n + 1)}}\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\(x = \ln \left( {\frac{{k \pm \sqrt {{k^2} - {n^2} + 1} }}{{n + 1}}} \right)\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>for two real solutions, we require \(k > \sqrt {{k^2} - {n^2} + 1} \) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2">and we also require \({k^2} - {n^2} + 1 > 0\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({k^2} > {n^2} - 1\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( \Rightarrow k > \sqrt {{n^2} - 1} {\text{ }}({\text{ }}k \in {\mathbb{R}^ + })\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2"><strong><em>[8 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p2">\(t(x) = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}\)</p>
<p class="p2"><span class="Apple-converted-space">\(t'(x) = \frac{{{{({{\text{e}}^x} + {{\text{e}}^{ - x}})}^2} - {{({{\text{e}}^x} - {{\text{e}}^{ - x}})}^2}}}{{{{({{\text{e}}^x} + {{\text{e}}^{ - x}})}^2}}}\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(t'(x) = \frac{{{{\left( {\frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}} \right)}^2} - {{\left( {\frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}} \right)}^2}}}{{{{\left( {\frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}} \right)}^2}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = \frac{{{{\left[ {f(x)} \right]}^2} - {{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p2"><span class="Apple-converted-space">\(t'(x) = \frac{{f(x)g'(x) = g(x)f'(x)}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">\(g'(x) = f(x)\) and \(f'(x) = g(x)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\( = \frac{{{{\left[ {f(x)} \right]}^2} - {{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p3"><strong>METHOD 3</strong></p>
<p class="p4">\(t(x) = ({{\text{e}}^x} - {{\text{e}}^{ - x}}){({{\text{e}}^x} + {{\text{e}}^{ - x}})^{ - 1}}\)</p>
<p class="p4"><span class="Apple-converted-space">\(t'(x) = 1 - \frac{{{{({{\text{e}}^x} - {{\text{e}}^{ - x}})}^2}}}{{{{({{\text{e}}^x} + {{\text{e}}^{ - x}})}^2}}}\) </span><span class="s2"><strong><em>M1A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\( = 1 - \frac{{{{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\( = \frac{{{{\left[ {f(x)} \right]}^2} - {{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s2"><strong><em>AG</em></strong></span></p>
<p class="p3"><strong>METHOD 4</strong></p>
<p class="p4"><span class="Apple-converted-space">\(t'(x) = \frac{{g'(x)}}{{f(x)}} - \frac{{g(x)f'(x)}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s2"><strong><em>M1A1</em></strong></span></p>
<p class="p3">\(g'(x) = f(x)\) and \(f'(x) = g(x)\) gives \(t'(x) = 1 - \frac{{{{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p4"><span class="Apple-converted-space">\( = \frac{{{{\left[ {f(x)} \right]}^2} - {{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s2"><strong><em>AG</em></strong></span></p>
<p class="p3">(ii) <span class="Apple-converted-space"> </span><strong>METHOD 1</strong></p>
<p class="p3">\({\left[ {f(x)} \right]^2} > {\left[ {g(x)} \right]^2}\) (or equivalent) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\({\left[ {f(x)} \right]^2} > 0\) </span><strong><em>R1</em></strong></p>
<p class="p3">hence \(t'(x) > 0,{\text{ }}x \in \mathbb{R}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p4"><span class="s2"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Award as above for use of either \(f(x) = \frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}\) and \(g(x) = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}\) or \({{\text{e}}^x} + {{\text{e}}^{ - x}}\) and \({{\text{e}}^x} - {{\text{e}}^{ - x}}\).</p>
<p class="p3"><strong>METHOD 2</strong></p>
<p class="p3">\({\left[ {f(x)} \right]^2} - {\left[ {g(x)} \right]^2} = 1\) (or equivalent) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p4"><span class="Apple-converted-space">\({\left[ {f(x)} \right]^2} > 0\) </span><span class="s2"><strong><em>R1</em></strong></span></p>
<p class="p3">hence \(t'(x) > 0,{\text{ }}x \in \mathbb{R}\) <strong><em>AG</em></strong></p>
<p class="p4"><span class="s2"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Award as above for use of either \(f(x) = \frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}\) and \(g(x) = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}\) or \({{\text{e}}^x} + {{\text{e}}^{ - x}}\) and \({{\text{e}}^x} - {{\text{e}}^{ - x}}\).</p>
<p class="p3"><strong>METHOD 3</strong></p>
<p class="p4">\(t'(x) = \frac{4}{{{{({{\text{e}}^x} + {{\text{e}}^{ - x}})}^2}}}\)</p>
<p class="p4"><span class="Apple-converted-space">\({\left( {{{\text{e}}^x} + {{\text{e}}^{ - x}}} \right)^2} > 0\) </span><span class="s2"><strong><em>M1A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\(\frac{4}{{{{\left( {{{\text{e}}^x} + {{\text{e}}^{ - x}}} \right)}^2}}} > 0\) </span><span class="s2"><strong><em>R1</em></strong></span></p>
<p class="p3">hence \(t'(x) > 0,{\text{ }}x \in \mathbb{R}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p3"><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (c) were accessible to the large majority of candidates. Candidates found part (b) considerably more challenging.</p>
<p class="p1">Part (a)(i) was reasonably well done with most candidates able to show that \(\frac{1}{{4f(x) - 2g(x)}} = \frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}\). In part (a)(ii), a number of candidates correctly used the required substitution to obtain \(\int {\frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}{\text{d}}x = \int {\frac{1}{{{u^2} + 3}}{\text{d}}u} } \) but then thought that the antiderivative involved natural log rather than arctan.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Parts (a) and (c) were accessible to the large majority of candidates. Candidates found part (b) considerably more challenging.</p>
<p class="p1">In part (b)(i), a reasonable number of candidates were able to form a quadratic in \({{\text{e}}^x}\) (involving parameters \(n\) and \(k\)) and then make some progress towards solving for \({{\text{e}}^x}\) in terms of \(n\) and \(k\). Having got that far, a small number of candidates recognised to then take the natural logarithm of both sides and hence solve \(h(x) = k\) for \(\chi \). In part (b)(ii), a small number of candidates were able to show from their solutions to part (b)(i) or through the use of the discriminant that the equation \(h(x) = k\) has two real solutions provided that \(k > \sqrt {{k^2} - {n^2} + 1} \) and \(k > \sqrt {{n^2} - 1} \).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (c) were accessible to the large majority of candidates. Candidates found part (b) considerably more challenging.</p>
<p class="p1">It was pleasing to see the number of candidates who attempted part (c). In part (c)(i), a large number of candidates were able to correctly apply either the quotient rule or the product rule to find \(t'(x)\). A smaller number of candidates were then able to show equivalence between the form of \(t'(x)\) they had obtained and the form of \(t'(x)\) required in the question. A pleasing number of candidates were able to exploit the property that \(f'(x) = g(x)\) and \(g'(x) = f(x)\). As with part (c)(i), part (c)(ii) could be successfully tackled in a number of ways. The best candidates offered concise logical reasoning to show that \(t'(x) > 0\) for \(x \in \mathbb{R}\).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let the function \(f\) be defined by \(f(x) = \frac{{2 - {{\text{e}}^x}}}{{2{{\text{e}}^x} - 1}},{\text{ }}x \in D\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine \(D\), the largest possible domain of \(f\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the graph of \(f\) has three asymptotes and state their equations.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(f'(x) = - \frac{{3{{\text{e}}^x}}}{{{{(2{{\text{e}}^x} - 1)}^2}}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use your answers from parts (b) and (c) to justify that \(f\) <span class="s1">has an inverse and state its domain.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \({f^{ - 1}}(x)\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Consider the region \(R\) </span>enclosed by the graph of \(y = f(x)\) and the axes.</p>
<p class="p1">Find the volume of the solid obtained when \(R\) is rotated through \(2\pi \) about the \(y\)-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempting to solve either \(2{{\text{e}}^x} - 1 = 0\) or \(2{{\text{e}}^x} - 1 \ne 0\) for \(x\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(D = \mathbb{R}\backslash \left\{ { - \ln 2} \right\}\) (or equivalent <em>eg</em> \(x \ne - \ln 2\)) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Accept \(D = \mathbb{R}\backslash \left\{ { - 0.693} \right\}\) or equivalent <em>eg</em> \(x \ne - 0.693\).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">considering \(\mathop {\lim }\limits_{x \to - \ln 2} f(x)\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(x = - \ln 2{\text{ }}(x = - 0.693)\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p1">considering one of \(\mathop {\lim }\limits_{x \to - \infty } f(x)\)<span class="s1"> </span>or \(\mathop {\lim }\limits_{x \to + \infty } f(x)\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>M1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(\mathop {\lim }\limits_{x \to - \infty } f(x) = - 2 \Rightarrow y = - 2\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(\mathop {\lim }\limits_{x \to + \infty } f(x) = - \frac{1}{2} \Rightarrow y = - \frac{1}{2}\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<div> </div>
<p class="p1"><strong>Note: </strong>Award <strong><em>A0A0 </em></strong>for \(y = - 2\)<span class="s1"> </span>and \(y = - \frac{1}{2}\)<span class="s1"> </span>stated without any justification.</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(f'(x) = \frac{{ - {{\text{e}}^x}(2{{\text{e}}^x} - 1) - 2{{\text{e}}^x}(2 - {{\text{e}}^x})}}{{{{(2{{\text{e}}^x} - 1)}^2}}}\) </span><strong><em>M1A1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = - \frac{{3{{\text{e}}^x}}}{{{{(2{{\text{e}}^x} - 1)}^2}}}\) </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(f'(x) < 0{\text{ (for all }}x \in D) \Rightarrow f\) is (strictly) decreasing <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>R1 </em></strong>for a statement such as \(f'(x) \ne 0\) and so the graph of \(f\) has no turning points.</p>
<p class="p2"> </p>
<p class="p1">one branch is above the upper horizontal asymptote and the other branch is below the lower horizontal asymptote <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\(f\) has an inverse <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( - \infty < x < - 2 \cup - \frac{1}{2} < x < \infty \) </span><strong><em>A2</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>A2 </em></strong>if the domain of the inverse is seen in either part (d) or in part (e).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(x = \frac{{2 - {{\text{e}}^y}}}{{2{{\text{e}}^y} - 1}}\) </span><strong><em>M1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>M1 </em></strong>for interchanging \(x\) and \(y\) (can be done at a later stage).</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\(2x{{\text{e}}^y} - x = 2 - {{\text{e}}^y}\) </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({{\text{e}}^y}(2x + 1) = x + 2\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({f^{ - 1}}(x) = \ln \left( {\frac{{x + 2}}{{2x + 1}}} \right){\text{ }}\left( {{f^{ - 1}}(x) = \ln (x + 2) - \ln (2x + 1)} \right)\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">use of \(V = \pi \int_a^b {{x^2}{\text{d}}y} \) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \pi \int_0^1 {{{\left( {\ln \left( {\frac{{y + 2}}{{2y + 1}}} \right)} \right)}^2}{\text{d}}y} \) </span><strong><em>(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for the correct integrand and <strong><em>(A1) </em></strong>for the limits.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 0.331\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The graphs of \(y = {x^2}{{\text{e}}^{ - x}}\) and \(y = 1 - 2\sin x\) for \(2 \leqslant x \leqslant 7\) intersect at points A and B.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The <em>x</em>-coordinates of A and B are \({x_{\text{A}}}\) and \({x_{\text{B}}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \({x_{\text{A}}}\) and the value of \({x_{\text{B}}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the area enclosed between the two graphs for \({x_{\mathbf{A}}} \leqslant x \leqslant {x_{\text{B}}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_{\text{A}}} = 2.87\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_{{\text{B}}}} = 6.78\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_{2.87172{\text{K}}}^{6.77681K} {1 - 2\sin x - {x^2}{{\text{e}}^{ - x}}{\text{d}}x} \) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 6.76\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for definite integral and <strong><em>(A1</em></strong>) for a correct definite integral.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="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) Find the solution of the 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;">\[\ln {2^{4x - 1}} = \ln {8^{x + 5}} + {\log _2}{16^{1 - 2x}},\]</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;">expressing your answer in terms of \(\ln 2\).</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) Using this value of <em>x</em>, find the value of <em>a</em> for which \({\log _a}x = 2\), giving your answer to three 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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) rewrite the equation as \((4x - 1)\ln 2 = (x + 5)\ln 8 + (1 - 2x){\log _2}16\) <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;">\((4x - 1)\ln 2 = (3x + 15)\ln 2 + 4 - 8x\) <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;">\(x = \frac{{4 + 16\ln 2}}{{8 + \ln 2}}\) <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> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(x = {a^2}\) <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;">\(a = 1.318\) <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> Treat 1.32 as an <strong><em>AP</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;">Award <strong><em>A0</em></strong> 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;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A more difficult question. Many candidates failed to read the question carefully so did not express <em>x</em> in terms of \(\ln 2\).</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;">Given that (<em>x</em> − 2) is a factor of \(f(x) = {x^3} + a{x^2} + bx - 4\) and that division \(f(x)\) by (<em>x</em> − 1) leaves a remainder of −6 , find the value of <em>a</em> and the value of <em>b</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(2) = 8 + 4a + 2b - 4 = 0\) <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;">\( \Rightarrow 4a + 2b = - 4\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(1) = 1 + a + b - 4 = - 6\) <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;">\( \Rightarrow a + b = - 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solving, \(a = 1,{\text{ }}b = - 4\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p 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 \(f(x) = \frac{1}{{1 + {{\text{e}}^{ - x}}}}\),</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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">find \({f^{ - 1}}(x)\), stating its domain;</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: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">find the value of <em>x</em> such that \(f(x) = {f^{ - 1}}(x)\).</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{1}{{1 + {{\text{e}}^{ - x}}}}\)</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;">\(y(1 + {{\text{e}}^{ - x}}) = 1\) <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;">\(1 + {{\text{e}}^{ - x}} = \frac{1}{y} \Rightarrow {{\text{e}}^{ - x}} = \frac{1}{y} - 1\) <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;">\( \Rightarrow x = - \ln \left( {\frac{1}{y} - 1} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}(x) = - \ln \left( {\frac{1}{x} - 1} \right)\,\,\,\,\,\left( { = \ln \left( {\frac{x}{{1 - x}}} \right)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">domain: 0 < <em>x</em> < 1 <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for endpoints and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for strict inequalities.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">0.659 <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>[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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Finding the inverse function was done successfully by a very large number of candidates. The domain, however, was not always correct. Some candidates failed to use the GDC correctly to find (b), while other candidates had unsuccessful attempts at an analytic solution.</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;">Finding the inverse function was done successfully by a very large number of candidates. The domain, however, was not always correct. Some candidates failed to use the GDC correctly to find (b), while other candidates had unsuccessful attempts at an analytic solution.</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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The sum of the first 16 terms of an arithmetic sequence is 212 and the fifth term is 8.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the first term and the common difference.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the smallest value of <em>n </em>such that the sum of the first <em>n </em>terms is greater than 600.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({S_n} = \frac{n}{2}[2a + (n - 1)d]\)</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;">\(212 = \frac{{16}}{2}(2a + 15d)\,\,\,\,\,( = 16a + 120d)\) <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;">\({n^{th}}{\text{ term is }}a + (n - 1)d\)</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;">\(8 = a + 4d\) <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;">solving simultaneously: <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;">\(d = 1.5,{\text{ }}a = 2\) <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;">[4 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{n}{2}[4 + 1.5(n - 1)] > 600\) <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;">\( \Rightarrow 3{n^2} + 5n - 2400 > 0\) <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;">\( \Rightarrow n > 27.4...,{\text{ }}(n < - 29.1...)\)</span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 11px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not penalize improper use of inequalities. </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;">\( \Rightarrow n = 28\) <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;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be a good start to the paper for most candidates. The vast majority made a meaningful attempt at this question with many gaining the correct answers. Candidates who lost marks usually did so because of mistakes in the working. In part (b) the most efficient way of gaining the answer was to use the calculator once the initial inequality was set up. A small number of candidates spent valuable time unnecessarily manipulating the algebra before moving to the calculator.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be a good start to the paper for most candidates. The vast majority made a meaningful attempt at this question with many gaining the correct answers. Candidates who lost marks usually did so because of mistakes in the working. In part (b) the most efficient way of gaining the answer was to use the calculator once the initial inequality was set up. A small number of candidates spent valuable time unnecessarily manipulating the algebra before moving to the calculator.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">The function \(f\) is defined as \(f(x) = \sqrt {\frac{{1 - x}}{{1 + x}}} ,{\text{ }} - 1 < x \leqslant 1\).</p>
<p class="p1">Find the inverse function, \({f^{ - 1}}\) stating its domain and range.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><span class="Apple-converted-space">\(x = \sqrt {\frac{{1 - y}}{{1 + y}}} \) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for interchanging \(x\) and \(y\) (can be done at a later stage).</p>
<p class="p3">\({x^2} = \frac{{1 - y}}{{1 + y}}\)</p>
<p class="p3"><span class="Apple-converted-space">\({x^2} + {x^2}y = 1 - y\) </span><strong><em>M1</em></strong></p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for attempting to make \(y\) the subject.</p>
<p class="p3"><span class="Apple-converted-space">\(y(1 + {x^2}) = 1 - {x^2}\) </span><strong><em>(A1)</em></strong></p>
<p class="p4"><span class="Apple-converted-space">\({f^{ - 1}}(x) = \frac{{1 - {x^2}}}{{1 + {x^2}}},{\text{ }}x \geqslant 0\) </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>only if \({f^{ - 1}}(x)\) is seen. Award <strong><em>A1 </em></strong>for the domain.</p>
<p class="p3">the range of \({f^{ - 1}}\) <span class="s2">is \( - 1 < {f^{ - 1}}(x) \leqslant 1\) <span class="Apple-converted-space"> </span></span><strong><em>A1</em></strong></p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept correct alternative notation <em>eg</em><span class="s2">. \( - 1 < y \leqslant 1\)</span>.</p>
<p class="p3"><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">Most candidates were able to find an expression for the inverse function. A large number of candidates however were unable to determine the domain and range of the inverse.</p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Compactness is a measure of how compact an enclosed region is.</p>
<p class="p1">The compactness, <em>\(C\) </em>, of an enclosed region can be defined by \(C = \frac{{4A}}{{\pi {d^2}}}\), where <em>\(A\) </em>is the area of the region and <em>\(d\) </em>is the maximum distance between any two points in the region.</p>
<p class="p1">For a circular region, \(C = 1\).</p>
<p class="p1">Consider a regular polygon of <em>\(n\) </em>sides constructed such that its vertices lie on the circumference of a circle of diameter <em>\(x\) </em>units.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">If \(n > 2\) and even, show that \(C = \frac{n}{{2\pi }}\sin \frac{{2\pi }}{n}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">If \(n > 1\) and odd, it can be shown that \(C = \frac{{n\sin \frac{{2\pi }}{n}}}{{\pi \left( {1 + \cos \frac{\pi }{n}} \right)}}\).</p>
<p class="p1">Find the regular polygon with the least number of sides for which the compactness is more than \(0.99\).</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">If \(n > 1\) and odd, it can be shown that \(C = \frac{{n\sin \frac{{2\pi }}{n}}}{{\pi \left( {1 + \cos \frac{\pi }{n}} \right)}}\).</p>
<p class="p1">Comment briefly on whether <em>C </em>is a good measure of compactness.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">each triangle has area \(\frac{1}{8}{x^2}\sin \frac{{2\pi }}{n}\;\;\;({\text{use of }}\frac{1}{2}ab\sin C)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">there are <em>\(n\) </em>triangles so \(A = \frac{1}{8}n{x^2}\sin \frac{{2\pi }}{n}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(C = \frac{{4\left( {\frac{1}{8}n{x^2}\sin \frac{{2\pi }}{n}} \right)}}{{\pi {n^2}}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">so \(C = \frac{n}{{2\pi }}\sin \frac{{2\pi }}{n}\) <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 class="p1">attempting to find the least value of <em>\(n\) </em>such that \(\frac{n}{{2\pi }}\sin \frac{{2\pi }}{n} > 0.99\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\(n = 26\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">attempting to find the least value of <em>\(n\) </em>such that \(\frac{{n\sin \frac{{2\pi }}{n}}}{{\pi \left( {1 + \cos \frac{\pi }{n}} \right)}} > 0.99\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\(n = 21\) (and so a regular polygon with 21 sides) <em><strong>A1</strong></em></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <span class="s1"><strong><em>(M0)A0(M1)A1</em></strong></span> if \(\frac{n}{{2\pi }}\sin \frac{{2\pi }}{n} > 0.99\) is not considered and \(\frac{{n\sin \frac{{2\pi }}{n}}}{{\pi \left( {1 + \cos \frac{\pi }{n}} \right)}} > 0.99\) is correctly considered.</p>
<p class="p1">Award <strong><em>(M1)A1(M0)A0 </em></strong>for \(n = 26\).</p>
<p class="p1"><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p1">for even and odd values of <em>n</em>, the value of <em>C </em>seems to increase towards the limiting value of the circle \((C = 1)\) <em>ie </em>as <em>n </em>increases, the polygonal regions get closer and closer to the enclosing circular region <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">the differences between the odd and even values of <em>n </em>illustrate that this measure of compactness is not a good one. <span class="Apple-converted-space"> </span><strong><em>R1</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">Most candidates found this a difficult question with a large number of candidates either not attempting it or making little to no progress. In part (a), a number of candidates attempted to show the desired result using specific regular polygons. Some candidates attempted to fudge the result.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (b), the overwhelming majority of candidates that obtained either \(n = 21\) or \(n = 26\) or both used either a GDC numerical solve feature or a graphical approach rather than a tabular approach which is more appropriate for a discrete variable such as the number of sides of a regular polygon. Some candidates wasted valuable time by showing that \(C = \frac{{n\sin \frac{{2\pi }}{n}}}{{\pi \left( {1 + \cos \frac{\pi }{n}} \right)}}\) (a given result).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (c), the occasional candidate correctly commented that \(C \) was a good measure of compactness either because the value of \(C \) seemed to approach the limiting value of the circle as \(n \) increased or commented that \(C \) was not a good measure because of the disparity in \(C \)-values between even and odd values of \(n \).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram below shows a semi-circle of diameter 20 cm, centre O and two points A and B such that \({\rm{A\hat OB}} = \theta \), where \(\theta \) is in radians.</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="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_06.17.13.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Show that the shaded area can be expressed as \(50\theta - 50\sin \theta \).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \(\theta \) for which the shaded area is equal to half that of the unshaded area, giving your answer correct to four significant figures.</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: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(A = \frac{1}{2} \times {10^2} \times \theta - \frac{1}{2} \times {10^2} \times \sin \theta \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1 </em></strong>for use of area of segment = area of sector – area of triangle.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 50\theta - 50\sin \theta \) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>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;">unshaded area \( = \frac{{\pi \times {{10}^2}}}{2} - 50(\theta - \sin \theta )\)</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 equivalent <em>eg</em> \(50\pi - 50\theta + 50\sin \theta )\) <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;">\(50\theta - 50\sin \theta = \frac{1}{2}(50\pi - 50\theta + 50\sin \theta )\) <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;">\(3\theta - 3\sin \theta - \pi = 0\)</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;">\( \Rightarrow \theta = 1.969{\text{ (rad)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(50\theta - 50\sin \theta = \frac{1}{3}\left( {\frac{{\pi \times {{10}^2}}}{2}} \right)\) <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;">\(3\theta - 3\sin \theta - \pi = 0\)</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;">\( \Rightarrow \theta = 1.969{\text{ (rad)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<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 very well done. Most candidates knew how to calculate the area of a segment. A few candidates used \(r = 20\).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) challenged a large proportion of candidates. A common error was to equate the unshaded area and the shaded area. Some candidates expressed their final answer correct to three significant figures rather than to the four significant figures specified.</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 Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \ln x\) . The graph of <em>f </em>is transformed into the graph of the function <em>g </em>by a translation of \(\left( {\begin{array}{*{20}{c}}<br> 3 \\ <br> { - 2} <br>\end{array}} \right)\), followed by a reflection in the <em>x</em>-axis. Find an expression for \(g(x)\), giving your answer as a single logarithm.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(h(x) = f(x - 3) - 2 = \ln (x - 3) - 2\) <strong><em>(M1)(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(g(x) = -h(x) = 2 - \ln (x - 3)\) <strong><em>M1</em></strong></span></p>
<p> <strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">Note<em>: </em></strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">Award </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">M1 </strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">only if it is clear the effect of the reflection in the </span><em style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">x</em><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">-axis:</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 expression is correct <strong><em>OR<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;">there is a change of signs of the previous expression <strong><em>OR<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;">there’s a graph or an explanation making it explicit</span></p>
<p> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln {{\text{e}}^2} - \ln (x - 3)\) <strong><em>M1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln \left( {\frac{{{{\text{e}}^2}}}{{x - 3}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[5 marks]</span><br></em></strong></p>
</div>
<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;">This question was well attempted but many candidates could have scored better had they written down all the steps to obtain the final expression. In some cases, as the final expression was incorrect and the middle steps were missing, candidates scored just 1 mark. That could be a consequence of a small mistake, but the lack of working prevented them from scoring at least all method marks. Some candidates performed the transformations well but were not able to use logarithms properties to transform the answer and give it as a single logarithm.</span></p>
</div>
<br><hr><br><div class="question">
<p class="p1">Find the acute angle between the planes with equations \(x + y + z = 3\) and \(2x - z = 2\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><strong><em>n</em></strong>\(_1 = \left( {\begin{array}{*{20}{c}} 1 \\ 1 \\ 1 \end{array}} \right)\) and <strong><em>n</em></strong>\(_2 = \left( {\begin{array}{*{20}{c}} 2 \\ 0 \\ { - 1} \end{array}} \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em></strong></p>
<p class="p1"><strong>EITHER </strong></p>
<p class="p1"><span class="Apple-converted-space">\(\theta = \arccos \left( {\frac{{{n_1} \bullet {n_2}}}{{\left| {{n_1}} \right|\left| {{n_2}} \right|}}} \right)\left( {\cos \theta = \frac{{{n_1} \bullet {n_2}}}{{\left| {{n_1}} \right|\left| {{n_2}} \right|}}} \right)\) </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \arccos \left( {\frac{{2 + 0 - 1}}{{\sqrt 3 \sqrt 5 }}} \right)\left( {\cos \theta = \frac{{2 + 0 - 1}}{{\sqrt 3 \sqrt 5 }}} \right)\) </span><strong><em>(A1)</em></strong></p>
<p class="p1">\( = \arccos \left( {\frac{1}{{\sqrt {15} }}} \right)\left( {\cos \theta = \frac{1}{{\sqrt {15} }}} \right)\)</p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><span class="Apple-converted-space">\(\theta = \arcsin \left( {\frac{{\left| {{n_1} \times {n_2}} \right|}}{{\left| {{n_1}} \right|\left| {{n_2}} \right|}}} \right)\left( {\sin \theta = \frac{{\left| {{n_1} \times {n_2}} \right|}}{{\left| {{n_1}} \right|\left| {{n_2}} \right|}}} \right)\) </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \arcsin \left( {\frac{{\sqrt {14} }}{{\sqrt 3 \sqrt 5 }}} \right)\left( {\sin \theta = \frac{{\sqrt {14} }}{{\sqrt 3 \sqrt 5 }}} \right)\) </span><strong><em>(A1)</em></strong></p>
<p class="p1">\( = \arcsin \left( {\frac{{\sqrt {14} }}{{\sqrt {15} }}} \right)\left( {\sin \theta = \frac{{\sqrt {14} }}{{\sqrt {15} }}} \right)\)</p>
<p class="p2"> </p>
<p class="p1"><strong>THEN</strong></p>
<p class="p1"><span class="Apple-converted-space">\( = 75.0^\circ {\text{ (or 1.31)}}\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
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<h2 style="margin-top: 1em">Examiners report</h2>
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[N/A]
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<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \frac{{{{\text{e}}^{2x}} + 1}}{{{{\text{e}}^x} - 2}}\).</span></p>
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<div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The line \({L_2}\) is parallel to \({L_1}\) and tangent to the curve \(y = f(x)\).</span></p>
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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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the equations of the horizontal and vertical asymptotes of the curve \(y = f(x)\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
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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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find \(f'(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Show that the curve has exactly one point where its tangent is horizontal.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Find the coordinates of this point.</span></p>
<p> </p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
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<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the equation of \({L_1}\), the normal to the curve at the point where it crosses the <em>y</em>-axis.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
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<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the equation of the line \({L_2}\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
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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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \to - \infty \Rightarrow y \to - \frac{1}{2}\) so \(y = - \frac{1}{2}\) is an asymptote <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^x} - 2 = 0 \Rightarrow x = \ln 2\) so \(x = \ln 2{\text{ }}( = 0.693)\) is an asymptote </span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
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<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(f'(x) = \frac{{2\left( {{{\text{e}}^x} - 2} \right){{\text{e}}^{2x}} - \left( {{{\text{e}}^{2x}} + 1} \right){{\text{e}}^x}}}{{{{\left( {{{\text{e}}^x} - 2} \right)}^2}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \( = \frac{{{{\text{e}}^{3x}} - 4{{\text{e}}^{2x}} - {{\text{e}}^x}}}{{{{\left( {{{\text{e}}^x} - 2} \right)}^2}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(f'(x) = 0\) when \({{\text{e}}^{3x}} - 4{{\text{e}}^{2x}} - {{\text{e}}^x} = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \({{\text{e}}^x}\left( {{{\text{e}}^{2x}} - 4{{\text{e}}^x} - 1} \right) = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \({{\text{e}}^x} = 0,{\text{ }}{{\text{e}}^x} = - 0.236,{\text{ }}{{\text{e}}^x} = 4.24{\text{ }}({\text{or }}{{\text{e}}^x} = 2 \pm \sqrt 5 )\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1 </em></strong>for zero, <strong><em>A1 </em></strong>for other two solutions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Accept any answers which show a zero, a negative and a positive.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> as \({{\text{e}}^x} > 0\) exactly one solution <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award marks for purely graphical solution.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) (1.44, 8.47) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
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<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(0) = - 4\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so gradient of normal is \(\frac{1}{4}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(0) = - 2\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so equation of \({L_1}\) is \(y = \frac{1}{4}x - 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{1}{4}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(x = 1.46\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(1.46) = 8.47\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">equation of \({L_2}\) is \(y - 8.47 = \frac{1}{4}(x - 1.46)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(or \(y = \frac{1}{4}x + 8.11\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
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<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>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
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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;">Sketch the curve \(y = \frac{{\cos x}}{{\sqrt {{x^2} + 1} }},{\text{ }} - 4 \leqslant x \leqslant 4\) showing clearly the coordinates of the <em>x-</em>intercepts, any maximum points and any minimum points.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the gradient of the curve at <em>x </em>= 1 .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
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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;">Find the equation of the normal to the curve at <em>x </em>= 1 .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
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<h2 style="margin-top: 1em">Markscheme</h2>
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<p><span><strong><em><img 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" alt> A1A1A1A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for correct shape. Do not penalise if too large a domain is used,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1 </em></strong>for correct <em>x</em>-intercepts,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1 </em></strong>for correct coordinates of two minimum points,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1 </em></strong>for correct coordinates of maximum point.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Accept answers which correctly indicate the position of the intercepts, maximum point and minimum points. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[4 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">gradient at <em>x</em> = 1 is –0.786 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[1 mark]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">gradient of normal is \(\frac{{ - 1}}{{ - 0.786}}( = 1.272...)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">when <em>x</em> = 1, <em>y</em> = 0.3820... <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Equation of normal is <em>y</em> – 0.382 = 1.27(<em>x</em> – 1) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(( \Rightarrow y = 1.27x - 0.890)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to make a meaningful start to this question, but many made errors along the way and hence only a relatively small number of candidates gained full marks for the question. Common errors included trying to use degrees, rather than radians, trying to use algebraic methods to find the gradient in part (b) and trying to find the equation of the tangent rather than the equation of the normal in part (c).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to make a meaningful start to this question, but many made errors along the way and hence only a relatively small number of candidates gained full marks for the question. Common errors included trying to use degrees, rather than radians, trying to use algebraic methods to find the gradient in part (b) and trying to find the equation of the tangent rather than the equation of the normal in part (c).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to make a meaningful start to this question, but many made errors along the way and hence only a relatively small number of candidates gained full marks for the question. Common errors included trying to use degrees, rather than radians, trying to use algebraic methods to find the gradient in part (b) and trying to find the equation of the tangent rather than the equation of the normal in part (c).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram shows the graphs of a linear function <em>f</em> and a quadratic function <em>g</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;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">On the same axes sketch the graph of \(\frac{f}{g}\). Indicate clearly where the <em>x</em>-intercept and the asymptotes occur.</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;"><br><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;"> </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;">correct concavities <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;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for concavity of each branch of the curve.</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;">correct <em>x</em>-intercept of \(\frac{f}{g}\) (which is EXACTLY the <em>x</em>-intercept of <em>f</em>) <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;">correct vertical asymptotes of \(\frac{f}{g}\) (which ONLY occur when <em>x</em> equals the <em>x</em>-intercepts of <em>g</em>) <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;"><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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates answered well this question. Full marks were often achieved. Many other candidates did not attempt it at all.</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Express the sum of the first <em>n</em> positive odd integers using sigma notation.</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) Show that the sum stated above is \({n^2}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Deduce the value of the difference between the sum of the first 47 positive odd integers and the sum of the first 14 positive odd integers.</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;">A number of distinct points are marked on the circumference of a circle, forming a polygon. Diagonals are drawn by joining all pairs of non-adjacent points.</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) Show on a diagram all diagonals if there are 5 points.</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) Show that the number of diagonals is \(\frac{{n(n - 3)}}{2}\) if there are n points, where \(n > 2\).</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;">(iii) Given that there are more than one million diagonals, determine the least number of points for which this is possible.</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable \(X \sim B(n,{\text{ }}p)\) has mean 4 and variance 3.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Determine <em>n</em> and <em>p</em>.</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) Find the probability that in a single experiment the outcome is 1 or 3.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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) \(\sum\limits_{k = 1}^n {(2k - 1)} \) (or equivalent) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px 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 \(\sum\limits_{n = 1}^n {(2n - 1)} \) or equivalent.</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;">(ii) </span><strong style="font-family: 'times new roman', times; font-size: medium;">EITHER</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2 \times \frac{{n(n + 1)}}{2} - n\) <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;"><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;">\(\frac{n}{2}\left( {2 + (n - 1)2} \right){\text{ (using }}{S_n} = \frac{n}{2}\left( {2{u_1} + (n - 1)d} \right))\) <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;"><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;">\(\frac{n}{2}(1 + 2n - 1){\text{ (using }}{S_n} = \frac{n}{2}({u_1} + {u_n}))\) <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;"><strong>THEN</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;">\( = {n^2}\) <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;">(iii) \({47^2} - {14^2} = 2013\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <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;">a pentagon and five diagonals <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">five diagonals (circle optional) <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) Each point joins to <em>n</em> – 3 other points. <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;">a correct argument for \({n(n - 3)}\) <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;">a correct argument for \(\frac{{n(n - 3)}}{2}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><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;">(iii) attempting to solve \(\frac{1}{2}n(n - 3) > 1\,000\,000\) for <em>n</em>. <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;">\(n > 1415.7\) <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;">\(n = 1416\) <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>[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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <em>np</em> = 4 and <em>npq</em> = 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;">attempting to solve for <em>n</em> and <em>p</em> <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;">\(n = 16\) and \(p = \frac{1}{4}\) <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;"> </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) \(X \sim B(16,0.25)\) <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;">\(P(X = 1) = 0.0534538...( = \left( {\begin{array}{*{20}{c}}<br> {16} \\ <br> 1 <br>\end{array}} \right)(0.25){(0.75)^{15}})\) <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;">\(P(X = 3) = 0.207876...( = \left( {\begin{array}{*{20}{c}}<br> {16} \\ <br> 3 <br>\end{array}} \right){(0.25)^3}{(0.75)^{13}})\) <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;">\({\text{P}}(X = 1) + {\text{P}}(X = 3)\) <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;">= 0.261 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[8 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (a) (i), a large number of candidates were unable to correctly use sigma notation to express the sum of the first <em>n </em>positive odd integers. Common errors included summing \(2n - 1\) from 1 to <em>n </em>and specifying sums with incorrect limits. Parts (a) (ii) and (iii) were generally well done.</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;">Parts (b) (i) and (iii) were generally well done. In part (b) (iii), many candidates unnecessarily simplified their quadratic when direct GDC use could have been employed. A few candidates gave \(n > 1416\) as their final answer. While some candidates displayed sound reasoning in part (b) (ii), many candidates unfortunately adopted a ‘proof by example’ approach.</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;">Part (c) was generally well done. In part (c) (ii), some candidates multiplied the two probabilities rather than adding the two probabilities.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A straight street of width 20 metres is bounded on its parallel sides by two vertical walls, one of height 13 metres, the other of height 8 metres. The intensity of light at point P at ground level on the street is proportional to the angle \(\theta \) where \(\theta = {\rm{A\hat PB}}\), as shown in the diagram.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for \(\theta \) in terms of <em>x</em>, where <em>x</em> is the distance of P from the base of the wall of height 8 m.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Calculate the value of \(\theta \) when <em>x</em> = 0.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Calculate the value of \(\theta \) when <em>x</em> = 20.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(\theta \), for \(0 \leqslant x \leqslant 20\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = \frac{{5(744 - 64x - {x^2})}}{{({x^2} + 64)({x^2} - 40x + 569)}}\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the result in part (d), or otherwise, determine the value of <em>x</em> corresponding to the maximum light intensity at P. Give your answer to four significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The point P moves across the street with speed \(0.5{\text{ m}}{{\text{s}}^{ - 1}}\). Determine the rate of change of \(\theta \) with respect to time when P is at the midpoint of the street.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \pi - \arctan \left( {\frac{8}{x}} \right) - \arctan \left( {\frac{{13}}{{20 - x}}} \right)\) (or equivalent) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept \(\theta = 180^\circ - \arctan \left( {\frac{8}{x}} \right) - \arctan \left( {\frac{{13}}{{20 - x}}} \right)\) (or equivalent).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">OR</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \arctan \left( {\frac{x}{8}} \right) + \arctan \left( {\frac{{20 - x}}{{13}}} \right)\) (or equivalent) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(\theta = 0.994{\text{ }}\left( { = \arctan \frac{{20}}{{13}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(\theta = 1.19{\text{ }}\left( { = \arctan \frac{5}{2}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">correct shape. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">correct domain indicated. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to differentiate one \(\arctan \left( {f(x)} \right)\) term <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \pi - \arctan \left( {\frac{8}{x}} \right) - \arctan \left( {\frac{{13}}{{20 - x}}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = \frac{8}{{{x^2}}} \times \frac{1}{{1 + {{\left( {\frac{8}{x}} \right)}^2}}} - \frac{{13}}{{{{(20 - x)}^2}}} \times \frac{1}{{1 + {{\left( {\frac{{13}}{{20 - x}}} \right)}^2}}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \arctan \left( {\frac{x}{8}} \right) + \arctan \left( {\frac{{20 - x}}{{13}}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = \frac{{\frac{1}{8}}}{{1 + {{\left( {\frac{x}{8}} \right)}^2}}} + \frac{{ - \frac{1}{{13}}}}{{1 + {{\left( {\frac{{20 - x}}{{13}}} \right)}^2}}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{8}{{{x^2} + 64}} - \frac{{13}}{{569 - 40x + {x^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{8(569 - 40x + {x^2}) - 13({x^{2}} + 64)}}{{({x^2} + 64)({x^2} - 40x + 569)}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{5(744 - 64x - {x^2})}}{{({x^2} + 64)({x^2} - 40x + 569)}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Maximum light intensity at P occurs when \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = 0\). <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">either attempting to solve \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = 0\) for <em>x</em> or using the graph of either \(\theta \) or \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>x</em> = 10.05 (m) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}x}}{{{\text{d}}t}} = 0.5\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">At <em>x</em> = 10, \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = 0.000453{\text{ }}\left( { = \frac{5}{{11029}}} \right)\). <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">use of \(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = \frac{{{\text{d}}\theta }}{{{\text{d}}x}} \times \frac{{{\text{d}}x}}{{{\text{d}}t}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = 0.000227{\text{ }}\left( { = \frac{5}{{22058}}} \right){\text{ (rad }}{{\text{s}}^{ - 1}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>(A1)</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \(\frac{{{\text{d}}x}}{{{\text{d}}t}} = - 0.5\) and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = - 0.000227{\text{ }}\left( { = - \frac{5}{{22058}}} \right){\text{ }}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Implicit differentiation can be used to find \(\frac{{{\text{d}}\theta }}{{{\text{d}}t}}\). Award as above.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[4 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was reasonably well done. While many candidates exhibited sound trigonometric knowledge to correctly express <em>θ </em>in terms of <em>x</em>, many other candidates were not able to use elementary trigonometry to formulate the required expression for <em>θ</em>.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b), a large number of candidates did not realize that <em>θ </em>could only be acute and gave obtuse angle values for <em>θ</em>. Many candidates also demonstrated a lack of insight when substituting endpoint <em>x</em>-values into <em>θ</em>.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (c), many candidates sketched either inaccurate or implausible graphs.</span></p>
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (d), a large number of candidates started their differentiation incorrectly by failing to use the chain rule correctly.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">For a question part situated at the end of the paper, part (e) was reasonably well done. A large number of candidates demonstrated a sound knowledge of finding where the maximum value of <em>θ </em>occurred and rejected solutions that were not physically feasible.</span></p>
<div class="question_part_label">e.</div>
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<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (f), many candidates were able to link the required rates, however only a few candidates were able to successfully apply the chain rule in a related rates context.</span></p>
<div class="question_part_label">f.</div>
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<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A particle, A, is moving along a straight line. The velocity, \({v_A}{\text{ m}}{{\text{s}}^{ - 1}}\), of A <em>t</em> seconds after its motion begins is given by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{v_A} = {t^3} - 5{t^2} + 6t.\]</span></p>
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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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \({v_A} = {t^3} - 5{t^2} + 6t\) for \(t \geqslant 0\), with \({v_A}\) on the vertical axis and <em>t</em> on the horizontal. Show on your sketch the local maximum and minimum points, and the intercepts with the <em>t</em>-axis.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the times for which the velocity of the particle is increasing.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the times for which the magnitude of the velocity of the particle is increasing.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">At <em>t</em> = 0 the particle is at point O on the line.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for the particle’s displacement, \({x_A}{\text{m}}\), from O at time <em>t</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A second particle, B, moving along the same line, has position \({x_B}{\text{ m}}\), velocity \({v_B}{\text{ m}}{{\text{s}}^{ - 1}}\) and acceleration, \({a_B}{\text{ m}}{{\text{s}}^{ - 2}}\), where \({a_B} = - 2{v_B}\) for \(t \geqslant 0\). At \(t = 0,{\text{ }}{x_B} = 20\) and \({v_B} = - 20\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for \({v_B}\) in terms of <em>t</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>t</em> when the two particles meet.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><img 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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1A1A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for general shape, <strong><em>A1</em></strong> for correct maximum and minimum, <strong><em>A1</em></strong> for intercepts.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Follow through applies to (b) and (c).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 \leqslant t < 0.785,{\text{ }}\left( {{\text{or }}0 \leqslant t < \frac{{5 - \sqrt 7 }}{3}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(allow \(t < 0.785\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and \(t > 2.55{\text{ }}\left( {{\text{or }}t > \frac{{5 + \sqrt 7 }}{3}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 \leqslant t < 0.785,{\text{ }}\left( {{\text{or }}0 \leqslant t < \frac{{5 - \sqrt 7 }}{3}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(allow \(t < 0.785\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2 < t < 2.55,{\text{ }}\left( {{\text{or }}2 < t < \frac{{5 + \sqrt 7 }}{3}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t > 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">position of A: \({x_A} = \int {{t^3} - 5{t^2} + 6t{\text{ d}}t} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_A} = \frac{1}{4}{t^4} - \frac{5}{3}{t^3} + 3{t^2}\,\,\,\,\,( + c)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(t = 0,{\text{ }}{x_A} = 0\), so \(c = 0\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}{v_B}}}{{{\text{d}}t}} = - 2{v_B} \Rightarrow \int {\frac{1}{{{v_B}}}{\text{d}}{v_B} = \int { - 2{\text{d}}t} } \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln \left| {{v_B}} \right| = - 2t + c\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({v_B} = A{e^{ - 2t}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({v_B} = - 20\) when <em>t</em> = 0 so \({v_B} = - 20{e^{ - 2t}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_B} = 10{e^{ - 2t}}( + c)\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_B} = 20{\text{ when }}t = 0{\text{ so }}{x_B} = 10{e^{ - 2t}} + 10\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">meet when \(\frac{1}{4}{t^4} - \frac{5}{3}{t^3} + 3{t^2} = 10{e^{ - 2t}} + 10\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t = 4.41(290 \ldots )\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was generally well done, although correct accuracy was often a problem.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (b) and (c) were also generally quite well done.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (b) and (c) were also generally quite well done.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A variety of approaches were seen in part (d) and many candidates were able to obtain at least 2 out of 3. A number missed to consider the \(+c\) , thereby losing the last mark.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Surprisingly few candidates were able to solve part (e) correctly. Very few could recognise the easy variable separable differential equation. As a consequence part (f) was frequently left.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Surprisingly few candidates were able to solve part (e) correctly. Very few could recognise the easy variable separable differential equation. As a consequence part (f) was frequently left.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the expression \(f\left( x \right) = {\text{tan}}\left( {x + \frac{\pi }{4}} \right){\text{cot}}\left( {\frac{\pi }{4} - x} \right)\).</p>
</div>
<div class="specification">
<p>The expression \(f\left( x \right)\) can be written as \(g\left( t \right)\) where \(t = {\text{tan}}\,x\).</p>
</div>
<div class="specification">
<p>Let \(\alpha \), <em>β</em> be the roots of \(g\left( t \right) = k\), where 0 < \(k\) < 1.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of \(y = f\left( x \right)\) for \( - \frac{{5\pi }}{8} \leqslant x \leqslant \frac{\pi }{8}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>With reference to your graph, explain why \(f\) is a function on the given domain.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why \(f\) has no inverse on the given domain.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why \(f\) is not a function for \( - \frac{{3\pi }}{4} \leqslant x \leqslant \frac{\pi }{4}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(g\left( t \right) = {\left( {\frac{{1 + t}}{{1 - t}}} \right)^2}\).</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>Sketch the graph of \(y = g\left( t \right)\) for <em>t</em> ≤ 0. Give the coordinates of any intercepts and the equations of any asymptotes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(\alpha \) and <em>β</em> in terms of \(k\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(\alpha \) + <em>β</em> < −2.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <em><strong>A1A1</strong></em></p>
<p><em><strong>A1</strong> </em>for correct concavity, many to one graph, symmetrical about the midpoint of the domain and with two axes intercepts.</p>
<p><strong>Note:</strong> Axes intercepts and scales not required.</p>
<p><strong>A1</strong> for correct domain</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>for each value of \(x\) there is a unique value of \(f\left( x \right)\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Accept “passes the vertical line test” or equivalent.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>no inverse because the function fails the horizontal line test or equivalent <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> No <strong>FT</strong> if the graph is in degrees (one-to-one).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the expression is not valid at either of \(x = \frac{\pi }{4}\,\,\left( {{\text{or}} - \frac{{3\pi }}{4}} \right)\) <em><strong>R1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\(f\left( x \right) = \frac{{{\text{tan}}\left( {x + \frac{\pi }{4}} \right)}}{{{\text{tan}}\left( {\frac{\pi }{4} - x} \right)}}\) <em><strong>M1</strong></em></p>
<p>\( = \frac{{\frac{{{\text{tan}}\,x + {\text{tan}}\,\frac{\pi }{4}}}{{1 - {\text{tan}}\,x\,{\text{tan}}\,\frac{\pi }{4}}}}}{{\frac{{{\text{tan}}\,\frac{\pi }{4} - {\text{tan}}\,x}}{{1 + {\text{tan}}\,\frac{\pi }{4}{\text{tan}}\,x}}}}\) <em><strong>M1A1</strong></em></p>
<p>\( = {\left( {\frac{{1 + t}}{{1 - t}}} \right)^2}\) <em><strong>AG</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(f\left( x \right) = {\text{tan}}\left( {x + \frac{\pi }{4}} \right){\text{tan}}\left( {\frac{\pi }{2} - \frac{\pi }{4} + x} \right)\) <em><strong> (M1)</strong></em></p>
<p>\( = {\text{ta}}{{\text{n}}^2}\left( {x + \frac{\pi }{4}} \right)\) <em><strong>A1</strong></em></p>
<p>\(g\left( t \right) = {\left( {\frac{{{\text{tan}}\,x + {\text{tan}}\,\frac{\pi }{4}}}{{1 - {\text{tan}}\,x\,{\text{tan}}\,\frac{\pi }{4}}}} \right)^2}\) <em><strong>A1</strong></em></p>
<p>\( = {\left( {\frac{{1 + t}}{{1 - t}}} \right)^2}\) <em><strong>AG</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> </p>
<p><img 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"></p>
<p>for <em>t</em> ≤ 0, correct concavity with two axes intercepts and with asymptote \(y\) = 1 <em><strong>A1</strong></em></p>
<p><em>t</em> intercept at (−1, 0) <em><strong>A1</strong></em></p>
<p>\(y\) intercept at (0, 1) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\(\alpha \), <em>β</em> satisfy \(\frac{{{{\left( {1 + t} \right)}^2}}}{{{{\left( {1 - t} \right)}^2}}} = k\) <em><strong>M1</strong></em></p>
<p>\(1 + {t^2} + 2t = k\left( {1 + {t^2} - 2t} \right)\) <em><strong>A1</strong></em></p>
<p>\(\left( {k - 1} \right){t^2} - 2\left( {k + 1} \right)t + \left( {k - 1} \right) = 0\) <em><strong>A1</strong></em></p>
<p>attempt at using quadratic formula <em><strong>M1</strong></em></p>
<p>\(\alpha \), <em>β </em>\( = \frac{{k + 1 \pm 2\sqrt k }}{{k - 1}}\) or equivalent <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(\alpha \), <em>β</em> satisfy \(\frac{{1 + t}}{{1 - t}} = \left( \pm \right)\sqrt k \) <em><strong>M1</strong></em></p>
<p>\(t + \sqrt k t = \sqrt k - 1\) <em><strong>M1</strong></em></p>
<p>\(t = \frac{{\sqrt k - 1}}{{\sqrt k + 1}}\) (or equivalent) <em><strong>A1</strong></em></p>
<p>\(t - \sqrt k t = - \left( {\sqrt k + 1} \right)\) <em><strong>M1</strong></em></p>
<p>\(t = \frac{{\sqrt k + 1}}{{\sqrt k - 1}}\) (or equivalent) <em><strong>A1</strong></em></p>
<p>so for <em>eg</em>, \(\alpha = \frac{{\sqrt k - 1}}{{\sqrt k + 1}}\), <em>β</em> \( = \frac{{\sqrt k + 1}}{{\sqrt k - 1}}\)</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\alpha \) + <em>β </em>\( = 2\frac{{\left( {k + 1} \right)}}{{\left( {k - 1} \right)}}\,\left( { = - 2\frac{{\left( {1 + k} \right)}}{{\left( {1 - k} \right)}}} \right)\) <em><strong>A1</strong></em></p>
<p>since \(1 + k > 1 - k\) <em><strong>R1</strong></em></p>
<p>\(\alpha \) + <em>β</em> < −2 <em><strong>AG</strong></em></p>
<p><strong>Note:</strong> Accept a valid graphical reasoning.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the graph of \(y = x + \sin (x - 3),{\text{ }} - \pi \leqslant x \leqslant \pi \).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph, clearly labelling the <em>x</em> and <em>y</em> intercepts with their values.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the area of the region bounded by the graph and the <em>x</em> and <em>y</em> axes.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><img 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" alt><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for shape,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for </span><em style="font-family: 'times new roman', times; font-size: medium;">x</em><span style="font-family: 'times new roman', times; font-size: medium;">-intercept is 0.820, accept \(\sin ( - 3){\text{ or }} - \sin (3)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for </span><em style="font-family: 'times new roman', times; font-size: medium;">y</em><span style="font-family: 'times new roman', times; font-size: medium;">-intercept is −0.141.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(A = \int_0^{0.8202} {\left| {x + \sin (x - 3)} \right|{\text{d}}x \approx 0.0816{\text{ sq units}}} \) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates attempted this question successfully. In (a), however, a large number of candidates did not use the zoom feature of the GDC to draw an accurate sketch of the given function. In (b), some candidates used the domain as the limits of the integral. Other candidates did not take the absolute value of the integral.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates attempted this question successfully. In (a), however, a large number of candidates did not use the zoom feature of the GDC to draw an accurate sketch of the given function. In (b), some candidates used the domain as the limits of the integral. Other candidates did not take the absolute value of the integral.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Sketch the curve \(y = \left| {\ln x} \right| - \left| {\cos x} \right| - 0.1\) , \(0 < x < 4\) showing clearly the coordinates of the points of intersection with the <em>x</em>-axis and the coordinates of any local maxima and minima.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find the values of <em>x</em> for which \(\left| {\ln x} \right| > \left| {\cos x} \right| + 0.1\), \(0 < x < 4\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><img 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" alt><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"> <strong><em>A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica; min-height: 24.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for shape.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0px 0px 0px 30px; font: 20px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>x-</em>intercepts 0.354, 1.36, 2.59, 2.95 <strong><em>A2</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 20px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for three correct, <strong><em>A0</em></strong> otherwise.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0px 0px 0px 30px; font: 20px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">maximum = (1.57, 0.352) = \(\left( {\frac{\pi }{2},0.352} \right)\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0px 0px 0px 30px; font: 20px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">minimum = (1, – 0.640) and (2.77, – 0.0129) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(0 < x < 0.354,{\text{ }}1.36 < x < 2.59,{\text{ }}2.95 < x < 4\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> if two correct regions given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Solutions to this question were extremely disappointing with many candidates doing the sketch in degree mode instead of radian mode. The two adjacent intercepts at 2.59 and 2.95 were often missed due to an unsatisfactory window. Some sketches were so small that a magnifying glass was required to read some of the numbers; candidates would be well advised to draw sketches large enough to be easily read.</span></p>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \frac{{1 - x}}{{1 + x}}\) </span><span style="font-family: times new roman,times; font-size: medium;">and \(g(x) = \sqrt {x + 1} \), \(x > - 1\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the set of values of \(x\) for which \(f'(x) \leqslant f(x) \leqslant g(x)\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><br><img 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unSpe7duzP71I9rWs4Z6rMDLkpJkg4ePNi8eXPGGCywEQRBuBDSKvWAOGVkZNSrV0+n0xUdgCAIQtOmTfl+9nyVWzckISGhffv2jKtkQRAE4SpIq9QDdtXDhw/ffvvtgoICLAD4JFq0aPHTTz8xexkIN/cBbt68uWvXrrDFbfPACIIoJ5BWqcdsNttstj///LNixYrZ2dlPjZVYsGDBxx9/rCiKVquFLW4oVzabDbRq+/btnTt3hi1uG2FPEEQ5gbRKPWBtXLt27d///vezdFPMyckJCQnJycnBqd8NNQDkVlGU3bt3N23alNnNLIIgCBdCWqUSSEJijJ08efKNN954qlaBsPn6+u7YsYPZ61a4oQyAVhmNxi1bttSrV09RFIhjJAiCcCGkVSqRJAnk6pdffvH19S0oKGBFxvWBCTV16tT+/fszu7HihmELoKlms/m7774LCAiQZVkURTccJ0EQ5QrSKpXg9L1jx46WLVvCFP/UAurZ2dn169dn9qQr94wDhFPbtGlTVFQUbHH/wvAEQZRtSKtUYrNz+vTpVq1awcan+vQEQejQocOBAweYG9fZUxRFFMWEhITevXsrdlw9KIIgyjWkVcVCUZRz584FBgY+1fKAUkyiKP7www8TJkyAeHe3taskSdqxY0efPn0KV+YlCIJwPqRV6oEZPDk52dvbW6vVPnVChxj3rKys5s2bG41GaL/rlJH+PaAG4M6dO0mrCIJwE0irVCIIAihNWloa5AJLklS0DxDCK8xmc1RUVEpKSk5OjhtqAHj8rFbr7t27UatcPSiCIMo7pFUqQZMoIyOjatWqUGOpaO3BGoCzZs2aN28ec8s4QBikoih79uyJiYkhrSIIwh0grVIPiNPly5erVq0KNZaK2Bk8aTDvHzlypEmTJswtaxfhkPbu3UtaRRCEm0BapR5Zli0Wy/Hjx+vVq6fX64te1+ErMOXl5TVv3vzYsWPOGunfALXq119/jY2NdefeJQRBlB9Iq9QD6zq///57ixYtQKWKntZhvQqKAY4ePTo6Oto54/xboKDu27ePtIogCDeBtEolaH8kJSVBzPpTF5/0ej0+PnToULVq1YxGIxxKEAQsxMfv5nxQqw4fPgyxFcwta+wSBFGuIK1SCSiToigXLlzw8/MzGo0YGVjE/sxesUKj0TRs2PD48eO4HR+4SUHbHTt2dO7cmYoBEgThDpBWqQSkxWq1nj9/HrRKFMUitAqThSGzijHWvXv3r7/+mg9zR7lyeU0jm822ffv2jh07mkwm146EIAiCkVapBl12SUlJwcHBT43oA02CV4HltHDhwri4ONwOq18gVy6sv456+euvv/bo0cPN20ISBFFOIK1SCcrJtWvXGjdu/NT9IQ4QtEoURZPJlJSU1KhRIzBcLBYLiATImAvzrlCWDhw40KdPH3jsnrWgCIIoP5BWqQTndNQqKPf3pP15+cHaEHXq1Llx4wbjIjXcZ31o9+7d77//PtlVBEG4A6RVxQJygcPCwpi9jF4Re8IDPnSif//+3377LTwGPXC5XYWDSUhI6NatG7o6XTsegiDKOaRVxUKW5YsXL4aGhj7j/larFS0nvV6fkJDQt29fiFznK6+71o4BZdqzZ0/Pnj3hMfkACYJwLaRVxcJmsyUmJvr7+5tMpr81oYPD0GKxtGzZ8sGDBzabzWAwMLtiuTxsXZKkzz//vFOnThjuQRBEuQKW5AVBgKnJ5ZBWFZfk5OSAgACj0Vh08J7DjG+z2SRJEkVx1qxZy5Yt458CuXIVqLjLli374IMPmL2rpAuHRBCEk5EkyWQy4axls9mMRqNrpybSKpXwsRWBgYGQX1X0/g7hFVarVZblxMTETp068Qd0bXgFatW6detQq9ywxi5BEKWN0WiECcEdZgDSKpVg0MGVK1eCgoIsFkvRZZYKV7aFsuuSJPXs2fPq1as6nY7Zhcod1ofi4+OjoqKYqxfPCIIoPZ5UcRvnN/j5i6IIlpazx8dBWqUS8IxJkpSUlBQeHv7U/rlFPLtp06apU6fCYygG6Nr1KrhAf/jhh1atWlHtWoIowzzpHhofu2JQj4e0qljIsnz58uXw8HDVX6osy/n5+S1btoR/XVixAsArdefOne3atWNkVxFE2eVJaxOMsfz8fPjtS5IE/Y9cNkrGGGmVavALvnz5ckBAgMlkUiczcJw+ffqcO3fO5QWWmP1iZYwdPHiwffv2jLSKIMouT4r5YowVFBQwxvR6/Z9//gnPurZOKWmVSvBrS0xMrFOnTnZ2tupeHoIgrFixYuzYsVhpybUrmSBOBw4ciIyMZKRVBFFuwFyaXbt2zZs375tvvgkJCfHz8ztx4oSrh0ZapRasUqHT6V588cUzZ86wYmjM/fv327dv/+jRI/jXhaaVLMvw7rt37wYfIHP1+hlBlFugqjX+C24PdNPBDxPuJh0CH7AlHmNMkiSoR4qHslgs8Fp4Ffzq79y5s2rVqri4uMqVKwcEBLRs2bJv375z5sz57bff8vPznXG2RUJapR747vPz8xs0aJCYmKj6IIwxs9k8bty4lStXyrLs8oYgwObNm1u0aEFGFUG4FqvVKkmSJEmFE/NNJpPNZoOVJGyLyt8xO9QosFqtfGKvxWLRarV//PHH+PHje/bsGRERERYWNnfuXBAnSKhyn/tU0ir1wEVgMpnGjBmTnp5enIMwxk6ePNmxY0etVuvyllGCIIiiuGTJkqCgIJ1OR7nABOFawJbit/D6hPvAv2azuaCgAFUNYs1xFQq0JyUlZfPmzYMHDw4MDPTx8WnYsOGyZcvS0tJgjcpsNuO8ZLPZoDOfLMuuTf0krVIJxiAwxo4dOwZfrYq8KDgIXEZt2rT5448/mKvXMOEqX7FiRevWral2LUG4G3xMuSzLmLELjj7czcEkSktLO3LkyJAhQyIjI995552YmJj58+cnJibm5uZijB+qEf9aN/n5k1aphI/1hJsRplarICSUMfb5559PmDCBMQbVbF3LokWLoqKi4FfhDlnrBFEO4ReZYK6AH6PZbC4cRA4rzYqioM8wLS1t48aNcXFx4eHhQUFBgwYN+uKLL5KTkx1C+0wmk8FgwJ+5RqPBY4JFBYYdxQF6MKBY6ClWdxBw+hmNxmvXrrVt2/bhw4clOcS/CfweBEGYOnVqZGSk0WhUFMVNltAIotwCNhM/yWD1I4PBoNfrbTZbZmbmnTt39u7dO3v27P79+7dr165Vq1a9evUaM2bMjRs3cnNzmd1ggqBlWO7i3wV+/vh7dyv/P2lVsRAEARY8MTJHBXA3BIo1fvz4L7/8siSHqJapU6dGRUW5Q7Ungijn8F44SZL4LkJZWVlHjhyZP3/+Rx991KBBg4CAgBYtWgwbNiwhIeHevXsGg8FsNvMOPd5+wgwZmL4EQRAEgXcwoveomFNciUBapRIQGPzyVBvIcGVgcM6JEyfq16+vOlWr+MAKrc1mmzRpUqdOneCkyK4iCJcADj3e0MnMzLx69eqECRO6devWoUMHX1/foKCg2NjY9evXb968OScnB6YURVEwXxOQJAndhuA7gcfgZkQBg8BCNyyuRlrlYlDtMHi9X79+K1asYHYBw1wrZ97UWK3WWbNmNWzYEP51eeUngnBniog+UBSF7xjuYNMwxsCzJ8syxjGhuQNqIctyenr6gQMHJk2a1KpVq6CgoKZNm06aNGndunVJSUnusLbtHEirXA9oEtxAMcYSEhLatm2r1+vhJggscafZN/A7sdlsn3/+OWoVxVYQxGOxWCyQaYsrPbiqJAiCQwoK7AxqhGm8vPkC5cxFUczNzU1KStqzZ88nn3zSsWPH4ODgyMjITz75ZN26dRcvXszPz+e7OmAwhbtZQiULaZXrAY8fFozQ6/WBgYG///47OovRYHdCXh5e7vPmzfP392fcjR5BEM+CQ6VXQRDAqwb/YkFYxmUy5ebmZmdnHzp0aOnSpYMGDQoLCwsJCalZs+bo0aPj4+Nv3LgBr3VIBwaDrJzcSpJWuQtwccOFu2DBgs8++4zPmQCLygmagdf9ggULAgMDGdUDJIgnY7FYTCYTlHgo/Evhk2fREwh3nFlZWdnZ2d9///3nn38+evTounXrBgYGVq5cuVWrVpMnT968eXN6enpaWhrYYXgEk8mEEwXmuiBl21dPWuVi4EJEvwEE26Snp3fp0gVqYWDUuHOMG7xx+/rrr0NCQhg5AAni2QBzilcs0Cqz2Wyz2R49enT//v2ffvpp2rRp/fr1q1u3buPGjX18fLp06TJ06NC1a9diWDljTKvVMvtPz2q1FtF2HMIiim6eVzYgrXI9eH1jNKAoioMHD963bx/j1qicE4yH6WKLFi0KDw9npFUEUSRWqxVyV3CLKIp6vV6SpLS0tOTk5IULFw4bNqxJkyZBQUFBQUGdO3eeN2/enj17tFptfn4+v84EIeaiKILt5RBdjBF6jDGTyQTVaTFX17kn7QJIq1wPygP6uAVB2LJly+jRo/kr1Wn3TXDdL168uEmTJqyQi5wgCAegYh5jTJbl7OzslJSUiRMn9u3b18fHB8IiFi1a9Msvv9y8edNkMvH94NEeysvLQ8Wy2WyQ5wRuQ1jucrhVLfyTdJ+y16UEaZWLgRsodPHBXRVj7ObNm0FBQffu3eOfdc7dE4jT4sWLmzVrxrjYWYIgHMA8y6tXry5btqxv376RkZGNGzeeMWPG5s2bjx07JkkSeAJh5ckhwoKncKtVhxLpfLElZq8qCzJWHm4oSavcFFmWp06d+tNPPzG74eWcyxELt8ybNy8wMBAzPEr7fQmilEC/BcKXY4Bob9gOooL1GvBVWM1BURS+7gNU2xs1alRoaGidOnW6d+++cuXKK1euYIHQwmDAFB4E3tShuB/4FZk9ChdC23Fd6qnzgMFgwHtf2KLT6RhXaFSn0+FBQOrQzsMge9gZovDxlpoxlp2djbMEnJFz+oaQVrkvGzduHDZsGHtc/mDpAW8hiuJXX30F61WsrMcXEWUYPo6Or/3q0HsQwh8YN5s7JOkzxkRR1Gq1d+/eTUhIGDp0aFBQUNWqVfv16/fll1/+/vvvqE+CIBSRn4uxVKyQPsFoHX5rNjvP/tsv3LmD15LMzEzYARbDsHISuhBxSUwURbPZjOMp7GDMycl5xiGVCKRV7sutW7c6duyYlZXl/AqSoiguXbq0RYsW8G95WLklyjY419tsNlAsvgSRxWIxGo18q1xm7/yk1WqvXr367bffDhgwIDg4ODw8vFevXjNnzjx8+LBDPfJn7EyIWf8w14uiqNPpRFHE3zj6/AVBUDiKPiaAK2cWi4XvYsUYy8jIgPcVBAHMLHgWggwLV4lDR46iKJADCnWb+DbEMMKnnnKJQFrlvthstqlTp8bHxzPOC+EcrFbr6tWrW7VqVR5iYYkyjCiKEMvwpGVXrVbLCwwYGTk5Ob/++us333zTp0+fxo0bd+zYMTY2dsmSJYmJiQaDAeLusMILpFjx93NFKxYMxuH+j9cJPnEYQE8gmEGFffL4LPyr1+vRutLr9aIoOph6RqMRlrtQcmA7fEQZGRl8oAezKxMMEuvsOHlpgLTKTYFLJCkpqW3bts58X7zc165dGxkZyd/uEYTHwc+noCu8gcXsmUyMMZ1Od+bMma1btw4cODA0NDQ4OLhr167x8fH37t3LzMzU6XQgMCaTCY+Ar8UDQoWkorWK78+7ZcuW1NRUfDkYN3ySloNF5aBJhbfDYTH7hbf8EhMT09PTsY29Q/0LjN6CTwwMKb1ej+t2IH64gC0IwsyZMw0Gg9PmB9Iq9wXc2eHh4ZAUzB7n4C5x8Le9cuXKJk2aOC0HmSBKAwjDw865jDGr1arX63HLvXv3du7c2bNnz+Dg4Hfeead3797x8fGJiYngJbPZbLAQxf8KTCYTdkJQ8QMBrbLZbPn5+fXq1fv+++8dSp7Ds2D6PCmiqrCZCDvz9hOcAmNs48aNUVFRb7zxRmBgIE4mzD6fHDp0yGg04nrbn4alGjsAACAASURBVH/+iVIHPsNJkyZdunQJdoD1CKj6BlW2eTksVUir3BS8nZk3b97ChQvR0Vza74v3TQsXLgwLC+OXggnCQ8FcXUVRMjMzr1y5snnz5iFDhkRERFStWnXQoEFfffXVuXPnrl+/zhcuEgSBj1OwWCz8zSLvWON9epg79STwIFeuXHn55Zf/+OMP+Dc9Pf2XX345ceIEHp/9tf84s4eEQAgGHxvCCoU74lyxePFiX1/f5cuXJyUlRURE/Prrr4yLltq/f//LL7+8aNEixpjRaPz4449bt27dp0+frKwsGMDRo0dfffXVffv24cHxTHfs2NGiRQunLWaTVrkpcDFptdq0tLRmzZphz2nnYDKZ5syZAzWW2OMiiwjCI4Be7zk5OcePH58zZ06XLl38/Pxq1KjRsmXLadOmJScn3759m9n1A5xvDoHsvA7BIg0/O6vLPgQ5TEhIqFKlCnRUEEXx66+/fvXVVxs0aABy5XBjCtaMyWTS6XQajUYQhMKF1SG2AhQUyrYtX768Tp06hw8fliTp/v37s2fPZlxAhCzLvXv37t27d0ZGBmNs796906ZNO3nyZEBAwJQpUyBUpGXLlkFBQVD8SZZlmAry8/MZY6dPn65VqxZzVkkd0iqV4E0NBPPAlVSCx8fsCpvN1qdPn+3bt6NTAneAS6Rk72vwaKNGjRo6dCj7q8sbmhqwv/ZqI4inUtgIAA3AHw5czDAVQvgA7M+vCWF9PLz2oH8gRr7B6o4kSRqN5saNGykpKePHj2/evPlrr73m7e0dGxv73XffXb16FZ1jzgdNMUEQNm3aVLNmTVigYow1bNhwwYIF8fHx48ePh31gnPDs3r17P/jgAy8vr1q1ar366qsNGzZs2rTpgwcPmN0/ieYaFhX84YcfatWqlZiYCP8eOnSI2T9DcOgZDAY/P7/Tp0+DAF+5cuXhw4eMsalTp/br1+/ixYt9+/Z94YUXNm3axOxfBLwXRBju2rXrnXfeYU7x9zDSKtXwX8+ZM2f4CsolAqY4MMZOnz49fPhwcCzA6i7vlCvZvjV4izRixIj+/fsz+80UurMdAoQI4hmB9CaIguNznvh+N6hGzG4lYPYPSBomsTokcphMpqysrBs3bqxevbpr1641atSoXLlyeHj4mjVrNmzYcOTIEZiFmRNzV58EOiTnzZvXrVs3vV4PJ+Lr6xsfH3/+/PlevXphsVo0gFJTU9esWTN//vwff/xx06ZNc+fO/fTTT1NSUrRaLW/WoAyfPHnSx8fnzp07sizn5+c/ePCgTp06er0eP3yDwZCQkBAVFYUvgY/FaDTGxcXVr1+/cuXKL7/88j//+U/cweGjW7lyZePGjZ3W7JG0qlhotdqHDx82btwYbl5KcF2HL8diNBq7d+9+9+5duFB4cSoNwdBoNHfv3p0+fbq/v39sbGzt2rX/8Y9/XL58GXPX0YIkuSL+FoVjtRHoJwCXFj7gwfJjgCRJeXl5f/zxx5w5c9q1axcREVGjRo0aNWo0bNiwX79+GzZswPg6/t2dmQ/0JLD8xLx580aOHInbW7VqtWDBgpUrV3bp0sVms2FbO9zBwdWWl5fHzxLooIPY3enTp3fr1u3Ro0eMMYvF0rx5cy8vr8TERDDjQCCHDx8+ZcoUxlWrgY+9Vq1aFSpUaNGixerVq2vXrv3gwQNw+sF7YVzJl19+2b17d6ctEJBWqQSrHefl5f3zn/88c+YMK2m/Ld5YmUym+fPnT5w4kRWKRyrxyMCePXu2b9/+3//+d+XKlb28vHx9fWfNmjV58uSrV68W1iqKuSCKA1T0KWzl8PdAaWlpeJnBosuuXbtGjhwZHh7+1ltveXt7d+3adcaMGcePHz9//jxMqQD05IUocDwClIV1Qjztk8AQO8bYTz/95OfnB4tkRqOxS5cukZGRrVq1Wr16Nftr6SNm/63l5uY6eFMBzL9EhWvfvj04/c6dOxcZGTl8+PCOHTvGx8fDxJWXl8cY8/Hx2bx5M7Mv1MGEc+rUKS8vrxo1ahiNxosXL1aqVAl2Pn36NN4rgy0VHR09ffr00v28OEirVMJndL/++uuXLl0qjXcxm83wRrdu3apfv/6dO3fAKY8/bz5Xo0QYPXp0jx49Nm/e3LNnz5CQEEmS4Pfv8BbgnyG7inhG+BmWr3XEA0uweCckSZJer9+2bdv+/fu//vrr6dOnv/fee9WrV/f29m7UqNHYsWN37tyZkpKCle7wThGr5+G/cGSXW1QAGECiKF65cqVKlSoHDx6E7f37969QocKgQYMKlzWCGKsHDx7s2rXr8OHDN27cyMrKgioSsAOfN8YYM5vNCxYs6Nix40cffVStWrX58+czxvr27Ttt2jTcx2AwVK9e/cKFC4y76czJyalXr15ISIhGo4GDR0ZGduzYcfny5Q0aNEhLS4N30ev16enpFSpUOHnypNNMVdIqlaDTXKPRvPvuu1evXi3Z2ApwFIAYwCU7e/bsjz/+GJ7FeAesY1ZS4H3fsmXLOnbsCG+N69vofizxWBKinABR13jR8qm14BkzGAwGg+HQoUNTp05t3bq1l5dX5cqVq1SpEhMTM378+MTERLz4HeK5oRAfLmhBZpXDVQph6C60q2w2Gx/ZMXXq1JCQEH9//1dffbVmzZqvv/46nF1mZibuc/To0fDw8LfffvuFF17w9vYODAwcNGgQv7AHQDsr1GyNRvPdd9/9/PPPR48ehR2GDRs2efJki8UCXrvk5OSgoKCsrCw8zt27d8PCwkJDQ48cOcIYy83NVRQlOTm5RYsWLVq0OHz4MP928+fPr169en5+fuHSwKUEaZVK+I4yTZo0ge+1BF23UBsGHsPlazabO3bsmJSUxLhFzlJyFkuS9O2330ZHR+MYICEfuu8wV1RYIcoAvLSgK4kxlpqaeuLEiXnz5sXGxlavXv3555/39fVt1qzZ8OHDv/vuu9u3b2dkZGAoNrObSng0eOqxd/cYJQh3V+7gCYDoBpjlGWM7d+5csGDBmjVrtm/f/uabb0JJJNgTft3Z2dnr1q377bffkpKSwFMHXg1RFKGeOna1t9l7i+N7Qa6LRqMRRXHx4sUTJ05EB0lGRoafn9+ZM2fAJjObzYmJie+8887JkyeZ/fYUPy6QfHBI6vX6+/fvN23adO3atc7MZiGtUg/eyLz55psYZVRSoK0NDmiQq40bN8bExMAvk/+tlnhck8Vi+eqrrzp16gQVORl31WItFrPZTHJFPCMQLsG76TIzM69evTp37tzBgwfXq1evVq1a/v7+o0ePjo+PP3bsGNzv860oeM8Yn/yE2euYwgGX5ZOcfvCbLe3zfRL8zxZrHeGWd999F5fc8A4V/sUof2b/KByOwxfmYJznAz0lvXv3njRpEmMMRI4xNmjQoGnTpkHWDWgevCk2+2BcoCbeK1gslgEDBoSFhYGeOa3BI2mVeiALxGQytWjRAvt4lvabNmvW7Pz58/wlW7LJIngK33zzTfv27d3hPpRwOYWr0uG/6ALilzAdOgpizVO9Xp+cnPzLL7/ExcU1atSoSpUq0dHRY8aM2bhx4/Xr19E1V4br+kOsB97wgQCA4mo0Gm9v74SEBJz91ckAhEIw7mM0GAzLli3797///euvv2IUn81mu3btWvPmzefOnct39yi66IZer4+KiurUqVNKSgrjWk2qGOffhbRKPXDHkZ+fHx4eDhG3TnjTKVOmjB07ltkDfjBluKSOj7dUM2fOhPWqMjxxECoAoeLbOxWeqvhcXZ1Od/PmzS1btowZM6ZZs2avv/56vXr1oqOjN27cmJKSAkF6vNWOqVRlGEVRoA8IboHHcXFxEESuKEox6+wZDAY45t69e2vVqvXuu+96eXlhnBR8QVqtNj09HVejMUm0iJ98SEjI4MGDT506xZxuoZJWqQesbI1G40ytOn36dEBAgEajgasEbkVL8LeNOchjx459//33wc9ZUgcnPA6IKYe6Bg7lheD6x2aGsizrdDq0je7du7d+/fqYmJiAgICXXnrJ39+/c+fOCxcuPH36tMlkgiv2sZ0vnHhyLsAhdcxms2VnZ8PjrKysnj17Llu2DJ9VsRoE+iTLMiTv79+/v2LFikOHDp0yZUrfvn0xgwoHw+xFb/V6Pe9ZfdLxz58/7zAqQRCKNsVKCtIqlaDHz2w2N2/eHNzQTvCY6fX6Dz74YMmSJeyv7eNK6vjowxk5ciSEG5EbkHgs4PTDizAzM/P8+fPr16+fMmVKWFhY1apVQ0NDx4wZc+TIEVjh5y8kPizCYrEUrsDkxPNwNuCj02q1WLmc2T1vTZo02bp1K84t6j4Hk8kExzx48GDNmjVnzpwpSdJHH320c+dO3Mdms4Hk4M0o/15P9T1qtVow0fi4+dKGtEolfFGJiIgIiKVxgrvMZrMdOXKkVatWeC9Tsj9sLG8zbtw4qAdYticOomgKN/eTZVmv12OXo7Nnzy5atKhPnz5BQUHVqlWrX7/+iBEjduzYkZ6ebjKZIFBN5oCDQDybgz9AsePME3QVmzdvHj58OORlwiknJycHBwdDuQ3sgqgOvV5/48YNb2/vpUuXMsbS09PfffddWNjGYEgHK5lxhayKgN/hsUlypQdpVbGwWq2ZmZkNGjRwaBddesC10rVr18OHD7O/psGXCBgTPHXq1AEDBrAi6+IQ5QS+gp8gCFqtdt++fZ999lnjxo1r1ar13nvvrVy5MikpKTMzE8vI8i/HaRfsMP5ZEDCsYwsmRdmWK0VRsrKyPvzwwwoVKnTs2HHJkiVLly5dsWJFt27dZs6cibupXreDCJdGjRrNmTOHMSZJ0vjx4z/55BPGmE6nc/DggVELtd6f8R21Wq3BYLBYLHxLFBXj/LuQVhULq9X68OHDunXr5uXlOcdXBhfTjz/++Nlnn0HzbFai1wrmUc6ZM6d79+6M0n7LN+gOslgs586dmzt3bsuWLStVqlSnTp0hQ4bs3LkzNTU1NzcXLS2+LDok58JjPncV9oQOTIVznlxeW7ZUQZ+bxWK5d+/e0aNHZ8yY0apVKz8/vxUrVjDGjEYj1m9T9xZ6vX727NmjRo2C6IxHjx4FBQUlJCQw7h6CX1lknLUEb1305+9QIANXH0sb0iqVoDxkZ2eDXeVQ+Ln03hcS+/v06QOtd1iJxlbgARcsWBAVFQX/0pJVuUWSpEuXLs2bN69Dhw7BwcHR0dELFy48dOiQRqPBAmAInz4FDzDsAiZouKnHQG18IRSzeFIP3LIEnLsoiphHhQH9KPMOERB/C6iLERERsWPHDjj44cOHW7RowezfBQReYgoan8EGFeOKPj4oKG8cU69FDwAcFwaDwd/fX6fTOUerIMNcUZTPP/987dq14DDBupN8lJE6ewg9MLGxsb169XKTVH/iSfDfDiTbwhY+57RwWDnevOPyJO4JL3/06NHmzZvj4uLatGnTqFGjgQMHHjx4EO6gy7DRUzaIj4/v0aMHXglxcXFbt2519aBKANIq9cBtoF6vDwwM1Gq1zlnXQafK5cuXW7Zs+ejRI4c3hSWB4gQlQgxrnz59YmJinFbsi1DH37rkJEnCPmSMWxEBZ1FaWtrevXs//fTTZs2a+fj4tGzZ8pNPPjl58uS9e/dwFfOxRb4Jt+KDDz7ASu3nz58PDQ19qrXkEZBWqQTjSgsKCkJDQ7VarXPmdLR7rFbroEGDVq5cybgoVZCZYiZUgkHWu3fvvn37Mq4wAeG2gNcI3GhwDUB9BFhO4LM7QWwMBgNsyc3NPXPmzPLly9u2bRsUFNSoUaOPP/5427Ztt27dgrsivioKun3oenBbRFFs167drl274Mvq2rXrvHnzXD2okoG0SiX4c83MzAwPD+dvV0sbbCZ9/fr19957D26KYT7ia4KpznuAyS4mJga1im6l3RbUJ4ftDvYWb/QrivLgwYNffvmlX79+b731Vp06dTp16vTDDz+cP38eK8vxB4QuSug2ZE4sAUf8XQRBaN68eVpaGmMMjCporujqcZUApFUqQUf/7du3w8LC+CZvTgAni+HDh0NzGjS2+NhiFRqDytSvX7/Y2FjnLMIRquG/Hag+DrrCGLNYLGjuW63WW7duHT16dOTIkU2aNHnllVdCQ0OnTJmyZ88eSE3lF7TwsimsSU5OqSFUUL9+/YKCgocPH7Zr127Pnj1l5vdLWqUS8KVIkpSUlNS4cWOs8O+E92X2WYkxdvLkycaNG2/fvh13wJo36uYUfNWAAQNiY2OpboVHgOWOHLabzeaLFy/Onz+/c+fOISEh4eHhAwYMWL9+/a1bt8B6xvw8qO2GcdJYMk6v1+NtGamU+2Oz2aZNm9a7d++YmJiRI0eyUmjC4CpIq1SCBfMTExPbtGmDoZxOGwCsl5pMpunTp3fo0CEtLQ2LrxcnhB3tqv79+/fr149R3Qr3BlQKW5gzxgRB0Gg0W7ZsGT16dOPGjQMCAnr27Pn111+fOnUqOzsb+1DwtyC4KMXPaw4R5HgPxOzXHuGGiKKYnZ0dGBjYq1evjIwM2OjMLlOlB2mVSvB3e/Xq1W7dumFbBOe8L97/gie6W7duR44cyc3NZdz9r+p1JvD79e3bd+DAgYxuqD2HvLy8/fv3jxo1KiIiwtfXt0ePHvHx8ampqeC448UJrXO8kPABH5UDlcPg7geki4xs90eWZWgrDK7gMpPIT1qlEvTv63S6tm3bOmwsbSB6GB7r9frbt29HRETAvxAAxoph+0PL0REjRrz//vuMgr5Kh8J5r6gEfGgDHyMOOzj8yxhLSUlZtWpVdHT022+/Xb169WHDhh06dEgQhMK5cWQiE54LaVWxEEUxKyuradOmTpvQ+eqf8EBRFK1WO2HChFWrVvEtQviwwGcHM4gnTZoEdhWujRElThEOW2jEZzQaIcITv274WnU63fnz57/77rtOnToFBQWFh4dPnDjx/PnzWJsAQtgdipfTbQfhuZBWFQtRFDMzMyMiIpxmUaFsOEw9V69eDQwMhP6eMBh1LbXwzv2///1vz549cWPxR07wGAwG/FTBF2c2myG8GL4C3u8KX7pOp7t169bu3bvHjh3btGnToKCgtm3bbty48ezZsxgiwUfWOHxrEEzhpNMjiJKGtEol2PRFo9FERkbC4pAT5gKHEkr8fDR8+HAofwlrD+oWVPGAPXv27NKlCzVaLFUgV/exlw3UsTYajXl5eQ8ePFizZk3//v2DgoJatmw5YsSI+Pj4CxcuGAwG/IIkSbJYLCBRhW01uLMhrSI8F9IqlaBW5efnN2vWDNYYnFO7FksoYQMFKE0ty3K7du0ePXpU2E/47KDC8bnANMeVOGBFFTZ8sY6RLMupqalr1qzp1q1bjRo1GjVq9NVXX925c8dBhwq3eWWP+95JqwhPh7SqWIiimJ6eHhQUZDQaneMowwo6/DQHLagZY4sXL4aSKoq9O/XfPT7qXPfu3QcNGkSLHE5AlmWIZ5Fl+caNG7/++uu0adNatmz5zjvvhISEfP311w8ePEDfr9VqLSgowEoEcI8CVWvxS+cLIwGKHWeeF0GUIKRVxUIUxbS0tICAAEyZLG3wBrnwvKPVakVR7Nmz5507dxhX5VbFW8iy3KVLl//+97/UaLGUUBQF9An+vX///s8//zxjxoyaNWs2aNDg/fffX7VqFbR+Z/av0mg08iLEvxwQBIGqHxFlFdIqlWAOU05OTnh4uNlsdmYJalAsuKHmtcRiscyZM+err75SbQ+hp2jgwIHQpZTK6pQSUPdo2bJlUVFRAQEBXbt2/fTTT0+ePIkpnIW7jDO7S5b/cjEiAw9bnPbnBOGekFapB9wyGRkZAQEBmC/pqsFgr9Xbt2+3atUKuqjxkxredD91kHCoXr16Qd/r8uw7KnxPgL2geD0oHIECKbTQFxy2YGmJzMzMw4cPjxs3rn379j4+Pi1atFi4cGFKSkq5/ZAJ4lkgrVIPrBmcP3++Tp06UNjYtSnioJ2KoixZsmTSpEnYTM9kMvGT6VPbJ4LC9ejRo2/fvuV2saoIXysAwl+4gnVhi1YUxUePHp09e3blypUDBw5s3rx5aGjo4sWL9+/f/+jRI9jHYrE4rRc4QXgipFXqgVns9OnTNWrUuHXrFnNi3YrHDgZmT6PRePv27U6dOt28eRNGyIvTs2gPvComJqZ79+6wpRz6AJ8Uw2I2m0GfYDuGTToUlZBlWa/X5+bm7tq1a8yYMWFhYfXr12/Xrt2nn37622+/4VIiLQcSxDNCWqUSmPThlrlJkybZ2dnMpTVscFE9KytLUZTly5fPnj3bwX1nMpme2skGZ+dBgwb16NEDNpaN/jd/iyflBsCzNpuNj2KA5SLIHNBqtdevX//uu+969+7t4+NTv379wYMH//TTT3fu3OHLf8BaFP/tOByTIAge0iqVwCwDk/i8efPAe+PaJQfeg3T9+vXu3bv/+eefUH4UZ8mnlgpEeevTp0/v3r0LH7mc8KScaz4SD6UL1q6uXr06d+7cRo0avfbaa35+fqNHj4YGu3wpWHjAaxJ8O6RSBFE0pFXqQf/P3bt3YT5ybZUHvheRIAiLFy+ePHkybIHewYwxs9n8VDcgWBKdOnUaPHhwEQs2ZZsn1bLCZ+FTkmUZ6vLVrl07NDR0wIABmzZtgirXjDFoY6goitlsNhqNfNdmZv+a8JiiKML+BEEUhrRKPby1AffFrtUqqJ1hNBphMFlZWd27d09KSmLctPgshZdgam7fvv2MGTP4gu7liifVCAaVevjw4cGDBwcMGNCwYcO33367YcOGCQkJycnJuPgE5iwrlOUG8ZkO7wWlZkv3fAjCwyGtUgnMSjgTwcTkDiYIOJpgYEuXLo2JiYHHfEv7InyAuNrfrVu3tWvXFr1zmadw75Xp06e3bt26YsWKDRs27N279w8//HDt2jV+f4iihAe8k1Cn06EgYYEuB4uN4iwI4kmQVpVNoIuVxWLp1avX/v37YeMzqg6oXdeuXUeOHAmTqQfJFW+gFLYIDQYDCDacEewMBYpwH0xKw4yo3NzcNWvWREVFeXt79+/ff+XKldevX0dv6mNrxRIEUbKQVpURHEw6mEBFUdy+fXtkZCRsxITWolfyYY2qd+/esbGxGAJXagMvLaDIHtYU5gvF8oVcMaXXarXykmM0GnNycnbt2hUVFfWvf/3Lz89v1apVWq1Wq9XiPnB8J54TQZRfSKvKCHxyD7NX4oGZtH379qtWrcISUBiC8VhgvhYEIS4urlOnTkxtbxFXAZHlj5UQXLHDRDS+MDlstNls169f37Jly6BBg6pVq/buu+8uXbq0oKBAlmWHz81isZTDUH6CcBWkVWUEB61i3HLIuXPn6tSpk5+fD6pTdBwgzPKyLA8fPjw6Opp5WnIVKDRvQoFppSgKmFAOwXhoJ124cGH06NF169atWrVqcHDwmDFjzp07xxgzmUzQwZIxBonAfI95gOrvEURpQ1pVRiisVQDkA7333ns7d+7UarVgNhVdgh2OM3To0MGDBzNPXvC3Wq1g/aC64EeE7r7bt28vWbKkRYsWNWvWbN269Zdffnn58uUnHbCIfvMlPXaCIP4CaVUZB8yI48ePBwYG5ubmwsai3Xrw7MCBA0eMGAHGmcfFDkDFqcJJBXBqoiju27dv0qRJ9evX9/LyGjhw4Llz5zA2j9nzcx2Sn0DtJDsWiwV6Rzn51AiifEJaVfaBkIqwsLDvv/9eEISnOqxQq4YNG4Zl8Zwy0hIAC4jw8SOQCi0IwrFjx/r37/9///d/Xl5esbGxu3bt0mg0GPWH4gSfAB9TDglqhTv5Qgl2UiyCKG1Iq8o4VqsVpuBz5875+vpeuXLlqS+B6T4uLi4uLg56W5T6KEsOlFV88ODBg4MHDw4ZMsTPz8/b27tZs2arV68GdyjsA4GC+Cq+zm/hnmSYQQX/emKEJEF4IqRVZRycTC0Wy/Llyz/88EPGmF6vx4gJtJzAOEBzZOjQocOGDWPO7V9VuF8UH8UgCILZbMawe36JTlEUPCODwQD7HD16tEuXLpUrV65Tp87cuXOPHDnCl6Eqt+1OCMITIa0q4/DesLS0tEaNGj169AineI1Ggws54PjCZZvBgwd//PHHThOqIvpFSZJkMpl4nx6/kqTT6XivpiiKGRkZK1euDAkJ8fb2/vjjj48ePZqenv5Y65DkiiA8BdKqMg5qDzxYsmRJbGws4yLReacZesNkWf7www+HDh3K+8dKlSf1i+I1BkfIF0GHB2az+ffff//uu+86dOhQpUqVoKCgTZs2wW58zL0kSXwNWVpnIghPgbSqvIDNLMLDww8cOMAYw3LgWIUdm1/IsjxkyBDwATpHq4ruF8UYK9w4w2q1ZmZmHj16dOLEifXq1atUqVJISMiECRMOHjwIQfm42gQxe3zmL7yRB9WOIohyDmlV2QdcZDD1i6L4xx9/dO3aldnjAyVJgkmcD9q22WyffPLJ2LFj2ZMzt0qWJ/WLMplMDmIJ4R7nzp2Li4t78cUX33zzzVGjRh04cODhw4fsr6lOhSMjcLsHRTYSBMFIq8oD/LwMKVYffvjhggULGGM2mw3CDTDoALVqxIgREydOZH8NjSs9iugXhcXOTSbT8ePHp0yZEhUVVadOnZEjRx48eDArKwsL9TK74tpsNr7ZvMlkgowos9nMG1gUxUcQngJpVRkH5mu+t4XFYrl48WJwcPD169eZPcwPpAKdbJIkDRs2bMKECcxZRRme1C+KMZadnX3kyJHZs2e3adPGz8+vZ8+eixYtevDgAewJpiEvb6IoPkubXVEUiy6NSBCE+0BaVS6wWq0YLAfxfsOHD588eTKs68BTfAyCxWIZOnQo+ACdGYBQuF/UF198ERkZWbVq1ejo6J9++un+/fu8V5DXUWhviC8HAcZ/weGJy1S0UkUQngVplXoKCgoYYzqd7ptvvoEtHhRXdu3abgoQ7AAAIABJREFUtf/85z9XrlzBzCpsrA47xMTEjBs3jrdXwGMG0XqCIBRtbz32WVEUwaPI9yFEUFquXr06derUsLCwatWq9e3b98cff4Tm7ph0RRBEeYO0SiXQiE9RlFOnTvn5+d29e9ezahEpijJy5Mg2bdrgFrBpsH9gnz59xo0bh0HkUAcWSuHhS56xpIUkSTqdDv1y2ICD2R1xkOSblpa2efPmrl27VqlSJSIiYunSpXfu3HHInfpb70sQRJmBtEolOF2mpqZWqlQpOzvbteP5uyiK8uDBg8DAQIhfZ/aWVxhb0bdv30mTJjnkV6ExhG0yngSEmAuCwOuKIAhgjDJ78w7GWF5e3sWLF8ePH1+jRo1KlSpNmzbt7t27er2eVykoY1i4fhJBEOUE0iqVQNwz2CLBwcEWi8Wz7CoIK9iyZUunTp3ARuTXqxRFGTJkyIwZMxgnDOCCA0/d6tWrN27c+CznC1UnsB88YwwrwF67dm3KlCn+/v6vvvpqaGjo1q1b+bExxnQ6Hawt8Xr5WP8hQRBlG9Iq9UB1H51O16RJk4KCAo8LgFYURaPRdOzYce/evYyrUA7Pjhw5EuLaHRoKg1TExsZ26dKlaM0wmUy8bcTrzbFjx7p37/7WW29FRUXt3r0bjiMIgsFg4PuVOBxfURSz2UwOQIIoh5BWFZeMjIzGjRtjVQjPQpKknTt3du7cGcYP0XEgKmPHjl28eDHsA1rFC0+bNm3atm1bxJHRSrNYLFqtVhAEi8WSn5+/bt26999/v0GDBp988smFCxdgH71eX3hgEIkOYXtgmVHBWYIot5BWqQSn19TU1NDQUJPJ5NAzyc1B4ZFl+YMPPli+fLnZbIbxg3tz9OjRixYtYnYBg0p6EMJ3+fJlb2/vESNGPNUXB4F/jDGdTrd69ermzZsHBATMnDnz+vXrDqojiiJIEdZYKuKwFHFOEOUN0iqVwGSq0+nu3LkTERHBPCpgHUC5PXXqlL+//9GjR+FfSZJEURwxYsRXX33F7BYSyrDFYtmwYcNzzz23cePGoo8PH4her1+9enWLFi2io6O///57CCaEHWCRjK/txP5aGAlWAeExvxzoQeuCBEGUCKRVKoH5VJKktLS0Bg0awCqLZ3moQDOgOtHcuXMDAwP1ej1q0rRp0yZPnuxgwZjNZpPJ1LhxYy8vr99++43ZPwcMl+CF5/79+7NmzfLx8QkODl67di0UoSAIglABaZVKcGrOyMjw9/fHUkauHtezgnXzQI1SU1NnzZo1b948xpjFYhFFsX///tOnT4edIeoBXrJ48eKXX365YsWKe/bsgRg/iLZAY6igoODcuXN9+/b19/fv2LHjoUOHYLtOpyN7iCAIdZBWqQRzZrOzs4OCgjxUq0wmE7ouL1y40Lp16+TkZPh3xIgRs2bNkmUZO4YUFBQYjcbY2NjGjRu/9NJLP/74I7NXbGL2cz9w4EBYWNh//vOfuLi448ePM8YURcEYdA9azyMIwq0grVIJylJeXl5ISIgn+gCZPUgBzB2DwTBv3ry4uDjGWG5u7vjx42fPns0KFSNPSUlJT0+vW7fuunXrQHv0er3RaNy7d2+rVq3efvvt/v37//777w5v5Jxi7QRBlFVIq1SCM29BQUFoaKjRaCzczMLNQf2AgHLGmE6nCw4O3rlzpyiKs2fPHjZsGMiYVquFQhVYTqJJkyYbNmyA4xw9ejQmJqZ58+ZLly7Nzs6WZVmW5fz8fFzS41OmCIIgVEBapRJeq0JCQmAxxrPSgWGRyUFf4+PjO3XqlJKS8sUXX8yYMSM/P59xcXd4guPGjZs1a9bZs2dbt24dHBw8btw4EDMHWUKnnyzLfOMogiCIvwVplUoUOxqNJigoSKPReGI9BV5foSchY6xXr14DBw6MjIxcuHAhs4cLWq1WrAGYmprat2/ff/3rXxUqVAgPD8ci6NgHC9ao+IhzgiCI4kBapRIQKpvNlp+fHxgYmJ+f71laBeNHHeLtoczMzC5dunh5eTVt2vTkyZPnz5+H3cACW7p0aatWrV555ZVXX30VtCo7OxuzpvR6vYOhBnlR8FlRbAVBEOogrVIJKpNerw8PDzebzXyjP0+hsN0DMXs//vjjiy++6OXl5eXl5e3tvXr1apPJdO/evXHjxtWsWbNz587/+9//Ll++nJiYePbsWbC3UPmYB6ZFEwTh5pBWFQur1frw4cN69eppNBrPWozhB4yWEIiNyWQaP368l5fXc88952UnKiqqdu3a77333o0bNxhjoijCUhZ0FmaM8SWmSKsIgihZSKuKhSAI9+/f9/HxycnJ8awgQMaYJElarRZ0BWoAMsa2bdvWq1evN954w8vL66WXXgKheu655ypWrHj8+HE4x8KhFnA0vn+8s0+GIIgyDWlVsbDZbLm5uQEBAQUFBZ4VR4D2EOP8maIoRkZGenl5Pf/886BSzz///Msvv+zl5fXRRx/xO9tsNignCOaUxWIp3O2eIAiipCCtUgnEJjDGdDpdWFiYTqfj6wx5BIIgGI1GB4ndtWsXqNSLL774z3/+E9yAFStWXL58OUqaVqt1aMzIP/YszSYIwiMgrSoWVqs1Pz8fYtY9epHGbDYXFBTodLpevXrx3r+KFStWqFDBy8vr+vXrsBvv6HPo2gUdQ1wweoIgyjqkVeoBG0Kj0QQHB3uoVomiCNlRjLFdu3a1adMGJOrll1/+xz/+AUZVpUqVateu3adPHwimkGUZjCoIc8eOiNAd0bMsS4IgPAXSKvVgt9yIiAidTudZ+VV8TtXWrVsDAwO9vb1jYmJWr179ww8/REVFeXl5VatWLS4u7urVq2lpac2aNVu9ejUYUiBacPqFI0psNhvfQZggCKL4kFapB/xdoiiGh4e7bQ97URSh8QeICnTxwGdv3rw5YsSI2rVrx8XFXb58mS+51KJFi2HDhuGeSUlJtWrVunjxIrPnYGH1dIIgiNKGtEo9qFUQW+Hq4TwRXENCdbFYLBaLZc2aNbVq1WrVqhWsRfFtTRRFiYyMHDVqFMZKKIqyZMmSjh07wkHAiKRe8gRBOAfSKvXAApUgCGFhYe7c9BYr9aGg3rx5s0+fPsHBwfPnzxdFUZIkUCBMn7Jare3atZs0aRK+HF74/vvvf/HFF/CYDwUkCIIoVUir1ANaZbFYQkND3VarsCckrE6Jorh06dL69et36NDh9u3b7K/JVdjOymazdenSZebMmYw7TcaYwWCoU6fO/v37XXMyBEGUV0ir1AOTuNlsDgkJKSgocM8QOL5c7MWLFzt06FCvXr1ly5YxxoxG42NtI9Cqrl27zpo1i3Hd7uEE9+zZU61aNYge9MTQR4IgPBHSKvVgG3iIWXdPrYJB5ubmTpo0CeL67t27xzhzymq1FhQUgEUFwgZl0aOioqZMmcLsUenwrNVqFUVx/Pjxbdq0oaLpBEE4DdIq9aBWQS6we2oVYyw9Pb13796+vr6//fYb47SHMabX6zE+AuIDMRCjbdu248aNY3aLCk4W9CkrKysyMnLRokVOPxWCIMoppFXqgenbaDS6s1YdPnw4JCRk8ODBUAAQUqMcCkxgopUgCLi9TZs2Y8aM4Q8Fa3IQhZGUlNSgQYPU1FSnnARBEOUd0iqVgDmi1+v1en21atUMBoPTArjNZjNfeRYRRRETpEBHly9fXrNmzeXLl4PNhKtTRactQzJW06ZNJ0+ezO+Jj6FQxb59+5o3b15QUMC/kDGGhTAIgiBKCtIqlWBYgdlsDgsLw/7upQ1m9eIwoLgRH+YA+jFjxozWrVtfuXIFJQrygtnTtAocfS1btpw2bRpvfuFbwEFu3749Z86cwYMHM86XCEJFS1kEQZQspFUqATeaTqdLSkp67bXXTp065ZzCQmi9SZLkUCgWXHn5+fm5ublDhgwZMmQI7AwdeyEy4lkclaA0bdq0gThAxuVdsb/2/7169WpkZOTKlSthPGDtUYIwQRAlDmmVSvjpu1WrVjk5Oc40JgRBwEUmXrFEUTx8+LCfn19sbCxjTK/XO5hcVqv1qRVmea2CPfnSfw79fw8ePBgaGpqYmAjrWGDnlei5EgRBkFYVj9zcXI1G8+GHH2ZnZzsn2QhC8lCfrFaryWQCecjKyvriiy+qV6+OpSUc5FMQBAcX4mN5kg8QX+hwhLVr177zzjv3799nVCSQIIjSgbRKJWazGS2bmzdvwgPnVK9ABYJiSLh9xYoVTZs2vXDhgizLRqPRbDZDaSVo2KHX65/RSwnHj4yMdNAqvrItY8xms2E29LBhw0JDQyHIkP216TBBEETxIa1SDyzMCIIgy7KTHYDwAKURUn0bNWrksMOTTL2il5TQBzhz5kz0AaIbkDfpsP2H0Whs3br11KlTmf0DKdYZEgRB/BXSKvWARGHBPac1bcI3AvOloKBg6dKlffv2heq0ICqyLINgQKF0XKDi/YdPArSqQ4cO6EvkvX8WiwWygx2Ok5OTExYWNmfOHPbXJTSCIIjiQ1rlvmCkH+QzwUYQEgxDt1gsw4cP79GjhyAIfEEKQF16MkhRy5YtP/nkk2dRHfT47d2797XXXps7dy7YbRhkAQ/QZUoQBPF3Ia1yU0wmEyoNRJyjqYR2VUFBQXR09NixYy0WC8T78eLksLz07MBx2rRpM2LECIxTL/olWq0WRHT9+vUvvPDC9u3b+aHy+cIEQRAqIK1yU3ABzGKx8Ms/0INKFMWkpKT27dtv377dZrMZjUZYPeKP4FBI6RnB9KmOHTuOHTsWVqqK0Dy9Xo+PQZMWLVpUv379e/fu4VNQUMNqtZJpRRCEOkir3Bqr1YpxEBj1Z7FYcnNz69atu2TJkidZPCAw6taN4FVdu3adOHHiU3cGbyQoK7RtZIxNnz69R48ejLHMzEzcjYpZEAShGtIqNwV8eig2EIYOwpCbm9umTZuBAweCjD02pqM4WgV606VLl4kTJz7LiheMCoIS0XIaPXo0xFkwexIYo5gLgiDUQlrlvvAlB3GWv3btWuXKlT/44APQBlmWH7sapNhR8b4Wi0VRlC5dukyYMMEhheuxgFsSBQkJDQ1NSEhg9oZYjBauCIJQC2mV+4JB57jwc/78+YiIiIEDB2ZlZTHGcnNzYXvJljUCO6l79+5Tp06FMhlFrFeBbceLUF5eHoznwoULvr6+R48e5fckCIJQAWmV+4KpvmDZnD59unXr1h9//PGDBw9gOxgrGo2mZN8XFpZiYmJmz57NuO71RcNnmIEH0maznTt3rkmTJvv37we5BQuMIAji70Ja5XqgTB+/hQ/8A7Nm3759fn5+mJxbeqDHr3fv3l9++SU8VuFLhONIknTp0qU2bdpkZmbyUewYJFJSwyYIomxDWuViHNx3EBAhSRI0goIKezdu3KhSpUpCQoIT6uyhVvXq1Wvu3LnFORSO9tixYzVq1Lh3754gCIqigL0IlpbFYqGAC4IgngpplYvhqx/xDTiYXcYOHTrk7+9/7Ngx57RzRJOuZ8+es2fPVhedAYAIgdxu2LChQYMGR44cYYxBRV321xyyYg6bIIiyDWmVWwCNEOExTNwQgHfmzJkqVap8+eWXTmsKhQEd77///owZM4pThdZgMIBpZbPZzGbzyZMnIyIifv31V9wBF+So5RVBEEVDWuVioGEHCpUkSRihkJiY2KhRo507dzLGdDpdQUGBE+wPGInVao2Ojp4+fbpqrcIVOD704+eff27atOnhw4clSYJOV7m5uU6r+UsQhOdCWuV60KqAWkTwODc3t2vXrjNnzhQEwZmLOjAASZK6deuGPUFUAP49PoYC1OvQoUN+fn4///wzs8dZ2Gw2KmlBEETRkFa5HrBdJEkCn5jVav3tt9/efvvtUaNGwQ5YQNZp6zqiKHbr1g0LT6irgQujRSWGf2VZTk1NDQgI2LBhA7PLVXFWxQiCKA+QVrkYXoFAk06ePNmwYcPJkyfjdgxGcBoWi6Vbt24YB6jCEwjFlsBg4nuawDmeOHEiKCho6dKljBarCIJ4BkirVAJzLtboA4q2P2DGh8p+jKs8ZLVa8SC7d++OiIiABruuAgYWGxv7+eefl4bvEU7/zp074eHhv/32G9a8wNZcKI20lEUQBEBapRLeGoCwbMYFYRfGarXm5eXxO8BjfG12dva5c+dq1qw5Y8YMJ+RRFQFkH/fp02fWrFkgG+p8gE/CZDLBYS9fvtykSRPwfGJEPsg2ZF9R6hVBEABpVbEAw2jNmjVQ9+hZfGXQaMpqtcJ0DC/RaDRnz55t0KDBt99+69oJGgoAKorSp0+f2bNnY1hgSR0f49RBnM6fP9+8efPk5GTGmMVi4Q0pCrggCAIhrVKPJElms1mr1bZv3/7UqVOsSPsDZ2G9Xu8QIpGZmZmRkVGtWrXRo0eX6oCfERDgmJiYzz//nN9SIoDJiPWWZFn+3//+17x588uXL6MzEGxNKPdeUu9LEIRHQ1qlHlSmoKCgc+fOsSJLiWOwH+88hAAEg8HQoEGDzz77TBRFNDtcTq9evWbOnAmPS9YHCB8FOj8ZY99++22DBg0yMjLAlsrLy4N3LE4mMkEQZQnSKpXw03e9evWSkpLYM7e9sNlsWHE8Pz+/R48en332GW9DuDCmwGYnOjp68uTJGA9Sgm8hiiJ8elarFY88d+7cTp063bt3DwohiqJIgRUEQSCkVcVCFEWNRlO9evWkpCRYiHrSniaTyWg0wsKP2WwGVcvJyRk8eDC6/sAJxgfCOR8QKlmWO3fuPGHCBDB0SnY8YDuiXGHW8Pr16xs3bpyfn6/RaCiqgiAIHtIqlYAZJIpiXl6en5/fzZs3+aoTRb8Kpv6srKwBAwb07t0blq/42D+Xr9NYrdbOnTuPHz8ePJYlvl4FcSVwWDxxSZLWr18fEBBw//59xhgUYSIIgmCkVcUB5vG7d+8GBwfzJYUeCzxlMplgjYoxtmLFimrVqmVmZuKk/NQmvM4BzqVVq1YLFy7EnKfSflNJkkDC16xZ07Bhw5MnTzIu4wrLW8DHqMLOwxeC1YjttaAtJOPsvJJNu4bDwqUiCALv2JRl2Ww2Q0FIuCpUpEWDja4oClw8sLFstGDGJp+FWxAQ5RDSKvXATHrz5k0/Pz8sbfeknXkZEwRh586d1atXP3HihNlsxqfAIebygAKYETp06LBw4UJ+Hi9V4EOAQrfr169v2LDh5cuXrVYrzOa4G6iLijndIQIelsr4j1qv1+O/JRguD9KI/8Kb6nQ6vkVySU3BDpE7ng6/nAn/kqldniGtUg/cz165cqVWrVqw1FT0pAN6ZrFYDh061Lx58x07djjsAD9O1y7VYABe+/bt582bh7e0zkGSpIKCAlmW79y506hRo02bNjF7wxSMG+QDCJ8dNFjxDh2MD95kxE++ZFO74HvnxQmAmvp85WIVOeBQZIS/xREEoQys9uFXIAiC0Wjk7ySI8glplXoEQbDZbJcvX65Zs2ZeXh74YZ60Mzyl0+kuXboUHh5+9uxZxmkbRDS4g4sDpk6LxYJa5ZycXAwOZHb9uHXrVuPGjTdt2sSH8hcnph9PrfBTuFEUxZI9X/RtQkMyfAtZlh3WAotjvPJaVQaECuF/EbIslw3fJqEO0ir1wKR27do1Hx+f/Px8vkJrYWBBIiMjo0OHDgcOHGB27xDUsHCHZSoAl23at2+/fPlyfhWkVMFlPJjBwVd2+vRpX1/fhIQEeArC2ZnasAuY6fgVo6ysLDhmfn4+LlyV3vnCOTpoiV6vh/c1Go34IahAlmWLxWI0GstGvQ/8lHDJymKxUP/o8gxplUpw1eTmzZt16tTRaDRFaxVjLCMjA4uXo32A+Uy4m8MKh5NBR1nLli3Xr18PUuq0d+f9eyAqJ0+e9PHxmTVrFqimJP1/9r4zLIqr/Xv/eZKYxzyJscWuNKWJICigiDRFUQRBRAQrWEARGyAoigW7MbGXmGjs2GPD3kVRjNhQUVARRNoC2/t5P9zv3tdhFtAsKLDO7wPX7jA7c+bMOXcvMu2EazT6YYVDuVy+ffv28PBwtLwhL6lBuUEqlcpkMriFVCp9/vx5RkZGVlZWbm7u7du3k5OTb9y4ce/evVu3biUnJ2txfU2XHlGHWdZrwLzB589siGZRN8HyKu0BRPzZs2cdO3YEwbyKkyUSSVhY2IgRI/h8Pn0mbTkE0R6NRbUCCEsjhNjZ2R06dAh6Fn8GSqFSqYA5QZ1A7H1VUlKSn5/fu3fvwMDAd+/ewTlasCuUADAgUKVSjR49Wk9PDzsXw01rXHgHWUQmk50/f75JkyaNGjVq0qRJmzZtWrRo0bVrV1NT0yZNmnz99dfW1tZXr17V4vpI05HT64atDGWI0tJSeCId4MEstAbLq7QHCLPp6emGhobgr6ri5LVr1zo4OICDHTYeqAjopgJGVRcsgUDTbW1tz549+zm5plKpRCMYzVcIIcXFxWFhYT4+PmlpaaR6gXPgGIPru7m5DRkyhKg5JUx+jdfLQB368ePHzZo1mzFjxpkzZ+7fv5+VlZWTk3Ps2LGjR4+mpKRAmS4tAMN++PDhkiVLdu/erTPBcrA7rly54u/vP3r06Js3b9b2iFjUJlhepSVAmJXJZJmZmQYGBqBXYct25DrgPDh48KC5uTlIzXSAU62NvnKAYpeXl2dkZLR+/XpSBywwMGMqlWrmzJn29vZoK8O+IR85pXC+RCKBd3flypXmzZsvXbqUYXGt8bBvmD2ZTFZQUPDjjz9euHABs7sIIUlJSRs3bszOzv7g+CsEXCozM7N79+5GRkYtWrRYtmwZXAc5Pcay180lVxlUKtWcOXO++uqrtm3bRkRE6Onp3b59G/vGwTkg/FXHz8eivoDlVVoClaE3b9506tQJI5LpYASgoXfv3rW1tT1x4gQYl9AGWDdTYYAW8Pn8rl27/v7776S248ogIJuoTXO//PJLq1atLl26hOQJ6K9AIKhan4AYClpnmj179o8//rhq1SqGSbbGCTq+6EePHv33v/+9ffu2UqksLCwkhIwePbpt27ZNmzZt3769dgIBzMP06dPNzMwePny4fv16BwcHog4/gdg5DBupXxCLxXp6er6+vgUFBTwez8vLy9vbm1DBL+ioY8PZvwSwvEpLYGOn169fGxkZYT8LJArofRk8ePCkSZPgIOpehJCPqcn0+YHFanv06LF9+3ZSBwgBCNFKpRIUo1OnTllaWm7cuJFo8FEMFKwQwDPgInl5eY0bN/6///u/X3/9lai9WVg3qwYHjzHrKpUqPT39hx9+uHjxIjCYoqKidu3abd++PTs7u1WrVjdv3tRuPRQXF4eHh1+6dEkikVy8eLFfv35wHPLS4DOdW1Zf8Pr16+fPn6MI4uTktGjRIkK9IFad+qLA8iotgQ6VV69eaeYCA0GUSqWTJ0+2tbXFdk0os9d6zm9lwKFaW1uDXlW7+h+M5927d/C1sLBQIpFcunRp0KBBUVFRqKoSQvLy8qq4DgRQAEMqKChwc3Pr3r178+bNkVeBd4R8miIdEolEIpEUFBS0adMGMhYgC/jIkSNKpTI3N9fS0vLVq1faXVwsFoOvSy6Xx8bGRkREELU3lKiNuuSzFB+pcSgUioKCggsXLnh5eXE4HFdX15cvX5Ly8gQbyP6FgOVV1UV2draxsTEdoQSkU6lUHjlypFGjRhcvXoTjSA2lUmld9hwANe/UqRP4q2qXxgkEAtQJ6Ij2vLw8V1dXOzs76CmMWUqVAXkVIaSkpCQ4OPj06dM9evRYvXo1nCCTyT6R8oGls968edOkSRModUjUEysUCsPCwvT19TMzMyEG8t+CLojco0ePkydP0lOBZs/6FXMBASnAZZcuXfr1119PmTLF3d09JCSEECIWi+Ffn8Jmy6JuguVVWgJl8NevX3fs2BFjvYBkiMXiO3fumJiY7Nixg6jJBB2bDh/qpmpFCMnLyzMwMFi3bl1tD4SQ8qUCCRWZ/fbt22nTptnY2KxevRoE7apVQFC8MAhQJpN17dp1xYoV8F/UP2o8lgRcU4SQ169ft2jRIicnh6i1AYFA4Onp2aBBg3bt2llYWFRtw6wMEBAvFov37t3r6uqKS3HFihWYdQ6PVr/IOrwmSLR6/vy5Uqm8fPny999/j5EpdAxtLY+VxacHy6u0RBVxgFC+zNbWdsmSJRikDolKjIvU2RIDxcXFJiYmGzZsILXNUFEbAIIL1FalUvH5fKFQKBQKU1JSbGxsunbtmpWVVcV1YKpByeDz+UAHHRwc5s6di+oU+iA/xYP8888/mZmZpqamyEtAi/L392/btu2LFy+GDx8eFhb2by8LC2zr1q3r1q3z8vLauHEjsMaVK1eamJiAtCEQCGC51lnZqEKIxWIGc42Pj+/Tpw8m/KG/iuVVXwJYXqUlKoutgGpJK1eu7NOnT1FRkaYxHSoqicXiuhkHCNSBz+dbWVlt2rRJqVRCCH4tDonH4zFynmgSxufz3717N2/ePA8Pj4yMjMoughEiSNeEQmFcXFxERATabD/FYwKPPHr0qL29/YEDB3766afbt2/jGEQiUU5Ozp07dxQKRWBgoGY5449BVlaWra3tf/7zHyMjI3Ds3blzp3Xr1hB+gtDOwFhbgI2jUqkwPH39+vV6enrnzp0j6nAb2EF1VuBjUbNgeZWWgOYUAoHg2bNn7du3B6EeSk6cOHGiU6dOt2/frr/VNgsKCqysrOLj40n52MW6A0apVh6Pt3r1aj09vdOnT9MnoAyOVcyFQqFKpTp37lx0dHTTpk2//vrrb7/91tLSEqsOkpp20cF9e/fu3bx5cw6HAzmtYIoEiiwUCnNyctq0aXPnzh0tri+XywcPHtywYUMOh7Ns2bItW7a0a9cuODgYraZEvVxr6IE+B86cObNo0aL79++npKT8+uuvgwcPNjIy2rt3b22Pq7oA/qpUKmmDQa2OqDaBifmV6f10wz+WV2lbM/twAAAgAElEQVQJZEIpKSktWrR4/vw5HvH09Pztt9/gMyxEmmrUCxQVFVlZWUHpQlIntxNjlRNCJBJJenq6vb39hg0b6AYcOPlSqRTV3/nz57u5uUVHR2/btm39+vUbNmz4559/ME24xqFUKs+ePduwYcOWLVs+ePCAECIQCEJCQh49evT27dvjx49bWFhs2bJFiyvDk3K53Pfv3x86dKhXr15GRkbjx4+HqEIwk8KZtZ578K/w5MmTzp076+vrW1tbm5iYLF26NDc3t7YHVQOgq00qlUqpVCoUCuugLPipAR5W/CoSid6/f08IgR1Nr1WI0SUsr6oOhEJhUVHR3bt3ORxOcnIy7KUNGzYYGxtDGYK6Uz394wHSd3FxsaWl5apVq8gnM45VH6DwgfKKgkJGRkZQUBBkhvH5fPRvcblcBrHGSAq5XF5SUiIWizFntgbNSmKxGBLppFKpj4/PN998c+PGDULIxo0bv/76awMDA2Nj486dOx85cqQ6d5HJZBCJqlQq37x5g8cFAgGqlfXRVpaXl4fpCjoDqVQKEkb9ssp+IhQVFVVY20yhUNBiKGF5ldbAnZ+dnd20adO7d+8SQlJSUgwNDRMTEwlVGag6LZc+P8BoVlxcbG5uDp75upwKhgMDjgVfs7OzPTw85s6dCzXIiYbvHQPzKtN3P5EKcv/+/RYtWuzcuRNuvWXLlsuXL7979w60PRzVvwIyaayFgR1G8ByssVSPVCtG6CxAi16UdQ0VZoPVU09BdaBSqbDsCEhyyJlwU4tEIlrAYnmV9hCLxRMnTrS0tORwOCAXu7i42Nrawn9xs9WvXEWgDlwu19TUdNu2baQOEziI1WbwUT6fX1JS8vLly8GDB48ePZrL5YKNBRa9QqHACu6YEof62afQg8FWCZm/xcXFwcHBS5cuxcqEXC4Xxg/sCk2U/woKhQLkIUYqOkAsFqNrpH4VesAIfh6PB49W42WFPz/QOg3PIhKJ6tdLqSmAAxX4k0gkAimkpKQEmmXjNoQIAHj7LK/SElwuNy0trWPHjiNGjGjYsKGDg0OfPn3atm0LmZ48Hg8TaEg9lJtKS0uNjY13795N6mqgM12YFeQv9F0BpS4rK/P19R0yZMj79+9ROpPL5RhChjIEXe2efIKXRSsHGRkZr1+/Jmr5GuQAjCnXAoyCQzQ1R/sn7SDR7i6fH2CSJeqnUCqV+fn5tT2omoFSqRQIBPh26h1xqEGAaeTYsWOrV6+mBTW6LxKucJZXaY9Vq1Z9991306dP/+6779zc3Bo0aGBmZkZX+kEDYL1zFRQXF+vr60PYVd2MrddsMAgAVoT5wpGRkV5eXhBfJxKJsBA+/Bcc3QxpXSQS1WDInEwmA0sjwxoJyQCEkPz8fDhYWlqqxVRLJBKG4g6anEQioQNMSP00oKHoTQiRSCQ6oFcBgCBgVa26KQ5+UkAXHhArd+7c2bhxY39//5cvX6Iyja4TlldVF7du3TI0NDQzM+vYsWObNm0yMjJOnDjRp08fJyennJwcgUCArvv6tcEg5TY/P79169a7d++uy+OnGyjT9m4AFhBZsmRJ06ZNMdkoLy8PnIvI6rA+ApoHa3yoWBAI7I1wC0wGkEgkwMm01nvEYvHRo0d9fX1hq2NyEiGEx+PB7eqXLRrtlnl5eTk5OfWrQFQVwCpfqampDg4Ohw4dqo8yRE0BaItMJlu8eHG7du2+//77NWvWAJfCaUH6w8Gz6dIyEomE9lJodqoF+z5+Rc8Bo8WtZuhhhRVCaYcB+AxwVzN2Ly3wyuXyqlcw+NsZY8CLVyY7A7HG+9IqEc6aQCAYOnRoYGDgq1evtm/fbmdnBz4DuVzu4+MTHR2Nej1NNbCbIj1LVQwDUFlLdUbIQ4UNfLFSHK1Q49gqk+Z4PF5JSYmdnR1EAcCiqXrSGMcZLxcfBEYCT0TPAwyMXoHQWoXBgeAnsNgYfS5wbFBcnF6x+fn59+7dMzc3j46O5nK5q1evbty4MSwM2ouLJgh6Ghnhs5o+LRgM2nPoR8DIDuCC+C7wiZB50BV46Z1FF26gK6bTHmn877p161q0aHH//n2irpNCj4ReHkp16+eqgRuQhuYCUJUHKU8u6EmmnRD0dTT9jnACnB8bG9u3b194KHhepbonJ3p6NDNDYKsivYNXwyj5SA8SI6HoWaVr5NPzhmQHi1VqAu9FPyYcgWEnJiZ+8803CQkJsKJgqjWnt8JuDBDViYuNcYJIJKKVUZre0rmS9HvRXF00cOcyyDuDlOFkVqEmwlRDnxr0S4HtYdOmTVFRUe3atRsxYsQ///wD58NUwxv5/3oVl8u9f//+8ePHExMTL1y4cPHixatXr968efPu3bv37t1LS0tLT09/9epVXl7es2fPXr58mZub+5H9pCFmVyqVikQiHo8HjhyFQlFUVJSfn//u3bv8/PyysjLG4zEoEYqlGKD8QQmUPkEul6P9h5R/N2KxGKxJXC6Xts/AB6AUQKFw80skkqdPnzZu3Pjp06eEkMTExP79+8P6EwgE0E/vyZMnRO1HRULGGB68Nnl5wIusUASGn/D5/A8+u0wmKysroyPE8F+wSkh5SicWiwUCAewZbFfh6Oi4ZcsWOJkeD3IdmUyGV9B8OgaBQ9BziyOkV3yFvBlsQYy7wDDg+rhD8Lf0yXw+H7KbnZ2dN27cyOFw1q5dCyfTxe+BNsFXoIxwBP7SA4NqTxh5SCiyKBaLuVwuXhOnCFksPg5RW0IYxfo0aRPEhgAYYiWfz4dbnDx5skGDBmfPnmVMAn01xi4D8VEsFqNYwHhMzbcAb19zt8JBLNJP6+JoaMWDcFNNlqlUJ8zJ1Y1plEplSEiIiYnJ+/fv0cOHjI3h6UFNmlDKMVhEK3wcnFKshIu2EMaZ+HLpMdNsj5SnTjgwsMSWlJQA3YPfFhcXFxcXr1q1qlmzZnQGeoXQZOqa8ijNM5RKJbI3enpxd+DT0ZVcaCkQuCwY6EpLS/l8Pn0dkAWBonK53IKCAi6Xy+PxioqKioqKiouLS0pKSkpKuFwuPGZhYWFxcTF8LSgoAC05JycnOzs7KyvrxYsXOTk5L1++zMnJSU5Ovnr16rlz5/r37//111+vX78eGFVxcTG8Uw4h5MiRI1ZWVhwOp3Hjxubm5mZmZt9++22jRo0aN27cpEmTpk2bNm3atGXLlvr6+iYmJo0aNWrSpEmrVq0MDAxMTU1NTU0NDAzatm3bqVMnQ0PD9u3bt27dunXr1m3btu3QoYOBgYGhoaGRkVHHjh0NDAz09PT09PSMjIxMTU319PRatmzZuHFjaDRnampqZWXVtWtXOzs7Gxub7t27u7i4+Pj4BAYGBgQE+Pj4ODs7e3h4DB482Nvb293dvXfv3o6Ojs7Ozm6VwNraunfv3h4eHu7u7r169erRo4ebm9vgwYPHjBnj4+Pj7e0dFBQ0fPjw/v379+vXz8/Pr1+/fsHBwVOnTh03btzo0aMnTJgwfvz4gICAPn36+Pv7h4WFhYSEeHl59e/fv0+fPt26deNwOMHBwQkJCeCpGjdu3IwZMyZOnDho0KBGjRo5ODiEhIRERET4+fmFh4ePGjVq1KhRISEhoaGhoaGhISEhI0aMCAgI8Pf3HzZs2LBhw/z9/YcOHTpkyBAYm5eXl7Ozs6ura9++fd3d3cG02LNnT1tbWwcHhwEDBvj5+Q0aNMjR0bFr164WFhbm5uZGRkb6+voWFhaurq79+/f38PAYO3ZsQkLC1KlTw8PDp0yZEh4ePn78+LFjx06aNGn27NmzZs0KDQ0dNWoUPLuPj8+UKVPi4+Ojo6NjY2NHjBjB4XD69OkTHh4+b968qKioWbNmRUdHR0ZGTp8+PSIiYvLkyaGhoRMnThw3blxISEhISMi4cePGjx8/fvz4cePGBQcHjxo1avTo0WPGjBk7diz+d8KECYGBgWFhYZMmTRozZkxoaOj8+fOXL18eHx+/YsWKpUuXJiQkLFy4MCEhYcWKFWvWrNm4ceMvv/yyfPlyOL5s2bLVq1evWrVq8eLF69atW7FiRUJCwuLFi5cuXbp06dJly5atXLlyyZIlK1euXLFiRXx8/OzZs+Pi4uLi4mJiYkJCQsaPH8/hcDgcToMGDTgczvjx4+Pj4+fOnQsPGBgYGBoaOnPmzKCgoAkTJkyYMGHq1KnR0dHR0dHTp0+fOnVqZGTk7Nmz4b6zZ88OCwsLCgoaMmQIrMkhQ4aEhYVFREQEBgb6+PiEhIRERUXFxMQEBwfHx8evXLkyPj5+3rx5a9eu/eOPPzZs2LBp06YNGzYsWbIkIiJizpw5c+bMiY+PX7ZsWURExMSJEyMiImbPnj1//vzFixcvXLgwKipq4cKFMTExM2fOjIqKmjlzZkRExPTp02NjY+fOnRsdHT1v3jxYk/369YNXHBYWNnbs2MDAwJEjR06YMGHy5MkTJ04cM2ZMcHDw+PHjQ0NDJ0yYMGLEiKFDhwYEBMCZI0aMgGU5ZMgQb29vb29vHx8feLpBgwYNGDCgX79+7u7uffv27dOnD/x1c3NzdXV1dnaG/ejo6Ojp6eni4uLs7Ozl5TV8+HB/f/+BAwf27dvXw8PDx8dn/Pjx06dPDw8Pnz59elxcHAwenn327NnTpk0LDw+fOnVqVFTUlClTFixYEBAQ0L59ew6HM2jQoPDwcNhNoaGhU6dOhe3p5eXl7+/v4+Pj6+sbEBAwcuTIIUOGBAUFDRo0qF+/fi4uLrDB+/bt6+rq6uTk5Ozs7O7u7unp6ebm1q9fPw8PjwEDBnh5eQ0ePLhfv352dna9evWys7Pr2bNnz549u3bt2r17d9h3pqamtra23bt379y586BBg+zs7CwsLHr06NGlSxcrKysrKytLS0tzc3NTU1MTExMTExNnZ2dbW1vwEZiamtrY2Dg6Orq6uhoYGPzwww8ODg6GhoYcDsfR0dHX19ff39/Pz2/IkCG+vr4+Pj7wOEOGDAGC4OPj4+fn5+vr269fPycnp/79+w8fPjwgIADG7Orq6uLignSvT58+AwcO9PT07NWrl7W1NZARCwsLNzc3oF2urq4wIS4uLv369evdu3fPnj179Ojh4ODg4OBgb29vb2/fq1cvqLFpY2PTs2dPJycne3v7jh07NmvWrH379p06dbKwsAAa3r59e2NjY2traz09vXbt2unr65uZmZmamurr6wML6NChg76+voGBgb6+fvv27du0aQMMolmzZsAC2rdv36hRox9++OGnn35q1qxZy5YtExIStmzZ0rp16ylTpiiVSnRccUCyePfuXbYahYWFr169ysrKysrKevny5fPnz588efL48eP09PTnz59nZGSkp6enpaWlpqampKTcvHnzypUr58+fP3bs2KFDh/bt27dz584dO3bs2LFj165de/bs2bx585YtW7Zu3bp58+ZNmzZt3rz5999/3759+9GjRw8ePLh///7ExMRDhw4dPnz4wIED+/btu3r16oULF86cOXPmzJmkpKSDBw9u3rx52bJl0dHRCQkJ69at27Bhw/Lly2NiYmDVTqwEoaGhYWFhsCtmzZoVFxcXHx8fHx8/a9asKVOmTJkyBcgQEPGoqKhJkybFxsYC2ZoxY0ZsbOycOXPg88yZM2NjY2fPnh0VFRUdHR0aGjpo0KCff/55zJgxixcvNjMz43A4Q4cOjYiICA8P79WrV9OmTf39/WfNmjVjxozAwEDgByNGjAgJCQkLCwsNDQ0ODgZOCQgICAgICBg2bBiwK19f38GDB48cOXLMmDEhISFAN8eNGzdmzBhgeDNnzpw/f/68efOAjMIIZ8+ePXv27AULFixbtmz+/PlwZOXKlcuXL1+8ePGiRYvmz58/e/bs6OjouLi4JUuWTJkyZezYsbC3HRwcQFCwsrLy9/d3dna2trbmcDhdunRxc3Pz9vYODAwEmuXl5TVw4ECQAIBawQfgqf369QNy1qdPH9hsfn5+Q4cOHTZsWEBAwPDhwwMDA729vYE3Dxo0CMgZUMxRo0YhJYXXB5gwYQJ8AA43adKk4OBgYPCDBg2C+wLFGTBgwMCBA8eOHQvnjx49eujQod7e3gMGDOjbt+/QoUPt7OxGjhzZtm1b2BgcDqd169ZWVlbdu3fv2rVrr169nJycLC0tu3TpYmtra21t3bNnT1dXVzc3t969ezs4ODg5OcEOBzLn6enp4+MDtH748OHe3t4BAQGBgYF+fn7Dhw+Hpxg1apS3t3doaOi0adPGjh07YsSI0NDQKVOmhISE6Onpfffdd8Ago6Ojp02bBlwf2MbYsWMjIiIiIyPnzJkze/bs8PDwpUuXxsbGzpgxIyoqatq0aSAWTJ06ddKkSYsXL968eXPPnj3/85//WFlZBQQExMTExMTETJ06FbbArFmz5s2bFxcXFx0dPXPmTGAPc+bMiYyMjIiImDlzZlxc3Pz58xcuXLhw4ULgGbCzwsLCxo0bBwMLVgNEE9hlINKhvBIcHDxnzpwZM2ZMmzYNltmiRYtg2DExMXPmzAFpY8mSJYsXLwbpBISSDRs2rFu3buXKlcuWLfvll1/Wr18fHx+/efPmoKCgxo0bczicKVOmbNu2LTo6GrZwQkJCVFRUZGRkaGhoTEzMjBkzJkyYMG/evISEhPj4+KVLl0ZGRsK6GjFiBDDI2NhY2O8TJ04cP378jBkz4OfAy2fOnBkZGTlt2jTY7AsWLIiNjQ0JCRk1ahSsxsmTJ8MVpk6dGhMTA5MZFRU1d+7c+Pj4BQsWLFy4cMGCBfBh0aJFIDYtXLhw8eLFq1ev3rRp09atW7du3frXX39BqRQTExMOh7No0aKDBw+ePn366NGjR9Q4duzYiRMnTp8+febMmYsXL549e/bChQuXL18+depUYmLi8ePHk5OTr1y5kpSUdOTIkcTExIMHDx4+fPjgwYOJiYnJycmpqal37949c+bMwYMHk5KSkpKS/vrrryNHjpw4ceLo0aOHDx8+fvw4kOvjx49fu3bt8uXLly9fvn79+o0bN+BvSkpKcnJycnLy7du3U1NT79y5c+7cub/++mvVqlXXr19PTU0FjpCWlvbgwYMXL168e/cuPT39/v37Dx8+zMrKyszMBAbx8OHD3NzcvLy89+/f5+Xl5ebmIpd58OBBTk7O06dPMzMz7969m5SUdPXq1bNnz165cgW00q1btzZu3NjJyYmodWUO6oOgxX+8Y7lC+7VK7ToGi5amrQA/g8OAYVKHjG7NEF7NUVXhO6F/JRQKaYdT1a14QUFGdbhCaxKgsLBQT0/v8uXLMpns0qVLXl5eUFJTLBbHxsbGxMTAaZg0QMobFkDXhsevUKOvzHhNqBrhjIFhhYIKgfY3tLGoVCrNorRgGCwrK8vPz/fy8lq3bh3YbRTlQRstSUXvAoxLtNkKlwRjYGjHg7hzTYuH5k+kUinmruEqQodEhWYujC+QSqUXLlwA7eqHH36AWrEqlQpD5jCdtjKbu6ZBSanuKQz2ZNooVJm/TSqVLly40NTUFOqbMK6MZiuGLZp2NmB6LyxvsVh85MiRJk2a7Nu3D2ZMqa7fIxKJ6AXDcLlp+jhx5tHwjlbcCieEATBv4iPA18rCsqsw0KEfvXXr1g0aNCgrK8MdIVe3dFGpVOiy0oxQQFcxWjWVSiW4AGlbNG3TA1+ApgUeI4xgABi/B6Hn8krS8hiODKK25cLnkydPbt26Fa4AbxP3i7x8VxqakDJqXqPJjlDWP/i5TCYD+7BSqaQdBwx/FS6JCt8CDSSPjGeknw7/iy5AJGW4Q+lNzTChw1e0FQ8ePHjEiBH4ZjnwCX+MPkaYMs2RwZ0q9L9VuKaR7tOuiypmhDa8MiYR3jTDbyyvBBWOgXbS0FVn4APOL16ZQdDpgt+BgYELFiygJ1omk6WmptrY2ECDouLiYnpp4qQhw4CvlbEl2idU4ZzDCbh78QoYPQG+EEIRU/rR8ANQNPrB4UxjY2OoXUs+FJ9WIa+q7GTgHHQ3B3Th0NfBr4yhViH94M/heTXPhNf06NGjzp07h4eHGxgYtGjR4sCBA3BCaWkp7HZSSSggXhbDQ6pYyTgAmUwmEAg0YymPHTvWpEkTyBnKz8/HKET6ofClw6PRnJjmpjiZ2NWz6hbJKo2wFFK+1SSDn+Fp9PPK1EAXV9UTQtSua8ZpKsoHhrycDjDp27cvCNcSiYQur65S+1foscGvgETgnFfo5oFJk1PVpeHVi0Si3Nzc9PT0lJSUa9eu3b59+/r160ePHp03b96kSZMGDhw4bNgwGxubY8eOwfuqkNkjGJQa7lVSUkLPbdX5VcBfMTYH5QCVOh6NvhSSlAqvQ8qLOzSRxEdAfoPBOJqrRVk+Tgr91kBR4SfgtNPkBfSNQIih3flwI5Anxo0b17Vr18ePH+N//79ehXMBqDAfCJ5TkyrBWBm05iMBI4Z50VzENNdhXFxFxf5WCIYeo6kk4UGV2jOMsirj7gqFghZOCSEikaisrMzIyAhqZkM2T3Z2tpub25UrV1CgwPMZy1FTGPn4eQMZQlE+DhOvo0nQaSmBHgA8AmNZw1fQWqysrCAOUKbOMKfVI4SqoogghUb8GILxOMDO6fdY4UICLqLpiscLMj4jj2cEL+HzqlSq7OzsoKCgn3/+edeuXXTUFi2h42Dg+vR0oX5JE1l4BSKRiM/nMwJS4INMJhOJRBKJ5MyZM61atdIMZFUoFOjqr0LahbsjjUCmDnenz0RRAMePUo6qEmWUAU3yVMX5SJqRtWsub+RwlYVr4/kFBQUXL15MTU3FqaDjWTABHIKtRCJRaWkpvNmMjIy0tLTnz5+npqbevn377t27//zzz4ULFzZs2DBt2rSRI0cePHjw6tWrKSkpaWlp9+7d++233zw8PLp3725gYNCkSZMGDRp8/fXXTZo0sba2BmbZs2dPcHgvXLgwLi7u0aNHGK1ADxtXPvlQ6GxZWRmuEDCK4BrTlLk1t0MVwgFSALBtwHaomlcxrkw0xDVgtLAyAR9JsiqUJnGcpDybhAl59+7duHHjrK2tnz17RtQiDiGEg6FuRC17KtWxIppkiKgFRmXlGhK9h2nSQG973DMMwiqrJPBaUT42ib511TSR/iG9n2kllEEXGNoVTaGQXMrlcqFQePLkSSsrq3PnzmVnZycmJpqZme3cuZN+AfLyYXsqjYidKogRPWOM45oTTkfG40yCXFMFX8QPjJMhwtPKyur06dOVvWhVeTPpxwP3AMO+p/nq6ZlXlRfuMK8WCTH+lh4tSiGEEh0g7A0+FxUVxcTENG7cGLpK0jnCjHnDIxXuUvqm9HoGLlKhHnbr1i1ra+v8/HzoUSKjeiKgEkxzuAq5Mi2yyNUlOeBBlOXVdxwnKb9OGOuhMvKnCQYLx11f2c9pyZKeQ1p3xIkihNDSoUwme/HiRXJy8v379/fu3Xvo0KG9e/fu2rVrxowZISEh3t7e4EDt2rWriYlJjx49GjVq9O2333I4nIYNGxoYGEDolpubG7hO/f39hw8f7uXl5e7u3rlzZ2tr66FDh0J0w4wZMy5dunTjxo379+8/ePDg8ePHhYWFNH2HsQFrrDC+l55YxleYW1i6eEFa+at65pWUdURTApNTMeU4n7RRR0FZ/PAgvg5UoXD+8f0ylGzG+seVjwZ8xsapglfBcgUKiSO8f//+4MGDXVxcnj9/TtQBt3A+mwusPXg83vHjx318fH788Udzc/Pff/+9tkdUA8CVamNjs2fPnn9Fv+ojpFLpiRMnunTpMnLkSLqKD2on6MrSrlhfZSguLnZzc4OsZIU6Ar4Gr/9vUdkrVlF5MKS8oqn5Q03ZC40utGSmmZUBsV5KpTIlJeXWrVuXLl26fv16UlJSTEyMs7Ozk5MTRKY5Ojq6uLj06dOnf//+gwYN8vHxgfgdPz+/devW7du378KFC9evX4dIgcePH+fm5nK53LKyMqjHqIVoRYNOKkCGWp0LfsmgxWJMf9q7d2+TJk1iY2PRIwgol1/F4t8CJSOJRPLq1auMjIyapWW1BaBEEomkc+fOf/75J5hZantQnxYlJSV379718PBwdHRMTU1VqvvgQcoIoVSZmi39sHv3boa9pRZpH8NhSWdxgQ0cEqRQPCfqqrggiQsEAjqWgc/nazbFBlclXYbxwYMHu3btWrVq1YABA1xcXHr27Nm8efNmzZp9++231tbWnp6evr6+oaGhiYmJL168QM96hSyHx+PR2g9DfWcol9oxLYhWwJRkFtUE6JSw1woKCtzd3Vu2bLlz507IWyUauinLq7QEODzBi/sxdvz6BZVK1a1bt7179+qwRgVQqkseiESi2NjYdu3aQUgnmObgHNADapyRYOIIXrnW5XSGDl2ZmZouqEGjwtUikUgKCwtv3LiRlJS0f//+JUuW+Pj4WFlZQSqSl5fX6NGjR44cuWbNmuTkZFCGMjIy6OIR8EEkElUoK2jyHpXaD1eF373SKagEDA8xOsn+7XVYINCddOjQoUaNGrVq1Wr//v34X5CY6RlmeVV1oaoo5KT+AheHq6vrqVOnancwnwEMcrZq1SoDA4M1a9bgvz6RZilXB16D91s7518NQkWVXaBJObIHZfmKFbTDSSAQ8Hi84uLinJyc58+fX7p0adeuXcuXLw8KCjI3N+/UqZOjoyOkSf33v//t27dvWFjY/PnzDx8+/OLFC7BGMDgfXXiXMfmMyEOlOhihCj+ZUiOwqIrdWpnFm35whvuchXbAWlBz5sxp3rw5OKiIWq3X9FWzvEpL8Hg8msxhekQtDqlGgNEuLi4uJ06cIBWVhdUlwKPRtPL27dvGxsbDhg2DnB44WOMGXlCh6LjT2vVXadrr6LgnOrujoKCgtLT08ePHBw8eXL9+/YYNGyIjIx0cHExNTZ2dnTt37mxlZeXh4REWFga5zDt37nzy5El+fv65c+fOnj1bWUtJiGmqMHu8FEsAACAASURBVLcJULXDia4RpRmzWnU4GA1NXqWiig/JZDI6w6l+lQOuU0AfVX5+vlgsfvPmjVzdLlUzwhk+sLyqWtAlux9Aqc5EdnBwOHz4sFKdcqSrYATOAh48eDBo0KAePXqkpaURtWEd+4zUCB49evTs2TM6LktWUeLz54RSqaSDJAkhUPPt2bNnBw4cWLVq1ZIlS4KDg7t3725sbGxqampkZOTk5DRt2rSEhIQ5c+YsWbJk586dGRkZ2JUcLwseI8ZCAvaMcXG4j+gUIjyTvhodfIghiB/zgCoKVUwCQwnD62uGk3zJraeqDzpjgY73o0ErWCyvqjFg7LhuwMnJ6e+//yZfQHMdjBuGSp14PD4+vnnz5lu2bCHl6+XXCPbu3btq1Sqg4zAAOVWC/fMDZRS5XP7u3bvjx49PmTLFwcHByMjIxsamQ4cOLVu27Nev34wZM6Ck04ULFx4/flxcXEzzCUwzgOhBRvVk+C8d8Yj+OblcThsb4QODZ5BKcrSB96BehYqU5stSUXUJKpsHxq+U6lw9sVh8/vx5aIRG1G1cXr58WdWcsqgcYONFSQX3F0bJy9VFLvCNsLxKS8ipgvy1LhHXIFDC7du3b1JSEqmyEI4OAKsPwFc0CcLxpKSkLl26DBo0KCsri9RoD/UtW7aMGDECPmOdpJq6uBZ4/fr12bNno6KiLC0tv//+eyMjowkTJvz555/79u0rKCiQyWTv3r1jPD6dcwMlshjHSfmQBHqSkeswMizpLDFs6KPJvSrTkBhH6Ah7BVVc4+NlDoVCAYxq4sSJjRo16tu3L/AnsVi8b98+d3f3j7wOC02g249u5qKqKHETlgHLq1iUg0Kdje/k5HT06FHdNgBWAVqEHzdu3M8//wzxgQg+n49UFaMwwIamonKQK0NSUpK3tzchBMLisWpi1aMCmz4tbNIcAu9IC1JQJgOO00MSCoVv3rw5derU1KlTra2tGzVq1KVLl8DAwGXLlp0/fz4vL09KtTqrU6CZGf2B/qrJyVBgV6ibY9HeewgyVKmTstE3Btf8888/jYyMTp8+HR0dffbsWfj56dOn27VrhxUgkZEz3giDvzJiVT7NDNUtwBzCW2NUKhEKhRkZGUQduV71emN5FYtyUKir2Dk6Oh4+fJhRfOuLAkQBgJvq77///uabbzZt2gTppXgOn88HL7GmKazqHOqzZ882b978/fv3+JOqB6NZC5GoX5ZU3bwOPEAydU1bBqWGk0tLSx88eLB161Z/f/82bdo0a9bM09Pzl19+gfbhjCjhuvnqaQ+fiioDSAepY3RlFTF7yorqBCJUKhUQ0Ozs7N69e8+dO5cQUlJSUlxcDBc8evSooaEhfMVbFBQU4M9xkDhgTLSng1Y06+bpGOClFBQUwFaC0m4wt2vXrv3xxx+vXr1KPqIfN8urWJQDkr/evXsfPXpUsxb7FwLaccXn81UqVWpqapcuXezt7aFELCTA4jkQwgQ14CvUYxh4+PChtbX1ixcvCCFYO/gj/VW0TZ9UHoSNWVACgeDcuXORkZHu7u4WFhZdunQZOHDgihUrbt++XVhYKNPocC9Td5is9XyvqsHIrAI+AalycATU3ApD++iaQyAH4DQiR4E52bFjh6GhYX5+vpwqiFxWVjZ//nxvb2+gv3Ac5xCSphn9eUEDUygUUPyeHswnmJu6gqKiopUrVzo6OtrZ2Y0fPx72DizLNWvWmJqaBgUFwZnI5isDy6tYlINSXaoZ/FW6lDr2rwDbCdN1wRWckZGxbNkyCwuLkSNHQjV9qEBaoS5SdRi6SqW6fPkyrf1Uzagq89BgVbqSkhLkrxKJhM/nJycnx8fHOzg4NGvWrF27dgMGDIiOjt6/f/+jR4/QaEb7jTQfoQ4CVSj4ijO/c+fO8PBwjNWEGhmEKryrpIrqKjTaseNnLBmKbGnYsGHBwcFEraqirW/ChAkRERFEHS2JV+DxeHhx5IgV2tKV6nLpdVwmqA7S0tK6d+8+bdq0kJCQ4cOHu7q6QmxtZGRkw4YNGzduDAVqYcaqngeWV7EoB9xmXl5eoJuTuk28Ph2wQi6tY0kkktTUVOioSafZM1p902ygCmD82wcd/hjABmfCD6H7EX0aj8c7dOhQSEhImzZtzMzMXF1dJ06c+Ndff2VkZIBLBnNsadAVVDEbSa5Rsr0ugJEPB2wmLy/P3t4eXgdEc2RlZaGcoaqkywmEn9FchO5Vj0csLS2XLVvG6BbE5XIdHBy2bNnC5/NLSkpEIhG0IsvNzYUr4zzTfilcSFXbh3UJfD4fPFKEkNzcXBMTk23btgUEBHzzzTccDmfWrFmEMurS1nVNsLyKRcXw8fFJTk6Gz1/IvtIEVlpSKBSYDgwU7fDhw61bt+7bt++TJ0+QpkPpnY/xmWMrI/gKERYfjGXQLNAAZTXKyspu3bo1b948Nze3Hj16eHp67tu37/Hjx5DSy2A5GByvVCoZkeX1RY0GzoH8+/Lly56enjweDzqBlZWV6evr+/r6wsnKivqZ0cDYCmBRyGagBUaPHj0WL15MCJHL5aC3SSSShw8f+vn5vXnzBqbL0NDQ1tYWWD6+UyVVoYqWRYRCIepewC91Joq4QsDLEgqF169fb9GiRdOmTZs0aQL9Da5evQr7paCgoLIGMQiWV7GoAEql0svL69q1a+QjRH5dBVAQHo8HH4DiAz2C7VdUVDR69OjmzZtPnDiRLsegKUdXCIaLiHwolY2OLVQqlfn5+U+fPj127FhERIS1tbWZmZmnp2dCQkJqaip9cfrdYbQV3euS5n+MIO86G6iG8SOEEKVSuWXLlmHDhhE1mykrK4O+zw8fPiQaBQBRX6QzvWhugQoZ/MrZ2Xn16tVydRdHaFyuUqkePHgAp8XExPTq1QvmViQS4dyCcQ/DVRjeNYwevHPnzubNm2t+juoG6LjKGTNmcDicoKCgly9fLlq0yN7eHs6BMijkQzkhLK9iwQQ4Wvr373/x4sV6JGvXLEBgZ1RQBQZA94aQyWQHDx7s0qVLz5499+7dC8f5fD5GPVRxC3CoCIVCPPljzIbQzGnbtm3e3t4tW7b09vaeNGnS5s2b79y5w+VyKwyEUVANZOm4D6ybTiirlEpd+LXOvnRMHUV+nJCQsGTJEvisUqnS0tLatm377bffHj9+HA/CB6lUyuVyc3Nzc3Nzk5KSdu7cmZycjD4/KBsPZ4KYL5VKjY2Nd+3aBdF6yNKgzx8hpLi4uHv37n/++SeGgyqVyuLi4oiICBAa8J3ev38/JCQkJSUFjqBqdf369aFDh37aKas94OPPmjWLw+FMnToV5i0sLCwuLi4jI2PRokWWlpZdunRBEaEysLyqWoAFvWfPnrdv35KPjuOq+1AqlW5ubidOnFBVXi+ABY2EhARjY+OBAwe+e/cOjjC0K6lUSls5bty4gbNKhw6S8vHrdNJVYWHhgQMHfH19mzdvbmBgEBER8SUUF2YA8/8I1Yd+4cKF06dPJ2qelJ6e3rRp02+++Qa4BTIYsVgcHx+vr6/foEEDDofTqFGj9u3bd+7cOTc3F4MgiNokiJGZ1tbWv/zyC6FK2GFDbZlMlp6e3r59e6xnAe965syZQ4cO1dPTg7A3OHPBggUNGzZ89eoVsli44Js3b2xsbLACCMNy+Cnn8nMAniUiIoLD4cycORMOikSiffv2tWzZ8quvvurUqZOnp+exY8fYmPVPBTRq5+bmcjgcNzc3MDjUd2CclZeX14EDB2p7OPUJXC43JibG1NR06tSp4Njg8XgYiYscCNo+HT9+HM5BuweEOCPTEggE8K/S0tI7d+6EhIS0a9euVatW8fHxr1+/rvXejLUFOjoclb+TJ0927doVPfPJyck//PDD4MGD6V5ZsLCfPn166tSpK1eu3Lt3r6ioSKFQwK+gxQ+hin8TtSTavXv3jRs30ncnVG/x2bNn29nZlZWVacYFHDhwwN7eHi64ZMmShg0bArFWqVR0B+cLFy706tWrpKQE2TAjH6u+Y9SoUXp6elu3boWvwM6VSuXFixevX7+enZ1NW02ruA7Lq7SHUqkUi8U8Hs/CwuL06dNEJ/QPoIBisXjYsGG7du0iOvFQnwegUaWkpLi6urq7u1+7dg2dWEAHhUIhUrTJkyf/8ccfCnVnd9reCOY4Pp9/5cqVmTNn2tnZtW/ffsaMGefOnYPU7LKyMjAzfrGvhlExpKCgYPz48f7+/n/++efq1au7dOnC4XDAAMiIe0T7IYgF+HPMeaf1toKCAolE0rNnz+nTp6NLiQ5UUSqVYWFhENGOogOEtovF4nv37vn5+T158mTSpEmtW7du0KDB77//TjvD4Cd//fWXqakp5PCR8t61Ousv/HjweLzNmzcfOHAAngUeGRViWuQqKCioOsaE5VVaAoiOVCrNz8/v2rVramqqDijshIoJ9vPzS0xMJDqxYT4n5HI5j8eLj4+3tbW1tbX9448/RCIRxi+IRCLwzE+aNGny5Mnwk5KSElChgGLevXs3OjrazMzs559/dnd3X7du3Z07dyoMH9elWsn/CjRjgA9CofDgwYO9evWaOnXqP//8Y2Jisn79eqI2o0GBR5hkHo/H4/HS09NzcnJOnToVExPj6+t7/vx5UK1g/WdmZt69e/fQoUPjxo3jcDhNmzadM2cOTW0BRUVFvXr1WrhwIe59kE7gRunp6d9///3gwYM9PT3Pnj37v//9788//ySEwAIgapK9aNGimJgY+rKYmKwD8YF0EUi6MiQd3cM4szKwvKpaUKlUr1696tixY0ZGhmYCRz0FbJKBAweePn2azuRnUTUYUUyvXr369ddfGzZs6Ofnd/PmTaKuU0cIUalUo0eP9vX1hfhmoI9yufz+/fsBAQHm5uY9evTYsGHD27dv+Xw+Xhayo+BdYM/4Lw2o92iSNpjGt2/flpWVzZ49+9ChQ3gQKWNZWdmvv/7q5ubWtm3bn376qVOnTosWLUpLS6OTslNTU52cnL777jtzc3NfX18o85Gfn0+owE64YFFRkYWFxS+//ALR7fSNJBKJm5vbd999N2DAgMzMzLKyMlNT0927d2u+tc6dOy9YsIB+HFCslZU0Za6PQMsq2j/pithgUFVRxRIrBMurtASfzwfzQm5u7o8//vjkyROiKyoIJKN4eHhcuHABnkg3nutTA3rtQAUdEJOVSuXff//t4+PTokWLwMDAtLQ0pVLJ5/PFYnGvXr0iIyMhdKKsrOz48eMDBgxo3769j4/P7t27i4uLaVuQSCTCrB26HMYXWFlYM8oc9Q9IjoaDwcHBmzZtosP20F6alZV19uzZY8eOQU4bUkypVMrj8UQi0YIFC4YNG3bv3j1CiEKhMDc3X7RoEZwDxBSj3sVi8ZQpU8AGSNQqAqyBPXv2fPXVV5MnT4bKW4SQoKCgpk2bjh49Ojc3F8vJv3jxwszM7NKlS7RVhk4b+ART+FlBCwFgu6areCCD1yz0pQmWV2kPKOOWkpLSqlUrELt0w90NwdO+vr6gV+mGbfNTQ7MeBGw8IIXnzp2ztbVt165dYmJiTk6On58fh8OZPn36s2fPVq1a1bNnT2Nj46CgIKg3Q9SvgNEJl67NSsrXAfpyAAVnGUeIOlgcjohEoqioqIEDB0JuHF2QCcL0sToflMavjESCfNCpU6dp06YBYyOEyGQyOp5z165dxsbGEFdVWlqKm2XEiBHjxo3jcrl4JCcnZ+7cuefPn8ffZmZm+vn5YcA6vdeQXWk7T3UIXC4XbAN0YXuQHhhZgFWnA7O8SkvgtN65c2fgwIFEV4RcFFFHjhwJVhTdYMCfB5hkStRWjoyMDKyElJiY6ODg4ODgwFGjRYsWVlZW8+bNy83NhQR+RmF7mmYBkcXPukHItABN4Bit4zDtKT4+3tXVFQ7yeDzMa6a5O0Zdws5l1J/F7WxhYYEB8TRHBOmEy+WamZkNHTp09+7dcBxsd0VFRXAFtArSHkfwSO3atcvU1PT27dv4OIxkYR0QE2l3FBj6lEolGsNR38XQkirA8irtAYs7IyPD3t5el/KQIDhn5MiRly5dAoEIux4wCvZAuJpMJktNTV27dm1iYiKIongOBF5nZGS8efMGVE8Ao+wNLSxDmwxNBknHC+EtZDLZq1ev8CIqdWlR9CtACguWsUHDmkQiuX379vbt2zdt2gSiLgwARJC3b9+mp6cDMcKsGkJIZmbmrVu3MjMzCwsLs7Oz09PT09PTX7x48fLly+XLl4eFhS1YsIAOSJk/f36LFi1atGiBB7lcbkBAAIfD+c9//sPhcAYMGADjx7vQJZp0wwpUs6BNdnTNWdBB8ciYMWMWLVpUYfHDDwLyq2BHi8Vie3v7CRMmVHayTCZLSUnx9PR89uwZ2n6r8DOpKoEW4/zSwPIq7QHE8eHDh507d66DVT61AxJHDw+P5cuXb926NS4uztnZOSYmBnegUCgUCoVlZWVLly5t3bq1mZmZtbW1hYVFp06dnJyctm3bRghRKpU3b96Mj493dHT86aefvvrqKysrq4kTJz59+pTRBvfBgwezZ88eNGhQXFzc6dOnb9y4QQgpLS0VCoVisfjt27dDhgzp1q2bjY2NkZHRmjVrCCFyufzFixfLli0zMTFp0qRJu3bt2rZt6+7u/tdff8E14RYHDhxwcHDw9/dfu3YtMCF8TevWrTMwMDAyMvL19Q0ICMCSo4QQiUTi7e1tYmLSoUOHK1euEELev38PP588ebKJiYm5ubmDg8O4ceM2bdp08ODB5cuXBwUFOTg4eHt7r1+//sqVK8hvoqOjo6KiLl26RAjh8/lbtmzx8fFp06bNN99889VXX3E4HENDw61bt2L0BF3bFD5UYaH6MqGZeyQSiXJycvbs2XP27FlCiEQiuXbtmoGBwfbt27W4Pl0WC3qFuLm5QfJGFcjMzGQMrzKwvEprsLxKe8BuefjwoZmZGS1913eAhjF48ODAwEB7e3sPD485c+YYGBgsWLCguLhYJBLhw6alpd2/fz87Oxur1Lx9+/bNmzdyuZzP54tEovz8/JMnT16/fj05Ofno0aOTJ08eN27cuXPn6J5+ly5dGjZsWFBQENxx7ty5eH1wzJ48efLBgwdFRUXp6elwXCAQ5ObmPnz48OzZs9nZ2Twej8vlQnNx2uR9//79ZcuWHT58GKqKwKjg6aB+KP3UUCcbIBQKcXi0ZlNWVkY3+sPQJox9QKKDzSkIIQUFBdu2bevatev//d///e9//xszZszp06enTp26b9++CRMm/PTTTw4ODocOHYKrlZaWYuNExhuh8cXSOIznxmcvKSnJyMj44YcfOnTosHTp0rlz50J+m3biI8gNXC4Xos8FAoG+vj6W/tMEvhpITAZVuIo6kCyv0hosr9ISaJ959uyZjY0NCPK6seYEAgGPx/P19b1x4wbojjKZ7MmTJydOnIATYH9C6ivyBh6Ph/uWngeaJahUKixBBHlI9E3xg0qlKioqwkhu+poKhQK93HAyaGBE3WIVI7VI+bRKmodp+iQQXC4XDmKZVwzAY9A+VfmKqHA1RtnTFy9erF69umPHjm3btuVwOE5OTnfv3oUTgBcqlcq7d+/GxMSYmZkFBgZC60VNaK4rla7EiWkHcH7AZ5lMVlxc/OzZs4cPH0ZGRgYGBq5fvx7SH7WwycNbxsj448eP6+vr03KMJmCF0HUrqnAlsrxKa7C8SnuAozU9Pd3Ozg6O6EB4BZI/Ly+vs2fPgicJa7ZqRgwzHhmUDCx+iqGoED2lWeiMrirEGAD4YIk6Q5YOIqLPROWGvgheEwyJWJNUJpMhY8OQZawugdyIoXJhPF6FhdrkcnlJSQl64yA69Nq1a8OGDWvZsqW9vf3u3bsfPHiwefNmaM/4+vVruBqyTJlMdurUqeDgYFtb21mzZl28eBFmVSAQVLaivlhehTPPaAEFCQPgy8RJ0y4/CcozZmRkhIaG2tnZLVy4sOrz6agNNhDp04HlVdoDaoTcv3/f2toato1u5O5xudy8vDxbW9u///4b46QxM1Emk5WUlKioGFOlUsnj8bDMF3YBIOoJoYsLEELAikg7HlBnAnkZUlKQEuH+Z5Qjwog4QkhJSQkY5bBQGwMqlQp7ugNoNqBUKul4ELw47SpHvosjxN7z+HQikejhw4f+/v7ff/+9h4fH33//DXokQ9CGC9J2Qpj2tLS0bt26mZiYjBkzBu1OMB7NwL8vk1dVXQAek5mUSuUH+yFVCNjU8PnEiRPQTbGK81GcgpWPX7W4NYuqwfIq7QG09dGjR926dUNqW9uDqi5wh9vY2Bw+fJgQolKpwLTF4BmwIelK/sAqcBLQKSWXy/Py8jRr/jO0E4YOASHaWJAGgbX1VBr102hA9zxCNWnF8b97945uScXlcrE5L4/Ho3vCwi2QqdCBZ3gjqVRaUlIC+tmiRYt++OEHZ2dniBBBugkOM1LeUoTmSlqN4/P5p06d8vHxadeu3ZgxY6CnKuipjEaLKl3Jv/lX0LSYwREsr0coQ67Wdg6BQECbfD/I9qDjJf1Vu/uyqAIsr9ISGCD7+vXrXr16wUHdiFkH0u/i4gKBVRj2TaiepyBs0uWi6VZPNA2lCXFxcTHdP4kuskIoGyPEX+GvMG6eIeGq1EVZkCfhADCZA09mdD0nai89KR90h2PGCqd4HI2NqPzRj7Bnzx4bGxsbGxusJw00FKdIIpHgpIEqyaBoMFE45vT09PDwcH19fT8/v/Pnz0skEsbEEl3xj2oBRloVUb9Emqkw1NaPh1QqRdsAvMSqZQKQhOBtlpaWsozqE4HlVdWCSqXKysqytrYmupK7h3lUnp6eiYmJDIHxSwNa/7C2LM4GMs4XL14EBwdbW1uvXbsW6GNldsiPATqigJk9fPhw4cKFPXv27NGjx+rVq1+/fk2366VTU+FXIEJ9ya+Mha6C5VXVgu7xKmw6FxAQcObMGVJRVZsvChh5AdEToNxgIurhw4f79u0LxjqcJXS2aSFia5oZpVJpXl7eunXrLCws2rdvv3HjRtpZCHoewwr6BdoGWeg8WF5VLegerwKIRCJPT8+jR4/CV515ro8H+M+AH/D5fGRUhOo6P3To0LZt227ZsgXnRy6XC4VCugCd1gOQyWRYPQFuKhAIduzYYW1t7erqevXqVULZV8HYWIVbhY2NZlHfwfKqakFXeZVQKPTw8EhMTPyS686B3wtVFugyDrOxffv2Nm3a+Pn5YSwGODnoBUCX/PlXN2WsIoVCATxJIpGUlZVlZ2cnJCQYGBj07t17165dZWVldC8SCGPTvO8XG+POQmfA8qpqQfd4FRK+UaNGQWxFdbwv9RdI1jGoDHDx4kV3d3c9Pb0DBw4QdSRhhUlm1TGcMpKHSPnaP4QQsVi8d+9eDw8PZ2fnrVu3YudPNh+Lha6C5VXVgu7xKoyFGzFixMmTJ7/MwGii5tnYhorP57979y46Orpz586xsbFgoKPDmqEjEaSRajqQPh50rIRIJEKLIupbdDqaSCQ6ffp0QECAnp7e6NGj09LS4LcQSMnmY7HQJbC8qlrQPV4FgL7Ae/fuhSTH2h5O7YDOwXrw4EH//v2NjY1v3boFxj1abaqwGqR28XjQYAm/MhK50IOFbZnAR3Xjxo0BAwYYGhrGxsZmZWURdVQ3m4/FQmfA8qpqQfd4FVaa8Pb2Pnz4MOYS1fa4PjeQG5WWlkZHR7dr1y4yMhJC0jH9C04AsxsyBpVKBVbT6jAGmHNM7sFyDKR8KTysWA+nHT582N3d3cXFZeHChWw+FgsdA8urtAfs/GfPntna2gJR0AFagDRx6NChV65cqcIFohvAKkpYFArZjEwmu337tpubm7W19cWLF8lH1C/4/MBidMDAFArFvn37+vXrZ2RktG7dury8PGRsEomEfptQtpFQ+p9CoQBtTNNbxoJFrYPlVdoDKNrz58+RV+mAjQWdIv3796f7beswkJozyridOnXK1NQ0Li6OaERY1B3QRTfoaodHjx719vYeNGjQgQMHcnNzGZoxXQeLDiMEQM4Wy7FY1CmwvEp7wIaneZUOxMuBM6akpMTGxubIkSNwUIdzgaEELVJ5bKodHh7esWNHqNwBL7puttNkWGjptsIikWjHjh0ODg7Ozs7bt28vKCiosM49o0IVofKLdUD2YqEzYHmV9oCdTPew1wG/DvhdiouLzczM9u7dCwd1vm40OITgMZ8/f+7n5+fp6Zmfn48RfVg8qZYHWhHkcjnyUaipAYnMaB48c+ZMnz59evbsuWXLFjhNs90wvHfwe4FGVVlRYBYsagUsr9IewJ9evHhhb28PR3RGDhWLxVZWVvv374evOkyzkCKDOrVr1y5zc/Ply5cTikNjblMdnAc6xp0R+AfgcrlFRUUqlermzZu+vr5ubm47d+6EvGbNx4GIErymDuvTLOodWF6lPYAugA0QY8Bqe1DVBVZhsLGx2b9/v8744aoGBJ3HxsY2bdoUtcni4mK6eHzdVC5pbxNY7bA9Ma0FYlH5v//+OyAgwNTUdPr06a9evSKEiMViOuaedlOxnQNZ1B2wvEp7wK5+8uSJtbU1Nk2v7UFVF0DUSktLrays9u3bV2HXXR2DVCrlcrm+vr6mpqbQYx7ZErbsYzSNrGtgFA8kVF8x/EAHMV67dm3AgAEGBgZhYWGpqalwGv6c0auFBYu6AJZXaQ+wojx48KBLly5Y4KC2B1UDUCgURUVFlpaWBw8e1I0nqhqbN2/W19cPCQnJy8sjVINEJO51mVUzqlFgZxBCCJ/PB6aLUelgJETnVnJy8rBhw6ysrIYOHZqRkYHaVTWTw1iw+BRgeVW1IJPJXr16ZW1trVAo6qaNSAtAp9p27dqdP38e6GD9sgWJRCLNRCjgN2KxmG7JSAhJSEho0aIFOKgEAgH0zdNhoFEX5+Hhw4dbtmzp0KFDXFxcZmYmfTK9yn+iZwAAIABJREFUpPEzKnCMdiSQBP0ZHoHFlwmWV2kJjJu6d++ejY0N6Fg64IuGhyoqKtLX1z906BCmi9b2uD4WjCrjkOTLeC9yuZzP50ul0v79+zs6OqakpBB1VXVCiEKhoDvN6yogNZgQolQquVxuVlZWZGSkvb39jBkz7t27hwxJqVS+f/8eo/bRClrhkqhH64RFvQPLq6qL8+fPo7+qbqbg/CsAWc/Ly+vUqdOOHTvqnTkIVUDkPQhQtiBiIj8/v1u3bpMmTbpz5w6hOv/WwUi/mgWt+tCfhUKhSCS6cePGlClT3N3dZ86cefny5aKiIrr3I0QJAruCyHiol/GFN49m8XnA8qpqQalUnj9/3tTUFEhkXXZsfCSAWBcUFBgaGu7bt6+e0iCJRIJyAzwRRscRQg4dOvTjjz9GRUUBf8JUJEZEnK6CjvRTqVSod4rFYvjw6tWrOXPm2NrampmZHT58GPpMItPSZOdgDPwy60ay+GxgeZWWQKvIvXv3OnbsyKhwU6+hUCjKysrat2+flJRE5x7VC4DXBImmQqHAthoCgUCpVJ45c+b777+fM2cOnEAHoyPHqo2Bfz4olUqxWMyQQtDDhzzp7du3hw8fDgkJ6du3b3R09KNHj3BWBQKBUChkXIRRe54Fi5oFy6u0BNY8zczMtLCwUKlUmnXV6ilkMhmfz2/btu3FixfrY2wFXZKcIemHhoa2bNny5s2b8BXYEnR/LykpgYO67ayiuwHQERYwaSqVisfjIbeGJf348eO4uLguXbq4uLgcOHBAKBQyWBQU/NUBowKLugyWV2kJ3OSpqamdO3fWmVxgQgjUA+zQocPx48cx1rm2B/UvgJwVjX6FhYWPHz8OCgpycXF59uwZJJCBAkEH/qFugT/UPTC0RggI0swbQzshzJJAIMjKyjpy5Iivr6+VlVVwcPDz58/z8/Mx/Q4quLM2QBafDiyvqhZkMlliYmLbtm2hDE/90j8qBLCl9+/fd+zYcefOnfVRXkYFF3hPSUnJmjVrDA0Nw8PDCwoK6Mri0AKDEMLj8eAx62y2b81CLpdLJBJ8s8BmgGlhA2KsPkXH/hUVFSUlJU2ZMqVFixZ+fn779+9///59bT0Fiy8KLK/SEiCfikQipVIZExMDkni9I+uaAPJUWlrapk2b/fv3f0zHJrqmA5pGGSW9BQJBjfuB0LMiEAhoTlNYWIgDUyqVCxYsaNmy5eXLl5GqolulfoU41imkp6fPmTPH2Ni4W7du69evh9q+EomEIa7hVDM6FH/OobLQDbC8SnugxePdu3f10a9TIYDH8Pl8Q0NDtAF+8HxCESD0fIhEIpyQGu+ZAkRQsw8T3BHC+V68eNG5c2c/P7+CggJ0R8FvdaYufm0B5lkgEOzcuXPgwIEuLi6//fYbFP6Ady0UCjG6HX5Csyi6DwsLFh8DlldpD7CPoeSoG4QP2IlAIDA1Nb1w4QJ9sGrQnZPog4QQqVSKnXZrcKjYvYJxO7lcLhQKDxw40LFjx9jY2Ldv39K/Yltd1DgKCgqOHDkyevToTp06jRw58saNG5AwAKlXhBChUAgKukqlKisrQxss+yJYfDxYXqUlkCyKRCKGWb9eA0h/SUlJp06d/hWvgl4SMC0nTpx4+fIlXg0jx2pQr0LFCMVzeAtyuVwsFoeHhxsbG1+6dAnVKQxXwyuwfW+rA4lEwpA8xGLx+/fvo6KiLC0tXV1dFy5cmJGRQSoJVIEEONYGy+LjwfIqLUE7cnA31q94uSrw/v17PT29pKQk+FoFTcHwBADwBhcXl2nTpjGYN+PMagJkc1pyB5dJfn6+u7u7jY1NZmZmFcXRIZSApZXVBJTBFIvFULpCqVQKhUKhUPjHH394e3sbGhq6ublduHABTLJQDpjH46E6pTP7hcVnAMurtAfDGUN0JY1UqVTm5eV16NDh9OnTH2OloYk+zEDr1q0HDBgAqTxIj2q8ABWakvDDnTt3AgICzMzMsrKyCCECgaBCPyLLqKoPKGFVoWIKoltZWdmDBw82b95sY2Pzv//9b+3atWfPni0qKoJzWOsfi38LlldpD6kaKpVKZxzF4AQqKioyMTG5ePHiR/5EJBKhipOdnd2mTZvIyEiiZmNwvMbJE7brBeKYk5MTEhJiaWlZWloKpeLp/9LF6zC2gkVNAdKKFQoF1sNFGaW0tPTo0aNOTk7//e9/DQ0Nd+zYQQhRqVQlJSUsx2Lx8WB5lZag48pgy+lG3QqIg+DxeF27doX6DnSlA03As4OOAprTpk2bOBzOmjVriDoeD/N1ajC2AhgVesIuXbrk4+Pj7e1dXFwMQ6K1OlqFop9FN/TgWgGEqIBdFzx/WAVDLBbjJIP7ED4/fvx43rx5dnZ2/fv3/+uvvwoKCmpt9CzqIVhexaIc0tLS3Nzcevfu/dVXX3Xs2PH06dMYxQD9NQghqCoBey4pKYGvQLlGjRrF4XDGjRsHF8RfYdrTvwLcAvkccB3QYlGXPXbsmKmpaVBQUDWfncUnBSjffD7/0KFDAwcONDU1dXJyWrx48blz54qKirBHCaEi2mHVwUFUlKHGIy1nsObcLwEsr2JRDk+fPl28ePHYsWO/+eabnj173rt3DzVIzdA7QrnHCwsLodZOp06dvvrqK3d3d2zrV80h5eTk4GepVAp3x1zs3377jcPhTJ48mehETxZdhWb+9fXr12NjY83MzFq1amVubr5o0aLMzMzS0lKIWlIoFMicysrK8M1ihRGAZslHFroKllexYKKgoIDP59vY2KSmptLHgUlgc3egPlwul8vl0kLu5MmTTUxMbG1tiVqUlkqlwPC0tgGCxI1cEwYgFApDQ0O/++67y5cvE0LevHmj3cVZfAbQzIYOipHL5S9fvty9e7enp2eHDh0mTpx49+7d/Px82t0Fy0Ymk+FFxGIx5ooQNlLjywDLq1hUAC6Xa2lpeerUKUKISCSCSnHAMJ4+fZqcnAzt3rHwK7Cx4uJikJr37t1rbm5eWFgIxzEIQjvgZYF+AV/MyckZOXKknp5eWloacESiE3VDdBh0kVxGeha4u54+fQqCjpOT05IlS54/fy6VSunijYRlS18wWF7FohyA6L97987Ozu7w4cOkvBHv9evXbm5uHA7HycnJycnJ2NjY0dExNzeXYXx79uyZkZHR7t274StW7NbCHojUDZQqqOl3/fr1/v37+/n5ZWZmQgIyJFexhKzOosJXD1Y+VMqBG2VnZ2/YsGHkyJE2NjZeXl67d+9+8eIFdHNGqzKwPYjtpDubsNBhsLyKRTlAtDePx+vRo8elS5eAfEBTXWA5Fy9eXL58+a+//hodHT1y5Mjff/8dfohldSC+a/To0TExMUQdMg7V4bQr7YEFJoBdPX782MjIyMfHRyQS0bGX0ACwek/P4lMBVV6xWFxcXIyqNjqlGIWX+Hx+ZmbmqlWrLCws9PX1Z86cmZaWhvZnBITzsBkIXwJYXsWiArx8+dLBwWHbtm2EoiZotKEtM/AVwpRRdpZKpbNmzfLy8uLxeJpR41pAJpNBC0Qul9u+ffvly5cTNfmDkTBc7izqIKCuEn5FjxSyHzwB2Q/IHzk5OXFxcR07drSwsFi5cmVSUlJ+fj7+hH3vXwhYXsWiHIBwCAQCS0vLO3fuELXtTigUYqIVMp7S0lKa+ohEotLS0sLCwrFjx7Zt25bD4WzatAnK8BBt888g1Ro+JycnW1hY7Ny5kzFaZKJgCWRRBwEtsmAJYeIwXSYfWRdDuJFIJNjvEbLoLC0tjYyMRowYcf78eTiHjf/8EsDyKi0BOUa0RYIudFavIZPJCgsLra2tIQ7wY/wBCoUCJeLt27d369ZtyJAhwcHBv//+O3aN+mDgA0ZqIOkBhwSUBdmwYYOlpeW6deuIrpQJZqEFQJFKSkoKCQkZMGCAu7v7tGnTbt26xefz6fY0tGGQZnuaAR30V0IZnOG/bOZW3QHLq2oAEIOgM1AqlVwu18bGBvWqKswsqC3hOQqFIi8vD7gX8ifMCK4MwPWxCjDWoiWEyGSyPXv2mJmZrVixoma7irCovwAukpycPGHChB49enTp0mXAgAFLly5NS0ujT2OkAwIg15hesdjRhq7SQquAn/x5WHwILK/SElBaBkhwnz59nj17RsoXX6/X4PP53bt3v337Nvm44DrY1eC4YoiiEonkY0oZ0boUHeMuEol27NjB4XAgiAMGw9p8vlgIBAKo2wRrAKItpFLp3bt3t27dOn78+P79+7u5uY0ZM2bv3r0Q5oMKk0Ag+KByr1SDPsLWg68LYHmV9oBtQwixsLBISUkhOlTrRSQSde/eHeoBfpBXSaVSmnnA18LCQuBbwNThX1UzLWB4YAmEuZXJZL/++mvLli1hJKWlpXApto4fC4RKpRKLxXw+H3RuPp9/5syZ0NBQS0vLVq1aDR48OC4u7tq1a7QARC9pWK7oFgVFil60LOoIWF6lPVBGc3R0hIDa2h1PDUIikXTr1u3atWsMm74moDfEBy8I16nClkhXToLqfzweb/r06dbW1q9fvyaEYPEL7CvB4suEWCyGFIgK+2BhEX2xWFxQULBjx47Q0FALC4vmzZvb2NgsWLAgNTUVS1MyeBIatDVbTrOodbC8SkugXbugoKBHjx4ZGRmQlljb46ousGJ6165dr169SsoXJtcE/hdK4ECGJtAOmUwmFothWjCRszLQPA+6zq9YscLOzu7OnTvQxQNC50GBwzB6Fl8a6HVCm5dLSkrA50RLTmVlZZjM8OTJk19//XXMmDGenp6Ojo6//PLL1atXgTnJZDK0kdAABYt1VtURsLyquuDxeN27d8eEj/oOzMS0sLC4cuUKHKyaXWkGCmKjEDoW64N2FQj5gx5IiYmJFhYW169fh38BSQJ/uEwmYyMsvmTAWqIjIBj+S7FYTPuloC47xo6+efPm5MmTbm5uffr0GTJkyIIFC27dugX/AnmLLjMIstcnfyQWHwGWV2kJ2uNqbm6ek5OjG4HU8FBlZWXm5uZQE5Z8yA9HK5TQ0ZxQLoGq21/RQG1p27ZtHTt2BBcgo8YSYZ1VXzYYkehQbwmOMIQYjOvDHzIaeefm5u7ZsycgIKBz58729vZjx46dP39+Xl4eerYg9l0HjCW6AZZXaQncA1wu187O7v3797phLgALXnFxcYcOHe7duwcHa7AmLNpwVCoVRqiDBwKIwqZNm1q0aHH//v2auiMLFprAPpyEkLy8vH379o0fP753797ff/+9jY3NrFmzLl++zOVykVFB8CFucLBLEyoPXTO0HcQsLMaBvljGMD7oEmYBYHmVlkB14f+1d+ZRVZXrH6dBXdVadgsHHBhkkklmwZREsSiXXrWbld3SW1euDWpmc2qDP1uVpZm20jRvk3VFFDWnaHDALAUDRFEJEJD5AGce9rzf3x/P4l3bozFswHPO5vn84Tpns88+7z7ud3/387zP0NTUFBsbW19fr5mVWEEQ6uvr77jjjiNHjvS4AwR+JZqVCXYYNZ6WLl3q7+9/5swZiAbUzE+KuCHK5S5wJDocjkuXLmVmZs6fP3/cuHETJkxYtGjRwYMHlW1ClZfr1U25SJvrm2VZp/YCEAxCY+LlK+ndU9UEqFUqoR1Lq6urw8LCKisrNbOIIghCbW3twIEDf/rpp95wuNEstMbGRqII4po7d66fn19BQYHNZnN6aEWQHgcq9F/TphEEoaWlJTc3d+XKlWlpaSNHjpw5c+a6detKSkrg4oS1VVAdURSh7juVHKe4RHgL/4oKMNSwS6BWqQdM/pqamujo6Lq6Os24tgVBaG1t9ff3z8vL6w0fhfLJlFbOXrp0qbe3d1NTE5SrgG/UxhIg4oY4JfxCvTS4FKmhI4qi0WisrKwsLi5+55137rvvvqFDh0ZERCxZskRZPxeg6cmEEKvVarFYrFarMrDeqRwGhsV3FdSq7mI0GidPnqyZBX944rNarVFRUefPnydXLl93H/rISdsKE0JefPHFUaNGVVVVWa1W5doYhmAhvcRf6QR0rnG64GFPjuMuX76cmZn5z3/+MywsLD4+/qGHHvr6668LCgroEix1CTh91zVnEPoAuwRqlXrg+jObzenp6RqIqqBIkmSxWCIjI8+ePUs6qgfYVegPRVuSf/3112PGjDl06JBTdSVayhZBeg8QEpZlleHpHMdZLBYQHmWIPJ0IOp0uOzv7hRdemDFjRlRUVFxc3CuvvJKbm1tfXw85W9TjB19BKzs7fTvGVnQe1CqVwPVNCNHpdOPGjQP7QBvPR6Ioms3msLCwoqKiXircqdPp4LCHDh0aNmzYwYMHQfhpRVHw/uF6FdJLgMdeOWEht++aIa/KNqHQ40bZHOfs2bOff/754sWL77nnntjY2HvvvfeZZ57Zt2/f8ePH8/LympqalN8CDnDlnMK+xp0EtUo9cAk2NDSMGTOmurpaubjq0YiiCHZVcXExrBv37PGp8bR3796QkJCtW7c69S4SBKEHo+QR5K9oJ0VdmUcBQGlm5QeJ4nFKEASbzVZfX3/s2LFNmzY9+uij06dPHz16dFxc3KxZs1544YVvv/02OzvbZDJBsV16ZNDI3j1PTYBapR6HwyHLcmNjY0JCAthV2rjmJEmCuhXFxcUd9vJoH3ChEEVQr9zWjd5gMERFRS1btkwzS30IQgG/X2NjY0FBwfbt29944405c+akpaUlJycnJSWlpaUtXrz44MGD8NymjCECFyI8qykLmFF5o5lhEI5I55fmC4+hVqkHrpLa2trIyEgIv9YGkiQZjcbg4OA//vijO0UOaVaKslUKOO4NBsM999yTkZGhLH6DIBoGXBRGo7G8vPybb7558MEHfX19AwMDp02btmTJkvXr1x88eLCmpobuL7ThdBxah4wGK8J2JytQe6BWqQeulbKysoCAgPLycs0ErYmiqNPpfHx8Tpw4ofrqh3q18Bq0SpIkKFTR2tr62GOPzZ8/n1psaFohGkMQBI7jIN34moWbBUFoamrKz8//6quvVqxY8eCDD06aNCkkJCQtLW3evHlff/31H3/8YbfbabEMSZIgLF4Z+87zPC3+onlQq1RClam0tDQ4OLiqqkozSyyCINTV1d1+++1HjhyBLSoUi36ERknAlGNZdurUqTNnzoQ8KvCdavt5EEEAWZYtFgvDME7PtSBsZrP54sWLP/7449KlS++++24/P7/Q0NAVK1a89dZbq1atWr169aZNm/bv33/x4kWLxVJdXQ1zB+B5nvbR1iqoVSqhV1tFRcXYsWNNJpNm8iR4nq+pqRk4cCDVKhXrcCA/tNcUmFYsy06fPn3s2LGQuUWwwy+iUWw2G8MwdL32aiALXum4U+Z1tbS0nD9//sSJE6+++urTTz89c+bMpKSkkJCQwMDAiIiI+Pj4W2+9dciQIUlJSQsWLKA1prUNapVKwFwQRbG0tDQlJQXeasMNyHFcXV3d4MGDT5w4AVtU21Vga8Jru90+d+7coKCg4uJiulEQBLvdro3fDUGu5uoSFRAZ71SHCRyGdEtLS4tTjUGo6kS3FBQUbNmyZcaMGSEhIa+88gqsDWs7JRG1SiVwYTkcjsLCwqSkJGh7o404QJZlm5qaAgICoM66OnuRzjTogGez2bZs2RIWFlZRUUFtqcuXL/fgsBHE3aDllOgW5YITacvcogF+ykJNpK3crVMSGMdxSmustra2ubm518/EDUCtUgmtF56fnx8fH2+1WrXhACSEsCzb0tIyevToc+fOkW4E4tMFKkLId999l5aWtmfPHjr3wD2oTO9HEM3gpDGkTbfoX5UCBlESpG06QNj61c4M5VMjxMQrhdCprLv2QK1SD8/zsiwXFRUFBAS0trZqY70KyslUVVX5+PgUFhY6ZUddE1ppgj4SOqVk7dq1KyUl5ZdffsEYCsRDuWZEOG3t4dTtvmevcxAhLVXGUQdqlXrsdjvP86WlpUlJSbBFG6GAsixfvHjx1ltvPXbsGDzidbg/fQ2ed9LmlHc4HDU1NeHh4du2bevFESPIdQEMIIiYgEKCyoufSlcPfiOUdHLaqI37TFdBrVIPGOxnz54NCAhobm7WhtEA862ysnLIkCGQC0w69zQH+zhVrBFFMSUlZfHixaSvTjBES1ydGu+0mATWVY/LFTwyQteSPuswR63qLkVFRd7e3uXl5dpIaAUBrq2t9fPzKykpgY3tyDC4+5ye/iC6z2KxzJgxY/z48UajkSiaziGIJ3J1mANpi9BTLkT1bB87Oq1o8Rdt3GdUgFqlHnB2lZWVRUdHK4OzNUBZWdntt9/+22+/dWgMwRRyKj4LC1evvPJKSkoKBGiAXGnm90H6Gk6+PqhGARup35vu2YN2FTwL1tbWvvHGGxcuXCDXsu36CKhV6oH7cmlp6ejRozVT6QScGOXl5d7e3nl5eTAhO5wb9KGPBiNt27YtOTnZYDAoC1H33rARpFdR9qd3Ch3qjV4EShiGWbFiRf/+/efNm0fVsfe+zm1BrVIPXDclJSXDhg2DniCuHlEPwDCMJEk1NTX+/v60ukQnrSuWZWEW7du3z9fXd8eOHYIg0JQRp0QTBPEglG0YqW459byHtiA9uy7L83xLS0tqauqsWbPuuece+KLORDxpD9QqlciyDBflpUuXEhMT4S6smWXPqqqqwYMHnz59ukN1UXrP4fSLioqGDx/++uuvk7bJTBt7Y3gF4qFQraKxf83NzadOnSIKk8tisTQ2NvasiwUeHIcPH/7DDz+kpKTQvsN9ENQq9YChUFZWFhgYqKWC/JIklZaWJicnm0ymDtUXzpr2zuE4Li0t7cUXX+z1USLIdUTZhB4mRUVFxcCBA3/99VfYgWGYzMzMQYMGbd++Xdk+ESpN0IbXsEVZV4w69OBJjmVZ+kgHrppdu3aNGTPmzz//HDx4ME0ZBsWCt9TxDsekk1Gv1yu7bMNhqbve4zQPtUol1KNVV1cXHR0Nod6aWZKprKxMTk7W6/UdCrBSzEwm00cffTR58uSysrJeHiCCXG+sVitMcJvN1tLSsnr16sjISCjEB13tn376aS8vr4yMDNj/6phAKLLudFiQLnJVHWdQIFmWX3311cWLF2/cuPHhhx9Weiaoawc+qywGSFvHsSwLQkWPRveB9NBu/SLXF9QqlUCsKiGksbExPj4eNnrW//01gdkIJ1VXV0cDc9v/FEy28+fP+/v75+bmXodxIsh1xul2n56e/tJLLxGFGzw6Orp///5vvvlmS0sLFR5Zls1mM9wZZFk2mUwGgwEOYrPZlPrkVG+M6tBrr702f/78sLCwrKwsWZbp6i9dLaNHEEXRYDBQg8kpdpEoMrSu2cXRzUGtUg8Ej1ZVVUVGRnbynu7+wKRqbW0NDw8vLS3tTI0leIiTJOm+++5bu3YttvlAtAdc1bIsw9Vus9n69euXmZlJCKmrq4N9EhISfH19T548SRTrW5cvX/72229ffvnl9PR0b29vHx+fmJiYTz75RPlcCzVqiSLtlxAC1TEcDsfs2bMHDBgwZcoUmst49afIVQn7BoPB4XCAjsJglJ5AwLMqNqFWqQfcgJWVleHh4Z2v7+DmwGVtMBj8/f0LCgqgPGA750V95Zs2bYqJiYEm3B7nCkeQ9oF5Qbv0Xrp0ydvb+8svv4Qa5zU1Na+++mr//v0ffvhhovCv6PX6DRs2xMfHJycnr1y5Mjs7e+vWrR999NEvv/wCbUHo6hEIiTIyHkqwE0ISEhIGDRp05swZeuTTp0/v3r0b9rTb7XAQpXeR9o0D4FM0H/Tw4cOwZuFZsWCoVSqhWUe1tbURERHwEORxZvXVwEnp9fqRI0fm5+d38qQuXrwYEhKSnZ1N2qrf9vpAEeQ6And2ZTX0hQsXJiQklJWVvffee4MHD548efKgQYNWrVpFP0JNMb1eD6qg7C1A2iwn0iYzgiDQkgL0EXDnzp1BQUErVqwgivrrixYt+vvf/04PQghpaGg4deoUtAaGvPvm5ubVq1cTQpRhHSaTKTc39+GHHy4vL/csoSKoVaqh1kZlZWVgYKDFYmmnB6hnIUmSXq/38/MrKioibY9jfwX8CLNmzfrwww+pfmtg3Q5BnKA3d4hi2L9//+jRo2+77bbx48dv2rRJEIQpU6Zs2LCBtPnZaDye2WyGz0L8Hn2uVcYKkrZyGIQQaPYhy/Lhw4cDAwNvuOGGr7/+mrrWL126NGzYsKNHj8qyDJJWXl6ekJCQmJg4YcIE2hPuqaeeCgoKEkURpIvOYp7nFyxYsGPHjs7k+LsVqFXdQpKkc+fODRo0qKmpSTPJQzzPGwyGwMBAyAXu8LzefvvtOXPmkDaJQgcgoj2gESI1iUBmDAZDQUEBrFcxDDN58uSDBw+StokAE4fjuKNHjx49elSn05nNZqvVarfbqb8OkuXJlR48+Jbi4uKIiIj3338/ICBg48aN8CeTyVRfXz98+HA4Dmw8ceLE22+/zfP8smXLUlJSCCEbNmzw9vbevn07UUgsSCAh5M0333zkkUc8zgmEWqUenucZhtHpdLfddltDQwP0CHD1oLoLPL6Zzebg4OA//vhDWZST7gPzChJHCgsLQ0JCzp07R3dArUI0DEwQ0CGIpoMICKvVGhoaevz4cdiHCoPNZtu8eXNiYqKvr29qampiYuKXX35Jy2Ze0xHH87zdbh8zZsy6detaW1snTpyYn59PHxkvX77s5+dntVqVIgf/fvjhh6Ghoa+++mq/fv1SU1OVkRcUQRBef/11f3//3vuJegnUKvVA9zOz2dy/f/+cnBxXD6cnMRgMvr6+5eXlSuGBZWSaYEgIaW1tHTt27NatW0lbN27YrhkTE0EosixTtx48lYKowJbjx48HBAQYjUY6C5SrtgaDoaGhQa/XNzY2Orn+CCF2u53jOBpNTghZuHDhyy+/3NzcXFZWFhER0djYCHsKgrBnz55JkybRt4QSorYPAAAenElEQVQQh8MBh5o2bZqXl5eXl1f//v0hJRn0Ekpp6PV68Afu2LEjODjYYDB4Vlk41Cr1UA/y4sWLi4uLiVbK9TMMYzKZAgMDjUajsp02rdoJl7gkScuWLZs2bRoNpaVeBc/ygyNIh8AalTJ/lpaqgemwbNmyBx98kLRlXrIsyzCM1WqFlWzloWiZdliUotuphu3atSs6Orq+vp4QkpmZOXbsWHgs5nneYrFkZ2cPGzbM4XDY7XZl3/pDhw4FBQUNHz58/vz5/fv3B1nleZ5mdwEmk+mDDz649957iaetK6NWqYRWqyRtgTeiKHrWc8pfAaG0UVFRVquV1jlUmk2EEFmWT5w4ERYWBmu5ypYo8GsgiMYAwVC+oN1AGIaJi4s7fPiwUx0jQOmFczgcynnk9FYURavV+vLLL7/55pvgXfzss8/uvvvuP/74Y+PGjXl5eYSQ9evXBwQE0I+At8Nms82YMWPYsGEFBQUlJSUxMTFFRUWgZJ9//nldXR3HcdQEfPzxx5cvX048rX4papVKwKiil5pTDxvPBc7CaDRGRERcunQJNoIwUzsSpuLkyZPfeecdoligcipHhiBawmq1UpV6++23v/nmG9I2Kb777jsoXkPnAkT6KfM3JEm6pm9c2VIEwjSsVuv27dtnz549ffp0Ly+v2267LTIycvr06TqdjhBy4MABf39/URQhl5EQ0tjYmJGRERIScvr0afiKxMTERYsW/fnnn48//vhTTz1FPSIOh+P06dP33HNPdXW1ZwkVQa3qDg6HA64ASZKUvjKPBq71+vp6f3//06dPOyVLUR366quvhg4dSoORaF9gWZY9y7GAIJ2BVtgjhOzbty88PBwyOgghOTk5kZGR27ZtI1c1aVO+FUWRFjfiOI7ePUhbDha8NhqNJ0+eHDFiREpKygcffDBo0KCMjAzlo/CZM2fCwsLAJ0lvOOfPn4c1LZiteXl548aNGz58+FtvvQWaBDP38uXLycnJL730EgzGs7ruoVapx263O0XaaCAEDirwNjY2BgcHV1VVwWRTluU1Go0mkyk0NBTiaGFumEwmmiaJWoVoFVCs3NxcLy+vqVOnfvnll6dOnZozZ05aWhohBJagSFsjN1qfjOd5eotwsmaUTX5BTqC5wZ49e2BjWlramjVrwJvX2NgI3bNuvvnm7777jijqU4Crw2w2w0FaW1utVmtJSQlM26amJji+IAjr16+Hj3hcwj5qlUpoQAG4mImG1mlsNpvZbE5MTKRbqHUFD3dPPPHE/fffT9rmIfUNwrNhn+2xjWgYnufpoqwoivn5+cuXLw8MDAwMDHzyyScvXrxI94Qd6BRQlgiAmcIwDA3CoiWwSZtLg/4JckKioqI2b97sVB999erVDzzwAN0Cs5L6PJw6QMJfYfULpAtsMo9bs0CtQq4ArmC73R4ZGQlmIvzLcRwo1o4dO3x8fMrLy4kmfJ4IogKINmIYRmlCUdSZLFRaaMF1nufHjx9/4sQJZYBxn/VboFYhzvA839TUFBwcDCFGRDH3/vzzz5CQEEjdwCQqpO/gJD/gUeA4jud5pzVddbWL4DhOX2GxWJKTk6uqquCwDofD44pN9CCoVYgzHMeZTKbExMTm5maYdVC4UxTFpUuXzpo1C3ZjWdbjQokQRB1OuVAwI6Cmn5MyKd16XTo+PQ58EcMwVVVVAQEBdXV19E/wgOhxS009AmoV4owoii0tLRMmTID5Q3ubrl27duLEiQ0NDUSxXOfisSLIdcFJq8hf2E+wUfW8AOWDyuiSJJWWlt55551VVVW05y/Lst05vkeDWoVcg7Nnz4aGhsJr2nRg6NCha9asIdfqh40g2uZqrbom3dQqp0fAc+fO9evXr6amBiSKXNXnvk+BWoVcATjEy8rK/Pz8TCYTDRZ69tlnp06dqtPpIMpI6bJAEASQ2+jqB2nTEHgNmnfgwAEvL6+ysjJCiCRJyr4ePTpqzwC1CrkCiPrT6/VhYWGXLl1iWZbjuKysrISEhOLiYjoJqZvCpYNFEI2grNkGtQQdDsdXX301fvz42tpa5T5EK3VHuwpqFeKMKIp1dXXh4eFQ66+hoSEsLOytt94ibfEUYFr15ZAkBOkNQISo/fT9998fPXqUXLkwrIGCA+pArUKuAFZxL1y4cOedd0KGx8qVK0NDQ1XkkdC/0rq3tJMpLcqOlhmCIJ0BtQpxRhCE2tramJiYxsbGn3766ZZbblm/fr2KPBJooEDNL6vVerXDXafT9c2gJgRBugRqFXIFHMexLKvT6YKDgysrKydNmpSamgoN4rqUR0LViJYso7As6xTO1JejmxAE6QyoVcg1YFl2xIgR27dvv/nmm0+dOnX1Wm5nYnPBogL3OpRTo4UwYIvRaDQYDH0zqAlBkC6BWoVcATTqtlgsd955Z1RUVHp6Ou1W4LRbh1rFMAx1AFKVgjoxSn3qm0FNCIJ0CdQq5AqoMXTDDTd4eXl9+eWX19ytwzwSpcOQuvgMBgOVt9bWVognpHmOCIIgfwVqFeIMwzDFxcU33njjgAEDjhw5Qq7qyd2lQ1GzadWqVVOnTp01a9Zrr71WWVmp3A21CkGQ9kGtQq6gsbFx7ty5Dz74oJeX14033pibm6s68IEmgoiiePLkSR8fn4yMjP/+97/h4eFLliyB4HXINe6x0SMIolFQq9TDMAwYBEuXLoVFHdX2h0twEiGIL7dYLBkZGd7e3l5eXgMHDvztt98YhgHHnXL9CRAEAQ4CBadhH5pBRa0lSZKKiopWr14Nb7Ozs/v16wctVrGoIIIgnQG1qrsYDAY/P7+dO3fSvpweAQ1woJXUQVoYhjl//vygQYO8vLwuXryo1DPYRxRFKlqwhWEYSBOmUu1UZ9NkMpG2UHWLxXL8+PHg4GCz2czzPKQe99lUfARBOglqlUqg7rIkSVardeDAgTk5OZ7Ve5BG4nEc52Tc/Oc//xkwYMBNN93U0tICqqOUYdAqeO20zgS71dXVUaMKpMgpKv3IkSN/+9vfzpw5A6aYZ/1uCIK4BNQq9dCaQ2FhYZDx6nE5rTzP08A8WZY5jnM4HBkZGV5eXl5eXrADnBTHcUqfHuzf0NBQWFh4+PDhd955Z8GCBQ888MADDzwwfvz4Y8eOgZ5RkWNZtrW11W63S5KUm5sbFxcHh3U4HFcnCyMIgjiBWtUDDBs2DPKHPChMACSKiis1bsrKyoKCgu6+++4RI0aUl5fDGVmtVhqhLssyFFsyGo1nzpzp169fUFBQbGzsrFmzHn300QceeMDX13fNmjXKlS3wAcJBmpqapkyZ8sknn8BxCCEGg8HjNB5BkOsMapV64PbN87yPj49OpyMeFSkA4gSKxfM8BERIkvTkk08mJyefPHnS19e3sbGRtHVWJG1FlQBCiCAIdXV1+fn5Z8+ehUAJOGZ9fT0onN1ut1qtoEN6vX7ixIljxoxJTk729/cnbSnA77333oIFC67/6SMI4lmgVqmEtppmWTYuLg5u0x6kVeDHg3+pf+/o0aMDBw7ct29fUVHRyJEjGYYxGo30IxzHgUo5nSYNAqSxFXQLIcThcLAsm5mZ6ePj8+yzz958880DBgxIT09fuHDhjBkzbrrppoKCAlyyQhCkfVCrVMJxHG2MFhcX19LS4lkB6wCMGXTFarUuXLhwwYIFsiwXFhaGhobW1NTAbrAD9XBCqLogCIIggMzAa0IIy7I0qA8CKwghPM+fPn16/Pjx/v7+n376aUVFxapVq+6+++6MjIxDhw554u+GIMh1BrVKJbIsi6LIsizLsgkJCbDRg9pbwFChjxS4437++eeQkJCamhqWZfPy8sAHCCaUartH2cLKYDDU19f30PARBOlboFapBALWeZ7neT4+Ph5uyh5UKwi0Fl5D1MPzzz+/fPly2JKfn+/r6wurUD3yFUSROIwgCNJVUKtUQsVJkqTY2FjIUvKg9SqiKHDOcVx5efnEiRNLS0sJIaIo/vLLL4MHD66vr2dZVrn41CUgy9iDbE0EQdwW1CqVKGUpJibGbrd71k0ZcpnpWWzZsiUjI4P+6bfffgsPDwfXnzIHq0tAVDoUxeipYSMI0jdBreoBYmNjrVarZ/UMBP2g6czp6en79+8nbRpWUFAwduxY5Z5dhTa4oqLYYb8rBEGQvwK1Sj3ULomLi/M4rQIgeA+sqJaWFujey7Lsr7/+GhISYjabOY5Td15gTjk5RT3LR4ogiPuAWqUeCKIjhMTHx9vtdo/TKjrg+fPnv/baa6RNugghubm5I0eOpPUAVaCss44gCNJNUKvUIwgCpBwlJiZCvpGrR9Q1YPBGo3HIkCGQSkUD2XNycu644476+nqoUtGdXF2IsIAgC7SrEARRB2qVSqjRYLfbY2JioB6gB63HUNlYs2bN/PnzSVtjDjAWjx075uvrC0UrQGxcOFQEQRDUKpXQJFm9Xh8REdHQ0ECuan7h5jAM09zcfNddd+3YsQNsLFok8Oeff4aYdZ7n0RhCEMTloFZ1C1EU7XZ7fHw8pM16kP0BibqHDx8eOXKk2WyGeki0quGRI0eGDh3a0NDgQWeEIIiGQa1SidLdN2HCBIPBQDzKBwhDXb58+XPPPUcUVZTAt3nq1KnQ0FBaqQ9NKwRBXAtqlUpo0QdCSGJiYl1dncfVrTCbzenp6RcuXCCEyLIM61VgSBUUFIwZM4a6ND1IgxEE0SSoVSpRVmWNjo6urq527XhUsH379tmzZxNFbUPSdl75+fmhoaHK1vUIgiAuBLWqu8iyPG7cOIgD9CBqa2sfffTRnTt3EkW9JWoanjx5MjAwUK/XY4UkBEHcAdQq9dCEofT0dGieS1s3uT+5ubkxMTHwGvx+YFfB67y8vJCQEJPJBCHsKFcIgrgW1CqV0AA5SZLi4uKqq6vdM2QOlppoR0TSpknPPPPM0aNHafQEdQDKsszz/JkzZ0JDQ1tbW8lVrT0QBEGuP6hVKqH1WAVBSExMhPwqNwRECMSGmkclJSVTp06lbX9JW6gIrVJRWFgYFBTU1NREFKWkEARBXAVqlXpEUeQ4jmGYpKQkt12vUtp/9N933333scceU24HHyatsVRcXBwSEuK2J4UgSF8DtUo9VKsSExPBBHFDlPGKhBBBEMxmc2pq6t69e2EjGF42m41aXbIsnzt3LjQ0FLUKQRA3AbVKJdQHyHFcXFxcTU2NO1cWh7aH8Pr333+PiYlhGMZisXAcR4cNO4iiyPN8cXFxUFBQQ0MDvMX1KgRBXAtqlUqoLAmCkJCQUFNT45792umiGt2ybt26f/3rX4QQKE1L2hyAhBCpjfPnz4eFhel0OhA5t9VgBEH6CKhV6qGm1V133QXuMjeMQQCZAQcg+AP/8Y9/7Nixg2EYqkC0PgXdUlFRERMTYzKZXDBiBEGQq0CtUg/YK7Isp6amQokHN9Qq0CfQKovFYrPZRo8eXV5eDlscDgcNanc4HKRNrsrLy2NjY2lPEM+qHYUgiPZArVIJ3OIFQbBarcnJySaTCe717gkoEMMw+/btmzVrVjs+PZDbiooKaHQCAeuoVQiCuBbUqm7B83xzc3NoaGhNTY3bNq9SRqsvX7582bJlHa4/Xbx4MSgoCAJGUKgQBHE5qFXdQpKkpqYmHx+fkpISV4/lLwF3n81mk2U5LS0tJyenw48UFhYOGzasoqLCDb2aCIL0QVCrVEKj41pbW4cMGZKXl0fctS8w1KQQBOHnn39OT0+HykntwPP8yZMnvb29//zzT+wLjCCIO4BapRKI7SaENDc3+/j4HDt2jLhlbAVRtNpasmTJhx9+2OH+HMedOnVq6NChlZWVNNaxl8eIIAjSHqhV3YJl2aampqCgoJ9//tnVY7k2tJqfTqebNm3apUuXSEe9E0VRLCws9PPzq6urgy1oWiEI4lpQq7oFx3E2m23y5Mm//vqrq8dybWCxihDy2WefzZo1i3TC+JMkqbi4OCAgALUKQRA3AbVKJco7/hNPPFFUVETc0gdIy9FOmzZt3rx5hJD2u/1KkiSK4pkzZ/z8/C5fvgyV19EHiCCIa0Gt6hPYbLbo6OjffvuNKIpTXBMIDzlz5kxUVJTZbIaN0P4KQRDEVaBWaRywq+rq6qKjo6uqqmhPxfY/lZ+fHxQU1NjYCPujXYUgiGtBrdI44JY8fvz4uHHjZFmGMrUdak9+fv6oUaMaGho6qW0IgiC9CmqVxgGZWb9+/SOPPEI6Wqyi+xcWFoaHh+v1enjrhutwCIL0KVCrtI8sy/PmzXv//fcJIQzDtG8koVYhCOKGoFZpH51ON27cuCNHjkD+cmeEB32ACIK4FahV2ic/Pz8kJKSpqenqPlXtfARjKxAEcR9QqzSOIAj79u0LCAhQtrFvp24hxqwjCOKGoFZpn4ULFz7yyCO0ZaLdbu/wIzk5OfHx8dCJ0T0L8iII0qdArdI+//73v1etWkUU/SHb2RncfTk5ObGxsVartZPrWwiCIL0KapXGkSRp5syZv/zyC1GoVDuxEqBnP/74Y2RkpMlkuj6DRBAEaR/UKo1jMBiSkpJqa2vhLahUO1oFf8rJyQkKCmpubr4+g0QQBGkf1CqNU1JSEhERYTKZQIQ4jms/qA92+/7770eMGFFTU4MRgAiCuAOoVRrnwIEDEydOtFqt4ABkWbb95lWQg5WVleXj41NdXd3h/giCINcB1CqNs3HjxmeffZbnedCqDgMlZFnmeT4rKysgIKC5uZnneYwDRBDE5aBWaZx33nln3bp1hBBoQ9UZn54gCLt3746MjITodrSrEARxOahVKqF3cEmSWJal7XddPh6GYYiiHfCkSZPy8vIIIZIkwcb27STQs927dwcFBen1+t4dNIIgSOdArVKPIAigEPTu70IThDr3lIJkMBgSEhKgZzFR9Ahu/1CyLGdlZfn7+xsMhl4cMYIgSKdBrVIPy7JgxMC/pCOTpVdx0ipRFGVZLikpiYqKKi8vp0HqsL39Q/E8/8033wwdOlSn0zkdHEEQxCWgVqlElmVZlmH5Bwws197QYSSyLCu9kQcOHEhNTTUYDHSZqjOV/ViW/eabb3x8fJqamgghWGYJQRCXg1qlEioJ1KhyhxgEQRCUWvXxxx8vXrxYlmU6NtCqDsss7dq1a9SoUbhehSCIm4BapRJ693c4HBaLpTOl9q4DPM9TLx/DMBkZGV988QVRWF0wznYiQSBcUBlbgc2rEARxOahV6gHPmCAImzdvLi4uJi5drwJFASkC5yS0WMzNzaViQyWqnch1yK/KzMz09fWFGkudjHRHEATpPVCr1APeP1mWJ0yYsGXLFkEQXGiCgEopV62qqqpGjhxZXFzscDhgn850A4GD/O9//xsxYkRra2vvDRhBEKTzoFaphEYc8Dyfnp6+e/dul7fPsNvtkOxFCLFYLJmZmenp6SqOI8vynj17QkJCoM46DSFBEARxFahV3UUUxfT09OPHjxOXLu0otRNGMnfu3BdffFHFoWRZzs7ODgwMpOtVuGSFIIhrQa1SCZgaPM+zLJuSklJSUkJcGltBl8oYhuF53uFw+Pj4/PTTTyoOJUnSzp07/f39W1paenSMCIIgKkGtUgloA8MwDocjJiamsrKSuEFsBSHEYrEQQo4dO+bn5wevuwpoVUBAAI1ZR7sKQRDXglqlEmX9vdGjR9fU1BBX39NhYQnWq55//vl58+apO44oillZWaNGjaJ9gXG9CkEQ14JapRLq7rNYLKNGjaqoqHD5DZ1adbIsx8bGbt261WazqTiOIAiZmZnKeoAuPzUEQfo4qFUqkSQJrKiWlpbAwMDS0lKe511rV9EKGsXFxUOGDPnhhx/oli7B8/y2bduGDh0KNZYQBEFcDmqVesANqNPpIiIiKioqXD0cAnlUHMdt27ZtyJAh6gIr4AhffPHFHXfcgT3sEQRxE1CruosgCLGxsTU1NS4PQJBlGTyTmzZtio6ObmhoUHccnud37NgRHBxsNpuVtQQRBEFcBWqVSsDgEEXRYrGMHj26vLzctYnAUBsJlqxWrlw5d+7czpRUvyaCIOzcuTMoKIjmAvfkQBEEQboOalW3EARBr9cHBQWVlZW53F1Gez8+9NBDGzZsUNemBKr/ZWdnBwQE0BpLLj81BEH6OKhV3UKSJL1eHxgY6A7rVWAA6fX6+Pj4X3/9VZblThYAVAJqt2vXruHDh1MvIroBEQRxLahVKgGTRRTF1tbWUaNGlZeXu7YeOZWT33//fezYsapLTsApZGVlDR06tLa2VrkRQRDEVaBWqYS61wwGQ3BwcFVVFXHpPZ1+9UcfffToo49yHKd6nUmSpKysrBEjRjQ2NvbcABEEQdSDWqUSqgRGozE4OPjy5cuuHQ/AsuycOXPWr18vy7LValUXXiGKYnZ2dmhoqNVqJRhbgSCIG4BapRKwq2RZ1ul0fn5+ly5dIi61qwRBkCTJYrGMHz8eir6rjksUBGHv3r2xsbHKnlgIgiAuBLWquxgMhri4OKPR6A739EOHDt1///2k3S71HWK32/fv35+SkgJvJUnC2AoEQVwLapVKRFGEm3hzc/OYMWNaW1tdWGSdtFk/S5YsWbt2Ld2iTmM4jtu9e3dMTIzFYnEHAUYQBEGtUgkkMwmCoNPpoqKiWlpauhPO0H14njcYDGPHji0tLSWKZvYqDsVx3IEDB5KSkrpjnCEIgvQgqFUqARmQZbm1tTUmJkav17u2bgXP87m5uUlJSWDe6XQ6dccRRZFhmIMHD44bNw60Sl1OMYIgSA+CWtVdDAZDbGysO6xXffDBB7NnzwZdMZvNRK1dxfP83r17w8PDm5ubWZZ1+XkhCIKgVqnE3ewqQsjjjz++YsUKlmXBHqJ9F7uKJEk5OTnx8fEWiwUD1hEEcQdQq1QC/askSWppaYmOjnZ5bIXdbk9OTj548CDVJ47jVJhE0IUrNzd34sSJ9OOuPTUEQRDUKpW4m11VXV0dEBAAXjtCiMlkUhcEKMuyLMs//vhjXFycwWAQRRG29PR4EQRBugBqlUrg9i0Igtlsjo6Ohvp71ycPied5GuYHLyRJ2rx58y233MIwjF6vh91oB/qu4nA4PvvsM39/f6vVCmeE+VUIgrgW1CqVKLUqJiamubmZXK97Ov0WqFVBCJEk6d13301KSoLtdrsdegSrQ5blr776ytfX12Aw0NPs9qgRBEHUg1rVLQRBsFqtMTExECN+HULmwCkHr1mWhdcMw6Smpi5atOjChQs2mw1Goi47Cg6YlZXl7+9Pi7WjXYUgiGtBreoWoija7fbY2FgoSX4dtEoQBLpUBmoky3JTU1NoaOiiRYumTJny3nvvgVEFmVJdPT4cfO/evRERERaLBVQK16sQBHEtqFXdQpIkhmHi4uLq6+vJdbmn08pJtF0Wx3EVFRXe3t779+8/duwYjKGbqvn999/fddddhBCWZdGoQhDE5aBWqYRKAsdx8fHxdXV11y1ejud5pSeQ47jKysrIyMjq6mqwqBiGAZNLRV9gQogkSd9///3kyZPh4FhpCUEQl4NapR4QJ0EQ4uPja2pqlPrRqzglTkmSZDQa09PTL1y4QBRxENB9qquAFbV///7U1FSiCDVEEARxIahV6qFalZCQcPny5evmK6NFcp0qqRuNRnJl8IW6gxNCDh06NG7cOLoR5QpBENeCWqUSpWcsMTGxsrJSG74yKFGxa9euhIQEGgeojVNDEMRzQa3qAaKjo6urq4lW7A9JkrZv3z5hwgQaRohxgAiCuBbUKpXIsgw1yE0m04gRIw4dOsQwjDbq5vE8v3379nvvvRfeakOAEQTxaFCr1APKJIric8899/vvv2vpnr5nz55p06bBay2dF4IgHgpqlXpooB0taKQBXxko048//jht2jRadVAD54UgiEeDWqUeu90uiiItEkEbR3k0EPKek5Nz33330boYmA6MIIhrQa3qLhCAYDQatbFYRQiRJCkrK2vKlClYZB1BEDcBtUol0CYKvGT0bq6N27rVav38888nTZoEbzWjwQiCeC6oVcgVgAbv3LkTYisEQeA4DnuCIAjiWlCrkGvw7bffpqamSpKERhWCIO4AahVyDTZv3pyQkEBr4CIIgrgW1CrkCiDq79NPPx07dqzchjbW4RAE8VxQqxBnRFHcuHEj1q5FEMR9QK1CnOF5ft26dTExMbSgO+YCIwjiWlCrEGc4jlu7dm1kZKTdbud5njYgRhAEcRWoVYgzsixv3LgxKSkJzSkEQdwE1CrkCiBI/f/+7/8SEhJgi9lsdumIEARBUKuQq7Db7R9//HF8fLzRaIQKUhgHiCCIa0GtQpzhOG7r1q2xsbEEoyoQBHEPUKuQK4AaSytXrhw0aBBsQR8ggiAuB7UKuQJw961Zs2bSpElms1mWZaPR6OpBIQjS10GtQq5BaWnp77//TkvWoicQQRDXglqFXIHD4YB4CgDqAaJphSCIa0GtQq4BNaRQpRAEcQf+HwjLyWOUHJd4AAAAAElFTkSuQmCC" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f'(x) = \frac{{ - 2}}{{{{\left( {1 + x} \right)}^2}}}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Alternatively, award <em><strong>M1A1</strong></em> for correct sketch of the derivative.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">find at least one point of intersection of graphs <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(y = f(x)\)</span> and \(y = f'(x)\) for \(x = \sqrt 3 \) or \(1.73\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(y = f(x)\)</span> and \(y = g(x)\) for \(x = 0\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">forming inequality \(0 \leqslant x \leqslant \sqrt 3 \) (or \(0 \leqslant x \leqslant 1.73\)) <em><strong>A1A1 N4</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct limits and <em><strong>A1</strong></em> for correct inequalities.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[7 marks]</span></strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Most students were able to find the derived function correctly, although attempts to solve the </span><span style="font-family: times new roman,times; font-size: medium;">inequality algebraically were often unsuccessful. This was a question where students </span><span style="font-family: times new roman,times; font-size: medium;">prepared in good use of GDC were able to easily obtain good marks.</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;">Let \(f(x) = \frac{{4 - {x^2}}}{{4 - \sqrt x }}\).</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;">(a) State the largest possible domain for <em>f</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;">(b) Solve the inequality \(f(x) \geqslant 1\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(x \geqslant 0\) and \(x \ne 16\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><img 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" alt><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"> <em>graph not to scale</em></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;">finding crossing points <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>e.g.</em> \(4 - {x^2} = 4 - \sqrt x \)</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;"><em>x</em> = 0 or <em>x</em> = 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;">\(0 \leqslant x \leqslant 1\) or \(x > 16\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1A1A1A0</em></strong> for solving the inequality only for the case \(x < 16\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<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 students were able to obtain partial marks, but there were very few completely correct answers.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(g\) , where \(g(x) = \frac{{3x}}{{5 + {x^2}}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Given that the domain of \(g\) is \(x \geqslant a\) , find the least value of \(a\) such that \(g\) has </span><span style="font-family: times new roman,times; font-size: medium;">an inverse function.<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) On the same set of axes, sketch</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (i) the graph of \(g\) for this value of \(a\) ;</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) the corresponding inverse, \({g^{ - 1}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(c) Find an expression for \({g^{ - 1}}(x)\) .<br></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) \(a = 2.24\) \(\sqrt 5 \) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong> </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) (i)</span></p>
<p><img 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" alt><span style="font-family: times new roman,times; font-size: medium;"> <em><strong>A2</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for end point</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> <em><strong>A1</strong></em> for its asymptote.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) sketch of \({g^{ - 1}}\) (see above) <em><strong>A2</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for end point</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><em><strong> A1</strong></em> for its asymptote.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(c) \(y = \frac{{3x}}{{5 + {x^2}}} \Rightarrow y{x^2} - 3x + 5y = 0\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( \Rightarrow x = \frac{{3 \pm \sqrt {9 - 20{y^2}} }}{{2y}}\)</span> <em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({g^{ - 1}}(x) = \frac{{3 \pm \sqrt {9 - 20{x^2}} }}{{2x}}\) <em><strong>A1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[8 marks]</span></strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Very few completely correct answers were given to this question. Many students found a to </span><span style="font-family: times new roman,times; font-size: medium;">be \(0\) and many failed to provide adequate sketches. There were very few correct answers to </span><span style="font-family: times new roman,times; font-size: medium;">part (c) although many students were able to obtain partial marks.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A particle moves in a straight line with velocity <em>v </em>metres per second. At any time <em>t </em>seconds, \(0 \leqslant t < \frac{{3\pi }}{4}\), the velocity is given by the differential equation \(\frac{{{\text{d}}v}}{{{\text{d}}t}} + {v^2} + 1 = 0\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">It is also given that <em>v </em>= 1 when <em>t </em>= 0 .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for <em>v </em>in terms of <em>t </em>.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of <em>v </em>against <em>t </em>, clearly showing the coordinates of any intercepts, and the equations of any asymptotes.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Write down the time <em>T </em>at which the velocity is zero.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find the distance travelled in the interval [0, <em>T</em>] .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for <em>s </em>, the displacement, in terms of <em>t </em>, given that <em>s </em>= 0 when <em>t </em>= 0 .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence, or otherwise, show that \(s = \frac{1}{2}\ln \frac{2}{{1 + {v^2}}}\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}v}}{{{\text{d}}t}} = - {v^2} - 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to separate the variables <strong><em>M1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{1}{{1 + {v^2}}}{\text{d}}v = \int { - 1{\text{d}}t} } \) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\arctan v = - t + k\) <strong> <em>A1A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not penalize the lack of constant at this stage.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">when <em>t</em> = 0, <em>v</em> = 1 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow k = \arctan 1 = \left( {\frac{\pi }{4}} \right) = (45^\circ )\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow v = \tan \left( {\frac{\pi }{4} - t} \right)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[7 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><img 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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> A1A1A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for general shape,</span></p>
<p style="margin: 0px 0px 0px 30px; font: 11px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> A1 </em></strong>for asymptote,</span></p>
<p style="margin: 0px 0px 0px 30px; font: 11px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1 </em></strong>for correct <em>t </em>and <em>v </em>intercept.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not penalise if a larger domain is used.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks] </em></strong></span></p>
<div class="question_part_label">b.</div>
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<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(T = \frac{\pi }{4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) area under curve \( = \int_0^{\frac{\pi }{4}} {\tan \left( {\frac{\pi }{4} - t} \right){\text{d}}t} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.347\left( { = \frac{1}{2}\ln 2} \right)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks] </em></strong></span></p>
<div class="question_part_label">c.</div>
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<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v = \tan \left( {\frac{\pi }{4} - t} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \int {\tan \left( {\frac{\pi }{4} - t} \right){\text{d}}t} \) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{{\sin \left( {\frac{\pi }{4} - t} \right)}}{{\cos \left( {\frac{\pi }{4} - t} \right)}}} {\text{ d}}t\)</span><span style="font-family: 'times new roman', times; font-size: medium;"> </span><strong style="font-family: 'times new roman', times; font-size: medium;"> <em>(M1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln \cos \left( {\frac{\pi }{4} - t} \right) + k\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(t = 0,{\text{ }}s = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = - \ln \cos \frac{\pi }{4}\) <em><strong>A1</strong></em><strong><em><br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \cos \left( {\frac{\pi }{4} - t} \right) - \ln \cos \frac{\pi }{4}\left( { = \ln \left[ {\sqrt 2 \cos \left( {\frac{\pi }{4} - t} \right)} \right]} \right)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[5 marks]</span><br></em></strong></p>
<div class="question_part_label">d.</div>
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<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{\pi }{4} - t = \arctan v\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t = \frac{\pi }{4} - \arctan v\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \left[ {\sqrt 2 \cos \left( {\frac{\pi }{4} - \frac{\pi }{4} + \arctan v} \right)} \right]\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \left[ {\sqrt 2 \cos (\arctan v)} \right]\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \left[ {\sqrt 2 \cos \left( {\arccos \frac{1}{{\sqrt {1 + {v^2}} }}} \right)} \right]\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln \frac{{\sqrt 2 }}{{\sqrt {1 + {v^2}} }}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{2}\ln \frac{2}{{1 + {v^2}}}\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \cos \left( {\frac{\pi }{4} - t} \right) - \ln \cos \frac{\pi }{4}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \ln \sec \left( {\frac{\pi }{4} - t} \right) - \ln \cos \frac{\pi }{4}\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \ln \sqrt {1 + {{\tan }^2}\left( {\frac{\pi }{4} - t} \right)} - \ln \cos \frac{\pi }{4}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \ln \sqrt {1 + {v^2}} - \ln \cos \frac{\pi }{4}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln \frac{1}{{\sqrt {1 + {v^2}} }} + \ln \sqrt 2 \) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{2}\ln \frac{2}{{1 + {v^2}}}\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v\frac{{dv}}{{ds}} = - {v^2} - 1\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{v}{{{v^2} + 1}}dv = - \int {1ds} } \) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{2}\ln ({v^2} + 1) = - s + k\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(s = 0\,,{\text{ }}t = 0 \Rightarrow v = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow k = \frac{1}{2}\ln 2\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow s = \frac{1}{2}\ln \frac{2}{{1 + {v^2}}}\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;"> </span></em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[4 marks]</span><br></em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = {({x^3} + 6{x^2} + 3x - 10)^{\frac{1}{2}}},{\text{ for }}x \in D,\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">where \(D \subseteq \mathbb{R}\) is the greatest possible domain of <em>f</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find the roots of \(f(x) = 0\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Hence specify the set <em>D</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Find the coordinates of the local maximum on the graph \(y = f(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) Solve the equation \(f(x) = 3\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) Sketch the graph of \(\left| y \right| = f(x),{\text{ for }}x \in D\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(f) Find the area of the region completely enclosed by the graph of \(\left| y \right| = f(x)\)</span></p>
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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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) solving to obtain one root: 1, – 2 or – 5 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain other roots <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(D = x \in [ - 5,{\text{ }} - 2] \cup [1,{\text{ }}\infty {\text{)}}\) (or equivalent) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> <strong><em>M1</em></strong> is for 1 finite and 1 infinite interval.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) coordinates of local maximum \( - 3.73 - 2 - \sqrt 3 ,{\text{ }}3.22\sqrt {6\sqrt 3 } \) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) use GDC to obtain one root: 1.41, – 3.18 or – 4.23 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain other roots <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img src="data:image/png;base64,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" alt><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"> <strong><em>A1A1A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for shape, <strong><em>A1</em></strong> for max and for min clearly in correct places, <strong><em>A1</em></strong> for all intercepts.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>A1A0A0</em></strong> if only the complete top half is shown.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(f) required area is twice that of \(y = f(x)\) between – 5 and – 2 <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">answer 14.9 <strong><em>A1 N3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1A0A0</em></strong> for \(\int_{ - 5}^{ - 2} {f(x){\text{d}}x = 7.47 \ldots } \) or <strong><em>N1</em></strong> for 7.47.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [14 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was a multi-part question that was well answered by many candidates. The main difficulty was sketching the graph and this meant that the last part was not well answered.</span></p>
</div>
<br><hr><br><div class="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) Sketch the curve \(f(x) = \left| {1 + 3\sin (2x)} \right|{\text{, for }}0 \leqslant x \leqslant \pi \) . Write down on the graph the values of the <em>x</em> and <em>y</em> intercepts.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: 23px Helvetica; text-align: justify; margin: 0px;"><img src="data:image/png;base64,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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;">(b) By adding <strong>one</strong> suitable line to your sketch, find the number of solutions to the equation \(\pi f(x) = 4(\pi - x)\) .</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;">(a) </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img 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" alt> <strong><em>A1A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica; min-height: 35.0px;"> </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-intercept</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>A1A1</em></strong> for <em>x</em>-intercepts</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>A1</em></strong> for shape</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica; min-height: 35.0px;"> </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) correct line <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;">5 solutions <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was well executed by the majority of candidates. Most candidates had the correct graph with the correct x and y intercepts. For part (b), some candidates had the straight line intersect the <em>x</em>-axis at 3 rather than at \(\pi \) , and hence did not observe that there were 5 points of intersection. </span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(f(x) = x + \frac{{8x}}{{{x^2} - 9}}\). Clearly mark the coordinates of the two maximum points and the two minimum points. Clearly mark and state the equations of the vertical asymptotes and the oblique asymptote.</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;"><img 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g21poEQx18y0vctdspKPaMo0wbwVbL0Yf6kI8+EaXVQnrettbQ7w16IswEAeNNSF+bHv0Ylp3rCTHO0+r5vmib1+DbGnDBtP1j2R6xxJmRWLzNvFSIfGFK94fRTp9n08gVcY5U6gFdNAyGKl4OnicP2eQlpf9LUVyS7OE4doqf8utgweh6gTCOId5lvPP041tqUtkz/MetYNU2k3Hew88bDWxrne7b7DQBXUmxM93g8rLXFJb20p4QzFb6NOBsAgDetxNm737GthwWpo4j3Pg3USv/uvR+GIdWXOedS6DltnU7HefMdfyGE7Aa9uF/y5LLGsuvhTqrFnn7qpTibwhngkuZv7XEc54th2y9bMcZ0uUmTh9M/tyyOpv5dxfhj6li9Ls2NTLPIlFJt2+57sgohnHyPzjTWNfvN0EobwO6KLenW7zaLzbLT2ZvpHdgXcTYAAO+IMS7Vjh288zfNe7TWpvaaWuuULyx125TPwLe9uZQN0GucgpjF2euvvazfSNo+L18VxS9Cxg1ciSy4c85tqcguDidUSn243Wdl5KMxJk2hmA4vjTv+5NttlIL7NADjgG+3UXEmm7yac9IG8LYQQtu2MptWSi0NLfDev1THDXyCOBsAgHcUa1qTg9PheXg9WTq24i3mPVuOjOMo90LuuG/9MNmTxnq5fRZep2IZ+ao4VXAD4BuKY2DXA1A5QXfp098IUpfi7FQ2/pNkNvX1TpfUE7aozlZkP19RAIAkm3mw5TxTvK9+1DmZBlUgzgYA4B0rLSwPfupOE6LSdu9Xs+xUzFVXAdfS0b70Uyzdc9d4w531zl5P5LPAyBhTrM6+bcE+cB/Fq9j6elh2ttnxFCqn2k7atn3va34o1aFPR5UqxJ1zbdt+sgy8yyVskvquzE/pNV7FAJxKCKF4gVjpK+W9L57D05iBEz5onPCQfuuTX0g2YWKPw9mEOBsAgHcsPXhrrQ+OAlM30tQ1OzUeScc2VWovzdR6Woh3WmkYVzaha7vUMVb+TopzIM//K8oeOVamWcYYZRpVfCWf/6cG8CF5NlBKrbz3QwjFq95kS6+SJSv9u3414KFpmvUV4pPs5nlpRRMApOzUXcyyV3aoLM1+PLKn/+c3rtlX4E442eX38KVfJnE2AABl60/1S9XZP3z2TsZxbJomFWunqm1rbdM0bdt2Xde2bdM06X9WWoGb5tIopay1Xde99NuOMTZNU+wDWG8P8ezHWa9kLNZiS9zEA5dXHPC1dBosLobNM4ulVqrbLX39X400GIZh2va09INba9u2/Tyv8d6/dwGSVe01ToAAcB7DMMiT3sq95dJ+x8ePVtdeuhLd/HZ3391CxyPOBgDgNd77lYlVj9Xy2GPEGNP0qmEYxnFM7URquTV5KvvlF8vhZYVF3/cp5V+KSyrNsv9ejLOXJtT//PEDwMHk4pYxZumDl7JmY8x8QuPbVqqzH79rA5WWP5c2Y829cQVJv7RpdVxr3XXdq19H3o0QZwN4mxwR/Hg8VlYrx3Fc6jGyy6UBWEGcDQDAa1bqshOl1G8LtC+sGHmk8nP/T4rv078756buK0tqn7eevSDXs4wt1dk8fgB3sD3OXhp9bK3dZSGwGKBkp7WfnJdCCF3XpQ7a60f49u8h+92mPVUpBlqZqxlCaNtW3o0opX6+oA6gUlkv/mTllLKUZdd+X429fPvCTZwNAMALis//8kHXOced3Dc8bd66XWqKmnLwX/9YH8mq89YHlG2ZFHrYkQP4IRlSW2uzj0nPoksbkt4ehziXXVWVUvMBjJMfNsgax7HrujSaovh7+GRYZXGJcRp9MY1QSz97CKHv++Lsh+RXuT+AqqUVsuIpZelTij1JHo9H0zRHnqvP3NkZ38YTCwAAa1Kdbxq36L2f37qlhsvDMAzDUJywJysauGH63FLDkFc1TTOO48pfpJY/VpaGrPc3fPprUUrV23cFwHbee/n2L37k0gaXz88VMlJPu9rHcZRBSZoq9tsz8zRJ2BiTJlJsb5xdPPKn+71St5M01fnpR87/IrVcwgD8VvEpJp1Sls5vxSxbKdW2bV1nnjRwyDl32MjKM0sX3+k6suVPOX1MCGEcx77v05XxmEcJ4mwAAMpSw2X7T9oCvHSfNwxDVqOttbbW9n1POLivLZnsilSRfaVuMFlBzUopzZYOsCufXtcjCoB1MkrWWssPW+pq/XmTfe99dlVVSk3bZYrxSpo5OQzDS8/bu3t7cqO0MkXtJWlxfZdDAnAfIYSlDR9LJ/mlKSw/n7zy6qCgtOcm7bLN+oPf6o43xpjKttLTbvptvLRSK7cNGWOeTjb6HHE2AACFyYFd160/YRpj5vdt6Vpe/BSt9Uq1wktL30i2zDOUrLXzEOQyst+GbBcwedpphNJs4D5k76ZinN33ffFc8eGFSca4Sql595JpRmJRlj6kB+9Kr5WyTH67VLVd9TRjAMeQZ8g03D61NspOLEsts5d6TxljfnsGjjE2TbO9bXfK8dPVJJ1I3+g9eIEEfBgG2TYzlXAtJdrzn3QYhqUr9SdtuDYizgYAIPd0XN7SNX5lnpW1tuu6tm2neu20GD798/CfsmKppm9eazx1Gk3/nv6ZRkQ65w7b9fYT2X3k0jC3LYkJM8SAW8l2bBTj7GKV9CdLX957uSSZMtnsI1fKBucX1nQOTKf6rutqvJ52XbdlsEH2G3vaMgsAlhS3hqSLQrG09m85y/75ilpa/kxn0Y1DHbIipGw99XOyUurpv2/8UruYl2HJ9YzkaR69fuXSWjMKEgCAQz19qtRar2zpHcdxuqPKTDFr6kMyLYan4DX1GpvfS/GMuiItA6Tf2DiOqbP5NLDLe1/7gMftsjh7qVvIljj7Pr80AMUuIjKSKO6Gea8QL520ix1XrbXFNCSEsBSgLPl5keAbvPep98vK7YdzzhiTmpiRYgP4RIyxWFRrrV1qJL20M9Ja+/PTUdd10+rsxuORD2v7xtnbpSea5BtfXP576ivydA11nkfLX+nS8/JUYLT+vLwL4mwAAP6nOH4qu7Q/vTZ775cS7adWOhcDRVnWs1RM8TTO/rx7AICKFEdBypOA7Emycp5ZkqKT4mVxfVNz+ty2bYtF4kVLO1ROLnU5S4uyaXk7dccKIXjvOTkDeMnKSSONtC2ejZci3aV9q9banw9RTOOLpqvYfAbDkhijrEw/ZvxAavA9DEOqv2nb1jnnnEuXwm9XNaX2MtOE4afX06U/btu2xT2yaU7yVKr17Zp94mwAAP6n2CT0vZu2NGBkaQPXEro94FVZvczSKJ6nIzQrzYAAbJQ9GxeXuOQ1rljE/erpYqWFlzFmy74Q733f923bPr2kMhERAIpWJv0opZZuIJfqcJd6khwstf+e/yBPH9ZCCHI6+levHWnWYtd1qcH3ymx259wn85bWjyErys7+XT60Fkvdh2HIPswYY4xxzqW15xTN0zsbAIDvyi7S8go9adv2jZu2tIO4bdvpAi+/8rRCvnIHAyzJcqKl28f1pZoH1dnAzciya6VU8SPlnvSXVl6LdXDTM/Crp510SW2aJj08z48ttdLmPAYARUu3gkt12Us9SdL59iQd6rIjLA6BmEvF0fJx78M4WzbLTr0Q09VqYzV08qWtulOVVXoanVdSG2PStCH5oJo9/KbRkfMPSIXY08U3fUDxkXb3qzNxNgAA/9H3/fxa7pxLfSp3+eJpcT51ee7/Sf/eNM0ZahxQnY1x9tMBp1prXoHAfchzgrW2+JEyzlgq4isq1sHt+MSeGnScJFgBgHOSQeR0Ki6eP5d6kpztjjHrufc0zv77+xvHca/q7GJEm5pTpwh7pRB7xTdauMwPKf27tdZa2zRN+tnnbVuSqXNLGn2RFcJPH5PdEhzWIIs4GwCA3NS88shpSxSU4T1ZJrVUNbllnNrPGyACOIwMqZdaiMhE46U4++/vz3ufPSSfZJc6AFxejDF1TM5SyKR477eypW97XfYxjzZZA42Nm372bTaSurgMw9D3vaxxLiba6ZiXSra/MZcyzRNOKbZzTm5m8t7LLiKpEmsplE+l2bsf6kbE2QAAABXLMqliwePKZv854uxrYG0MW8je2UsPpTLOfqPVftp2PW2+5lUKALuQbS7m/zNN/5Oxadd1aZOo/IJyAXJywuEEb1RnF/cMfZIgp3Lv1DM6VUAXW1RPvT7SR6Z+WalEOjuYbyz3Tq26Vq6/2etEKdW27dITRPrgA3pkLyHOBgAAqJXMqYtxtiy4KN6Vslu/XisPJyGEVDQUY6QeFpONZ48Qgjx7fKmzJwBgR6nrhbzlW8l8l+qylVLfKBn+XLZJsfijyVFJS101ih//VBq3nppQT1F1KoJO/9I0TVo/6LpuWtz13ocQYoypnXe6Iv/w9/x0aHzxhfTDZwfibAAAgFoVNwam/2t+L77UuzZDdfb1eO/TltLUOmkcRxJtTLI4u1hjFWOUcfYPNxcDAP42RK7jOBbrao0xS2f7bIDQRCn10gTgI2U7jbZUZ8teW0tNV7brum4YhlQ6kKoH0h8o/vP0K8QY093aJ4fxiaWxnyvemOe8I+JsAACAWg3DkN1Zaq3lnWUI4Wmzkc9v5XE2Mca0SzRNAkhTAYizMcn2aL/UeZ/NHABwWkt1DFprOfwghNA0zUqaedos+6+05rreEUU22nqwQ3G1W/qKNzqP7Yg4GwAAoFbZFstEptIb4+yb38pfyVQK1HVdirPTeFs5+Qf3If/0G+Ps4nnmzOkGANxZyrJlnG2tzaLetG2r2JBkujk8Yb/sjHMumwa59JExxqUf9qUf88hbqQO+10q39OllUHxFUZ0NAACAF0z3jsMwFMf7ZB8/juPT3tkPyi3rl9ovWmu11s65vu+bprHWtm3btq1zrmka/spIYoxZnC1PHUmxaIt+IwBwQtO5PZtGKJPHvu9Xguzkh4P+tsuuZUqppY+UmxqnT6niJ/2S9ZdB+uWkHX7y/6J3NgAAAF5W3Ewq7yyLqbe8JaUNRdXSZuHsz2qMMcZYa9O/pIz710eKs8geTT+Js6n6B4Bfmc7AIYSsVDlpmkbe463fGZ529qMkRzumI88uTKn92tIPm10B972orbfPntptp3GRSwHxl66zXdetvBKyl4H8Bf5wNDRxNgAAQMWykoqlQOrpgBfi7KqFEJaKa7KnFHpEYJLF2Uu1acVyNq01lf4A8BPFZDO1jJDRZDFwHMdx/bZw6X7yhFJLvfkPPh8k470fhqFt2/V74O9d0dq2Ta3Jm6ZJbd9SbD0MQ9/3Xdc551LNQToYY8wxv/wY4/rTQSrKnn9K8X7gV43siLMBAAAq5r2fckzn3NIN5ZZ55YRTFcn+0E/3C0+KcTaltfe0sXd2CEHmIwyPBYDzGIYhu9NL/Y6XosbiUIT559Z1Tyh3pznn2ra11m7ptvd4sXf2dukCWlxmWD+wrxYfpGLwpUcDpVTa1Vf8xGKFu7V26U7ye3eYxNkAAAB1S5N8+r5fuWWUN/oS4VSlXppHb4yp6xkV35OdFpb2lS813+eMAQBHKt7mLeWSK/2gr1SanaTr1JbkeuljvtRZJXUF3Hhs2XF+IwiOMaamK7IMIjVYT31p0pNF8SuM45jVwidt26aUfPdjXkKcDQAAcH3e+6e3znceg1O1LWsVc845GsvgT2zaWHp2Lfbor652DwCq8zTQnLLsLF7UWqd4sfhZ6zv25NDIKqR68/XUWGudpmTL/+t71dDjOKZ2ItPVc0u0XSyOfsP8T5mmhRfrxLXW238DaWNo8esopZqmSa1Uuq77Us17QpwNAABwCzKQylRXjHM3xcfLpcrZdU3T1Piwin1lj/RLcXaxV+ZeT9oAgPf0fT/dAGSdo9fv6FYalFW9VNk0Tfo9FO+Lpt1pMUb5G8jmG+8rFTs75/Q/akYe5zAMu5cdLO3kS61FVtoVFqVEu9hEJSMbcO+FOBsAAOAWnrZXJs6u0Zau6EsPMMMwEGrfWZZTr+wslq8fRkECwK94751z8yQxFaBi0GYAACAASURBVNhqra21T0fzFRtna62dc18tpz1AqoOex8RTyfA8IJZ7Fle6P+8lhdpt2zrnrLXW2jQiMjWqTg1A2rYtBtkfHluMcamo5e3JkyGE1LdkCuiXbji/dMNAnA0AAHALT1tSfKlvIL4kxrg0yml7vXbXdTQeuZX5I/H8nKCUWnoleO+L5WOshQDA8aYZ4DLO3rj1KlvLVEr1fT+O4wXO6iGENBVTa50y4qZpZJYqRxwfEGcnMUbv/TiOIYRxHL33B9yGFXdZPR4PrfUnCxgxxmEY0sjN9T2gzrkdf5yEOBsAAOAW2rZdTza/ca+JLwkhTJtqpeLc+SXGmPU5oriqbOvxSvGUfEVxugCA4/V9n07IWfVxupRv/CJpOXzKH7/XNvqHQggrF7UYY3Zdu/aWo6VOI7sUsqSAvmmaVKld/EbfmNpCnA0AAHAFT+PIpUpe8qnqyMew7JHs1Q4kxhhqtG9oXq6ltV46h4QQ5OuNybEAcLBhGIrz96y1b9TYhhC6risWLxddadk7xpjdKVlrs45bn/f3+OwY9xRCyIY3KqV2v46nevNUr51K49u2TeXn3/htEGcDAADcgvd+fSfgV8fg4CUr9/0xxpW+MemZ9unShXwYJs6+oayZZvYamF6EclP2g1b7ALCrp3lf27bZqTjVZX+j7vUOsjhbKXX561qKm1Pz7i+NZzwScTYAAMBdrKecF7i1vR75fLtSeT11fnzaJ106VRkRDjPF2UqppdeAHJn1+O8OZV48ALAXeUZNnRxklu2cY+rJ2+SdUu1jMO+GOBsAAOAuirHUlIT++ujw3FL3w8d/G4akIVFLHyYbR/DXv62V6uzJOI7yhXTJXqsAcCrzJtdZpwhrLUXZn8jibKXUhXtnXxJxNgAAwF3EGFdSzl8fHZ5ommapXUzbtvN6rqURkY/Ho+u6EMJU4p3Ku3iEu6352sZSMlLcEMAZAwC+SvZ3ni7cTdOwLeZDMs6+5CbFC79OiLMBAADuYqU6+0G7iXNbqcuW3R5X/sppY3KMMbXY9t7zd7+zeSH/0qb1YpMipdTBhwoAtzKf1jsxxpBl76Jt2+yiRhOtuhBnAwAA3EWxacCEXaunVXymffybXCQfulaajdAaEnPzl8pS/5Diy885d/ChAsBNxBj7vpf7sZRSXMT3IqsELlmdfWHE2QAAAHexEmdrrSlFOa2l8Y9L5bQr4yJ5WsPclji7eN5g/hgA7C4F2XJNWimltZabsfA27/18weCqzUYujDgbAADgLkIIK3H2r48O/zNfWogxyuGNK+Hjn+gISZyNJfOVj6XXRrE6u23bgw8VAK5tHMemaYrTL8iydzcMQzZdkxukuhBnAwAA3MU4jkuzBK21vz46lHnv5cPt+iC+peYkWmv2KWMynw27sqBV7J1NsxEAWJHteHu6Aa7ruqU7NGMM1+7dZXH2g25stSHOBgAAuJFscyXh1Pmlmnqt9fTcpZTy3q9/VvGvbK19+om4MBmvWGuVUusvDJqNAMBeZK6duosUi7If9Mv+Gnk/zAiZuhBnAwAA3Eux1pJNrGfWNI1zTimllHLObdkPW3wwJs6G9PQlUWxSRLMRAPhQCGGpu0gKso0x3J59ifc+6+TGDVJdiLMBAADupdiJgo6BJzeOo3Nue0lssd22tZbiI7yquABGeyIA+IT3fqUom2bZ3xZCmG9601pzg1QX4mwAAIB76fteVgA97eqIn3vpb7QUQfK0hlcVX0tKqV8fFwDUKmXZS0F227Y0GPm2rHe2MSabwv3DY8MWxNkAAAA3krrlZg9OlGZfTzGCNMawlxavkgtgj9XRkQCARKaiqcGIMUbWZSuluq7jMn2M+UiSByNkKkScDQAAcCNyqht38JdUjCCNMSxd4FXFUZBZ72wK2QBgsnRKHMex2AosrRE2TXPwcd6WvEeiHL46xNkAAAA3IhtnE2dfUrFDunOOZiN4lfdevpZ48geAl/R9r7WWp1OllLWWk+qR5DItRfHVIc4GAACoWFYB9LRGUvagyKoscQ3F6uymaaiixauK1dlUEQLAZP3aGmNsmiYl19m5VGvd9z0rzcebl8kzB7JGxNkAAACVeSmRzD44PVDN0X3ikorV2cTZeEMIQUYw7OoAgC1CCEsNRpRSFGX/inNu/ocgzq4OcTYAAMBdhBCyja5KKfLNS1pqNsJ2WryhbdvstWSt/fVBAcDZ0Sz7tOa3ScYYboarQ5wNAABwF977LM6mxPKqiv2OnXM8sOENsneN1pqlEQBY0XWd3Noy5ad93//6AG8thDD9OWi7VyPibAAAgKtZiSznmytliSVZZ42Kf7VigwhrLdtp8Qa5sYPFMAAoXn9jjKlZdnHwY1oOpM/bGYzj6JxjSnaliLMBAADqFkLw3m+slMx6Zxtjvn14+Ini+D6e2bBdFtPI9jXGGF5OADCJMQ7DYK1dCrLTmZN+2cDniLMBAAAqlh6cjDHGmC2D/rI421pLRfYlLfXOJn/Ee2S9P3E2AEy899baYoSdTp5aa266asGf6fyIswEAACqWjWh72v4ve9ZinttVFauzrbX0O8Z7ZL8RZmcBwN/f3ziOTdMstclWSimlrLVt2z49Z3JS/TZ+w5dBnA0AAFCxLJ5WSq3klTFGRkFe1dPWECl/7Lpu5bOAJakVbPaKYpQZgPuQV8wYY9/3S0F2uivTWrdt++pacgih+O0++gGACyHOBgAAqFVx3N9KT8YYozFm/sFN02Qf8P2jxhHk0kUxzga2k3G21pp+IwDuKQ0SXAqyU5b93gTmEIJzrus67sqAJcTZAAAAFZOPUitxtvc+i79Joy4sW7pIj9ZbGqwDRX3fy7yGBRIAd/O0KDutH/d9/94Ft21brbVSihMssIQ4GwAAoGKyXnJlQ6vsp0z326sqVmcrpZxz/MXxnnEcZXzztF8/AFxJjLFt26UsW2uttc62vj39gtO/hxCmLDutQH/hJwCugDgbAACgMvMnHxlnj+O49InFOPuQQ8bRYozFh23ibLzNey9fUaQtAO4jhJDNLJkvGDdN0/f92yOXQwhN00xL0Vpr5hMAS4izAQAAKvY0zp5nlzLOttYefsg4gvdeVmc/qKXFB2Tz/ZTg0LAIwB147+U5MJ0G02iKl06G2dJy6ped3aFxdgWWEGcDAABUrOu6LLVcHwWZVexSnX1VckyoUkprTZyNTxTnntHdFcDlybg5Sa1FVm69togxyuqE4vWa/VVAQpwNAABQMTmMaH1rarZJlursa5DPt3LpYiof+8kR4hqK0yDpNwLg2lIbEHn2WwqdX+K9lw1MOK8C64izAQAAKibTpfW8Mntkcs4ddqg4Ugghe2FQnQ3p1UI/773syU5DdgCVys5dxVPZUl12apb9+dlPBuW0GQGeIs4GAACoWNd12VPQenV2FkXJcJNY6hpkn3Sttdaa6mz8bX6byw8rxtlUEQK4sKW67M+zbO990zRyK9WHrUuAOyDOBgAAqJiMs9fzyqzRNr2zryrGWIyzeUi+s6fJy5Zopjhi1Hu/0zECwFmM4+ick2t46ZL64fV0GAY5WJLLNLARcTYAAEDFXm02kj2VUVZ5VUvNRtaL93E3McZXqwuLm+7JXwBUZMt5bxxHGTdPF9MPT3py8EnKssdx/OTLAvdBnA0AAFCxEEL2RLQeZ2fPZvTOvpLs+Vw+gVtribMxGYbBOWetbdt2e6hd7DdCT3YAV9L3vdyJopRK/bI/DJ2Xsmy6gQHbEWcDAABUTBbhrjwOee/ls9mRR4vDyBeGMcZaSxUtkqzIevtGDdnHhjgbwJW0bSvj5mmc8nv9stNnxRiLG1ycc7RsAl5CnA0AAFAxmVCv5JVZZ5JUrpt9DKMgr0HG2Vpr4mwk8uXxeDy2v/flBnyKCgHULjVf6rpuqVn25ye64hdXSpFlA68izgYAAKjMPHUahiF7Llp5KMo+WClF64mrKo6CtNbSlxN/f38xxmwfvdZ66SPlf5TVhXThB1C7GGPTNMUsWyn13h6UqSg7hNC2rfzKD3a3AG8hzgYAAKjYOI7Zc9FKXinnRhJCXVWMMXsmT81GiLORZJH0S230ZSjDmQRA1cZxtNaqf+ZBdsqyP9m7ttRjhCwbeBtxNgAAQMVkQr2yGZY4+z5k+a1SyhhDnI2k67rsbLD9c4ud2ecfQM8iALVYaTDy+Lexafs5beOOFrJs4EPE2QAAABV7KaFumoY4+yZk4JhapdOgE4k8dWx/bchNIY/HI4Tw1QMGgM/JuFneGs2z7KZpPrluxhhlU7jH48HlGPgQcTYAAEDFZDvspersGKMc4MZgwKuSM0J5fr65LMTJ4myt9fbyw+Kri8J/AHVZ6Wf9eDyMMZ/PFylm5c45trAAHyLOBgAAqJiMs1cSamtt9kzFKMirkqMgU3U2mSMS2Wxkfup4GrXIjfmcTACc0NLZbBgGrbU8lSmltNbOue2rv8VvEWOUWfmrrUsALCHOBgAAqFiWSWmt5Zb/9OAkCyqVUtTqXsz0kCybjaTnc+JsJB8ubslWsMUmsKQ2AE5oHMdsvMQ8y26a5sNzl/e++PXp8AbshTgbAACgYll1djHOTmSrXGvtwUeLwxRXL5xztJdBIvPol5Y6aMQPoFLee9l7bX6V/DzLLg6W1FpTQwDshTgbAACgYrLZyFImJTe9FqspcQ3F7sZUZ2Mip5O9lLPIXiXOue8dLQB8LjUAKWbNr/bjWoq8+74vZuVcf4F9EWcDAABUTNZcLz0vZR9Jp5FrK8bZxpgvVWdPD/Y0l6hF1o7m1ROCfIEZY753tADwnvnlSe5KmU6AxpjPr18hhGKWTb9sYHfE2QAAABWTcfZSXpnFT0op+XDF41aNin+1cRzlE7XW+htxNi+bGoUQ5iWKxpiX4uzirFFqDwGcUwhBDgyYroy7rPUW+3GnqRVLXeAAvI04GwAAoGLb42zZW4Ds6cKW4mz+6EiyOPvVE4L89Af9iwCcQ7bIOo5jsWg6rcN1Xbclbl5fuC1ec1MzblZ8gW8gzgYAAKjY9hYi2UeuDI3EBcjVi8fj8VJjUFxMFqnIbiGvdh+S0yBpnw3gh7bvVVJKpQYjXdft8n2Lpd+v7noBsB1xNgAAQMXers7WWvOUdWEyzt5rPzWuQfbOfnWpQ558ZPtsyhIB/Jacgz1dEN/LsuXSoGzJnVp7UTQAfA9xNgAAQMXkc9pSXtl13caPxAUU42znHGsYSEII8zavWutXo2d5SlFKEd8AOI+u61JbpHlzJK31xgYjT/V9L9suKaW4vwK+jTgbAACgYnK//1K1kSyllB9JKWWNNm6v1lpba4mzkchmI33fv/QV5MlnpdkRABwsy5rTvxtjXj3XLRnHsZhl7/X1AawgzgYAAKiYLJBcirNlHTdPXBdWrM6mdzYmcsHj1XJCub/+wYBZACcQQpBL+Eopa+1ezbK7rptvcCHLBg5GnA0AAFCxvu+zB6qlRzWZb+7yUIdzkmGlUip18/z1oeEUQgjGmE9OCMVxo0Q5AL7q6TayYRiyk1uitd7lBBVjLC7mkWUDRyLOBgAAqFhWnb2y2V/2FjDG0F3kqrz32SboFGdTPIvEe58lPm8sdVhrs7MKLzAAR5rfxsQYlwY/Wmvbtt3lO8pdcQklAsCRiLMBAAAqls1zU0otJdQhBPmAR5x9YbI8jTgbkxhjFkbP6wo3nhnkchovMAA/EWOUDf0TY0zTNG/c8GSfkuJy2WNEa71XVg5gI+JsAACAus1Ty5U4O8aYPYM55w4+VBxGhpVKKWMMaSMm2X75N6qzZSEkZxUAx5PbTeZZ8y510yGEYo+RlGVTHAAcjDgbAACgYllPCaVUCKH4kSGErPtE8QGPR7IaFf9q8sGb3tmYm79CVk4dK4rts1kyAXAkuXz7jSy7GJdba5c6vAH4KuJsAACAKqUEM4uTtNZLH9913ZY4G5dBdTbWzV8hK233V8hFsgfTIAEcaBzHpcGPzrldLnlLcblzjgoA4FeIswEAACqWxdnGmKWPHMcxexJrmubIQ8XBsif8NAuL6mxMsvr993IfuQnAWrv7oQLAn9iKJNfp08VOa900zRs7TorfsdiSW2tNXTbwQ8TZAAAAFdtenS3rKCmivLDi5E9rLdXZt5XFQNkU2bfjbNk+mxmzAA6QjaKdGGP22nwWQijWZdO5C/g54mwAAIC6ZXHSSrlQll4RZ1+Y914+ftNsBBO5ff69E4JMlN5rww0A243jmN3STFl23/e7rKiFEIp12SwMA2dAnA0AAFC3vu/nD1rzIGn+RCfLdemdfWGyGD/F2eSMmGRx9nsBkJwGqZSiOhvAh+ankeyU4r0vZtlvFE1nX3n6n+M4yrpspdReWTmADxFnAwAA1C1rkbxUnR1jzB7MKC+6Ntk7m+pszGWjIN9b6ihOg6SlLIAvWWoAopRq23aXb7GUZVMEAJwHcTYAAEDFZEi9/SNJNi8sxpgVrymlrLXkjEi89/MYOmu7v738MMaYLZxwbgHwJd57ecJRSu2YNfd9Xyz9pj8bcCrE2QAAABXLWogYY1Y+OHtCa5rmsOPEwWKMstmI1po4G4lMhd7eQS/TJWoYAXxD27ZyO0jql/3S11k63S215OZ+CTgb4mwAAIDKzB/Dsol/1tqVT8wez/baloufk0/mchSkUsoYQ5yNyTyG1lrvGGdba2kvC2BHIQTnnAyad9x1JCcBTFk2JzTgbIizAQAAKiaLcFceuuY1R7LLJE9rV5INCH38q86mC8SdZe/xrHf225FQ13UyAOKVBmAvwzBky2bpzmfHNdpiS26lFFk2cE7E2QAAABXb3hE7a0vyYPPspck4m+pszGW9sx+PxzAM732pYknj218NAP5my2/FBiPporZLP+sYY9d1cpeJ1pp+2cBpEWcDAABUTNZFLnWtlXG2c+7go8VhZMJojCHOxiSEsFecLddOOL0A2MUwDMUs+41+2UUxRlmUnZBlA2dGnA0AAFAx2UpyKa+U+eZ6o21UbRxH+fC/Y49R1G77xo6nZKF3EkLY95gBXFjW0yOE0DSNPLcopfZqnDWOoyzKTphnC5wccTYAAEDFspB6JaGW+SZx9oXJUZDE2ZjbvrEjU2wjWxzRxosNwNuappFnlZRl71I3PY7jfKDIHHXZwPkRZwMAAFQsayGyssF/Y+9sRh5dg4yzrbXOOQpmkcgcR2v99lcrToOkfTaA9wzDoLXOSrO11s65Xeqy27YtBtlpyMTnXx/AtxFnAwAA1G3+VDavr8yC6Rhj9mTIXtqLmf/Fi9XZTdMQZ99WdkKQHUI+6XZd7DfStu3HRw3g4oqL6Nba7JSSguZdVtyLy28swgF1Ic4GAACoW4wx7fRff9KTk98Imy5Mxtla67Ztqb7HJOsQ8mGOI8epFfd/AMCKGGPbtjLLttZ+sgafrn3e+2JnpPQt6DECVIQ4GwAAoHohhLZt13fgFst1CTevSg76I85GZmpNK/fvv/E6kY1u6c4P4CXee2OMUmoeZ38++zHG6L3vum5p8OPn63kADkacDQAAcAsxxqxb7ie9BXBy8s+tlKIeH3OpUHGvpkOy5lEptctXBnAHfd/Lnv4py/5krqz3fmnkY1rXf1oNAOCEiLMBAABuIcaYdQOQtZOU7lZK/uFknP14PJqm4U+MLymWPWYfw8sPQJKdDZb6WRtjPuwBstRdJKEoG6gUcTYAAMBdzIdGFuNsXEYIQcbZVGfje7LTy+Px0FqTXwOYk+eEEMJSlq21fi/Lnr7LMAwrWTb9/YF6EWcDAADcRZY3GWNCCL8+KHyFjLO11nu1lQCkcRxlFPVJiwAAl+e9l233p1uUrus+uUuRIyWzE9SOPwiAgxFnAwAA3EVWpsQoyAsjzsbB5LDZx+NBR1oAS0IIS7MZrbUfLobJBba5D4NyAD9HnA0AAHAX3vt5pZIxhtrJq5IxQRoFyQIGvkf2qGUFBcCS4vxYpZS19o2W1hubcT/oMQJcAnE2AADAXYQQso23xNlXJSd/KqUYBYmvkuEUDfoBSDFGGTcrpYwxTdPscmeyFGcrpbjzAS6AOBsAAOAuZDeArBUAWedlxBizbFFr7ZxjezW+p+/77AwjOxpxkgFurtgvW2udmmXv+F1kkE1pNnAZxNkAAAB3kfXO1loTLV1VsdkIcTa+SjarVUrRPhvAZBiGbK5DOlG812BkRXYRNMb0fc8VELgM4mwAAIC7yPbeaq15tLuqpTibBQx8j2xx83g8eNUBSNq2LWbZzrlvNAAJIXjv27Y1xuyblQP4OeJsAACAu5CtAIizL6DYzEHG2Vpremfj22S/WmPMrw8KwEGKl5j0H9u2fQhpqAO3IgBeRZwNAABwF1mcba0l3LyqLM5WStFsBAcIIcjqS1kXyZkHuJW+77NJ1OnC1LYtZwMAbyDOBgAAuIusNspa++sjwrcUq7OttcTZ+KpinN33/a+PC8BvhBCcc0tZ9q+PDkCtiLMBAADuIusDoJQi3LyqGKPsnU2cjW8bx1HmVqycAfc0jqNc33r86zHyjbpsar2BmyDOBgAAuIus2YhzLvsAngMvI8aYhQhaa7Z149uK7XHpawTckFxVTUF2uhj9+ugA1I04GwAA4C5CCPPCSWMMGdNVyRyBUZA4wDiOMsAizgbuJvUYKdZlM8UBwOeIswEAAO5CVuySMV1VsdlI0zS/Pi5cX9M0WYCltZbTIAFclffeGFPsl02WDWAXxNkAAAB3MY5jljERZ1+G/FNaa6nOxvGGYSi2z06vPV6BwLWt9MsmywawF+JsAACAu8h6Zxtjfn1E+CJZnU3vbByjaZos0aa1EXAl8u2c/kvf93I1a9oeRJYNYC/E2QAAAHfRdV32ePnrI8IXZT0fUppApIgDhBCy8kylFEkWcG3DMCzVZZNlA9gXcTYAAMBdZNXZj8cje7wk67ySrNmIMYY4G4fJXn6Px6Nt218fFIBvKXYZSqy1ZNkA9kWcDQAAcBfDMGQPmYSbF5blidZa+pbiMMX+ueM4/vq4AOxvpS7bOee9//UBArga4mwAAIC7yEZB0mzkwmKMWaGc1rrrOhYwcJise/vj8ei67tcHBWBnbdvKLFsppbVmDRXAlxBnAwAA3IXc/s9z5gUsJdRZmKi1ZhQkjpR1b08vwl8fFIA9Lc1+fDweT/tlcz0C8DbibAAAgLvw3mdPm8Mw/Pqg8C1ZnG2MIc7GkeQJ50G/EeBCuq5bmf3I5QbA9xBnAwAA1Cd7Stz+0Jg9c7L3/8KylCH1MKUeH0eSO0Kapvn1QQF4x/xOI4TgnCvWZSulaGwF4NuIswEAAK5j/gBZfJicP3wqpaiUvJIsa5C9symXw8HoNwJcknxrJ9ZaBj8COABxNgAAwF3EGLMSKmp1r0r2eTDGPO1kCuyrbVsZeBVfhCy0ALXouk7WZWutrbW8kQEcgzgbAADgLoiz72MpziZrwJG6rpNxNi37gUrFGNMaVRZnG2PY7AXgSMTZAAAA1du4tzeLsx//HctG0Hkl3nuajeB4sq1/NpL08W8qKWtpwPnN39He+2KPEaVU27Y/PEgAN0ScDQAAULEYY9M0qfD2aagdY8zGA1JOdVWyOltr3bYtcTYONo5jMdH+9XEBeEHf97LBiFJKa83gRwDHI84GAACoWN/387wy28UvKyWttfNnUUY2XYOMEmKMcjM41dn4CblXoLiWxosTOKdi16AUZ3dd9+ujA3BHxNkAAAC1SqXZ82dLa+36x2dlkn3fH3a0ONI4jrIellGQ+JVsIe3xeNCdADg/eZuxsoIOAIchzgYAAKiVjKebpnnp40mUrkrG2dZa5xxxNpIY4zAMfd/3fT9lUt+rj5b9RpRSNDsCTqL43o8xOueKWbYxxjl3/HECQEKcDQAAUCvZPGQ9zpZb/qnOviq5N9xay/w9TKHV/BVyQJVlsVmBMYYXJHBCIYS2beUqVFqIstb2fU93IAA/RJwNAABQsSwk0lqvxEMhhCzOZqfwVWXV2SmAYBQkkmJr9W9/02KZJytqwAnJ7kDzlVH2VQD4OeJsAACAimWppdZ6Ja8MITztnU3ceQ3DMMhK2K7rKIbFX2mjhlLq24NhZQMcVtSAE4oxLmXZWmuybABnQJwNAABQsSy1XK/O/hMlV2RJ1yAXIfq+z2IIpRSt0jGRtdJd1331O3rvtdZylWX+6mU5Dfg5eflIVxBjzPpFhPcvgMMQZwMAAFRsGIZ5QmStXXmelCWZlFldlayEVUp9O69ERdq2zV4hB/T9KPYb4SwEnMc4jlrrbOVJa+2c460K4DyIswEAACoWY5z3D3HOrXywDLC+3V4Av+K9z/7WWuuu66iew9/fX4xRJssHxNmyff/TRTgAh5nODPP3abp2/PrQAOA/iLMBAAAq9lJ1dtY4+/F40En5qorV2TQbQRJCkKPeDoizizH6Md8awIoYo/denhbIsgGcE3E2AABAxfq+n8fZxpilhFoGSU8bbaNexVl/bdtSBotEDgs9JlOWA2kfz7aVANhddi3Ilsanm4Smad6+asw/cRiGcRy5AAHYC3E2AABAxbKRTeupEHH2hclsQsbZFNlhIuv3DyuR7rou+9bW2mO+NQBJNiLbcQU0LaUrpVI4ToszALsgzgYAAKhYlkkZY1YePrN9xEqpLM6mcuoyinE21dmY/DDOjjH+pNUJAKlpGpllPx4P59zn14sQQvb1eacD2AVxNgAAQMXGcZynlvL5c/4/ZddaqrOvShbApsq4Xx8XziKEkPUWODJmkgka/UaAr5LZ9FIve6WUc+7DMuoYY9u2WutsYZURDgB2QZwNAABQsaxF8np1tnxwHYbhyKPFYWRnZK011dmYyDh73ovm26+TrEvSg95HwLGKgx+ntaXP34xLRd/TeYaLEYBPEGcDAABULISQlT6tPCJm6dV69o2qFeNsemffWfZmzzZ2PI6tmiyWhY7jeNgBAJe376ulFgAAIABJREFUdH2PMS5lzelK8fk7UW4PSqy1rFoB2AVxNgAAQN2yAqulZ8ViM2Xi7KsqVr8SZ2MiFzwObvchAzWa4QAHKA5+nC4TnzcdGscxWzufbjnYEAZgL8TZAAAAddseZ8vHyw+bY+K0sjhbKWWtZQYXJnJ963txdnHZTMbZWmsW2IDvCSEsNRhRShljPo+bi4Ne0+mF7RcAdkScDQAAUDdjzJY4W7YlUUodfKg4jPc+SxOstVRnY+K9z04dB49oY4EN2Nf6apB8y093Akqptm13aQNSbDOiteatDWBfxNkAAAAVizFmIfXSQ6Oc/GaMkV/t+4eMb5n/+WScnUZB/vDwcCryhHBw3hRjlOFadgyckYB1G98j4zjKommllNZaa900zefvtWEYlkq/d/n6ADBHnA0AAFCxEEL23Liyn1dWZ1MwdVWyGJ84G5ksTT6+F40Mv2itC+xiHh8Xm1mnLNs51/f951lz3/fFftlN04zjyPhHALsjzgYAAKiY3LC/FGfLcl1ZnY1KyTBCrnMYY2g2cnPz14mszj4+Spbtsw8eRwlc3jiOchvE7g1Gilk2C6gAvoc4GwAAoD5TLOW9nxfhrsxSizHKsqkDDxmHylYvUiEe4QLmsgTq+NUOuRrHNEhgR6kByPwmIQXZWuuu6z5/r4UQ5KJUYq3lvQzge4izAQAAKpblQSsF17I6m0LIC+v7Pouzqc5GJqvZPH59S1aIs8wG7KXruqzlVFoxMsY83YqxMYleapZtjKHBCICvIs4GAACoWJZaaq1XniG7riM2uom2bbM4O5Xj/fq4cCJZnG2tPfgAYozFOGzeMYkCT2CdfI+M4yiD7Clo3mtmRrY5bH4m2ZJl89YG8AnibAAAgIpt750tP5g4+8KyDeDE2ZCyOPsnvWi897JAm644wNuaplnKsq21e2XZS+Mld+lhAgBPEWcDAABULKvOfqw2wM3ibJqNXJhsNmKtJc7GXBZn/2o2rEzflFJ0KgDekO3LybLs94Jm+VnDMBQT877v9/ghAOA54mwAAICKySLclerscRyfxtnUVV1DtnSR+qWSNWASQjhJnC3b+pOLAW9YmsqolHLO7XJxjzEWE3Ol1NN+3ACwI+JsAACAimWPr+vdb2VsdNhx4nuKIUW2dKG1ttYSEWLu56MgJ7LSk70jgLQUSccYV7Lsvd7aMUbnnPwWxpiVdXQA+AaeYQAAACr2dLrj/Ok3hJA9he7VRhNnk20GT3E2zUYwl41hPH4U5KSYxNFvBNjCe58tTb23TDXdLRRD85XvwhwOAMcjzgYAAKjY0zh7Louz1zuToGryb+2cI87GXBZn/3AAYwhBjpX7YbwO1GKpYjo1mNrxnF/8Lr89bwC4M+JsAACAimVVjesPllnEqbWmOvuqsmYjaRQkzUYwl7X4+G2JZZatJyzAANK8jLr4xlFKtW271/Xde1/MsndsYwIAryLOBgAAqFg2lGm94WyMcR5gKaXmj7sMgbwS2SedUZCYy84Gj19PX/Tey2CO+XLAkmEYilm21nrH1vMxRrlzIn0X3psAfog4GwAAoGJZs5H1h9gQQtb7kmYjVyUr8anOxpxc8Pj5Xo1sS8H00mWlDchkl/4sy97rLTOOY7Ffdtu2vCsB/BZxNgAAQMWyZiPGmPWHzOwZmK6X1yD/6CEEOQqS1QtMZHX2Gc4GxZ4GvG6BSQihaZrszTud53d8F8sVr8e/MQyMaQXwc8TZAAAAFcvi7KfD04ZhOFuAhW/IkoiUQRALYi5b3DpD64C+72WCxq4C3FBxZbrrumK59O5Zdgih2Mnk6ZI5AByDOBsAAKBiLzUb+SPOvo3iKEjibMxlZ4MzpMYhBNmod2mVjlgNt7LUYCSlzK/OTV15+8QYZWiulKJfNoDzIM4GAACoWLY3v2ma9Y/PUs6n1dyoVFblSpwNmV5lL5L52eOHSXG24+Tx34GQRNi4vOKL3HtfbDCSdt58mDLPv+MwDMUC8KZp6DEC4DyIswEAACqWRT9P4+ys+FFrzQPqJWWFtynOPkP5Lc4jWww7yV6NYsfep/tOgAsLIRTbyqehCDtexLMLx/ZbCwA4GHE2AABAxdq2femZM6vwUkoRZ1/A08JbrbUxhjgbk2xY6Hni7D9xWksvYPYW4J5ijCnLzq7dSql9K6azzVssJgE4M+JsAACAimXNNOfV1sUNy7In5qsNN1EF2bEhDQqjVwOSEEJ2KjhPAab3XnbQZgYdbijGKFd3lFLGmH3P5+M4yjddyrK993t9FwDYC3E2AABAxbIH3afNQ0II2cPqeUoysaNsZ3qKP7quIxDEJCvhP1VeXJx6x/YC3IrsMZLmMWqt912Hlol5+l6sdgM4LeJsAACAimWhjzHmaZyddRjgefWS5DrH7tV8qN28t8DZoqusy/90fqNQFNcjT8vee+ectVZGzGmfzY7fvbgZgtUjACdHnA0AAFAx2WxkPe6Rg554ZL2krKYvxdmnyivxc1OM1TTNCdc5ZMOcB218cXWpu0gxX05n8r7v3363Zp8YY2yaJms6lJyn9RAAFBFnAwAAVOzVZiOy2iuLh06YauENcp2DOBuS9/6TdOyrYozF6lRmQuLCin0/ptP4S+fwp+/rpdmPZNkAzo84GwAAoGKyseb6EywD1u4gxiirs621xNl3VuPb3HufJdpna4oCvE2+JcdxzLqBzc/h+26l6vte1mUrpdiwBaAKxNkAAAAVk/vxh2FY+uAYo3xUttbWmHNhXRYCpjibnALV6fs+O2vRQRuX1Pe9tbYYZ38jyy6G5qwVAagFcTYAAEDFZJy98tDrvS/G2en/Xe9SgtMqrkbImlZr7cpSB3BOIYSshlQpxSsZVyL302RZ9r4NdoZhKIbmZNkAKkKcDQAAUDFZY5XVLc6zzmKcnR6VU10YIdE1yKbDSinnHH9fPHXCvRqym/C0CAfULoTgnCvmy0opY8y+ddld18nvRY8RANUhzgYAAKiYDHpWHkqX9hdPsrGQqFSMMWuSTpyNuRNm1ivkOpxSin4juIBhGORAi+lF3rbtLm/V6YsU7wHoRw+gRsTZAAAAFZOjnFaeS7uuW4+z27Y98uDfU1cS9xMxxvkLQylFnI2qya5KzLDFORVflsX/uJRla62NMV3X7fsKH8exOAt6304mAHAM4mwAAIBahRDkk/BK0eIwDOtx9mnbZ5NbvSSrzlZKaa2dc8QWqFQxiZM7UThRoAoxxqZp5Es6LT02TbP7tbj4DlJKcVEAUCnibAAAgFp572UkvRLoPK3OPm2cjVdl1awpzqY6G/WSpy+t9dIpi1wbp+W9l9uqUjsdrfXbRdnZZ83/Z9/3xbpsrggA6kWcDQAAUKtxHHeMs5VSRx48vir7W2utm6ah3TDq5b2XkRx5HCoSYyxOYpzy5d1rpUMITdPI77hXV24A+BXibAAAgFrJOZCPx2Plebj48ZOmaY48eOwryyZkdTZxNmpHB23UoviylC/gRCllrf3G7qhieq6UYicWgNoRZwMAANSq2At7pVxxPc6WjWjPifRqC2ttll+0bUucjfNbeYOHEF4afgucQYyx73v50p1Ozittcz5R3I+ltWZPA4ALIM4GAACoWN/32ZPqSmQZQlja5vxYnSGJ6sg42zlHRR5qNwxD1nLkS1EgsIvUYGTpspuaZe/+Ag4htG1brMsmywZwDcTZAAAAdUudMVM3iaeVy7L5bNK27TFH+x4qsl/lnJNxNr9G1C7GmC3VPB4P59yvjwvIxRjbtl0pylZKfWNTlPdevkcSsmwAl0GcDQAAUL1xHDfWVmcpJ0+5V1XsMkwBPi4gzYTMKk93n6EHbFRcJhzHcelq+3g8tNbfGPz49/fnvS8G6F/6dgDwK8TZAAAAN1KszmYI5PXIJIVmI7gM+fKupfU/LmNls8swDEt9vaatVN84G4cQinXZzjnWMgFcDHE2AABAZT5pGVGMs5mlVrXi60FWZxNn4zLkGABrbfq/6KiD3+r7Xu4emBhjvnQeTrsWZHpujGH3FYDrIc4GAAC4kWLpFoWN1yPj7KZpKNDDZchXOL0U8FupWXYxxU6dsnfv+DEt3mRDoScnn4oBAG8jzgYAALiR4sM2Kef1yD+0tZa8D5chC7SNMb8+KNyaXGKZXpnOuWEYPrnUrmw7KNZlk2UDuDbibAAAgBspDqeiOvt6ZLBirWXdAlci12zI7/ATS4MfU1H2V9t5dV0nG5sopay1NN4BcGHE2QAAAHcRY5TNRowxPPReTzHOpnc2rsR7LwNE2gTjSDHGvu+LnbJTB+1vZ9ny+z6YhwHgBoizAQAA7qL46DuNUEPVsjUJWSpIdTYuJoSQ9VjQWtNyBN82nWxjjEsNRrTW1tqmab53GLJfdmrPTZYN4A6IswEAAG6hWJpNnH1VWZz9jSlkwM8VhwFQoI29rG9dWhn82HXdMAz7boiZH8w4jrJfNldzAPdBnA0AAHAL3vvihmgaZ19SlrOkVqpUZ+NiikPwKNDGt3nvi8vD6WS7Vw93GaZ774dhaJpGXs211pzhAdwHcTYAAMAtLFVn8wB8SfMt8EqptPOd6mxcj2y5wCodvmrpYpoy5Q+z7JV68KU16bRayWgEALdCnA0AAHAXxS6fbMy/nhijMSbLO5xzLF3gemKMslO81nre4Pi3R4gr8d4755ZmP35pHSXGOAyDfJ2zeAPgtoizAQAA7qI4HvDXB4X9yeLBVL7H0gWuSr7gm6bJgmxybbxEvn7atl2pj/5SrOy9Xxo4+Xg8nHPf+KYAcHLE2QAAAHdBnH0TWZw9NRshzsZVyZYjaUcCETY+F2Ps+152aX/8m7Lb9/2Xen30fV8M0Kcsmx4jAO6JOBsAAOAuxnEkzr6JbOliylx+fVzAV8gGO8leQ/lwW8VuNtN59aszCZaaZSfzjjoAcDfE2QAAAHfhvc/qy9infFVt22bBh3OOUZC4sGEYZOTHih0+EUIoLpNMF9CvnlS7rlv61o/Ho+u6731rADg54mwAAIC7CCFkpV4/eR6eF5Qxru1LshyEOBt/pXdZCGEcx3m/gqrficXODKR+eFu2LjgpNmc/7Ls/Hg9jDG1GANwZcTYAAMD1paduWepFM+UrmWcr2eiwFGd77394eDibYRjSdg2t9WUa0ciheSvJY9XZPb4qhLDUY+RxVBObbMDp/HzOyRzAzRFnAwAA3IWclpY9EhPuXEa2dJF6vJKAYHKSvRq7CyHIkX1aa7YmYIncMJRN083OpYc16VqqzqYjPAAQZwMAANyFjDjZrXwBxUWILAdJEQxxNiay0/Q1MrIYoyzQftCcAa8ovoTSomDXdYet+8rpzcYY5xyvZAAgzgYAALiLLM5mSNqFZZX4Kc4mBMHEe59VZzdN8+uD2sdSaS2Tb7EuhDAMQzHLTlHy8e255g1PjDFsMgCAhDgbAADgLrI4+1fhDqHqAWQl/gGDy1ARWfhprb3MK2QpkVxqqHKZHxyfmLrJF1lrj794pRbe1tq2bdleAwAT4mwAAIC7yCKeX6VXxWdy4qR9ZXG21rptWxYS8DfrDmyM2RL1Vqpt26z8/PHfJtqcczAJIRRfMI9/W1v6vv/hC4bXKgBkiLMBAADuItuAf7H0CnNZ72ytNdXZyGQnhOv1Mej7XgaUNNFGpu/7bGlnnmUf32AEAPAUcTYAAEDdsoxyJbLMntivMfkNRcVmI9fLK/GJbLvGJde3vPeyfQSJ9uXNr4PFa+L0H7MxAxmukgBwTsTZAAAA9XmvzDYrxrzM5DdIWVJJnI3M5ZuNTLqukzXaSyW37GC4lWEYVrJsZocCwGkRZwMAAFyTzGVOMgoSB8givBRnM0kMczfZrhFCkK0ktNa8He7Me59dEDNt27K2AQCnRZwNAABQtxBCjHFLNJPtqpbFmDy9X0YWZ2utnXPkd5jLQt4Lb9domkYWaFtrV1qOcDK8pPRnLTZVz9Z6eQEAwJkRZwMAANStaRrnnLX2aTVZtrHaWnvYQeJgsjrbOUezEUxCCFmid9VmI39/fyEE2UH78XgYY9IaD9nlfaxn2f/H3r2dO64qaxh2CqRACqRACkqBFJQCKSgFUlAKpEAKpOB9wWptZiF7+Cwhfe/Ffuba3WO0bB1s/ZSqyqWS1uoAsHPE2QAAAB2LMarK/UBKVGdrrX+2nfgx8Ry91tpaS5yNmmimP03T1lv0RdM0GWPaHHNJtHEMd1Ymcs7DMNwJsq21HAwA0AXibAAAgI6VItwlo1FK3bkbn+dZ3MD/clPxS+3ShbX21vg7nNM4jiLY3XqLviuEsFqWq7U+cGU6rtdrSqmsZ9zJslnYAICOcA8DAADQMeecyGUej7MPn16dTV2WKKqzaTaClrh6nKH7kPd+tevI5ejF6Wc2z7N4EKFdz2DvA0BfiLMBAAA6JtphXy6XO49axxhFxEmH0KNq42yqsyEuDqLxwhni7Ov1GkK41XHizlpg/dbRaHtv7uyR+0XZ5dpIbT4AdIc4GwAAoGMloV6eoL/fDrvNvodhEH+HpOYYROEt1dloiZJV59zWW/QjOefVPtri6RYuhr0LIdwqxl+WcFjkA4AeEWcDAAB0LOcsbtfvFFyLfsqrcTa6sxq61XF26a5OnA1BlPDXNaqHT3JTSqsNKIwxPLNyDHcay5RO2c459jUAdIo4GwAAoDN10iT6h2it7+RQYvKbUoqGoUdVJ5VKKa21c444GzXRhGEcx6236KdijKtx5zAMh0/zD088niJQlA0AvSPOBgAA6Ng8z/Uj88aYp3pn0zP0qMTShdbaWsvqBWoizD3hsxplSGDbdcRaS6LdqZzznSy7FGXfaZIOAOgCcTYAAEDHREJtjLnzl1NK4t6ect2jYhQk/iQmIp5ztSOltDoq8H64T9i9E2JHzPNcFmnaJYrSYIQgGwCOgTgbAACgb3UWo7W+0wy0bbR9zgDrDNr6ROJsCGLN47RXg3mebyXaxNa9SCndH/zI8AAAOBLibAAAgI7lnOsSS6XUneqzlBJx9km0zUZIcyCIOPtsvbNrt8YGWmup5925nPM0TW05dn31G8eRlQkAOBLibAAAgI6llOrbeK31nfDlz+psbvgPY5om4mzcJw4S59zWW7SlWw2XnXN3HnnBtnLOq5X1RZmCy4gIADge4mwAAICOzfMsUsv7cbbolst9/lGJwlvibLTE1eDkvWjujBA8edC/ldXl1fr/GUK4lWUrpcrAAIrrAeCQiLMBAAA6JuJsY8z9CmuR19Bs5BjanS4Kb5VSxNkQREcargbXZh1ocX8yJL6tvcTd75RdFvB43ggAjoo4GwAAoGMitXw2zj55PeaBtc1GnHMUKqImDhJWO4pbNdo8y/Ibf2bQ8zyLBwsEay3NsgHg2IizAQAAOhZCeCrOttYSZ5+BKDKlOhst4uxVbVOmxZmnZe6E9/7W1MfSKZsgGwDOgDgbAACgY1RnY1XbO5vqbAhiMYxmI4t5nsXK34Ia7U3knKdpujP1sXz8cYkDgJMgzgYAAOhYG2enlO78fRFnE80cVVudPY4jWQ/q5S7RO5uBh7VSo90WAiulOI9+KaX0Z5CttSbLBoBTIc4GAADomIizrbV1XNVWahNnn0RbnU2cDUFcDeikIaSUrLVtoi0us/ieGOOdeY/1Hrm/jgsAOBjibAAAgI6Ju32t9VPNRgiwjmp1FCS9ZVATHaJZ3GqllFb7aLeV7ATcn5Vz9t7fz7LLKt00TV9aqGOfAsBuEWcDAAB0pr7HFnG2Uup+kZqIZoizj4re2fiTuBrQO3tVznm1jzbp/8tETNymxnd6ly/+7Kz1JSkl7z0nCwBsizgbAACgYyml+ln4Z6uz/2xOgk6JHa2Ucs7N87z1dmFHRGJIQndLSmm1dzPdxj+ujHxsG7wIWutNnjWJMZYjYasNAAAUxNkAAAAde7bZiAiwqM4+KuJs3JdzFqMgiefumOd5tfEFl9APCiHcH/molCpTH39/rJYP1vqUoTwfADZEnA0AANCxZ5uNiLCA6sKjEkmlUmoYBuLsM2sXukSDdeLsYnVFMOe82kRbKcVp9b4Y4+rbWysdk372bq+eL3XZOJ+eALAh4mwAAICOzfNc32D/GWeLAsNhGH62qfgqEb60vbPHcSR3Q02U8HN43HerCQZ9J15TLlkxxkdGPjrnNumUvRALhBeqswFgU8TZAAAAfauDAGPM/b/cztdiPOAhiejtx4WN6IKoh+Xw+NM0TbeKiEm0XxBjvD/ysTxWsu17m3MWCz/lispHJwBsiDgbAACgb3Uc8GecTYnZSYzjKOLscRxJ3LBIKYkkkUvBI3LOqwms1pr1gMfN82ytvTXyUSmllDLGjOO4bVF2e5pcqMcHgB0gzgYAAOhb3Q77zzg7hCDuzBlldkiinLBUZ5NXYhFCEGGi1nrb6LAX7Vu3vIEnr9i9P4i49mdR9jiOj/+2d4h/pf6fq0sXxhjWLQBgc8TZAAAAHcs5iyLcP39ETIOkyuyQ2jh7GAbibCxSSm3DYnK6B91KY8U0gt8Espu78zLFH6WUpmkSn0GCtXYPV6rVLNs5d5J9CgA7R5wNAADQtzqTeiTOFkHnNE0/2Ej8mNjLxpidhETYj7YjMNXZD8o5e+9Xa7SZr3u9EXCP43h/5KNSyjm3hwr31Sx7GAZOEADYCeJsAACAvj3VbOTa9BtxztV/SunZMYgsxhhDdTaKco6nlEQaS9+hp+Scb42FFBfVk4sxlk7ZfwbZO3k4YHVApbWWLBsA9oM4GwAAoG/1jbe19s+/n1ISN+p7qIbDO9pFCBG0lTibSnzURHU2ad2zYoy3+mZYa7muFveD7OJnnbL/lFJq9ylzPgFgb4izAQAA+lY/vt1WBbYZAXH2GYgIyVrrnCPORm2e53J4KKWo3L/lfswaQjDGrHYdMcacfDLBajRcK0XZ0zTtJMvOOY/jSJYNAPtHnA0AANAZcedf33g/0rY1xihu10k5j0ekSCXOJpSB4JyjI/CbUkrW2tVE+1KVae8ksf2q+jXO8/xnp+z9BNnXf/vx1u4DAOwKcTYAAEDHcs51jPJIs5Gcs0gZiLOPR4Rr1tpxHImzgW9IKQ3DcCvR1lof+xpbR9I551KxfifIttYOw7Cry9Fq3xhr7X7SdgBAjTgbAACgb3U2/Uicfb1e6+eptdb0GTiYtsywxNknb30AfE9KyTl3K9G+XC7OudUq+B4D01vbvDpEUTDGpJT28KqXbSirEW2WTV02AOwWcTYAAEDf6gBFKfVI34ClZ+6Ss/xgO/Ezbcta4mzgB6ZpulOYbK29f33eJOS9/48+uEkpJe/9nTR/+YTa9irUvpxpmla3cw+BOwDgFuJsAACAvtXpyWtx9iMdt7FnbfIiMrVhGIizgR8oZdp3Eu1dNdkQXstw53m+312kMMbs7bV771c3dRzHrTcNAHAPcTYAAEDHcs51jqC1fiHO1lr/YFPxS22zEe89z84Dv1Eaj6xWKxtjdrKw9GYBcoxxHMe2TYegtVZKjeO4t3rnaZrajd+8fhwA8AjibAAAgL79WZ3dhggpJZGzLEVze0sc8JrVZiPE2cDP3Ml5tdb3T8Y9X4dzziXIFiOFW+VTZm9TH6/Xa0qpzKsUrbq01nvbVADAKuJsAACAvtUPthtjHoksc84izqYe7WDaOHuapkcq9wF8RIzROXcr89Vaj+O451OyjtTneXbOTdM0jqO19s8e2SUdNsZ473cSzdeDH1dbo3jv97w7AAA14mwAAIC+1d0/jTEPZgd15WB5Evzb24lfEnmNMWaaJqqzgV/KOYcQSuef1Qh4n9fe5UMk55xzvt8N/Bbn3A4vODnn1ap57/3WmwYAeAJxNgAAQN9E0PBgdTZx9oG1kU3pnU3tIfBBD64dxhittXdacwzDsJNzM+dcOkprrZ1zxpjS+fqpILs8C7L1S1mRUlptlv34MOSdVJoDAIizAQAAOiPuqMX9+YNxthgVSJx9MPX+VUqVgGmHxZLAGczzfH9kYmnNEUIo1dDXf9f5+mp/679bz6aupQr7kXbYtzb+crmUBHw/Zc7iTVity9Za7zN5BwDcR5wNAADQsZRSHUA82GwkxigK7oizj6Hs/XbUZ2k2QmkhsJVSGvzI+ERjzDAM5f865+Z5jjEu5dsler5erzHGJfte/uiRLSl/bZ5n7/0wDPdz9key7P235r+VZTM0AgA6RZwNAADQMVFnba19JNEQIfjlcnHO/WBr8TOi+p5mI8Dm6lbaL6TGpfbZGGOtLXl3UVLvEEJKqYTdMcYQwjRN0zSFEOZ5LnFzKRJXSj3bP2SVMWYcx/0/81HmWLbbT102APSLOBsAAKBjMcY6mNZaPxIuiJ/ixv5gcs5iFGR5pp44G9hcjLFkyu8HyoLW+v1q6z+VcmznXBdPe8zzvPpW76cpCgDgBcTZAAAAHWvrrFeD6baLqIg7ibP71YZK7VFhrR3HkTgb2IlSpv1ar+pNLF1Q5nnuIsi+Xq/e+9V3+PHZjwCAfSLOBgAA6FhKSQTTj7QNaeNOWogeiWhBo5QahoFmI8DeLN0/vpRBf4q1toyp3PoN+9uyke0IgYK6bAA4AOJsAACAjrVDHR+ZBtn+1DzPv9lg/EBKiTgb6ELOeRzH0gX7S2H0a0o5dgghhLD/BtlCjHGapvZFUZcNAMdAnA0AANCx9o59HMc/f2qeZ/FTxNlHQnU20JeUUozRez+O4ziOq6MLf6PMnCwRdhfl2K0QQhmYKV7XOI4PvqJOXzgAnAdxNgAAQMfa1OORYLqdjsXz10eSc67HwZUqy3EcuyuxBE6rpNvfa66tlFo+Bcp/j+M4TVNfS5tt7rwMOq4/40qZ+SZbCAD4BuJsAACAXrUtsC+PDXUMIbzwU+iFqM7WWltrvffE2UBfcs6Ph9pl4aqkt865kueKlctlcSuE4L1fCrGPcXEIIbTvlVKqr4weAPAn4mwAAIBe9MpaAAAgAElEQVTOLPVoOed21NWDzUbonX1sddl+6R5AsxGgUznnlFIIQTTQWBhjSkOh0jO6XM9Lfbf3fhiGYRgOfxHw3rcfiEop6rIB4HiIswEAADrWphsvVGdrrY9RmofFOI51oFOqsw+cZAFnUIq1jTF1DTKtoq7X6zRNbZbNmwMAR0WcDQAA0LEY4xJJl//7SGTJKMgjWZ1aVsfZl8vFWvv4GDQAe1aKtWOM8zxz6U4p3Zqc6ZzjogcAh0ScDQAA0LfyFHlKaZqmB8tvl2FZlLAdlfe+jbOpzgZwJLcaixtjpmkiywaAoyLOBgAA6Ntrd+xlYthiGAbu/I9ExNlaa+JsAIeRcx6GYbUoexgGrnUAcGzE2QAAAKcg0uo2zt5qw/AN4ul7YwxxNoDX7HCxU6zYFUqpp7oq7fB1AQAeQZwNAABwRmIa5OVyIes8kjrOVkoZYxgFCaAjd7LmEEI7+FFrTSdxADgJ4mwAAIAzSimJOICs80istfXOLb2zY4xbbxcAvKgE3KtZNlMfAeBUiLMBAABOShTwkgUcSd1MRilFnA1g/+5/DMUYrbVtls3sBwA4G+JsAACAkxrHsX5Me+vNwVvu9EZfmo2Q+ADoTrlw5ZzFyIfCGMOjRQBwNsTZAAAAx7eaY07TVIcCdB09krbZCL2zgUM6yXldr7/WVzYeOgGAEyLOBgAAOKl5nutcIISw9RbhY4ZhaHtnnyT2As4gxjhN0ziOxpjDtxKa57ntMWKt5ZoGAOdEnA0AAHBSothtHMettwgfI6qzjTHDMFCADxxASmmaJtF5QynlnDtMqL08UZRzFotzBf2yAeDMiLMBAABOSjQbsdZuvUX4GBF1aa2HYaAAHziAYRjaUuVl4eowifb1ek0piZW5wjm39aYBALZEnA0AAHBSIs5WSm29RfiYtne2tZY4GwsqW/u1OhGxvpJ775/9nZscD3/+o6t12c45jl4AODnibAAAgJMKIYgC3q23CK9YTXbqwEspNQyD9/5IZZt4zZ85IEHhzuWc72TZi3EcQwje+2mayolft+/Y9BXcJDZMTHcolzI6JgEArsTZAAAAp9VWZxN3HkPOue5FUOLsaZpIgiDM8xxCYJ5eX1b7b9xnrdVal4mRXVznxWiHy+VijOH5EgBAQZwNAABwUm2cvduqPTwlpST2rHMuhNBFjIWf8d5rrUvWSaLdEfFgzQs2H/x757Mm5+yca7eZQxQAsCDOBgAAOCnvvah923qL8BkxRjEpbhzHeZ6Js7FIKdUHCb2GOrLaUfpZbX/tPSxnhhDa2vNSV/7Ij+/hJQAAfoA4GwAA4KTE09xKKcrfjiGE0MbZMUb2LxaiwpeHMzpyfxTky3H25qZpEheuC12wAABriLMBAABOSjzQzZStw4gxliYSC+dcSom8EguxmmWM4fDoRdtX+ilKKWPM3jJismwAwOOIswEAAE5K9M4ehmHrLcIr2hQypVTH2UqpUp29yeZhn0R0SG7YEXHpFssS97PsaZr29pTGrWbZfCoBAG4hzgYAADipGGMdHDjntt4ifIboI6G1ds7RbATXavFD1O/zcEZHblVna61zzjHGtrl2WdOapunHm1ovtt0q/199OaWEPITwqy0FAPSEOBsAAOCkRIhAHdxhzPMsQi56Z0MQiafWmsOjF7dqmZdxvjlnsVxxuVwenKb4S6vJe3kh8zxzQAIAbiHOBgAAOCnvfZ0gUJ19GCLOvvwbBUlzZCxEJKq1ptlIL241G6k7xrSR964K8HPO8zyvZtl8EgEA/kScDQAAcFJUZx+VaDZCnI0WoyD7FWNspyYWS2A9z3PbR9tau+2WFyEEa+3qSyDLBgA8gjgbAADgpERlHHH2YczzXEdFxhjv/TzP5JVYiIczaDbSkdVeIpfLRSlV78QYo7VW/J1hGFJK7aXgZxeHlNKteZVk2QCABxFnAwAAnJSIs3fYWRWPq9MoUZ1tjKE6G4KozqbZSF/anPrybxRk/ddijMYYrXW9vvXL1Fhsz60GI20WDwDAHcTZAAAAJ0WcfVQizi6jIImKUBPV2btqrIw/rbbPXu0lklISSxeXyyWE8Pttvt5I4fkAAgA8izgbAADgpBgFeVQizlZKee8pzUZN5KH0zu5LKbsWifCdhlEiRzbG/H59K8Z4K8veSVNvAEAviLMBAAAOok6jHkmm5nkWgQJ51jHEGOvWulrraZqozkZNnP60zu9OSsk59+CaRDsetjTR/uUG34qzlVJbVYsDADpFnA0AANCZOrBIKYUQXmuLLPIsyjMPo2024r0nzkYtpVSveRhj6J3dnXmey04srbGHYbhzDW+bVjvnfnnNF584yzJqp1k2H5cAsCHibAAAgI6VpqhKKWPMs61vU0r1fLDL5ULz3GMQsVHpnV3CSiIYFCmluluFUqqOszlOeuG9N8ZYa51zfy5IiERbKTVN0/KnP9jpYgPu5+8AANxCnA0AANAr0VPihfJq8ax6p1VyJ9fu9NVmI9TeoibGA4o4Gx2JMT74gM48z6Lj9lebaLebVK+08UAAAOBlxNkAAAC9CiHUqeXlcqlL7R4hxsE9++PYJxFaGWO89yRHqLVXDx7OOANxzb9cLuM4/nIDQgjTNNHNHwDwDuJsAACAXi2NUxfe+/ov/Fmvl1Iizj6e1d7ZxNm4VtcEcfVQShEvnoT3XlwfuDg8RXyw0i8FAH6POBsAAKBj1to7cfafRPts59yXthO/JKb8KaWW3tlAEWOsz32ajZyKqNEehoHFDABAR4izAQAAOjZNU51JPRtni5mB1tovbSd+qU0qibPRqhfDqM4+lZyzGARKq5kXUJcNAFshzgYAAOiY6BbybCQh4uwXhklih+Z5FnG2c464CoKYBMsRcipi7/Nozqr6A3H575zzNE3OuWEYxnHkxAH6xZfefhFnAwAAdEzU4YYQnvpx0WxEKfWl7cQvtXE21dloiUCT6uxTaUcvMDvhETFGa6365/LzWZoA3kSEfQzE2QAAAB0Tz4w/22wk5yyaLH9pO/FLMcZ6t2qtibPREg2UOULOZpom0XKkJNpkPbfknIdhuPwXcTbQtZTSNE1iYjaXwf0jzgYAAOhbHVwOw/DUz+ac6zJerfWXNhLfVt96xRjrlMoYwxPxaIlBsvURwp38SYjpC8aY1VUNjofrjSz7hVVkAPsxz/MwDOVhC5am+kKcDQAA0LF26N9TPy66UlxoOHAIdZyttS7V2c82osHh1WsenPunJVY1GAi8qvTLFh+X7ToQgL6M46i1LnG2tZbPwY4QZwMAAHRMxNla66fK6HLO4s6chgMHEEKo9ynNRrCqfrDDGLP15mAb7aIm+WxRf5g651az7GefiAKwIfENubTCL3F2+bLEN6WOEGcDAAD07Z1Mqo2zCTIOQPREpjobq+rqbGpyz0wMBTXG0F2kFkIQYzMvl0sp5+S6CvSrPMq2rFRprTmjO0KcDQAA0LGUkuh8+tSPxxiJs4+H6mw8ou4yQc/QkxOdZ7hcLNrq9ZJlXy6XMjkTQKdyzm23Ja5+vSDOBgAA6FhKSVTVPfXjooyXFOMY5nkWRwWjINGqE0x6JpycuGgMw3CqAu07L1akXUuczQoQcADee3F2n+3q1y/ibAAAgI6J8mrn3FM/3n6PZwxOd9r7LrFKYa313rNQgVrO+Z0HO3AwOWfRT8N7v/VGbaO+orYrviXLPu2bAxxMznkYBnGCs/zfBeJsAACAjr0ZZ7f36sTZB9BWZ0/TxO0ZhLo6WylV/xG1aSckVje11ie/aOScRQ+WcqY45zhBgMNoGwpZaznH9484GwAAoD/L92yRR4s4+8+v4yK/UEoRZx9AW51NnI1rc0Goozqqs9FWKZ68n0b79FJJ+cm5gINpF66YCbl/xNkAAAAdG8fxTpz9J5F7EmkdQ9sGlzgbrbq5hNaapSzEGK21S6HimR+6TymJ7ivlI/K0bwhwYN57rXVdo02B9v4RZwMAAHTsfnX2n5xz7/w49knE2dbaEAK9syHUt+6i2QhOS5Qkn2FGaBtapZTaCZBKKQo2ga7dSqiX5avlY9EYQ5y9c8TZAAAAHfvsKMiTP1p+GCmlOoIpcTZFhRDqzhJa6603B7tQXz0uZy3bF489FdM0rf5lMi/gANoVLL4S7xxxNgAAQMdEHa5z7vEi3HbO1a3bdfQlhFDv1tI7m+psCPXDGdbarTcHe1HHOkqpE2Y6os3IOd8E4FSmaWoHQm69UbiHOBsAAKBjbZz91I+LahSepD6GttnINE0nLLHEfXV1tvd+683BT92pKY4xipmQ9UfD4YuRRWl26ajL9fPH2sPs8Afe4Yk9uMMdKtaxmPu6c8TZAAAAHWuH/j3+sznnujzzzFO/eifuuGKMYqJRCCHnzI0ZavXpz1IWaiml+tmdW1WKx7ukiHEU5ZOR55aA71kuI5tfT0SFx61vxZtvJwribAAAgI69U52dcxbf3Ymzj0EcFcaYcRypLoRQV+CeYeIfniKKlM+w4NE24CqzB7beLvxHHSYSLOKDyjiZpRqg7jLEkbZDxNkAAAAdE12SnyoiyzmLJ8qJs4+hLjBUShFnoxA35PXp/2yfIhxeSql+9N5ae+BrSDk12trMY7/qLhAj4mfEN2oWeneOOBsAAKBj4snoZ8dVifo7Hqk+BlGdrbUex5FRkBDqOJtJd2jN87xaqHhIpTBTXDn5TNwbPsi609GCRM5ZtM/m4Yw9I84GAADomLgDfzZuELknt+7HICqMiLOxql7NogYN8zwPw+C9r68V9YrpgZOdlJLIspVSPLKwKzHGcRyNMd77jhJStHLOKaV97kRjTD16RGu99RbhJuJsAACAjok423v/1I+nlOov7scuvjsPEWeXZiPE2RDqpNIYs89wAb8RYyxliaU90dJ4KsZYJ7zPfsT0YhzH+qOwlKJzRuyE994Ys+SM7YMC7KmOhBBKh3pr7Q4b3JUJycuRppSi3dBuEWcDAAB07M1pXaI7KpFWj9pdRpyNR5yk8BZ/akcgLnGhWPI0xhwv3ClPKdUvcxgGPgp3om0Cc+Fpkj6V+vr6RHvhW+u3la9PJcgu/7G3LcSCOBsAAKBjpZBkKSgTkeUjN+T18KvXfgP2ZrXZyA7LoLCt+jhhKevAxJ5t/2f9OXJpql/F9aT3h3ja41ysCm/VMnvZsJxz+e/Sk+H3W7IhsXfq7u3nibNfuxR/9QJeH5yPbMByAMcYQwjjOA7DINpSL6fbrl6vWNuj6dCeEWcDAAB0rB7mprV+4db3zfpu7JAYEEqcjevazX9d9kg56mnVHyLL2oa4XIgPmiNdTET5+Tei0gfPrJTSNE0hhGEYjDHDMDjnylt9znMzpVQvt2++3vCCWzuuTX6f/T37OSSWLUkpzf94751z1trV1YiaUmr1tWz4AuvLnVLq2GsnXSPOBgAA6FgdRre11c/+hgvTIA9BxNmlvOhICRTel3Ouo6LXFsPQtZyzuP5fLpfVxkQxxrpicWlNs59M7WViHvLlt+XnyxsYQlh6l9cbc9Rm5bVbaWa70LJcrA5w4HUtxljKrkMI0zRN01SmdN5OrW8yxjz4j/5spy8LvaXlyCE7LB0DcTYAAEDHxEPiL8TZojEloecBiH1KdTZay+i/d64e6FfbY+RytzC5XiTTWh/mOR4R6P+4Ve5Si32riPW1VeoDEIM9lgNvGIbDHHvdSSmVsus7R+xTlFI7LKFY5t+W19g+rYKdIM4GAADomHgU94XbPFHJe4ZasMMTcXYZBcn9GGrLHftiiRWofDwD0RH78ldyKlrKWmsPcJy0MzCNMT+Lj1eHHArDMJywMnS1NLs8ZnSScH+1u8i2TTnKAtgyI/FZSimttbV2GIbShMRau8+9KZZSlFJ8Md4n4mwAAIBetZ0lX4izRYEeXQJ7JG5oxT4tcfY+7xuxlRijSCWoeTy2epib917s/UeiJTF5uMeIp500WL8JWmvn3Pfi43oXjOO4OhmvfoedcwdYM3hB2wHm0u0KyiPbHGNs15vLHMXSUd1aq7X+85D47Psjfts0Tc9m2SXCNsZYa8dxrAuxU0qPb236r9XN+ywxI73Ha90ZEGcDAAB0TFSWvd9sxBiz56FDeIR4fN4Yc56iNjwo50yzkTNor97iiZzLwx025nmuwyytde/HTP3xV6K6cRy/+nlXpuSVD+76zRQpYblin/aTt61b/3ETmC8pe38YhjLncxzH8h8lqh7H0f8zjmMpYW4bUm+1zlF2yoNxdnk54zg657z37ywRlarwEouXBacPvqhbxBHIqOR9Is4GAADomAikXmgo0Y4N5Ft779olimEYaDYCoS62XV3HwsHcmv344K5vnwfq+mmelFKdFZbuB1/t7NEuJCz/tKnssJvwjz3V1b0LSz3+R1pObzK5d57n0jK79AwZ/xHXhOJTpfQhhPZg+MEqmujFRJy9T8TZAAAAHXu/Oru9wT5hp86DaUdBOucOUNqGz6rjvHEct94cfF2bZT+bOs3zLB7D73edrO0e/u2WAm0/aGNMCCGlVOp253nuNzWrt3z579Iu4/6LEn/aDoH8cx7m/t+0GGNbZ/2yrc67pf/J8oa3S1zFm8sP5fffWv5pl50+fgCIUcn1v7j/g+08iLMBAAA6Jm4kXkiiU0riVoE4u3eimqk89ttv6oQPapOj0otmq+3BB93PWdoGDsaY1672dSzbb0djES9+qTS7DnbbQPPb9eAfd78X2TRNpVeG/afUvNfdrv48WtoQ8wCLbS80nr5vJ+vT7XlUvP+Z0vb3/+UhIYaRHqCx0iERZwMAAHRMVHu1N8aPBA37vE3Cy9rq7HEc2a3AqYjZj+I6/06BpyjJ/Ha/6W8IIWit6wLMb7+KtjT+0sliwCNbGEK4P9yyNLz681eJDjBvHqgbEq+0PQHf8fJC1Me1pfSXTzQ6L+n//Tfh24m2OGGZBrlDxNkAAAAdE9XZL9wYxxjFTQLf2nsnFjm01uUx9q23C93Yf8SGB5VBauIir7V+84JQZz2bdPJ9U9n+JTL7dmZ6q23CJjP9PiuE8GAbDWvtn29y+0Z1kfj/qfTOFr3a6zNoYYwphe231gZ2NRWz7dhzefs75DiOD5axr74PnzpaxCWOjvY7RJwNAADQsfebjbQ3oqs1Lwe4nzwPcVSUOHs/N8AAfkM8Mn//Iv+UGGN9nekulm1nWn51+28Fvl1nZDFG7/2diuxnX+9qqe+RWiGV5yRKVK21HoZhGIZpmuI/KaWUUowx5zzPc5vqltZhq7/5Sxt8/y+srtO805fDOfd4S5av9gCpX9qulhCwIM4GAADomLgnf/abfVuafblcrLVf2lr8RtsT1ntP50fgVEIIq8HQp6LblFL9+x9vjry5tvPDJqXZjxSx7vPNTCkNw6C1frYZdDvUsX6Bq0svWusyLfPnr/JbykDFklnf/2ttuL+3WvXV6uxnV8uWV3Srx4hSyhiz+kffWxBaTtvy73a98nRUxNkAAAAdq+NspdSzdUyrtyLGmC9tLX5DHBXGGOJs4FRutYD4bBxW/xN7C9ruEN1Xvt0sZTWl7a6efRFCEOvot8LH1cLtW1nnanpb76M7zc07fSf/1J7CewtV217nL59QOef2uCrPlpXoP6XU9k0ahuEbr+t6vc7zXBZsSpxdrwIe9XjrDnE2AABAr3LOov3is49DrlaN7WfKEB4kbq7qW76SLIQQiLPxJ+7S+1Xvu9V1yssXWmqIdKmLvhA5Z9HC+NvjItqQTinV14fsctjcOrSW1zUMQwihFCBP09Qm1Lfe7ZTSnd+8fDk51RCI9t3bW5wtzqbFC983vPei/np1d4trTlvv/yklzr78q87+Xm6OlxFnAwAA9ErE2S/cId+6Nd3bLROeUt/vldFSxNnAYdyPpGOMbcD0pd6v7b/VfnbsbY1ENDRQSn378261Ovv3sez7O+LO1MdSPS0+ZVa/YNyp4l/9ze0/dJJp1UucWh+rO1wFaWPoy0srW2LV59Ylq63ir8/fD15txHiAb7fXxwuIswEAAHolqpm01n+2YhT/89at6akKoI5HNBux1h6s9yiA4pGr+lfbgMQY6zDrfg3jHvIgUd1prf32tdE515bZGmM+uMT4vTd2+c1iR9dfPEo5dvuzMUbnXJvmr8aUq5M8Vn2vIHdX2qL+z57IL/+q9prT9gC5PFkV0T4zcesLbTsh8/3Btqvmea436Uv/Ct5BnA0AANArEWev3uPduWOZ5/nW7WJ7e7+HGAIPquMD4mzgJEIIbXRYHs746r/bV8sRkRL+YPTxrZmc1tqvxrKf/dRerTEfhuGRlyDSfGNMu23jOLa//9aK+xmyxfa1P/Kq6ze2zZ0/v5XX6/X2EyGPH97tOtytF9seJ1+q1o8x1sNOz3DIdYc4GwAAoFcpJfHQ9FNV1d771RtFpdT3thk/IKqcrLXzPBNnAwe2mgZqrX9Qx9o+J7Tn53vqaPVLPViEnPMwDKtzDnuZL7damv14+a04OLXW7d9pi5G99yml1Qbcfz6LdgDtq/7BsfqyeZ6HYRAHyeOPPoja/DvXkLYO43vV2fXLoQXfDhFnAwAA9Er0EHz2CdxbjbNXbzWxW+1dfR1nl97Z8zzvOWAC8LLS0qG9kjvnfhb5iQ0oaVSMcW8BnFgDXi0T/obSuEAp1YbCn63Rnud5mibv/TRNy699/zW2U6OfWvZu187bTRLV38aY5Y9SSm3YvbdD67Par2dvHqs5528vaaeU2hrtB1tOi9d759ts26r7g9XZ9aaKkvNjH2+dIs4GAADoVdtD8KnIsr0/LIize7danX2GZqPA2Yh8dvGlLPvO72xrM0sD3F3FQHUsq7X+ZV+UUqNdLs7ijTLGvFP7uewU0e33g4dBm0fXcfOfxGrH6khDUYwsSm7bePd4zR/qPdW2dnl5QTrnPE3TMAzW2nEcvxpqxxhXa7Svf62piG+zt+LslNLPxmOWZiP3twfbIs4GAADoVfvQ5a0qlfZGop0O/9ptKnZIJBqlOptmI8DxrPYY+VIz2ftufabsKnasc1Wl1O/fqBij9361JfT72frqzMmPzLps5zQ+FfCJtXOlVPudRGx529NchKT3h452rT2V3gltxVJE+T6w/EOf2+r/1x7ef67WzPMsXvLquTmO488OA+/9sknGGL5B7RBxNgAAQK/aurynvnCvTna6UJ3duZxznR3QOxs4npJD7SfLLla3ZzW73Eo9200ptVU/3NIPui2rfzP6vxWUv39IlDhbbPCD7177RWV1yVx8IRHhfs5ZvKgDx9lt76B3DozVIY3vNB/783Rus2mt9eo3kLpxvNhO8b1lnuc6X15eyPce/ijdgS7/vkR96V/BO4izAQAAetU+d/nUHPlb1dlP/R7skKhAtNaGEIizgY7UmVGbH60OXtuk3FhY/VjZycWn/dT7eBb2eHBf2jKIN6r0P1nermeXAcRaZn1gPPcy1n7zku7VvPf3vy2sHqir4Wy7FlL/adts5FOH+v1RnJusxLS7752vZKsrHM8uBjz7PrR7s+79vfrb2mcLyuQP55y1tj32yneb7+2g5R9VSu3qERMsiLMBAAB6JaYzPfI4at1ks73DWTA2sGviTtI5F2PcSaIE4E2ltre9bu8hc1kt0N5D++ycs/jU+3Y/3Jzz/aytdNNu365hGF6+XN/6ZH/tt9VKbWybKmqttdbWWu99GUE5TZNzznvvnGv//q2Rhu33mRCC934cx9Xfc9RF93bq5pt16KtzYt9f4bivXcP488AOIayOAbjlwSGTLytNWsr41j1cwdAizgYAAOhVe9vzeL3SrQFil//e5O/nIXE8qH1o1zk3zzO7EjiAdijf5XLRWn873HnQ6ieL1noP2yai3m/3wy0x4jAM95tyTNPUVtm/nGCuxtmfyi5LrPxU5ti69dJWO1Tc+iW3MvEDaN+EZ1viiHem/Urw+CFRniEoT3ellB5cF18N0C8PdO3w3q8WYre01p9dz2gPp7LU9O0acLyDOBsAAKBX7T3D4/fAKaUT3igekthZYmZXSUaIs4EDaFsuXP41md160/5fSqltebGH8kbx7n21MUsdK2utQwh3rsDtEsU7fWNEgfwLeegdMcbVfiYPMsbcORJW22K0tNbizTnMp1v7cMNHjtJ2kueDc0eXfa2UKq0/Sj+c1eM5pTTP860sezkA/txZq8X4y2ZYa8sK/a0f/8jBsLxj7cGG/SDOBgAA6FKMsf3G/+AtyvVudfatoT3ogtiz5fYvxniYG37gnGKMbb2qMWaHXRfa2H11+t+2W/W93iyrH69lWbH9m9M0rca4dfH4s1fvEIK1tgR/3zg8bm3zfX+uu7Sz/lpKqce/53SnHXX4qZWqkjKXPPrx73h3CqWttaUPzDAMzrlxHB/Zdw9er0qZ9tLcpoTppaHNb76djuNY/mlrLd+Hd4s4GwAAoEurbTdvFWGt1tHcueXYYT6CB4l1jnLzT3U20DXvfRsg7vkpePHx9MFg7mV1e66vpqKrRfTLLiuVrSURvpMAlpruL23h+8qMx/uhdokvy5Kq9/6RY/VOrwljzA+eNLo/gvWr2kYxb3bNrpVDLuccY3y8Wv+dSvzVPeice/BdzTmXcu8QQgjhl0vyy4ViD8N1cQdxNgAAQK/ae+bH71JW2yku3+CJs/sl4uzyaDBxNtAv7/3qSL2dlw0uiXYprtx8UqX4xPxenH1ntXi5LP/ZhLqLLgdlwOY8z9M0hRBKlW6ZA1lSyJJIPv7pk3MuKzeltcXyFt3vUnIM7eMXm38Tuz8z/HHlClDacG/7ih6xhPg7afqPW4izAQAAetXG2Y/f/d6Jsy/76HOK14hbYuJsoF+rT+FcOmkJlXNehge+M97wU37WbOS61gT5KeXt2v8u/pKUUghhmqZpmrz3v/n8SimVLH7DxwhENfRWm1FLKb3QWKYojU1K05v77eM/4v3fn0s7W0oAACAASURBVHNeztwu1pNObhdnCAAAAF7Qts9+auLTakpSbF5Gh5fVN59LivSDO0kcBofKJlbf9tVUtKOgc4mH9ladrZT67Pa0u6/ubfIUa+00Tb3s4mNYPjdLHfEHh2c+LucssuDfb8OqlNJqs6M7yvk+z3NKqaMjeblEKKU2OQbwFOJsAACAXrUV1k9VFd3pikhNSr9ELVV5wrc0zdx607CxO21hOTx2yHvfXpw7yrKLGONOmgzM87wsAN+Jsz94LqSU7iwbC2XpkSdpNiEq9621v9+GGGO9DZsv/whlbOnSgLt0tfbelw4z3nvv/TRN4ziuTj3dvxjjsqRx4HGjR0KcDQAA0LEyrX4JLttOi3dujOuWFKLKu72P4ga7F23/TecctX5AX1az7HEcuRS/ow6Xf9P8pHRcKV0XLv+emCkfuOX/ljrWcRxZdPyx+t0Wp5sx5vd9q0XL9b3F2ccWQigd28tCF9+XukCcDQAA0DHvffn+/cLjsaKyuxTXlC/0e6ikw4NEAhJjrOvuS50RQQlaKaUYI/fte1Me7W+zbB6aeV9dhPv7WZplLmL4J8bICbgT0zS907rtI1JK9TZs3mv+VEpReenYvvW24FHE2QAAAB0rE5O89y8U8ojOniXCjjHSZ7lrotmIUqp0YmWforY8WF3a0ZCp7cQ8z6ttoCjV/Ii6Q5fWuseWCPiGdubq0m/klx+d9ToWcfYv5Zz5jtQd4mwAAIAjeO2LeH3/Rk3KMSwx5RJnD8PgvedWDbUQQl0JSKvQzeWcp2m6lWVz/n5EfXlUShFnYyHibK31JifdNE2lNQ0PyQH3EWcDAACc1zzPy82bMYbE5ADmeV6Nsym/RU08nHH57yBZLgW/t9pghIXGzxJFuKs17xz85yROwA2L90sbqE3+6W/j5MIHEWcDAACcl7h/o1TtANo4uzQb2Xq7sC/jOIpesRQDbqhdXSh675e9w/Sqnp/8jTY7O3zJeES7ntT72fcODmPsH3E2AADAecUY65s32rMeQM5Za13H2cMw0DsbQoxx89FnKMT41qU49Mxp2veUZg7L5fHBVRyun4c3jqM4B+leDewZcTYAAMB5pZTqmzf65x5ASqmOKZVSzjmSSog8bp5nEWcTnv5YzjmlNI5jvf60XIrpDvQlKSVr7XLwG2OO2tgBq1ZXJlJK7WnIAj+wZ8TZAAAA55VzJs4+GHFbTpyNVVRnb0JEaXXji4W1llrgrxIdmYwxNNo6tj9PqLY0+/HKfQCbIM4GAAA4rxCCiFG23iK8or5XFzGl1to5x205hBCCiLOpUf2xtkD+crkMw0CW/QMhhDrRXn3b2REnMU1TeyYaY3hCAtgz4mwAAIDzEnH25cKXw+61D02X3tlbbxf2pa3OZs3jx1b7ZbOo8DPOufoUeOThJALu41ntXM/CErB/3LEAAACclxgFeblcuH/rXRtnU52NluixfqF39g/N89wmaFSD/lhKaRiG+iwYx5FdcB4xRu992zK7LCzRfwbYOeJsAACA8xK9s5VSW28RPmC1OpuFCtRyzlRnb6Jt81JOUoLU30spiRptrfU4jtTIH9s0TasV2csXIZ5nAvaPOBsAAOC85nkW5YFbbxHelXNuR0GGEIizUR8DbXU21YjflnOepqmNz8jONhRjNMYs54JSSimltWaB4ahyznXbdEFrzfkIdIE4GwAA4LxE7+xhGLbeInxAfa++xNlbbxR2R1TxE2d/2+rsRxYRN5dSGsdxCbW11iXRNsaUi2dKaZ7nW+k2K4V98d63p2H5rDTGcBkEekGcDQAAcF4izh7HcestwrtE6VmJs7lFR0uUKHKQfFwJOlNKbVMLLrl7E0Kw1qp/6ktoCbuttZwjnVqWHMTTS2I5nyYzQEeIswEAAM5rGIb6do4a3mMQcfYwDOxZCG2sQ5TzAlGZu1qoOwzDanMDehrsUIzxTlflpXqXiuxOteOvS5A9jiNrFUBfiLMBAABOKqVU39EppcizjqGNs7lRh9A2caZT8MflnMV8ArLs/cs555xXJ3aWRJszpV/t00t8OAKdIs4GAAA4qZxzfZfOY++H4Zyr96y1llGQENqYlYD1s7z3q0XZpXnF1luHv5VQ2zk3DEPpQOKc895zLe3aPM/zPMcYWZYAukacDQAAcFKiOpsapa7VCYvo0luajRDBoCZOfxFnc7S8I+cslpRq3vutNxBPK9H21luBp33kUsb1ENgh4mwAAICTEs1zibMPQ/R+dc4RZ0Noe8hSnf0RMcbVouxlbemRX8LZCgDAHcTZAAAA5zWOI3H28dQTPssD8sTZuP43JE0pidbAXAFe0I6CFAM2a1rrrbYT38OlFQB+jzgbAADgvOoKTR6BPwzR6KA0G9l6o7AvYiTahe75nxBCuJVlO+dYMAAA4COIswEAAM5rmqYlbbHWbr05+ICcc12dXeJscjS0RFMa4uz33Woz8mCPEQAA8AjibAAAgPPy3i+Bi1IqpbT1FuED6h4yVGdjVTsKkjj7TW078nqxkCUlAAA+hTgbAADgvETuSeh5DPUqBdXZWNVmr7QbetOtONsYMwyD9z7GuPU2AgBwBMTZAAAA5yWaLFOeeQx1D5lSGcpCBYS2Ots5t/VG9a2dA6m1ds4tKTYzAwEA+AjibAAAgPMScTZ51jG01dnE2RDmeVZK1cfJNE1bb1T36nbk1lraNwEA8A3E2QAAAOclck/i7GMIIbTV2SRrqIkSfqUUHWneF2Mcx3GapmmaOOMAAPgS4mwAAIDzmueZZiPHsxpn0+gANXGQGGOIX3+MUxIAgNcQZwMAAJyXqM4mzj4GsUqhtfbek52hJg4SpRSDCgEAQBeIswEAAM6r7vR6uVzIs3rU5tSijwRxNlqiOlspRYN1AADQBeJsAACA8zLG1HkW3QaOoe0jMY4jO/fkxHrGOI6X/2I1CwAAdIE4GwAA4LxEpMUsuGNYjbOpzkYthKCU4vQHAADdIc4GAAA4L+dcnWfRbeAYpmnSWtfNRoZhKLW3hNooYoz1QaKUIs4GAABdIM4GAAA4KZFnEWcfhpjwaYxxztFKArWUUt1riOpsAADQC+JsAACAk5rnWTTPJc4+hmma6j4SxpilOhsoUkpiEiynPwAA6AJxNgAAwElN08QsuEMSe1Zr7Zyj9ha1nDNxNgAA6BFxNgAAwNE82B9ZDAy8XC4ppW9vGz6u3d1iyl/pnU2cjVrba4jVLAAA0AXibAAAgF49Elvf+Ts5ZxFnMyfwGMZxpDob94mDhDgbAAD0gjgbAACgMx8MnYmzD0mMgixx9jRNW28XdmQYBnH6s+ABAAC6QJwNAADQvZRSjPHZMLqtzqbZyDGIwltjzDiOdEZGTTTOJs4GAAC9IM4GAADo2zRNwzAopYwxT1XgxhiJsw+pHA/LblVKee+pzkZNNM6+XC7e+603CgAA4G/E2QAAAB0T4xzHcXz8Z+mdfVSi8NYY472nOhuLnLMxRpz+HCEAAKALxNkAAAAdizHWVZbOucd/dp5nqrMPSSSVpWyfsBK19uEMRkECAIAuEGcDAAD0rc4ujTGP/2AbZ39vI/E9bU19G2eHEOiMDHGolKY0SimtNZ1GAABAL7hpAQAA6FvdJVlr/fgPivLMp34WeybibGstcTZWvTBCtjt/vsDDvwMAABwMcTYAAEDHUkoiuKz/9H5MI36WOPsw2urseZ6JswEAAHAAxNkAAAAdE+Mcn+qdff3vzEDi7MNoq7OnaSLOBgrKsQEA6BpxNgAAQH+WOCalVDcbeTbOHsdx+Vml1Be2FBsQcbZzbp5nBv0BAADgAIizAQAA+vbyKMjr9TpNU517hhC+tJH4pWEY6t06DEMIgTgbj6N+GQAA7BZxNgAAQMdyzqJhSErp8R8X0yCfLe7GPok421pLdTZOiCGQAAAcEnE2AABA30R2+VSLZDEN0hhDvnMAbZxNdTbOrL6szfPMYygAAHSNOBsAAKBjKSWt9TsNQ5xzL6fh2Kd2FCRxNlipSik554wxxhjv/dabAwAAXkScDQAA0DHRbORyuTwb03jv3/lx7E17SNA7G4gxir5M5PsAAHSKOBsAAKBjOWfRWeKp6uw2+hzH8Xtbiy+pg7nVOHueZ8I7nNk4jvVJoZR6aswAAADYD+JsAACAvtXdQpRSzzYbaRtTfGk78TNihaPE2YR3ODOxxqO15nkFAAA6RZwNAADQt3dGQV6blGcYhi9tJ36jLdinOhsnN8/z5b8YewsAQL+IswEAADrWZpdPxdntJEmqsw9AjPcsoyCpzsapLGl1jFE8g+KcE9dJom0AADpCnA0AANC3OrvUWj+VWoYQRNGic+57m4rfECsczjnibJzTPM88gAIAwMEQZwMAAPTNe38nzr5fdSjKeC+Xi/f+y9uLrxNT74ZhIM7GCc3zLJ4+UUrRMhsAgN4RZwMAAPSnDqnr7NJa+/hT8zln8Qz+5XKZpuk7m4zfEXE21dk4oTbLZrkOAIBjIM4GAADoW51daq2fqj0Uj+Ffnp8kiR1qq7OnaaI7MHr35lrdMAycBQAAHABxNgAAQN9EJB1CePxn60Yll8vFGEPc0512l4k421rrvWfP4nhWj+qUUttGyRhDmxEAAI6BOBsAAKBv78TZMUbRleJ724mfaauzvfdkeTiDEIJS6tKgzQgAAIdBnA0AANCxlJJ4pv6p1DKEIHLP720qfma12Qi9s3FsOWfvfZtlK6XIsgEAOBLibAAAgI7FGEV8I1LL+y0mRHW2MYbQ8wCIs3E2OedhGNqibOqyAQA4HuJsAACAjqWU6jjbWvvOjyulaElxACLOds5574mzcSRioU4c84XWepqmrbYQAAB8CXE2AABA37TWdXzzVGqZcxbF3aQ/ByDm4NE7GwcWY/Te15fBZW2PYx4AgEMizgYAAOibGAX5bIIjWm8/NUkS+8QoSBxS2zppmqa1/iIX59z9PksAAKBfxNkAAAB9q0txlVLPhjiikreuziYP6hTV2TiD1QYjl8vFGMPRDgDAgRFnAwAA9KcOmuvsUmv97K8S5Y3DMHx0S7EBEfMZY7z38zxvvV3A024tqq3WZVtrOc4BADg84mwAAIC+iW4hS/rzYG21915EQswM7F0bZ4/jSL0qOnL/8jXPc9ss2xhDlg0AwBkQZwMAAHQshPBmGN0WORJn904sUVhribNxDCmlYRhW67JpjgQAwEkQZwMAAHQsxihinWdTy5yzUoo4+0iozsZRicm3hfd+6+0CAAC/Q5wNAADQsY+E0aJdCblnd0RdqhgFqbUmzkbv5nkWB/ZSl731pgEAgJ8izgYAAOjbrd7ZjxMFj9M01X/KI/zdEQ1kSnU2bYXRL++9WLcrhmHgwAYA4GyIswEAAPomwugX0mfRi3YYhm9sJ35GdFQvvbNJ/dCplFIbZJcrFZ2RAAA4IeJsAACAvtVhtFLqhZ4Sor5ba/2N7cTPzPMsdug4jiGErbcLe7G66PX75zAe/BfbHiNKqXEcv715AABgn4izAQAA+lZnPVrr9+NsetH2TsTZxhjnHHE2Ws65ffbrKEl3zlnMNX150Q4AABwGcTYAAEDf6jjbWvtCMtU+wi/+Au2z+yJ6Z5dmI6IlOk5InMjee6211to5t9UmCWILRSelgoUZAABOjjgbAACgYzlnrfU7fUJyzmLGGtXZvRO9s7XW3ntCQAjjOCqllFLee/FHm69gpZTaLNsYw6oMAAAgzgYAAOhYOyTthdSyDsSJs7vTJo/eexFn0zsbLeecMaYUaO9tpmKbZSulOIYBAMCVOBsAAKBrKSVRW/3shDRR3325XPbTeQCvEe2GS7ORHfZHxoZijOofY8yGcbZYj4kx1uNtl2OYLBsAABTE2QAAAB1rw+i68/UjHQNyziI5Is7unajOJs7GtbkalE4jSxOPrbZKCCGs9stm9iMAAFgQZwMAAHSmjqVSSm/WVscYibMPRlRnl97ZxNmo1WseWus95MXt1exyuSil6JcNAABqxNkAAAAda8PoZx/Jb7tv1/Xdi81Hw+Fx9M7Gn+o1D6XU7+Ps9pLinGuzbI5bAAAgEGcDAAB0TASXL8TZbSC+GmejI+KoMMZQnQ1BxNk/qIC+sySWUmqzbK01WTYAAGgRZwMAAHSszYBEq5A/q6pzzsaY+jc8O0wSeyOOCmMM1dkQREca7/2X/qE/L0HzPLf9sp1zLMAAAIBVxNkAAAC9yjm3cfYLVZbil9A7u0d1aNg2G/HeE2ejNk3T5otYOWfv/TKRcsEDIgAA4A7ibAAAgI6FEEQS9EIPXBFnW2u/san4mXYU5DiO1LqiFkJQSi1R8pIg/7JLftsr6XK5GGPo1A8AAO4gzgYAAOjYPM/vx9nDMIg46Rubip9pm414738/6w97JlbCfv9Mhvdea91m2ay7AACA+4izAQAAOtaWN74QBok421pLdWTX2mYj4zgSZ6Mmmo38sr9HjLHtklSybI5SAADwJ+JsAACAXqWUxBTHj8TZPOzfOxFnU52NluhI85vq7JTSapBdFl04RAEAwCOIswEAAHrVNs5+rbBaBExKqTZXIuDuSBtnT9OUUtp6u7AjP+6Yn1Ly3ltr2yBbKWWtJcsGAAAPIs4GAADoVc5ZxEOvtb1uO5YQLXWkXWkQSaXW2ntPnI3aN6qz7yx63SrKLkk6FxwAAPA44mwAAICOiQJtpdQLqaUIti6XSwjhG1uL32h7Z9NsBII4SMZx/Nm/JVbgODIBAMBTiLMBAAA6lnNWSr1ZYil6ZxNn9y6EUB8VSilGQUIQ5dLe+4//E6VYO8aotV7Nsodh4KEBAADwLOJsAACAvtX9Rl6YA3mlOvtw2pp959xrxwYOQ3QCEWe9MeYbyfI8z7ey7NUe/QAAAH8izgYAAOhbCKEERqvtAh4Z4diOlPxGqSZ+Zpom4mzcJw6SjzcbSSm162QL+mUDAICXEWcDAAB0L4Tw5iQ30XlgGIbljx4JxLErIkbUWhNnQxAHyTRNn/39Ii4XByQ9RgAAwMuIswEAACALtK21W28RXicWJ7TW9M6GIDrmf+SBjHrpSxyExNkAAOBTiLMBAABwjTGKvImi7H611dnjOFKdjdq3R0HeaZn98UpwAABwKsTZAAAAJyUCaxE/kX72SxTeljibeljU6hGyl083GxHLYwvnHE8JAACANxFnAwAA4HptqjXfbMaNDYldqZSi2QgEY0x9kIQQPvv7xZpKuaTwzAcAAHgfcTYAAACu16ZaUylF9tQpEWcbY7z3xNlY5JzF0xgfbwCSc14uKUop5xzPBwAAgI8gzgYAAMD1ulZNSfzUKe99vR+11sTZEMTy1TiOH/8ncs7DMAzDwLEHAAA+iDgbAAAA1+v1Ok2TyECpzu5Cu5uozsaq+lARcfbHR0G2/yIAAMBHEGcDAADger1eQwiiOvvj/QfwG6LQnjgbrXEc64NE9M5+LYYmvAYAAD9AnA0AAIDrdS3OHoZh643CK8SUvxJnz/O89XZhR8SaB2tXAACgF8TZAAAAuF6v15SSiLOttVtvFF4h+kiU3tmi/BYnJw4S4mwAANAL4mwAAAD8j9a6TriUUnQP6JEovLXWUp0NQcTZHB4AAKAXxNkAAAAn1UbVSilRoE1Jb4/qOFtrTe9stMSaR0pp6y0CAAB4CHE2AAAArte1ZiOXy8V7v/V24Wl14a3W2lobQiCvRI3qbAAA0CnibAAAAFyvN+JsrfXW24WniaTSWjvPM9XZqInOQhweAACgF8TZAAAAuF6v1xBCG2cbY7beLjxNJJXDMIQQyCtPTjQXulwudXMhqrMBAEAviLMBAABwvV6vzrk2zrbWlj9lJmRHRJxtjCHOhiAa5S9xNmc6AADYOeJsAAAAXK/X6ziObZytlKLnchfqFNIYI9YkiLNRyznXax5KKYa+AgCAXhBnAwAA4Hq9Xud5buNsmur2iDgbfxIHyTRNW28RAADAQ4izAQAAzqsu6V2Ns5VSxKDdGYah3omldzZNJLDIOdfNRpRSxNkAAKAXxNkAAAC4Xm9XZzMjrjuiDXqJs2kagxpxNgAA6BRxNgAAAK7X23E2TXX7klISfSSGYZimiTgbi5SSOM2JswEAQC+IswEAAHC9Xq8xxrpgkzi7UymlesofcTZaOWdrrThItt4oAACAhxBnAwAA4Hpdq+olzu6R2I9KKZqNQMg5izUPegoBAIBeEGcDAADgf8QIQXKuLogZj6I6u8TZVGejJqqztdZMCgUAAL0gzgYAAMD/iBGCNNXtUYxRVGdba4mzIdQnu9Z6680BAAB4FHE2AADAAb1Wa+m9b+Nsmur2ZbU623tPnI2aONlFTyGKtQEAwG4RZwMAABzE+wlUCKGNs621X/rn8A1ipOfSbIT9dXLiABCPYnjvt9owAACApxBnAwAA9GrJp3LOHwkrRRK6NCKIMb7/y/EbMUZRne2cI85GrR0FyUMYAACgF8TZAAAAfQshOOdKf+T3f1s9IG7hnCMM7UVKSfTOpjobwupzGOM4br1dAAAAfyPOBgAA6Ng0TUqppaT6/Y4Bq9MgLwyE7EeMUaxJlKUO4mwsVletjDEcJAAAYP+IswEAAHpV6nDr9iDOufov/BlOtX9hNecSlZtkXnsWYxTV2dZaMegPJ3frNKetEAAA2D/ibAAAgF61dbjv11cOw7Cacw3DQIq9T2K/rDYbYdAfatM0rZ7m8zxvvWkAAAB/IM4GAADoVUophCBGur0ZOq821S2pKJWbXWhHQZbe2VtvF3Zknuf2HKfZCAAA6AJxNgAAQN9EnP1+feUj/UYW5F97k1Kq96DWehgGmo2glnOumxQVHCQAAKALxNkAAAAdizGKTOr9fPlWnE3Dii60zUbonQ0h51yf5kopzm4AANAL4mwAAICOiSpLpVT9R6/9znEcV+Nsa+2Hthrftdo7mzp61FJK0zRZa4dhSCltvTkAAACPIs4GAADomyimfj+1vDUmzhjzkQ3GV6WU6hUOrbVzjt7ZAAAAOAbibAAAgL4Nw/DZBrhtA5PF+4258W0559VRkFRnAwAA4ACIswEAAPomqrM/0gNXjJe8k5UTku5NzrltNkJ1NjhVAQDAMRBnAwAA9E3E2THG939nnYd+tvQbP9BWZ9M7G0/haAEAALtFnA0AANA3UUn9kalut+Jsinx3SCSPKSWajQAAAOCoiLMBAAD6JqLnj8TZzrnVONs59/4vx1e1vbMZBQkAAIDDIM4GAADoWx09a60/EmeP40ic3SkRZ2utibMBAABwGMTZAAAAffPef7w6W/zOxTAM7/9yfFtdsF/ibJqeAwAA4BiIswEAAPomGoN8ZBTkPM+rcfY4ju//cnzbMh1UKUWcDQAAgCMhzgYAAOjbMAwfj7OvN6ZBUp3dhXrfGWNKnM0oSAAAABwAcTYAAEBnRC65lOKWalzRbOTlEFOk5KvV2SSk+6SUqpuNeO/ned56owAAAIAPIM4GAADom2g28qngcrV9ttb6I78cXyV6Z4/jSLMRAAAAHANxNgAAQN9EGfWngstxHNs4u63+xg61oyCnadp6owAAAIAPIM4GAADo2zRN36jOvhVnf6o3N74k51z3n2EU5GHUvX1u/TcAAMDhEWcDAAD0bZ7nb1Rni5R8ibOdcx/5/fiSnHPdO7vsMuLsfq2m1TnncRydc977P/8yAADAkRBnAwAA9C2E8I3qaZGSU6C9WyLBzDm3zUZCCASdh1EX4GutWasAAACnQpwNAADQt7oryAez5pRSXeRbx6PE2Xt2K87eervwMfX0Vx6YAAAAZ0OcDQAA0Ld6FKTW+oOjGusWzPU/QZ3vnone2SXunKaJvXYM9dMY3zjrAQAAdo44GwAAoG91qaYx5oPBVh2UL6y1ZGc7Vxfsa63HcaTZyDHEGLXW4pSkOhsAAJwKcTYAAEDfvtRs5PrfoLwYhoG2FfsnDgni7GPw3rdZtrWWPQsAAE6FOBsAAKBvojr7g9lWnYqWLPtTvxlfJeLs0mxk643CW8TJuJTez/O89aYBAAD8FHE2AABA3+qc67OlmiJBIxLthYizh2Fg33VEnMI5Z+dcW5c9jiNtfwAAvVs+9XjYCI8jzgYAAOhP/Y2/Hg331VGQ1IHulrgDFE3PaRHTNe+9UkoUZX+wpxAAAL/0SGxNtI37iLMBAAD6Nk1TXYr7wThb9M723n/qN+Or6h23VGdzZ9ijEEKbZbM4AQA4gJRSCOH+Ai3fXrCKOBsAAKBv3vsl6vps72xRnW2tbf8Otxk71DYb8d6zp3au7TEyTZPoMWKMoS4bAHAA8zwPw2CMMcaUmdVbbxF6QpwNAADQt7o6u46z348vjTEiziYS7UJbne29p89yX1ZnP97vgc7pCQDohXNOPH7Ew2R4HHE2AABA3+rqbKXU96qztdbcY3RhdRQkcXYvcs4hhHb2o3OOExAAcAApJWutUkok2kqpcRz5sMOfiLMBAAD6Jub+iV4E79wSiN7Zn50zie+pDwmqs7vTzn4sWfbW2wUAwMd477XW7dqtUso5x5cW3EecDQAA0DeRXX6wpEXE2cMwfOo343tyzuKQcM7x9G4v2tmPnHoAgEOKMYqajKV+YhzHrbcOu0acDQAA0Lf6TsAY88HfLEpmqM7uRVudTbORHWpnP672y7bWsu8AAIcUYxSTWpYvtLdGH7M8jytxNgAAQO9EDfUHv+W3Nxh0PNgnsdNF7+xSnU0kumc5Z9GqnjMOAHAGpY/2/U9AImwIxNkAAAB9E3H2B1PLNs7WWn/ql+N7xCFBs5GdSymtPm1NjxEAwBms1mgrpaZp2nrTsFPE2QAAAH37XnX26kg6UtH9o3d2R27VZZNlAwDOI8bYfhrSbgu3EGcDAAD0TdR1fvB7f865jbNDCJ/6/fgS0WxkGAbvPXH2TtQ7YvXu/XK5OOfYXwCAU4kxiqktl8uFAm2sIs4GAADoW12drZT6bNzc2jva8gAAIABJREFU3lfQzHf/6r2mtS6jILfeKEghhNX5V+wsAMA5tSORVwu0WfEFcTYAAEDfRHX2Z+NspkH2qI6zlVLWWhLSvck5r2bZnF8AgNNaxkLWTweO47j1dmF3iLMBAAD6VjcrUErFGD/4y9sJdcRt+ycOCaqz92ae5/a5B2PMPM9bbxoAAFvy3mut6zh7GAbKsSEQZwMAAPTNe/+9OFvMmbwwoa4H9SKE1to5573feqNw/T/2zrbcWZ2JwljAQizEQixgIRawgAUsYCEWYiEWYuF5f8y7c6YzQGnLR2jX/eNc+/RpIYQAYc1kzb9//3LOS1r2vlfu02actq8bsaVb0HUAAHAolKDNFe3dnfTAFwA5GwAAAADg3ogEaqG2fCi+cK18dsknxJ0K4S4Wbdt675GdXQl932ste9YY9DhyzrPSOa5lAAAANTCOo3hWIkEbCCBnAwAAAADcGzHj33e6P00TsrNvhzYbQVpTDegKV+e/ovd975yjIMeZGvodgXQCAABX4b3nfiM6QRu36B8HcjYAAAAAwM0QM3ihju0rXIYQIGffDi5nk9lICAEvfpdA3R5C0L49xJkeI957in61bWuMwbW8EVw7AABwMjFGka7hvcfdGBQgZwMAAAAA3JicM89eaZpmX5fklJLYvrV2x+2DXRAveJR+S6ol5eGGEJCKexUxRnERFZxzZ7bkabIbAAAAUAn0zCqPLRRMBhzI2QAAAAAANyalJAQy4W29+/YhZ9ePyM7u+x5y9lXo/LJyHQ3DcPJJGcdRNGP34rFfAAWHcs7TNEHuBwCAq5imiQpClgj9vlNccGsgZwMAAAAA3BhdqnHffE+d/Q05u354dVB6/YOcfQkpJR5aKHRdd8npyDmXzH1+RWtF+8cXdE/TZK0lDYUCQvT5j3cLAACcjHOOh4SNMUjQBgTkbAAAAACAu0LilFDKvPf77kKIX8aYHbcPdifnbK3l52sYhmmaoMSdDKWVaS17GIYLz8Wswo4V3Bztcm6txeUDAADnMwwDJWgfNMsF9wVyNgAAAADAjen7Xigv+67EzDkLSa5t2x23D3ZHyNnWWsrOhh53HLpvQwizWnYN1RenaeJupGWc/HL+fjmDSxU7hdz/y1eTOPZf7goAzmH2Ktv90lvaIP/8/Os959x1Hao+AA3kbAAAAACAG6PNcMdx3HH7KSUtZ0O/qBmdnd33fYwRZ+0cyHNZa9nGmHEcKzkL4zjqVRcw0dbeTQUYtm6hkuENwMmcOfJPkLZf2toWEfxDioN2uSEjQRv8g5wNAAAAAHBrQgjrmtSHbxRazuaKOcSLGtDJkrNy9lXN+zVEHtlBcabP0dLtjw8SHRostG0LMxYAwGncd3J1UMv7vucPVmEAdd/uAp8AORsAAAAA4N70fU95K5T++fkGxUuCdtpFomLNCDmbSkH+uFJ5Djnn2fTetm1r07L/qUjYD8rZ/EYXY1zRsodhuLCdAIAb8Z60eqEgewstuCRok6gNvxHwD3I2AAAAAMAXEEIYx/Gg/MGj7bnBvoiEepiNnMaSll3tWzcfJz+egKzvcs1fGdVf7pYt/FoUBADw79+/GGNKKYQQY5ymKYTQ9/2hBRiccyVBu23bruswq/lxIGcDAAAAAIA1tNDjnLu6UWARmI1cwjAM2mPEGFOPlq1NafjCi7Ztf3aQUG1Mce66rvvZDlmHBlKMcRgG770x5peLiALwfaxf0SmlYRistRQQ5TfPvWodz+rU5DdSqOrxCi4BcjYAAAAAAFhDW8paa69uFFjDe89lSu99CIHeD5HNdATTNOncXmtt5Ym9fJw09bl7n8OsnxIKY64jnGq6ruv7vox23GTAr1HJmP+8GSEEilFZa6dpSinFGGnxH2Vhk7udKMxYcM4d1xUpJWstCkKCAuRsAAAAAACwhnaVPfSNBXyOSKjncjbYnaXc3so7XFd5/U0TIW0RQ3bzV7erUnLO4zguKVlXtw6Aa6CEZefcLnd+Eo7JwWM2rkYuH7uHS0W5RQrslcfE7FUvODoK2HUdV9Jxz/lxIGcDAAAAAIA1KCNGvLRUnnb643A5mywmcb4OIoQwq2XXb7+QcxZyNl8nXrkWvxcxRtEJkEhWTn3OedZknHhaMHN2y09H2odDUVQ2/mRT4N8X9eHSgbxxgMMwlNsIGe5/0rAQAvl4kKWGvh15751z1lpr7Y6eSDFGPdPbjjFmL6eRFUQszVr7m4uKAAE5GwAAAAAArDG7GB+vEDXTdV05U8Vs5OpGfRvkHay17Lssf9ZC/O8MkqJY6Tvbb97cnkp4lHyqpf/COSGcJW36DQkSMvcKP9UhSwdLydHTNK3rxbPL1z5pTDGkJkWbTD/KF/h9m1Kn91pKIryntkOa+zmPD5qOlgRt59zs7fqnBvAvAzkbAAAAAAA8Qa/HPyENB2xEl/jjcrYxxnuPikk7EkKgJc/6xf4uWvY/ZX/cNM2vDZJZx3PvPaQQIuecUpqmqeu6dZ+Bvu93zHU9CDqcGOOSgQPQ1HxadRv2ClHEGMk/mob9+mxH30ittW8PMG1dZYzhiq2uZbLXZExP87ZwmpBdiDFS3nrzt/iMPq9hTIKTgZwNAAAAAACeoBM527at307hNxFyNr3v/ZpSeRyzGihxLyWURAHe/l/LSuaXCWGtxW3t359Btvf+qflA27ZvWCuU7Q/D0Pf9MAzDMIzjeETGdM6ZFlLwInKU9Dprc3yjSxgcgXZhWg9S7ihnl4kWvzO3bcv1Yi06W2t3GbRLcnaxPREuH957KhH5+a5fgiew04X8O+uKgAByNgAAAAAAeI5elX+jRNSfIqUkTha8s3dEa6A3vRxSSkI0+amU1dmwxIemt7dDq2Ck/D5Nx26axjk3DMM0TS9JaVTjbsnWgDQy7/0nQ7G0h0TzrutWRPlfO+OfULnQn3M+SNVdT3/W6dLGmPceuGRMLy49YeNzaGnuWfMlCvxYa8nlo+u6YRiunVHwGwjZqV3YGHAhkLMBAAAAAMBztIoHv5Fq4S+l8M7ekZXU7Prz34XkIZIKf03O1hLnjqrQTaEadEsjXPTVq2nsZFqy4r6tny9v37VSSn3fz2pzei8/ftJvhzhf5OpOKwkoxPLJAgudmt08m+roh4Ix5r17Kc2yuJytrbF3l7P5b3WhVzqW/EdKqYbrpRSELA7aV7cIXAPkbAAAAAAA8JzZFbU1vNgAgTAbaZoGcvZeLGWV7lWM60yEg5Ax5nd8NnZUoL4GvaqjUYmiRT57daj0ff803VtDvv9P9yUeQ9M0bRGyC4jL3pSc8zAMs4O267r3nnqzhhvrKfw6O/s9dXXW0s05J+5LOWcRcyr3rs/nY1rNr1MpFp2AuejPAjkbAAAAAABsQmh5xhi8QlRIzllnZ9efO3wLZrOz76hl/5sTbn5Hz9US2I+bTqSUyGBEl6Fr29YYY4yh7Neu617yWNfRtVfZOCxzzk8TwOlY9DH+TiBnBW7SQnm4IYRpmirsnFKhdH3kvGqFn1KaXbSx/it9I33vZjJr5a8HvzCJolG94/NdNOMTpfi4+aGY5HxSexPcGsjZAAAAAABgE/q1DTm/FSISrChV7deq/B2HUELvWzzwpy5nLqzohSZvp2YLveaISobnQKnZRc4ulRLJLZdqvo3j+EYvafsCocQ9tTchqe5pf4YQtFTNaz8W299xHPkd0hjzrdE+rlBv+T6ZtOiamZfcGZauJsq+3+JaM7uMYOUi1XeGZkOB3F3kbKHPNk2z0u1Ccd5XzhZZC9WaUAn77NID97rxgg+BnA0AAAAAADahhQks066QGKMo8Qc5e0fKknBKe7/vy7PONP9iObugl+rTBXLoebzFICFVzlrb9z1Vg6T6b29UWivHG2OclR2LuBxCoCzgcRz7vicH5Ff1xNJ+kV1O/2uMIUtlrsqJZ5motvc7lDOVUpp1UqI+rKfU3np0RPDquhm98aVoJb+itZytR6y+A2iHHBGJWUqLnl3usOOtm8JCfADUufyonCwaopjh/CaQswEAAAAAwCa0RyQsCytELEYmNWccx9/Ua46AFuNf3YpPEVJjtVl4bzN7jrT2pN1pf5Oc8ziOIYQQQt/3Ymy855+gFVJSx0IIS32unzJCqFq69Mp45jnmdOvTPxGxHD34v+ACX0FkKI/juJ4jX0mVVIpYrLRT8FKYSudHbxz2eizxX+Wc6Zpaf/7OJoYv7X09O5uu4n8fjGGdoN33/crWLhkbFFcuVzrk7N8EcjYAAAAAANiETuess0zQjyPyvEp2dg16BKiHnDO/lq21V7focFJKOln4W40m3iOEoHM/KST2ajzsPaN5LWdvXwPU9z25e3dd1/f9SgwvpSQEux+M9qWUxnHcUjZTnLXzHyUxxpfKe24fb3wXQtPfOOZ1hIyMerz3fLXB+taW1jF473XgR1yh5JZTvOOpAeM4kq/OxsPniARt4uglLK/CAwBvx9vA3YGcDQAAAAAAtiJectq2vbpFQCLMRqy1VAqyqndRcDnCY71pmq9X9IpRDL86fva60AdODtozomDTvOGrM2tO9XQj2w0flg4qpfR0L9rb4deiGiGE7QLxtXYTWmguA4OiFzHGpe9sH7ohBLGFjTeH7f4n654tS5Utybye/OtTSrNHSgGn2Z+/p/POKtpVuY7waNndjb/A20DOBgAAAAAAWxGJSJCz66G8y4mkSDLD/QVbZPASwpSmbduvlwP0Ivq9RMwv6DoyWxD208R7fixadHuqSs/mqB5RoUELl79jOEP1Hl9y7bjQO3vWKpqfMm7UPqtot2275fE3TZMee0+zm2eXICyxLgeLCqV78Xax4tlBwjvk2psej0hVa/ANjgZyNgAAAAAA2IpeCf71GZ23Q7hwGmP6vv+13MMLqVbZFA3T0iFX9Ko9ik8Qx2uMOej2JdzVb9GZs/mYJIe9d/cQW9vivzybYWqM2bcDRTnQtm3fPsbb8VJS9glXylO0lUfTNFREVH+ZjKpn5e+nivasbk5pv9M0kds7Jf6TSQuVS93YgeSGIYaxHtVPTczf4JOiCNr7vhIX9X/sfoVSkL8M5GwAAAAAALAVnYsEy8LayDmLUpCQs4Hm18xGhAlPc0DO6TiOfd93XWetJf/c/o/6+7ZIVzzn0Tn39q1DOxGvf18bgBC7G8LooOwvpHbmnL33T5Oy27adjWpc0kXjOOoGd123fjXNGm1vaf/TpHVjjLX2pcT25sXFDaRozy6SeIMl3X8jujxmU82Ur1zFNGIxw/lNIGcDAAAAAICtxBjFu40x5upGgQdE7iGZjeBlDwi0nP3dfgs8zZOkoo1Cj9ZSl9TVlcxKY4zIH6wkyZEQNw3Ce/+JFiZyV9fLLcYYV7yDd+yr4qlStj+bcFrV2dmFYRhmFVIKWozjGEIYx5FuAjot95P7gzjvs307+6HWUr33WyJDKSUxnvXw03ukhN/PdWTq0hhjCOGNqhUxxhIVe0nXpnUG9BOqBvk0H3z9c+pJfWFeFf7h7eStMsZ898MLLAE5GwAAAAAAbCXnrF+ivt6j4HaIUpB93+NlDwiEKU3z1dnZOs1wd69w3Z9abKq2h8WSDuJDw32tRS4ZRHRdt+IaPOt08fa500LtL4T6lnyZKa1Vd+ZsgvNLfg7FkcN7b60NIWw/ZfRNbWbtnNt+BenM7i0nmhLYP0yO3sv4gjK1qcwj/dGwxRPiPA7DEGPMOZM1yo63mllHe3Etnzzx4z7pbdtuqTELvhLI2QAAAAAAYCs6O7v59qTO25FS4mcHcjaYRZtvVCu2fo6oe0nXxY7bn1V8jtO5dkf3T/OxGYt2PS6uCznnGKP3nuTOp/22VyVbMeYpi/brhbAlFxfv/cpzQa/e2F6Tc7Yq46v1NsXAeNX3JqUk2r/FteZpcGULOz5tSZ4ehqHve+ecWFhQ6Pv+pWhBSumlu70Oh7xXHnYvRHu0/8nXX9SAgJwNAAAAAAC2opP4dk9yBB9Ckk05TdbaYRj20oPA1yBWWrRte3WLdobfl7S0+t4VMetKMQzDRv2rEttZzZITxSeZy7MSP1mKv1rvbq8E6p+qAFnG6myFwy2RFV0qY6OCuRSiEDGk9ZmDSA9/I7gimrFxrpJzHseRhGORpq0nP7NXzXFxwZRSCEFfPi/dWLz3xphX/abFLYJyol8/gn3ouq40xhiD6c3PAjkbAAAAAAC8gH6VQuZvVYgMeucc5Gwwyxtaz00RuuqOjv9L+ZKzaLeESvqcpGd9IGRisNGBV0PC2cbOWeHz2EPOWRT6I3PhNzZ7O/Qp2H7g4rcbT8SSDXrTNBsHj84NfyMU9LYc/+8vLXqaJrKx7rrOe++9p2AMVXmdNXxv2/boGZEOzm03s+aLt15dmqAP9pL4HAn6ZXj8wgILsATkbAAAAAAA8AJbXmnwdnEh63I2Ts0vIwQ+EZr61rGhLZJ2ySskX4LmRV61XDgUkcC+pMsvWdNuGTBbvEQIYwz5LOt/+rD0nJYd27a9qpzdyWjPDefc9p+LFOmNOrjWW8vg37hfbZz9hnKqL/z3kvFXwjlaMW+OD/Dr7t2eui6ux77vU0pkur3yq5TSNE362mzb9vz1DeRvfmEDQD1AzgYAAAAAAC8wjqN4pdkx1RF8jniHpzwyvPIBjZAnvjWFv+97cb/6PKlQq4QFy5j9woee1MexVDCwaRrn3NvDY9YeQdB1HYmAsxU1P4mYzu79dwwKPozliMf9xqGrK682f2UntzdbDEUyOt/e8n9z5QGOyMd/WiZxd7TWv/2c6mvBOWeMoXKdVEMyxhhjJAm773uy7dZXZfn5yXFQfgizdWLB7wA5GwAAAAAAvIAuGgY5uyr4amKSAGA2AjRCN/xisxFh+bqlItw62gmhbJwnMpNfgU55rtmmPMZIVuCzxiNvK0cppdlMdvJt4CqnsHQn3o7GUUqprgL6I6nZ/+YyeV+Ss8XPt/+WzjhdJuRR/tLg0VU6mtdTcUUcq2Gu1jve64RAfILZiL6rbD8v21dLbKFtW2PMmctNuGUQrec4bdegQiBnAwAAAAB8IYcqU1qYQPJvPXAhoMjZ9fgbgErQ+cVfmebGozvNWzmemlkvhVmb6X8LSu7G8NJs5ckPG7+FEMKs7EUpnO9tM+ccQqBMT2OMc27Jw0Tv942dLpXofGqZLQx51r+wIwdtVp/Hl8I5ogNfUg9zzjHGEMJ7hzbrfrOxiOW/uRTmgyJ24uo+Qd7VGffb72lLPjBvQJUwz3FPKieOLxf4ZMkI+A4gZwMAAAAAfAmnJVfqpKffSXarHyFTQs4GS/ALuW3br5SzxTEaY141HND31dnU7JXN6lTTz827n6quK9/fuP1xHLXJwC657SmllY1oP4R10WophCD6nHLnP5HjN3740haORpuDPe1P/luxsuFk9XBW0XbOjeM4TVOMkZK+aTiRS8Y4jrPBGDr7RzRSXCMnLFbTJirbdxpCWHEOeQmSs8/Mjw4h8DGJLAoAORsAAAAA4N7EGPu+n33PPOj9WSQ8Nio56FtdC+pE9LaWs5eGB/hxhOgjPB8ubNheaGcka61Q7d/QebWy81QiF0mRbzgSkFQ3DIP3/rTLOaWklcGDZMGCLtv40vHGGEmw06f+O0b1q2j5Usj6S0q9+OHR532WaZqW5Fd6zBljKNl/yZ+dhsFxScT6Ajk6ePxh/RJdGfVVKCnbOee93/1gly7SlBIt7KA26Ds5+EEgZwMAAAAA3BKa9McY6S2Oko/Omd9rmwLYZ9dDSom/2JOcjexsINApw9+X7KZX5X+eSzhbq/Dp9SVa8qpEm3MWBdDeXnLxhnzP/WqJQ5fjfKIPio7it8H3YgBUEI84IopwgsJeJgliBPZ9vzRhCCHo9PbPC6i+R8652HC/SvvHcY0XavvnXkZP0Wfzjdva0+qsuiepYuQwDJQUf2ZwiFuxU2Pgmg3+Qc4GAAAAALg1wvfjnPyp2UpoyP+tBJFVR++fkLOBQMuyl2RfHoqWs191GtHotSlbgnnawvvV0ONsbcbTIhDC9oEMgg/Ss3Qm+/bDXLIG9t5v7HAyNBiGoeu6rutKtJi2c3RZ3eMWVM3KwVQVcxgGsuyYpmkYBh29aE6pcLjOkp/7OkWBPa5hQs621h63L0KXgnwjj6HME7qu897Tee/73nvv/iCne++99774uhxxREstLH/zMblLOV/wHUDOBgAAAAC4MeIF7zQ5W6//RbJMJdCaXP52PY4jluUCgdaGvu8S1qvyP5ezp2nSktmrvzLGvHRJLiUdv3HDJzX2DWXKWstFtOOeNTrQstEGZ0m0bVhR3JJYSm7LxXCZTC3EMc7yxlKkGqS3WRNtflArXfe0fqbmuFCH955au3SmKI+YzmbXdUer8Nq444TTzcM2b1+JFMDYt2FHEGPkg9Nae4tmgxOAnA0AAAAAcGNE+iElzZ2wX63pnJCUBLaA7GywBS1nfy711obO8/08tXbWbOSpvCLExDccCWYdhNu2fUk7oyRxUgMpM3d7hwjZzhhzUJ6yzn/fODJF6cLj+FyvvETgnqZJl3Feh5w6alMPKQgRQogxDsNAGnfXddM0USpxKQ55QmOOiJlxloYKxbeOuwwrIecsHlUoPA4KkLMBAAAAAG6M0FZOWxGs8+B2kYrALvDXP8pJRHY2EIQQxCX8fYNEyNm72NrOWi2tb1kvZ3nV/YDsg2cFxw99pcmGe/3U55y1UnycH/Hbru7USGK2r3ZhNhn2JXk650xmJpdEGYdh2JKE3jQNGU3UpmXPQun2V+2a3xBejTB9st9feLLTfY+GqzGm67oa1jqASoCcDQAAAABwY0Tdv+YsD+tZTef7sjtvCpezrbXe+2+NNKy82eKl9ykiVfPLUvi1iLxXWh95126UXFNKQlV/z/M6xjiraG+/687etIsGRxa6emshhKXE8IOkJZ3uutFOgRI5rbXvlQ3UGGOKlTA5C+9Sb5mK2pE29+Gm3iOlNI4jHRp37TB/kE3HLYTsGuAP3Dds8X+Z9RsIv3OSXxAe64ADORsAAAAA4MYIo+RmcyLb5+hly3jZqAGh4pEi82VK5SwYe6/CL2FjzPd1oNB/95KzZz2aKVtZFEictb94uxm6suWryvjTYnpt247jSOUBQwhLlRWJg+Ts99zJieKFTULt+pHO/k16rljUsuNhxhjJ3JniAdfemXPOIYRpmsg9nOw7Qgjfdys4lJQS3UuPW7Lw9egh573n5R+/3lYFvAHkbAAAAACAeyMkG/E2deh7qc7a+wXZtHKEpcCrDrm3AGrLLuxST+wp4mSdee7EvXHHWpfTNM2qpZRCSAa+fd9rc48PY34hBEqqpWTqLde1kNdXFN7tUHL6cQv/9ZNFq/bruyahthgrk7cyicgE/W3/KMnpRz/CUko8GxoZ0F/DaW7dv4C20YNlNtBAzgYAAAAAuB/lTV7boZ75erxFdAAnI/xnyGwEYQYwm/5Wxsn3OQVps5Ed5eycc9/33KhhC68mGO4uFlNq8PYGL0Fy8HGJqDor/JNwC3VjznmapmEYyDNkGAbKR6aU5De6+lW/bPqjpPaTmI4nJgCCYRiEHfmOt27wTUDOBgAAAAC4N5d4ZxPabwQFIS9Hy9l933+9nB1C6Pt+HEckbm+nyNm71EiskOPkbIL8rDcKxMaYGmIGMcZpmp66jixRMpr7vj/uWtNZ5N80RGnRQPEbOcLSBIA7QmFCccNB+UewBORsAAAAAIB7IxbUH53tJd4r9Gp6yNnnw09KjJFnNlF29ncvgubOD845JDxuhyrCfes1S/fGIjcfsVw9pcQ9Xmex1nIj5hooOcIbCydSOjY5Sp8gLWn77G9Kz+RiPbkoQK0DIMaoF/x573F1gCUgZwMAAAAA3BuRzHJyJSItZ6MU0rUIP4FfKAUpUk2L8oXX4B+HBgZ5JR8nieacqfagqC5IeYV939cZXylWvyklqgdIXhxd13VdV0ylyad7HMeTYx7Cb2Tp3N3xGhcFnKFogx9EDPhxHEVcja6LpSggrhfwD3I2AAAAAMDdEdnZJxfMGcdRZCZ+06rwOxJC+Ck5W9vsfmuu8U25UHfo+75o2R/eG58eRc45xhhCGMeRKgq+58hcA3Qs1P7TDmHd2/3LCsGJIDRqQoKfhaI7YhqJ2o9gC5CzAQAAAADuzdH+sE/RCdpfLJ7WT0qJvxk6527tJrGupgntvvmsZBwo8G7fImjq71DOctd1xhhK7925iRsQFsxLC0duKjr/At57a20NnuNPmb0Elr6sg3DOOYxD8FPQM0KbHbVte46pEbg7kLMBAAAAAO6NkLPPT/IKIYi3kaW0GryfnICQs6lo233lbAEfQsMwCC3bGINQyjnMincppWmaxnEchkFHuay1J1e92yhnA3AmIQR+ddACAngEg6+Hj/AQgnbKbqopmQtuAeRsAAAAAIB7I2SjS4TLdb8RvKWfyayc/X0r2XWxuLZtv0a1vxExxmEYvPez2oTgZJ0ihMBT/7quw70IXIu25zLGWGu/7xYNwL+F6V+MUcc7jTF93yMgDbYDORsAAAAA4N4IFakGObtpGshGVyGS5ekV8ct03mmauEzZti3MZ88h5zxNU9d1VDPQe6+Xii/Rtu1SXa/j4KKJMQb3JXA+KSXvPRmn6GcllTfAyATfTYzRe0+VZvVTo+u6L5ulgBOAnA0AAAAAcG9Eksv5glHOWb+cIMXmKkR29vfJ2cJBommacRwhBh0HFQYkPW5WidjIJfEGXk6wbVvcl8CZpJSGYVhauEA2I865b7o/A6ARBjscMsc/f+IKvgDI2QAAAAAA90aoS5e0gWtGRWG8pCUgxsiHhDFmGIZbZy4XqTrG2HWdGGmo/XgcKaW+740xb0jYZKHQNI1zruu6JT/9o+HeDm3b4r4EjoaH1tYdeCDkgV8gpTT7BCGbbISiwdtAzgYAAAAAuDfiPeGSd4NhGMSLivf+/GbZgQqJAAAgAElEQVSAfypZvm3br/HO1tqQc25dDMKr8qvEGPu+996P4+i9194I6xhjyIQkhJBzvrz/hUmrc+7yJoEfQfv788uk73sI2eAXyDmLjAeyq8L4Bx8CORsAAAAA4N5wsaZt20vaEGMUr+tt20I2Ogfdz18pZ+sVAE+1bLCRlFJKaRzHWW/fdfG6+fNMIIWiwqv+qX12hW3+Tb7sRCylZnvvceMCvwYtroJHNtgRyNkAAAAAAPeG2y8YY65qhn51H4bhqsb8Mjo723tfs5y9pGHxz7VfdnORF3OF8I562pniC9M0vSphN01jrbXWkio3TdM4jjWfC2FQAzEFnEMp/1gumWEY4N4OAAC7ADkbAAAAAODe9H1fg5ytBUfnnPjOlyXf1Ynwzqa02btIeHqExBiHYdB6K4IlW66mpe+EEIZh0EbkK1AKNulxKaUbXcvFPpsO4SoXb/Cb5Jy7rkM6NgAA7AvkbAAAAACAeyPq/ol/PU11yjlr/eucXQNOSomfBWNM5dnZ68xKrtCy3yPnnFLarmJTOcdhGKhg3U0lOVqvQIo2HdHVLQK/xU0vHAAAqBnI2QAAAAAAN0Zol9cqNcLdGHL2JaSUeC7zfb2zKatRa6xd113dtJuRc44xliTlpzjnjDHjOMYYb5SFvULf9yVB21r7HQcFagPjCgAATgNyNgAAAADAjck5c4lK+3ucyTAMQheDT+j5pJREwv4ds7NntWzyAYdmtBFyte77fqkknehbGiokYX9ZJ8cYS0HItm355fBlRwoAAAD8ApCzAQAAAABuTM65yDTN1dnZWjW7nYr6BYgIxx2zs6k+odZb4TGykZQSt9RfV7Gdc33ff00i9hLe+3JdIEEbAAAAuDWQswEAAAAAboYQYngS64WlIP8ps5Hm6mzxn4VrwfcqBfnv378Yo1Zdyfvi6qbVDhV49N7rYIBWsa21P1WhLoTAwzwoCAkAAADcF8jZAAAAAAA3JufMc6KvlY+FYNRcnS3+mwjv7KZpvPd3kbNTSjrH3xgD15oVyBfbe89NZmYxxjjnhmH4HRWbUwpCNkj2BwAAAO4M5GwAAAAAgBtTVSlI4XxCmtFdhNSvQZwF8puu9izwpQYiNlMU2PMbf7ITxdPdLX0hxtj3/VMVm+4MwzD8eFRAF8NEyj8AAABwRyBnAwAAAADcmGmahPZ3rSesLt/nvedfgGXtQZSOFaUga5OzVwaAtns2xtzL9XsLGy+Bpa/lnFNK4zh2XSfEWY1zruu6YRhw3RHcQZtYUvnRYwAAAEC1QM4GAAAAALgxMUaeinu5nB1C0Gmhv+lscBXCe5q8sysXhVNKeuQ0NRkcn3NZre8l50ymIk9V7ObPbRyarCDnPBs1QZo2AAAAcCMgZwMAAAAA3Bjhz3C5V7VIDSY59cctDk5GJOw3TVO5nD2O46xdRt/3UGOJEMIWa+ymacgaO8aIGNISOWfdk5ffOQEAAACwHcjZAAAAAAA3Rhgli1KQl6iB2m+kHqeLX0DL2c65aZoqlIZTSnq0FC376tZdDGWsT9O01EUcY4z3HunYG4kxCpd2Y8zVjQIAAADAViBnAwAAAADcmJSSMBu5PCtzHEehtQ3DcG2Tfgrt2kFy9tXtmsF7r5VZa22drT2NnHMIYUsuNnXXOI6XX/V1si7uj+NorW3b1lqL8AkAAABwIyBnAwAAAADcGGGU3DTN5VKgzg4W1SDBoYQQuLdytd7ZOuxBQ6UqZfa4ZGe9ZVKxnXNbrLG7rhvHcZqmT5x8Yox93/+ybXTOGVZIAAAAwO2AnA0AAAAAcGO0Jni5cKkVdmMMNKPTENnZZENRm9+Lzj5u27bv+3q07BjjMAze+77vD72mSMUehoEyhZf0a/qntm2dc7sI0KUiYtu23nu4lAjQIQAAAEC1QM4GAAAAALgxRZMq1ODsod1+a2jVjyDCCUXOPl+eW9qjyB8nRfXMHOHZzGj+v7o65foA3ti34msppXEchYnzEsaYruv2CgvN1gvdZcsAAAAAAEcDORsAAAAA4MZw42yiBhNY7YkMv5HTEEplJdnZRcld8hi5tnmcYRh0C0WR1SWeCuVU4LHv+67rtrhjU+p0jHHfaMTsMV6+sAMAAAAAYAuQswEAAAAA7kpKSStiNdh66NzPjWog+BydnU12GTWYJ+i87OaUAIw+9pTSrLHJrM7bKMH9jc6cpmmjhE0qtrV2GIaD3FdyzqIl1lo6qBrGCQAAAADACpCzAQAAAADuilaNK5GzU0patayhYd8KlyDFqCBP6ho6f5omPSouycvOOTvnrLV93w/DMI4jJU1rk5zCq245VGMwpUQe3FscRdq2JWvs41Rs3jzRpKoS5AEAAAAAVoCcDQAAAABwV2KMWh+83FaC0Ppd13VI/DwBkV9MbhWXj4rZrOerJFQdbllPmnbObYkHUMZ3jNF7b601xqyUdhR7d84dXXOSo28dZ3qXAwAAAAB8AuRsAAAAAIAbo2W4Gryz/83ZZzdI0D4FIRyT2cj5cjYPXYzjOJuXfXQO8hJLjiJLWvPTduac+76n9OqXtmytJWvscw68oBd2wDgbAAAAAHcBcjYAAAAAwI3R9ghd113dqH//Fir+verYAN6gEjmbt0enQl8rnuoCqku0bbuStjxNk3POObfREZtwznnvx3HcvcDjdoTBeoPsbAAAAADcB8jZAAAAAAA3RmiXzrmrMl4Fs2UqURDyBERevDHmKrORlJLOg27b9nLnk+3qs5bdc87jOPZ9v10TLyeC4go1WO5ouxV4ZwMAAADgLkDOBgAAAAC4MSGEIqu1bVuJlk3MJmiLFtYg7X0Zfd+LPu+67ohsaH7u9HkMIczWPzw/C1i3TXfRLGIxARV13C6Ft21LptjDMEzTVNW1GUKAnA0AAACAmwI5GwAAAADg3lAO7DAMVellhM5ghd/I0Qj/mZNLQZJ2PGuW3bZtJQbN2jl6VoymZGrKxZ6V5mcpEjZVhrz6WBcR1yYuTAAAAADcBcjZAAAAAADfzLXpz7NpsLOF75CmvReiz9u2dc4VOfuEfo4x6hTmruvqKQSqHec/xBhDpi4X2mG/ihDoIWcDAAAA4C5AzgYAAAAAAEcx66Bdj6z5lejSi97709Kic846Jb/rukrylHPO+2rZlPmec76Lil0QHuswGwEAAADAXYCcDQAAAAAADkQ7aPd9f3WjvhnR4VSB8Bw5e5omrWUbY+rRsoWG+x7kJTIMw+U1LT9BVOk0xtxOkQcAAADAbwI5GwAAAADgltxFe5pN0L61Dlg5WqY8R3idrfxZj8dI3/fbqziuQI4iVx/NDghTGmvt1S0CAAAAANgE5GwAAAAAAHAs2t7BOXd1o74WIVOSnH10dvZs7ceu6yoJukzTpJv3Bl3XXX0ou6E91svJquSsAQAAAADMAjkbAAAAAAAcyzRNWhlEgvZBaDm77/uDEopzzjHGWTdq730lqmhKyTm3S2r2N8nZ+qq8ukUAAAAAAJvArAUAAAAAAByOc05oZ/Dq3QvRjcL0w1rb9/0nwQO+ffG3c05nPbdtW5U9es55l9Ts5rts38U4wYIJAAAAANwFyNkAAAAAAOBwZhO0v0kcrActUw7DsHt2dghhNim7aZpxHPfd14cUOVuI2rNCvLXWGDMrf1trK6lpuQvCY/2bEs8BAAAA8N1AzgYAAAAAAIeTc9b6YNu2R3s6/yAicmCtHcdxdzlbWJqUE1pniCKE4L3vus5aa6313o/jmFKKMaaUxnH03k/TRL1En4cQpmmy1tKhGWO+zB4nxijCHle3CAAAAABgE5CzAQAAAADAGRRlkOO9v7pd30YIQcjZ0zTtm1bc9/1s/nL9ZzPn/JLFTc55mqaidH8TQs42xlzdIgAAAACATUDOBgAAAAAAZxBCmLV3oKRX+GjvhcjONsZQJvKOuxA+FYUvy1/+blJK4kq8ukUAAAAAAJuAnA0AAAAAAE5iVgat057ivujs7N3l7JSSjkwMw7DjLsBBlLiRkLObBi+GAAAAALgHmLUAAAAAAICTyDkbY7Si/U0V9i5He2d/WApyNnE+peSca/7KJ9ZW/hE8RYQ9RHY2VksAAAAAoFogZwMAAAAAgPNAgvbRjOPI+5bMRo6wfk4p9X0fQoD0eUdEdda2bRFVAgAAAMAtgJwNAAAAAHBvuJhYv7CYUuq6TsjZs2Xo6j+WOun7ft/s7L1474Q+/RXGyXtAzgYAAADATYGcDQAAAABwM+6u3wk3DKIGvfU7EHK2c2537+x9OWg83/0yORphNtLAOxsAAAAANwGzFgAAAACA76RaOS/GqAsJwm9kL4SdSz3Z2R9yr1UI9SOiSsI7GwAAAACgWiBnAwAAAACAU8k5UxVBobpCo3wP0W9fIGd/MhIwijYisrNnDX8AAAAAACoEcjYAAAAAADib2YKQXddd3a5vQGTdGmP6vr/EbGRWWYbcXAn6GpymqfwrThMAAAAAqgVyNgAAAAAAOIolUWw2Qbtt23EcT27h9yG8s9u27bquZu/sLeScU0oppWmaKNkc3iMfIsIeWB4BAAAAgLsAORsAAAAA4N4UEepeybAxRp2gDU3tc7z3oku7rqvQbISf6BDCMAzTNIUQQgh933vvnXNd1znnrLXOOWOMMaa4rhtjvPchBAyY99By9tUtAgAAAADYBORsAAAAAIC7knMehsF7770fhuF2ul7XdVrRRk3IDxFytnPucu/snHNJry5qdcE5p0uDbsc51/d9uRC89+M4QuZ+yjiOohuvbhEAAAAAwCYgZwMAAAAA3JUQAtcB+76/l4Qn8kOJtm3v7oxxLULONsZslLN3HzwxRkq4Hsex67q2bT+Rrd+AsrkpubvruhDCEYd5U7THOq47AAAAANwCyNkAAAAAADej6HExRmNMEaTatiXB7i7knK21QoK01kJW+wQtZ79RCnLdmVr8K6Vd55xJv04pxRj7vueDsxJI19YW7Ssa97fK38JjvWkaONcDAAAA4BZAzgYAAAAAuCspJeHX0XXd1Y16jVm/kSLKf6uSeChCprTWcjn7wy6d/gghpJT6vrfWkqu1tZaCE9zhulqcc+M4rpQq/aSXboGWs6dpurpRAAAAAADPgZwNAAAAAHBXdHazc+5eSpww8C1HcXW7boyQKSk7+/NRIRKuycRjV4X5Atq2pZKSv7AgQIyBYRhEV9xrbQcAAAAAfhbI2QAAAAAAN0ZkN2sD3MrV7ZSStqQwxlxbuvDWaLORruvek2tzziEE7/0tEq4/wTn3a2Ku8M7uuq7yewUAAAAAAAE5GwAAAADgxoQQuBxsjLmdJjVrsvyG3TMgnHO8J9u2fVvOnrWCOQFyuHbO0R9934/jSPUkxddKsUdr7eelJodh2P10VIvIzr6dTxEAAAAAfhbI2QAAAAAA90bIl7dLMs05i4TiIlbeTpq/HO0/07atc+7VbHdty74XRXG21pJgba0dhiGEME0TKdcr5z2lFEIg5276hA6NKlJSOcqifdOWXzqQHzEe+afuG3phBwAAAABAnUDOBgAAAAC4N0Ktu6NNR4xR59VaayFnv4pIuW3+srO3jIqU0jRN3vu9hOwiWHddNwzDMAxFej6+Jx546bi07cb3jcOcs1gS0bYt5GwAAAAA3ALI2QCAQ1h58fu+d0IAALgWIdJN03R1i14m5yxyRYlxHK9u2p0Yx1HbtpA+uy5nk0H2K0r1AxSKIN8PYwylWtcZVtFy/yxfn6MdYxSHjOxsAAAAQFPkC0gcVQE5GwAAAADg3tzdbOTfv38ppXEctaoIP9+X6Lpu1jx6xWwk5zwMw3uW013XjeMYY4wxkvtHtSp2Iee8MUfbWlv5sWxh6QV7Vta/YyQMAAAAAD8I5GwAwJ4svTUhXAkAAMchEnJFObs678C6VeM4zoqqWp2v84guJ6UkXLO5MrsU5HgpKZsqLjrnSMW+6YnQ9uIrx3tTRXvLqZmtv3pC2wAAAAAAPgRyNgAAAADAjQkhCE1KyNl3YclvxBhzU9n0ZFZsNIwxRZZNKVE+9Us1EslChE7EF5wOOvwtovYX1yPVkQx4+wAAAADgFkDOBgAAAAC4MVqTum+KZUpp1voZKtsWZoMBRNu20zTFGMdxdM61bfuSu8jGSpK3g4xWnh7+fS8ozTiOVJZz1ma9eGd/q4IPAAAAvEfOue97PiPFs/JaIGcDAI4Fd3kAADgUnWF6a/Vt1vvCWosidevknNcV6r7vt+di856/oxX7S4QQViIBxHd0Arenp6Kd4lxjzgYAAAAU6LGYUvLel6kCFQ65umkAcjYAAAAAwJ3p+14Ll1c36n1SSrOyrPf+6qZVTQjhvXKOGsrd7rruOzTcjUzTtNInX2A5EmNcHyFt2979GAEAAIDd6fteP0CpjgiSLS4EcjYAYDdyzjHGEMIwDN57iluGEKZp8t73fX/fslEAAFAtKSUxw76pd3ZhGIZZ3Q25MCsYY3aRs621vyZkF9az128dJfo3F/cStG2L13IAAACAMwzDrA8ePTettXefdd8XyNkAgN3w3gs7zvYP+l9jTNd10zTN/lwo3RuF742/4p/vJam/uh39/V1astIDWzrnpW7f0r1PN/LeN7fva8s23xtdG7/z9mnduKmV7X9+Eb03APb6/vaff9gzn29w+6be2PX6J/pfdTrz2xPrHTv26XGt98yS+YOQ256O3jfuGJ8MpHV2v6Xwf3rDSES/lf14CvxSMdIyhxFX1qsP3PVdv/HhS3tZqntp/ui6bnvbXvrChz/ccsg7Xps7ntaVvby0tZcezS/dxvd96H/yq3O2trLlS27vG7/8+QDY+M3Tso6OG1r7zvfeuzNvacYb31z/+S6vuudcvPteeh/uYsvZfBoMbv4ytT9/XCLz7yUgZwMA9oGKKQlJZTZTrG3bkmH36rzk7Yngqxt/W874cDJxwgP+DT6c777aJ1e9CG086fvOUK86xbvs9yAd8Mz3q4Pearb/fBemaRJC1ZIoedB5P4Il5wfv/ZlX1ifbOaidSz+Z9RzfCGVkLwWbf4qU0kpgwFq7V0nM82/+S0q9tdZae8TShzcenZ93y/Yb+O6n4JNnxC7xjw9/eObjbGW6e/Kd84hfbf/5CfeBo5+G51xHR+90C0fPB/4tXwg7Hu8J2vGHO91y4EcED1b29bS6RmHjHPWlhoEVIGcDAHZgS9BSQHWBQwghhBhjSimlFB+hfyqklMIfcQ4yNhnHcRzHaZrof+n75X/LvxbKF8ZxHIYhhMAbU/4Q+81/pJTK3ytdJJ7Nrz6G953T1PbI3N51v0nls9i3ud3bSM1tEKsgL1n2uPtx8bJ1HLqN77uvTzjonfNVllbCHvf2tZ0arrvt5JxXOvNDR47TgnN6R7MyvTFmHMdXNfpKntqXj6tDG3D50e3FyXOYXW7I9c9Prh0e50RTvvL6utdL3MknpVpI0RZr0Jcg7xE+T/jNTjsHyNkAgHcQk8WlFaxPadvWKOhpYYxxztlH6HNrLX2T/qB/ok/KZgt8m/rD0gb+t7XWOVf2XhrG90u5bPSd8s2u67z3ZBTe9z393XUdfZN/n/637/vhEVL5y9/030LZjveef2cYBtLoiwTPYwNa0C8/pL+pkaXNfI9lL9SwaZpKU8sGCdoXjxCMDP55CQBsGWZ0LCKWwGMMItJAO6Kdlp4p/UOt4r8q0Qs9qmeH+kojeWCDvqljGOKb+icb+0TLFrPxFb7TnHMZG+XYqa+oQ3jz6Pt8FKU5yuevHsV7zB41b/B6Lx3amB2/vH2bZZjpRObd5Ww9pE9g5eHylZ4Yn3TvugK79PylEheVHMKOG/l8C+M4rry1nmCifYSIMLviwRjz4Wb34jjd5JukhDpFzO0TmF2bc+xmP9njzw65Cg+8wiZVwnE985V9nlIiRXvjFMsY471fD35/ZUedDORsAMCnxBhfKj/Fv8z14iIol69xObth2rd26OZ/cMPu8hOSwmmDzZ9TJFe3yw+bv6oO9JPmUe/Wx8J/K7zC+TZL88qm9IHMdtHSF0TbRACA6+zlO7yfV45r6YhmIwT8D34qRZfy3uYBAPqbFP8i/Ze/6Z9K/ECEE3T8QzRVt5m+I7bGd1rUfNL3xSclliACFSWsUo6l/MEjGfwnfAvi+yWoUL7D/7XrOtFpOmpS/td7r2NCzrnSG+WMlyhLCeTwQxMxHh7psQrehnIg/Lh4kKPES3iEpoQieDiHjqi0hA6tzCz559Ty0u0lVMO3XOIrfKEGj3mM41hCPqT4lzgQD/bQEfGQD/2QR4D4QCrfLOd6HEc6Fn7S9U/of3l38ROtZ9je+xKroPK8vIW0Uz54RPCMj3w6ojKcypfLz3noi3qy9Bt9rYSySthJrMvhARIeI4kxLtk+0HsCbVlsh4dwlgIt/Dv/mFi/stpGb+Efi6nw325/evJ9fR4wIMuvLbR/lYvOVJ91wGk2ELWytdlA3Xo47ZMDpBvOUh/esVTmbHzofDkbL/BnclVvf99Zvjy4cl/xsYYI5UG7+zAI/fZvf5bLO41eB+hNast0yxhDK79fnR+CjUDOBgB8SoxRC6DizZlri0V2LJJZ0Z7K/9I/6XRmoetxAU6IkuI7WjTsHvXTsv2iixXhryh0Qq7lEh5tzTC02KezvLnGKoQG6tLyw6ICFy2ybIQnknOpWgvr/BTMqpDlYMUh8Ebyk6hfjIWQXZpU9sjVVfpwZeSIITQrvrdzlN6gPTYssNH8aevmMZ6hN97ORUfauQAGHUsRf/lm+c9LZ84eMv/bsHUGRXPnHagbJpq9sguCznJpf/lffghc8hYdzptXDqp8MrtrPXhmR+xKt/D+KTZ2/IyUcVs2LvbLxwBtROyRb02PMX2A5cv8Ypk9HaXlejv6ZM32MO+9ZgOleeKI2rkrdyPrbeD9zLtI3PTK4ZSzII5On8EV+L2lQB/yez5fd0IypbgNlpu8ZeEi8YTiS1hI/S/PhXITWAovlcUiPJ4x+/grUR8Kt5BYv/4WRBn6208rNZIHlkpoh1pYjoKHPXg4hF7PShBIBIdE1Iq+xuNb/G5jH2Ns5eFbwifiMV3gz1/Lolml8fYxCOdYTLH7W+RUlu+URTwlzEZfW+lGOq0lfkN/92zJVFnGpJ3TyuoWEcIpSj1fikT/5Yucyoor7YTG1yeJvYcQnDIA7bqubJCvtaKdlkGojd34xss6p/IrcbAUnSqfiJgTjWHRMyJGtRKa0kEp3lrx2/i4go1HpHiYRCwF4x+W49VeeYHBT584itJa0QkfIrqIH1Hp/8SWZ4nxMxsa/LxV6XE5Gh8nYoTos5A3xCZf6hk96sSR8gtQX7nlEtOXnh66eW61nG5Y2bsYCStH+uF5EcNDD8u92HdrT/fy9u6Oa+c5PbB979e2Z4m97n67b/PpHmmesGVO3rZtmQryp0OdZ+ReQM4GAOxASQrjEg+/iWvJprxBCcQLj3ifTwo94+SzZJqi8Zcr/UJCmxWvfPzLPH+zvKMKIwv+SlySQMU3+df4P5U8Ry210+to0Re4HCNShsvbPldnuDTDJQmR9No/OpwIeEKoUxSFgv9djoU3kucacwm+iFZFzDIKvjvxcxGxKEfKZaxOpevyDfK+4gNVSF1FH7FzWcm6/y0LitjHkAyX0txcprN7TIs2LMSiv2keYyfuMYHaqqCRU5Eh3mO8T2YpOy3nlM5y2Tt9XpraKJVTaJrNn8AqRGHek0XQ5zKl+LIeV7xz+AaLlMZPaDkox9TV9jHU0bJQkxixfAjxhtE9UEh1/NSIVrUsCNQqgV4MDPpkVvMtA9ioQIv7W7RRflgOUIiMSzvlzbbKA0oo2vxE64fC7N/ldC8dnT7Y0s9b3is4vP/1BnWzzaql8soP+Rb4Xa59DGCUr/GG0bDk9k3lXk1X7kuH3D5GrUpjmseeFH/wAV/+SZz09jHYM3to/JMynMTFW0YafwrMbmRpF/xr1KRyXdN+WxZRM3/rt8quX+1PvqNmLoDEb3riSMUNhB94+W1R1fnJatiyJ95jLXuK6Ut79nQI+OHwQcLPSPmmfQxa8xHC7wCGxRFbdsMvNxk9AMSNjiNiFeLwRXtE9/L/NWx24VTWQvN4wfKepAMvx+JYPKYgxrDYnf2LtZcLoTxSaZbIJ8YlREELa/q/9UwUlCpTNX5ndo/LsMT1wo+In2vz+OR1f9E1HuwhMXdWhaFJe7lBdX+Bw9nhzQdD6SI+R+IjzTwGrQ1LNCldKpYK8ZVSpc/LmOTDRvSJfZyUlgEgxhi/QOzjOkj98/K3Y9FWfuCOzdy6R8QRiZcF2g59rQzj0i163RV/X3CPs0Gx3Ipb89HrT1nyxV9k+r+FaCKEqYX+8r7G3914EEVEYnggJKqSRTx4EB/Dbzw4VwLDtK9yUNyZkDdJhFiyim/xd88SH+JvlyI+FP9CjLwZInrEvyxeisXey4VW3ot1p+nG842IGAa1nwdgykHx3/Lvp8c4kw7DlD/KT/79he7on1ZaWP5Jf02HXsof/ISSaDA9VsaaXY7JFxHSMObnsQgIXBCYFc0pWVs/W59OG5q/7Jxww8Ve9QA5GwCwAyGE7ffxtm27rksfVFL6MsQTnavtT8O2YkrBE0Z4chafc4j9vhQc5nOd8kojpjizMx4+7aO2lfBAz4wm/KO7QpklL5kVlAkK7zQ+L8yPSSilk/k8MrC0RBFpEJ/o/+U/FHMm3sJy7OL75X9ngwc8/DAwo/P+0TCdtsZfOPmkrTSDv2DwVwjeD/Exq05P7tNfgKeMLv3mwLulV8Yp/K1JJH7q+AcfCTzoMv4ZlfAQkRhaI/MVKT3Mm8G337GMTh43GpilhngD5OOznIL+0aZDRKp65pXPzyOXJstB6f7hskX5cvlEaHD6lbi0hG+BvzCXzhdf060t7dRnlr9d08t/iT2Il2fHIlJFwigSQ4lC0XbWnylc8xJaGBeSuKrIdZYSw+D6lMU8cGoAACAASURBVP4VlzP4f4tOylUYIZdwgYPrNVol5B9ylaRZFW1fgqs2ooVc4zN/yxeEHFO0nvKFRkm64lj4/wrFTYhcRXIyLAzDRR/R/2U7/CR2KkjpHkOJXAYVp6BlWn852PX+FIfARw7/rdC2xGbdY5CpVVElMxdFK9vhvV12V7bA22lUYIAfuNidHjZiMIhTxs9R6T3DolP2EdJzzeqKFv4h/yYfeGXEGnXBNiyayLesPyndy7dvH9eIlJ4pQ4uPH7Hxgtgy35d9jBeWr7VM5BWf873ozTZ/98OyF8t0fzFEObO7aB5lF70X97dshW7jRkXFeA+Uo569BHi3lNMqDpMPs3L66Ljoj9mWz37Izy8fruKH7eMNQbScX27r+6Uvlwdfy+7qS99f+nwJfvnz08rHuZmL2pb/5Z0jzpf4SavuPw07xfwyFMNYN5V/YtQNRNzw+Ugu93wxJFb6X7RQH2aBtlmEfvN43xPfbP9unvqI9E9ES/jxzjae/8qqyJl9DJF2c8ko5SZDm7KP4UM+YNzjUjn+DHJzIUB+RvhUmaLshj2/yjHS99vHiYF+LjgWsyyb5YfZMd9Fyx7T/KQY9WRZv6ZK/9Af/M5cTqieuPKpxcrG1+m67m0NAUDOBgDsQ9/3G2/Z4zhCywZb2K6zfyU832Hj949rzOfkOf6xxbY8I0PkobzaFVv2zlMwyq5X9iJCIyt74bkq6TF95u1m8//VR/RP+Sb3fV/iEFmFspZ2kVkiUtpWk738nOcKieCciJGIiJSI6xTRXPxTt2z7QC8e9F7BM9F4kmCJ9xR4SIBHjGZjDCVrUoed+BbE3zwAQC8/S/Eq/qvSbB5EKS+ET1/J1mmZgiZCHTySxFsoIjody+YTb8vlLHTMaX14zA3s2eolET4c/hL9eBiM/1AHnMppFR3OAy3lfVhEs/xfaQH+RkqH4B99TuxqQEW82JdO4MoLlwPE51ym6ViKpehVvR0u+vD9dixf1T2mr3ZsXQsXF8qx24W1F1rU4G3mvVp259lyrvJ9IV6UqFL7qEHzRvLf8k0VjYl/p2MLbtrHuBS1pOhHvIt4P/DLjZ8Cq2Q1odGXTdnHaJw4lXzL5lHf1HsXihI/F/xr5Ts8NCg+KSeC97/ohLIpHl8sHzoWMOCaUaFoWIWO1T7hx2IeQ0rmMUfesjHPz/tsf5o5jY8rULNnvPSJGNhixIprU3/NK1MjvcHyr56t8NM74oOZ36WFzEq/4qKb+RP9ef+ITfGzwOGDio9Dcfi6efwnYnBy+bU8dBoWdS6tbZj42MzJ9y1T4flBlcabuRBLq2IShO6NlmnZZsPSLv79Rq0VsCz0tbIp/QSf/XKrIgfl/IoLsHnsavuo7W5pwOxO+akpzdi4i1nEVbm0R73ZpeEhBls5ufzC2dIwfrBmTpJe7y7zFz7kl8CW/QqQoP02kLMBAPuQUhqGYVZxaP/Sc6ZpqlxxAwCAOzKOI7/rjuN4dYt2Jsa4/jLQtq3/KyKf1YLQzx89In5QPvxwm3wjutm0DoYkzqV3re0454a/xQ20zEIs0chsWTc/av43j/2IZRzpcfW3iHB8chZ4FIrHZrZscGUwiMU6YrkPX/Hd9/1S5zvneD8ktnKcr3Dn60j4WhYeTSmrPYouz9da8RgAD6vwIM0wDKUlfKmQXgxEQqdYTFPiQKUZ5ROxCEmvlREHxT8s3+fb4UGjgS02Eoulxr+CurRZvjCIt5lHsHizeWxDfz6osFlpmD60gfmk89U/5ft6U+LElZ4cHtel0eSZnxcu4Iq4kVPhmRJ9ER3CV/YMfzG5Xi3kCn9WEsOjQYeICQmJtvsrGFMETR4S69gaLN454gSVPYoPCRG46h+Di+VwRGsHZd9Xvsl/orewdH2Jk8uvYr5qsFyn5b9iCzqAxz/p56Kq/eMiqtk282HAv+/Zorfyt2cBVE75hH47/IWBPbOh48EqPizFh92fiUr50CujQj7IO7Vep32MUdnHGAwPmIlQTfm8tKr8l4dDRAPE9u1j8IYL6OJiLC0sB94ql0L+twg5lJbon/COEn84FRQsEmppjGVxCx5p4L2q444ilsbbX37L2yAOzbCoZMfKk5Rdl7HBD7N8h3ds+5i7LfblvZ/tIvsYoRdDlB+muKPav7uZGBJiDPBjaR+T3N1jTNQ+LsgTSv3K9HVl3gJWgJwNAHiHlUQ/evHjM0h6wTu5hQAA8Dt47/nk+Pvk7H///k3Pqh0aY2KMVzdzZ0II3vv38n1E5yD95xOmaVrq2KubBp7wdPFNbeS/yjFcHC9euiL+lJS17ts7/Te3kqlotTwSw9VPIVu/cROejZ89/bL+nAe9SpBJ9NXT7VSCPhEbg4Kz39Hh2Pxnaiw+KQI9DTkS3HXkssTt0qORdImlTczdrvyv9uIrHnFc3OexHx7QWrkiuI0ebxj/J/FNvkRMtGF8XPGjw2wDi8ANj9G48p2gCuRyu78SSSrHKNar8X4roZQS5yiXWzlH48Kyp7L96TGGKgJapTHTn0elWEVHR8R3NDDX6YHZ0A1zy9R4kIkHF4lRBVYHFiws2yxfEwOJiMzhWlz1BX1/KGOjHN3Eoq0DCwTyP3gErmemfPx/6TtF3Z6dP5TgzTAMe99CfgXI2QCAQ6h8mggAAF9DzlnovF8pZ//79y+ltK5oO+e+IHoaYxzHkd793tavxStT3/dXH9btGR/XQBQQJwC/ySdLLgCoHIztdUSAZN/N7rvNcxDxp38bpqykZU/TdHXbbwzkbAAAAACAG5NSEk4IX6xdppScc+uvB977GymM/M1tmiZawv+GZt2wgk7anbPv+5u+IlbF7NgzxnxBEAUAAAAAu0CrCpbysmm25r3/1uyT04CcDQAAAABwY4bHOpBN03z3ukV9vLOvCtUmvOScywpWy2xG12X6p3Rd9+9vwbgwn2maBnL2LiwlaAvjSwAAAAD8IDnncRxXPOKstd777zPHuwTI2QAAAAAANyaEoLXLqxt1LOQovS7vluKQlci45MxI5YY2qNMvQLWM+KuRUF2NMeM4IoN4F5ZOH15NAQCHUsmzDACwRIxxxSaO0hdutHywfiBnAwDeATMqAMAR4N7yBjoNxDm3/pMv6OenpoQEidrXHu/TIpbvYa1dyrkWCewkZ3/BSa+BGOPs6fjuJREAAAAAWCHGuDTZM8Z0XVftqsH7AjkbAAAAAOCu6DqQTdO0bfsLuaIrbw4C59z5BoUppb7vdxey27alXOwVeVrI2eSdjezsXZi94pqmMcb8wkUHAAAAAMFS4kKZs53TDD0z5J8s/T37yS1yICBnAwAAAADcFV0Hsmkaa+3V7TqJ9XWd4o1iGIYdJd3ZiX7OOYTQ972ux/g2bdu2bUuOIhuTrLXZCOTsHVl6ayX7cgAAAAD8Djnn2Skf1Xu8unXfDORsAAAAAIAbM02TmEBba2+RVbELOedpmrqu2yIfU55yjHGaJkpwLh211GNLn9NGQggppRhjCGEYhh1zsSmjZxiGEEKM8aXUHiFn1+C48mVM06THGxK0AQAAgJ8ipTSbV+G9DyFcNfWi+W099WMOAnI2AAAAAMCNSSkJZe03s0RDCG+oydR1bds650g7Xtevx3Hs+77rOkqKb9tWZ8e/gTGGit1Pf3wijGqzEaqK+fYGgabve30eIWcDAAAAv4NIIGj+lgNepSPHGL33ZY7qnKO1fV85P4GcDQAAAABwY3Rtur7v+Re+OzWDk1Jyzn0uLlPFnnEch2GgN4Gu6/Z1wS7+IcMwTNO0bwaN917sq+s6yNn7EmPUCdq/GUkCAAAAfhMxOXTOhRCuaoxer8kxxmjbvVu/I0DOBgAAAAC4MVrO/mVNLefc9/1evtX7QinYlAZ+qLgs5Gzyzr71G0udiH5umsY5h34GAAAAfgHhmt227fmFxwt6saaGcimGYbiqkfsCORsAAAAA4MboXAzn3NWNupilYn1XQes9p2na2H5u6v0GWs6G2cgR6CXGTdNc+CoLAAAAgNMQM3BjzPa51u7B7xDC9nmpWMe53rxq4/SQswEAAAAAbowwSm6+Xc7eOKuOMc4W5zkfY8x2Ifvfv3/jODrnrLVUtfKNLhJyNrlyf6Vt4rWEELRz+tNXRAAAAAB8ASKqfW3Wc0pJz0natp1N2W7bdn1qmnOmIudkiHfaUbwE5GwAAAAAgBsTQhBT1dsJagflfVA9nF3ctJ/S/mGtNcYU9+1xHF96DZimiZ9N59wbbxGiSiG1B3L2EeiQCfxGAAAAgF8g51zWAhpjLn/6l+kfFSovk9JZUbtt2zLDFLnY0zR1XVd+Yq39cNXgQUDOBgAAAAC4MSI3hCadVzfqBVJKWzTfTw5qGAaazX+sWkvoDYGqxqeUqKLj200dx1Fk1ry0cJUfr9gI5OyD4K+yhVt39b3uHgAAAMCF0FpAKlJydVv+xRhpeR8lczjnYowxxnEcSZ4Wk0zvvXjop5S893ouWqdnHeRsAAAAAIAbM46jKERzo6rlIQTKniZraWrqEQ3OOaeUYowkbb8nXts/jDFU0XHHNZizNXzeS/XV2dkwGzkO7fZD9tk1X3f/qm8eAAAAcBeqeqSWeamYoA7DYK3lU01jDJ8cUjX12QmwMYZbqVRyvJCzAQAAAABuBp9HkoEvn57WL1xS+2OMQsDtuu6EKXKMUYjUlFnDP2zb1nvvvSf92ns/DEPRxI9opLateDul2jknXlcgZx+HrsXqvb+6Ua9RyXspAAAAAI5jmiY+3eVyNuVlLxltO+dCCNc2XgM5GwAAAADg3pAaa4yx1t6oDqSwSSEos5VYUtn056/qcdwgohTDCSH0fS8KJ5KE/dLGX4Xq7ehXiLcFaKGMk5xd4XvI16BDERWuyQUAAADAEdwoKjwMA59wlln37JycLPXISqXCY4ScDQAAAABwb0IIXdcNwzCO412ScHVqdsFaO45jCIFSoUMIpCmHP5xzZFf99sEWg4i2ba+doI/jKJKpSw+8vU2hrlpr+76/y8C4I9o+uwYPze18Hh8CAAAAQP2IFYpd1/379y/nrAunk7FezfkQkLMBAAAAAMDZaIuG2ZQQ/r/6C8L17yVijGQnsu9xvUQIQSuhnxuDiHcSSqup9m3kCxD+9USdCdpFpy61oSiaci/9HQAAAABvoOXsnPM0TWIaQ2bZlWdCQM4GAAAAAABn81TO3gjlldwUrWXzSjtvo0vSQ84+lNnB/El+/dFodxRjTJ36OwAAAAD2IoQgZtEhBO+9mBXcwroQcvYt4QsAVxYDYp0gAAAA8JQQwjRNKwkIeJ6uIDpne1+J9JC30XL2Lc5XjFGXj98rVVxkZ1tr60+xuTs6MjEbaKlhcC5Fkqy1VzcNAAAAAC+zfXYhPLKHYZimSc9hag7JFyBnAwAAAOAXoZkfuQRQBcUalKb6ebuXtPD9jnqt2CWd+Xx0euyOI1BkZ3ddN00Tcm8PRaQ7EXXeUnQSFtG27dVNAwAAAMBR5Jz5/LNt22mapmkS80Zr7S0mjZCzv4c6Z8wAAABAtaSUrLVkwUzl8srDFE/VXVhfQ6bLzrzBNE1nHtHnzC7q3PdARJaNc24cx1u8mdyaGxWEFC+uhavbBQAAAICjGIZBlKUJIYh87aZprLW3eA/CrAUAAAAAPwrJ2XxW13UdVL+DyDmnlFJKfd93Xae1v/e41/nSxXaapjHG7LuoU+zCOTcMw7066o7oKIUx5upGzdP3vR6HDeRsAAAA4EvRj35yRdPlrCFngwu4xZgDAAAA6kHM4chl+OpGfRU5577v+7631hpjltJC3+MWlWqIlJJzTh++tXZ3V2tkZ1/CrCd1nRU4KbCk9XcYrAMAAABfQ1EI9RSl6zp66McYdYrJLeYDkLPvx6xmTQtXyRvx/CYBAAAA90WnsiI8/DlU6pAk7O3y9KtUXqmGDyRtlt0c5k4o9oVSkKdxI7+Rf3Mvt1x8x20QAAAAuBfi2R1jHMdRT0HbtuXzT/2FvYqTHwrk7NuTcx7Hkd4VqZhVUbQxDQUAAACeolMUa1ag6iTnTMVkhmHw3pOQvU2Rnsc599RZu23bCiXa2dnXrJbd9/1B7RddBzn7NLRALN4YqyLGKFqLdwcAAADgO5g1uKOZiViKWhRFTuUpI/8gZ9+daZq892Lk3SKQAgAAAFSCLoFClb6vble9kOaVc6YU7K7rPknBNsaQlbb3fhzHEEIIgSy213/Ytu3VPfGcEMKssn/obE3I2cYYeGefQ875Ri+EOWfRVMjZAAAAwN2hLJNZLXupSpD3Xnyf3oZqnhhAzq6dldETQtCJS23bIqcMAAAA2E7Oues6XQWlTtPbt3k6H904YSUVW0fTt0MO2tZaMkkr4jjfxTAMT7dzeXb2eo/R+rlZLfvoqZrOzh7HseYXkm9CJ2hzh/fazoJoKlL4AQAAgFuTUppdFEgz8KXkhpyzc04r4GT/sGX2cv4MB3L2Xen7Xr9GGmO897VNlAEAAIDKCSHop+p314R8KsXyvynLYxxHPv2YTfpYwlrb9/0wDH3fhxDW9z5bUm92mzXPeXTWP3G0lp1zFho65OyT0a+R1cbGRFMhZwMAAAD3ZRiGFbO+9VcbSsJYyummCXxRw8koYpqmCxf/Qc6+HznnWS27bVvvPVaSAgAAAG8gHLTbtu267upGncGKyplSotnqq0bYbds658hEexzHjZPd4l6yUShf8nCoQbdNKelOc86d4DuRc9ZLDXhmTQ39893oSIa19upGzSOWQcBkCQAAALgpMcaVpZNbpqBUN3JlHk4OgbrkuLX2/Ig45OybsbJwAB4jAAAAwNuQxxyfwBljqs2pPJTiiL2Uo6Fp25YsRETuxnamadroXkKJ3jWnkepjoZyD4/bIFeqU0rqcDY5GJ8g3VSrF2um7wkYCAAAAYAtLToBk7rdxI287Cp7/0gQ5+06QuaceN+SXjbcUAAAA4BNEgnbz7X4jghCCsBNZp0jYwzC8PQnJOaeUdM9rSCsfx7HyhWja9fvkuiZazjbGwGzkZLRhTp03E7EkudqqlQAAAABYh9IpaH5OiRTDMLyhMlMNG3oj2K5rnx8Rh5x9G5a0bHqNvLp1AAAAwO0ZhkHogF3X/YIISIIyzX2fzlZplrxUGP0lxnHcMktu2/YuKtusln1y41NKolfhnX0+MUYxEnhByHro+543Eu8UAAAAwH2hxBQy+vt8a33fO+e2LNa8xCsCcnbtlHeP2cQlWj16bQsBAACA70D7Hbdt+61+IznncRydc865dU2ZPFiKl8heLh/k7rI+Ob5qfvwGVNpEz9POHz9aznbOfZJBD95DpKG0bUunoKoTId4vIGcDAAAAoBBjHMfRe++9p7cGcsqm9wJa43VV0gnk7EoRM13v/ewr313e8QAAAID6oYVQ4oH7ZfpOjDHGOAzDxuqO1loqXL6vBhdCeJqX/V6B60u0wlm/FGPMJQbfKSXhIIHs7EsQBSHbtq3QJ0do7ndZBgEAAACAqyjh+RjjhXk/kLNvQN/3Wsumtat4MwHvgZEDADiB9VvNjjcisalPtqztL6y1XISq/P651LyUEuVWbHEUMcYUFfsgAU6bcogGVCur6R4OIejYQNu2VwVCZs1GhmGoUEv9bkIIYlRUGBsTYZhqrzsAAAAAAA7k7OtZfzFeWoqL6SYAAIB7cZx+vSMxRucc2WsUafWSHNsCP9ilv1fYnotNjthUNOZo6XNJzq62IshSb8+mmRtjLsxVoTGs5ezKIzHfh5azrbXXNklH/lAKEgAAAAB3BHJ21cQYxTsSJftc+14NAAAAfDGUoM1jyXUKrBytVFI6dtd1T9Ox27btum4cxxjjaYonGWLwhpEx970yiEMIQg1smmaXIpmfoC3gyTv7Xn37BaSUxKXXtm1tc3ienS3KliL+AQAAAIBqgZxdNeJND0kTYHfwrgIA+Fbevr+RdwRP0HbOzW6ttltozplUbD1/mFWxyU7kKn0txtj3vff+ZCV9L3QSdFNHUROdcktJ97fr4Rux1LfaUb222JhYJ4EXDQAAAADcAsjZdcFnw8JmhJKnLmwbAAAA8JQ33DAqhNRArmhf6B2xhZQSOYpQLva6lt33/YUq9ncQYxQ19CjscXW7/o9oG7yzr0JUg2yaxnt/daMe6Pu+tngMAAAAAMBTIGdXSs5ZLBS11uLNE3zOfdUlAMB92ffOc0KFyZKxWHTh2nIq//37l3MOIZQCjyv6NR0IOU5gLvESs8OJnFK0TFnJE3YpO/vqdv0iuixnPTGPf3MjGeMEAAAAALcAcnal6BJJWP0HAADg1hyRHHqQgBhjFAnOS34j5yB2nVIKIWgfgyUhu+97qNh7kXMWCa2XDw+BlrOdc+M4lhbW09RfQFynbdtWtdRDNA/Z2QAAAAC4BZCza0RUQofNCNiRql6iAAA/AllhdF03TdMRonaMkayBd9TpRE6lMWavLb9NSinGuCUXu2maruu897CY2B3tMVKVQEmXALKz60GHneoZLf9UKUjEvQAAAABwCyBn14h4U3LOYXIJCKHUaOFmXcohQ/au697OvnmpGNouuhKSyAA4gh2vrKebyjl3XWeMIVtnso59ejdb+VeSradp8t4757g3lzGm67pdHppHiFBb+kp/UkomUoHKJf26/aPrOqzoepuVc5Rz1ovn2ratUCmezc6+ulE/yjRNYszoc3HhVIcPFcjZAAAAALgLkLMvRs9fdWp2ha9J4F6QGkJyEh9XW16fDpWqD90gAN/KERfLxm2+sWvSsrkIa4x5I184xjhNE6V4kzLeMGNrwS5LmoZhEEnQrz6OV7qLPK9XviBKOy5J2OWWTno3TEWOY6n2Y50drhMjIGdfhZazrzX0ELcdIWdjMQcAAAAAbgHk7OoQhozGmKrWJIL6yTnTgnSSS/q+X0roI2nm6BJt65luO+4agF/j1fUZs6SUXvoV3V7GcdyoevR9L+4/LzkzhBBIwtYC7rrIS7v45CYTYxRy9ocqed/3ZHhd0sl1ojrl/3ZdJ8pBz4LqjmeiB2HXddVqf6K11lrI2VcRY9Qj5+pG/YcYKnjpAAAAAMAtgJxdFzln/vIM12ywBdKvU0qUukgqD0kh64pP5QV/IHYD8DYb1170fU/uHFzqWvIUKlIsPadIil2H1hvxu1Dbtk+zs+meFkLQUvh2dhFlysF+fs+krhD6uLW2GKd0XbddxTbGOOemafr8GMFTZms/9n1f80NKZ2djqd9V5Jx1XdmrG/UfwlUJ4wQAAAAAtwBydl2M48j1R2MMXlbBOiEEWsg/K/qsK0F1BktOszcB4JcZx7G4WFAAbP1xk1IS6zzatuU/mb1CZ42Gn4rCKSXn3NNqhytf2Ktso/AbEUL89ptSSkk7cRPkELJ+pLwBXdeFECiEucsxAoE4rbPnrn7JT8vZlevv340OU81ev5ecIHGXRhY/AAAAAG4B5OyKyDmL0j2VJ8+CM9GV0MZx9N5vTF3UX7PWQg0B4DugUoHbTSfESqDmz7Zi5SdamDbGPBU+xEON0opXWvXvT2dfv6EZY7z3lFQ+jqOWivZaLz9NExfx37P/2nJES/DSjtsNXsBexBi1lr1lXcLliGZbazcWzABHoJ1q6slWEdbeMBsBAAAAwC2AnF0RMUZRLKueyS6oAVp9PwzDMAxLiX5l8BQdhPIuhZztvT9aFnn7tZnW3Y/jGEKIMUK+AWAFslou5kJPk6wJ8bgpv135iRamt1hga9F8fVHINE1blF9xjFQlkiJ8dId82gMbSSkVHYoO+dUw8zRNb/ilcFPsV83NwS6QwYiIlLwxAK5CxJ+MMcjOvhBdDbKeJOhxHHnDMOkCAAAAwC2AnF0RYkJpjEFxJ0CQh+xSRcfymm2tdc7Rf51z5MQ6DEPf9957WtI+DMPbL1E5Z6ow2XUdbZCUI/rwE+mZtlwKV/KrgF7C39ssAN/NOI4i6e9pknX5oZazV1TgEMLsCo+nO9La9PrlTOLvuun/lv3uiPe+uLI0L3o0zWaOr0ByP3mJHHdEYAs6nba5g8dIAXJ2VaSU6rHPFsNADBVkZwMAAADgFkDOrggxoYQXRIHPvFdexjZ+7Rbw9ocQlgQRkq6899M0TdNEAyb/sW+TKEuRvAJEM0jroX/y3o/j+DQSU5pHuaXr+Zgk8Syd37ufayBYP6Hadefg5uzJvq3VGdbNn5vH0x3p5R1t2678SkRbiS3Snm7hejitJJtTKG5WUjzZ9L/U1y23u+3nkevg69CdHA/9c1g5g7QKanbgVVW+7ynCkJ3iVRhgFyIWuDTV5EGLoYJMGgAAAADcAsjZtUCVr/iE8hbmjBeSc04pke1G13XWWu/90iz8XpoXh8qvLSkgfd+f8zoUY9yYY0i6j3PuqeMBmYroF7wl4L0DvpIttU/1d5buDBtXM5TfFrF1XZvW8vcWVTfnrHPAt9yyyndmJXtjzJlJsuR/8p599nqaObHRH2YjlQhkN6Xv+77vZ8OrXdfdq2+FIk9XzX3nQl+A9hupJA9aPEruNc4BAAAA8LNAzq6FGKOY5sJgYYmUEi2x12pO27YrojZxr9e5lNJS5vIJK+6pr9Yl9SWstfxVTSfVUq739g3eKzMO7MK9rtbP2Xi8dPksXSZbEtjFpWeMWZcwdKbnxoCr9s5+VcFZinidFt+iKs1kfESHsN2vidyTrLVFEC8Bv1IIYa9BTuVA1yO7YJ2lJ91LKfmVIC4cUQrydofzBeScxbji8/wLz4gY9uXWikECAAAAgJqBnF0Leil3PVVi6oHWoT/VQKmC1nd0YIxxSc4+KD9RvMDodQPbWRG8dJpSYSmf8Q0hDPwU93r3/qS1wpmq0HXdFh0z5yzuKtZa3R7+iXhCLUm6eiNaH/Tev3Ts4zjO3gOdc6eJtmSfXZrx0topqlFJflDH3cFE4FNHNcBTRMyGj/Y7hgfEpUfuPUi8vRZxUk4uAzBL3/diHm1HRAAAIABJREFUxoVBAgAAAIBbADn7YsoLp3iPcs5hQimIMTrnXsrn/QJ7iqXM6Fn56Qi0yUDDyk567ynxcLb/V17VQgiz2zTGUBFL2nLDzBAaLFkAf5DXUErpLprdbDvLIaSUYowUhNvi4DF7T3jpqSGuWWPM+vd1/GmL94Kufkb76rrupWtZF64kzgnp/fvzG+FdXdvA0yeIxxtqa20l8G5JKc0+xV5Kxq8KEYd2zvV9f0dd/pvQM5/zfQV1HUhxd71RvVMAAAAA/DKQs6uA1jLz2SRkO86WaoFLL6J3X3a9lJ19zggJIWgVSSRF5pxpkbtu5MoCbZ7sScXrKHeMbzmlJMR0GMr/AktjhgTfruucc8458nC4o9JEl0zXdcYYHQ2iyq5kiz/bFbMrG6y122902sLo6ZWl7bCaVQGdBPolR5Rmg72JYClz9pwBIIoHCCelGtBuMLW1sHJmR/hN87IJnQgM7+zL0X4jT0OJR6NHPozdAAAAAHALIGdXgZYs76jRHETOWa+F5G+bJAnN/mt5W9iS81gts5LQOcKulpCWqpZpt5z1kUxjvtjILkkGIjldaHb3PafgJSheMhvXsdbeayHLNE0bXePp6tCBq1k5+6X4lq6vuKUbZ02HqPLkNE35D9LinzoUvaS/E2QMrRtwjm7Lj6ht29oSGLX/DILir6IH7X217H9KziYTNjw0L0cE6S/XjvXk7dZRHAAAAAD8DpCzq0AsP8RUkkOKqlZ/2rbtuo6EDErfXpFOmqa5S5q2ftucVYrfEIPeaIl4vV9Rjpb6f8XvZRgGsitZ0dGEnN227RcYyICXCCGsr8y4y5CIMc5a96xDyim/RmZvCFsMqSkrnK47vYWnovBSfjRByfIbzaA21qvUTNOkFe2u644W6XTp2q7rDt3jq+ggB+TsVxGXZ20Ri1fht02aLyFPogb0pXptjEEnTLRti7AHAAAAAOoHcnYVTNPE35MP8uWc3Sb/8O2dfr6RJWlD9AzvIsoH5L+iFM6u65aStbeYva40L6UUQtilx16Cjkv3w9EL3rVF75I/AGk9usOf+gk87UCdRnoX7RI8ZePl8zTP96UhsbLT9wTWjcz69myHH+OsK0Lzd1ek21SMkew+QgjDMHjvvffrPSnUT334+mLc5XBeRdhYEycoj+QwW6jNPlt78kK7fBWyxyEvoy/oPXG10kFVNWh/E+3Sfq0vkJ68Xe5/AgAAAACwBcjZVSCy3i7PCdIvPOdruMTsPPvpeyZlQc4KrK++o+acx3EsFrdkxj1Nk9C1+fdf2v72ZuhyPdQbx+Vo6+zslXUDs0rZ5wmMwocH2dlfj7jVrGcEE/UPiRDCuiHSU7gZyJKfPscYQ/er7bvYkuNMNQxIz337WD5ffqRvhgeVxuXbpGMvh3/C+piX0BoZsrN/FrL90dfIOI73smb6SvSlem3sBLcOAAAAANwUyNlVIJa4fkFa0C6Qjizm2du1/lnT7VeddpfSw5u/wkorisa+8ooWl0szdlFVZlurxcTZwbmUefr5SP4fe3d75qiOhGGYFJQCKSgFpUAKpEAKpEAKpEAKSkEpKIXeH7XN0ZSwG9tgEDz3j71mz/S4sfkwvCqV8kYT588usYlpmv6syxaqz8b6827Xkbn5xR+dua+ar13zZIitaqXFyrGxaZqkh7WsW/De7/r8LM4/gcUIZsNdLD1e5ij/bENrMUa1O8ik7iyfXCW9s4mzD5ePNBxewpLeKj9ZwRsAAOBUiLNPYU134BveX+bl1a8+n8u6ZOqhbv2Tw5r+ALIS2nf2jsyyX6zRHobBe7/5ZuS7ID84n8SOn+fsakCiuHX/8J7FoawnztbIeBZjfNQv21rbNI2smtj8kmklj0q55wvgXO79dqK9+A/XXxtlvcd5zsri69d1vdUsmTWf6rbdPxbXMEjL0uu6PlWcHUJQ12G1XPANbyHu7FGczWFwBupUPUMJiyyrIHeSR28LAADAKsTZx8ufOrbto7drQ9j95B+LMea9KFOl0n82dH70D59Ysw7bSs9fZxxH59yjpM85l7+1TzYsj6Jk+c20J++jj+jzlgJ5QPOFNd9wLJlU8egIlyYPi391qmxxlq/6VS2t7piaF2zM/2Ga2kviv77vx/yTdV0/uoa8OtVjvghIBC9Nh9u27bpu7tK72Brlz9z8eYvzxRY0u3Ze+vl9I2mcfWzHWyX/xlRxNm4lr9aX+WSMB5+BurM6Q5wNAABQHOLs46n1tc7WkTONFea1xaZpCiHsGiyGENTD+ScFmOq5bn0Msb5LwNeijRDCk7xv2/KrR4WlaxK0z6esSjlk+ppMn7+e9CB53mO6bVu5Ng7DkP/YtpX7m6yL+/Og+//K5D0PbVVAGUIYhqFpmke5dv3LOdd1Xd/3EjSHEEIIi9v29reP935xgshir5XFi3nankXIspbTNI3jOI7jMAxPLn17x9nzyIR8zmdbCjIfNuBqeWf58IbE2ac6aG8iryl5PpECAAAAaxBnHy+EMD+FSu3h98tnnpfCSbWg1AWntWlSqLvTNnjv84ext5/E1MPD+ud8WQpyTaj95eJQSfTyAMsY0zTNVhuzZtG5R4wxnxwe0lklfcHFckgezi8j7ws0yw/pxTR2cXbCE5Lq7ncIpdf22fpCvHx2yGLqEUJI015pWtJ1Xdd1smjtOI6L71GaQSt7DMvlo2JPLubTNM19V15aP3PDKTKL1DoKZ+tvM3dUnxFn31kIIV84hDj7JA6Ps1ceBhwtAADgzIizj6eqs3ddhiWE0Pe99GyVKeHSLE9SD++95DvTNA3D0LatTB6XBqmLCcJ+teTSaEJN7n7vk8lDpVcX3vHeS0mjBEaL6cz3J54/aVptjNkq3FlsfbvGq9mimgeQv7XDl0vCfhaTXzmS57YV+T/J484/Izyp+ZWO1VK5LBfDPQYR1bW9enFMLo+b/0w9ZPRx5esvNkLZ4zqW79lHn0Pf9290A5c+3XtfgVXv7LMVVOZxNh0MPlR0lrcYZz+6luLL1MwbRp4AAADeQJx9vLyz807PG6q8+lEoMCfIK2OF9a2oX5UHqe8Fmmo5QQnIPty2cRwl7pe+sV9bDVKR4vHFMu2qqpqm+XywIa+SVh4dVG8/ock6b+o1N+mazZN8+gksfhrPJ2o8/8k/X/yJxbY2c3eRR/KDc83slsXOy845GbJ6abOfy/Pol66W+WeybUC5WJ29+SyTPFarHiyEsBivryE53babnZPvkTnRPlsff9XBYNdxcZxfPtr3ndMEa6ilEYizAQAA3kCcfTzVz8E5t+3rz8+0T5YQ/JBKQLZ6is4r9d5YXTCv+vywCcZMerDMbV4/f8G3ee+7rpOl2Ob3KH9Y36j3kbndymJm7ZzL28KI956cJcvOM8qX9vudc5z3ln59nk3vR37LYq66cuxKNVhfs2Ds4q8T22aUeW6+Ps5WrS3eu/o9t7ja5OZzIKZpyn/LYmnz4jDDc1Jcv/kMofwYmOeLzDvlJJNF5k1VNxKHdC3DeeTV+tJs5Ojtws9PdlU8W+ciAACAIhBnH2/vOHuWV7x+QrZZqrl3emyOMa6fpb7+XV/1OX8OtdWicJs0hJmmST7J+ZXTFGkxH3wvzla/RWYM/PlS89CCfAht20o3YRm3eC/hvR7pgD8Mw+ZlyJ/Ilyx79eBRqc2f4zfPq4Al0d7kIMnLq40xf25ejHGx58bm5cDfqc7OuwY9yuXXx9kydLdHkP1IPmh3tkLX/Dwiu7w5depZa9NpZLf9HjwDNWdl86FKAACAOyDOPt7Xmo3IL0q7Ub9HCn5l/TFpRLvH1oqmafKtXdMVWrqE5zXFm3QaWeOQZ0UJc/N3vUmbV+k43Pd93/eqvP3DJe/mz0riePU6TdMsHmMxxumXrBq32En8bKnTIcZxVKdSXdeyH1cuhzjvAvnY5dyX0//D5/DF5UZfSuLeWAHv+TyVrbowq8rx+ZNf7GAre8F7/6hb/eZH8mKsv+2Fa3HnPtpBsgjk83ZYG65z+xJVLH/O+On5iUB8eSv5+hPOOZaCPIl8zgqDTwAAAK8izj6eeuDfteWlFFPPBbyqjLf6nUld/5KlIFWN4U5LYC2+a1ntMA84pDSv6zpZwVIqc2WpRlnc8tGyco+y0ZOTKLlt2zVBW95D4Ash/iYrNz5adFQWL50bU7RtK/m1DM/kP68OlR3ebknUgFlOrglt2/Z9L/8rS54K+Y/yA/KHeWbG/OdPrgmLiedLTXJUirdmY6ZpWuyQI7Y6WfL5/rOmaWQkRrrwN03zZMXdDz/hJ5unfuMevyX/BJ4HwXKtk2u7/GGebHFggpwuwGCMOeEUH9U7uyIgu7fF3tlHLfIB9bHnqwTTbwQAAOBVxNnHk1mHczD3ajONl0jy2/e9pFRzYiUtCCRbkYJNiYnnAsw09diqdHElCZ6eBD3yt+LRz1S/XVbPlkH8SQ6G+bm0rmsJd7z3ecsIqVNe/Bycc7u+97zaaE00lh7qf6ausvbmS+uUyk/u966LsLjK4ubevizkMZyw1q55zbzHwsowWtLS9N/Oh9aGlziZJvLo0rTyMHbO7fSloPqN7FH4rFqIlLjoWZ4MnjMpVufRl7+pcSr5dbVpGqqzT2Jx7xy9UQAAAIUhzj7eHBZLG5BzzmKWnFQeh77/26Vv6Sc9Uuq6Lrou6VEcJmXLXdcNw/D8I9q7QDvGqH7jq49nbywEt0Zd1zu95XPKD/JHBcLbSpPQV0+0xaYc1YpEO4SQh/UvDdtILXDTNE3T7HeJG8fxvWV4jTG75r/pUOV+025kHx319fG5aZrUDKpzDouqc+GQriw4j3wpyKLvgi5GDSXOVxV2EAAAwErE2cebA4W5RvvoLfrUHrfj0qp7sbPq85hbGoyUXqeW9w95iRxXu34IIQT1S621L72CWgTy7Xfa9733XhqzyJyDnd5yKT48eNZ85h9etSSVXtz1xpi2bb330lpaOndLO5S+7/OGIW83a5JpKB/GlE9+9eLqjk/IPIwvHL3S7WTXXyRTggqNafLS7NO241f1nsTZN5cvBVnuaXg9+XS0Qkf7AAAAjkKcfQrpU0deRcvjR2oYBudc2n5kMSSSn5G+HBf4AL3364OwnGSCu34OeZz9arAobVLWtMNO35f0sZ1LawtNcNQH9ehze3sPzv2vP18JtqqqudG2tCqSFkbvbVjqUcv76jcxl27+z7dt7+P8E7ISwPPDWw7pEtsilev5AdM0TbrL9mv88qG8E/olR/JWfvjn3EdfpqqznXNUZ59HflNHvxEAAICXEGefgswRnpdhLLG76DfFGKVSW9amk8Uqu66bI+xhGKSQ8+gt3Yx0pn4viPxCli1U1PjqYTw3SU//91G9tiSbMntastQr7e6dSE98WeZR0m3VoEb9ef6/sjtkloOcXDttoQS+bxzk1VkX6FOkujydiDBPypFeHLJ6wdGbeV/q2FZdYs58gOVV5IWO7a2XX4j4FvhJPoS8Opt7y1NRJ+y83jUAAADWIM4+BWmiN4dHzrmjt6gk8wPAxSLslCT4K2u055pl59w3G62o1SDfCFMkLZW8dS64lrGKefFSaTQh3Scun9fsKoTgvR/HcR4Kktph+YM0ZB/HUQ68N1K85yfjk7+V9hcvJNlJT5JXN/IoElvLGrzjOJ42JL0z1Q1g7+UHPnfbZiPyXXCf97vSYpx91Xuk88s/edUHbNd14AEAAK6HOPsU5sdm+V9rbUG5DL5JukbMx4lzToLItMZT0t7vb5ua7X7y6Oeq3n4elubU4de2W/WqGKOE7H92xp97TBME4FVPjpm8s+35h5lVc4mbtOIdx1EuFHVd86UzU1/H0sKI6uxTCSGoi8zh37wAAAAFIc4+i/RB9PxVYDhW3pFAVsY7vE1BOjefYxgfkkkJ0hclfeyfS8jPcMzjYmKMwzCoPgCLY8xnG0GRaV63irPTb5y6ru/wllea1xhPx2OIs89G7SPumgAAANYjzj6LruvSm1qeOlCoEIJ0Czlb1nNmfFbPSVOUvu8lwpbhHD407CFfkPa0LbPVKaB6F1wv203fr0zgSEe5GNlK5UuDSnf+o7cL/1DDZtz5AwAArEecfRZSZDQ/m9FvBLinNLKZY9xhGKZpOmemppAyo1xqAQCp+S0lJ1WD4hfOLqdpUp1VrLVHb9S5LMbZFP+ejTpnz9/RCAAA4DyIs88ihJCu20OcjZMjtdzbOI6qsWbTNHzswE5CCKrrV9/3BZ1xN5njlV8YL/xm35b3ZSbOPtCjy4gaP6vr+ssbBgAAUC7i7BNp21ZuZ+UhpG3bo7cIwPbWBGR551O5ODDKBWwuxtj3vcqyi/sKVleMcquzn1whh2HIs+y6rouYufJleZxd7iFxVfl0kFLmggAAAByOOPtEpN/I/ETqnOMJDbi2R8GNaoNLESKwkxCCjCXPrLUlBn93WFYuncTGIN9zKs5u27bEo/raxnFUxzP9RgAAAFYizj6Xtm3nJ5C6rnn2AG5osQKROkRgczFGlZCW2+nr8r2z8wYaxpimaY7erjOKMebLDF5yhKNoeYvzqqrUV3xB/Y4AAAC+iTj7XMZxtNYaY+SZrWkaoivgMtY8l+azj1WczcMtsBU53ay11tqmaYr+zlVTOlTXghKvG+k25/msxNk0Z5ipjyuvzibOPiE1ClVVPJcBAACswm3T6fR9PyfashTVT5kPogDeILOPpe+Qcy6vRhzH8ehtBK5jHEfvfaEV2SkVZ1+sOls1hLnke9zQNE2LvbO5mTybvLHYBa5FAAAAX0CcfTohBMmwhHOO4iPgPkIIXde1bTtN0zRNqiCROBvAomEY0mvFZfrsxxgXs+zLvME9qKbMsrQp6f8JxRiJswEAAN5AnH1G0zTNibbUaY7jSE0NcEMqzq7rmvEtAEreBPwa2aX3Pl1TZH2WffNbJu99+qFJnM0AwDmp0RpGrAEAANYgzj7Yoyeutm3ruk6XhWyahpINoHQhhPU5y+I6deX29gWwE++9Gvpq2/bojfrUOI75QnnUZa+h1mCo65re2ael4uwLnLkAAABfQJx9UlKRlD7IGWOapskLMxejsZvXJQHnF2P88zydpkmlOc454mwAuQuEYuklUbXLmGNZMtk1vPd5nH2Ngv3rUatBWmuP3iIAAIACEGefVwihaZo0zp5D7XnpKu892RZwVekVYI6oGKwCoMQY1eWiiBLmR1ezcRzzBiNVVdFqaaXFODsdCeB75DxUnO2cUz+w0856/rIcIQAA4OSIs09NHlDnZSHVw4l0I7HW8oAHXA/rQAJYSTWXKCXOXrRYl22Mobh4vRCC6p3dNA0f4DnlBzxRMgAAwJ+Is88uxjgMg0q18sc8Em3gSvq+z5vGNk3DUy6A3DAM6nJRaLMR1TJlHr/nJuclMcb0G0SqsxkNPS11wH+5o840TeM4DsPAdE8AAFAQ4uwyeO/7vu/73jlnjElXiSTOBoqmEuoYo5p6LJiHAeARFV8WGmfnqwVwh/OexTibj/GcYoxq/uU3p1bMteF1XbM4BwAAKAhxdnmkX/Y4jl3XDcPQdR2PKMAFyKhV3i9bAh0WQAPwiOqVXFVVcZ0lFvtl13XtvT9608qjmo3Udd11HdXZ55SPRX0tzo4xOufSX900zXd+NQAAwIeIsy+IdgRAcaZpUk+Vc5AtScTRGwjgvPJELF9Q7syGYciz7KZpqBV9TwghbVJHs5GTU8PY1tr0b/e7q8+vG3Vd8xABAACKQJx9ZdySAieUdxcZhiGfYl/9rt9FBgHgucVYqogsWGal5AuEMIb3iRhj+pEaY4izz0wt5WqM2W9SQnoHooY9ihsGAwAAd0acDQCHedQp2xjjnOu6jkEpAH+aG+CmBZ5znH3ay4jMSskH89KNxxtUnF3XddM0dKw6MzU962vNgtQdCHE2AAAoBXE2ABzDe7/YYKRtW9rFAlivbdv8MnL0Rv0nzdPnP4cQ8gugMYZhvM/lzUaapmGdlTNTsfLXelj3fZ/2+flanxMAAIAPEWcDwDGGYVBRTl3XxS3gBuBw+TqKp4qzF/V9n18A27YlQdtE2o6ZvlXnp+Lsr/WwVoX8LAUJAABKQZwNAMcIIfR93zSNtVayBnIcAOupSmdJtI0x1tozz/BYbLJkraV8eENp5bv0zubjPTM1uvO13veqbTc96wEAQCmIswHgSDHG9Sk2eTeARdM0NU3jnDt5cBlCyFujOOee1A5z3XtD+iHLYgxUZ59ZCEE1kf/OVC3Vdv/8szoAAAAEcTYAfAmhDID9xBjHcTx5XXbaBGPOsln4cVuq/l3i7DMPciCfsuCc+8I9g6oKpzobAACUgjgbAAAAu8vrso0xxKxbSdNPNWxgraU6++QOKdD23qdt9+mdDQAASkGcDQAAgB1JjxG1XqUxZhiGozftmtLe2X+2c8EZqFUZv1MrrSZMGGOYKgEAAIpAnA0AAIC9hBAWe4xQl70f9YE75xg5OJXFRiLDMKia+i+Ey2rkg+MEAAAUgTgbAAAAn1IJnfzfaZpUC4XqW32B74ylIEs0TZM6U/YOl2OM6vRkkAkAABSBOBsAAADbm6ZJ9U8gy/4O1aac6uwi5HH23v1G8g4nZ15LFgAAYEacDQAAgI0Nw5DXZVtrycv2FmNMO0gYY5qmSeNshhNOSLWxFm3bbv5b1H9JT1KGmgAAQCmIswEAALClEILqyVvXdd/3LDT3BSrOruu6aZq+74/eLjw0jqM6X8QXWsSkcfbm6TkAAMBOiLMBAACwmXEcVQcDay09eb8mhGCMSauz27al2ciZ5T15xN610upQIc4GAAClIM4GAADANvIeI8YYirK/Sa3vJ9XZxNmn5b1PM+XU3ieOOlSMMTQbAQAARSDOBgAAwKek+a8K5owxBKlflldnd11Hs5FTSVPjcRwXs+zqK0tBqsEn4mwAAFAE4mwAAAC8Yw6/vPf5wo9VVZFlH0INKtBs5OQWG2dXT7t/bJU7933/zXpwAACATRBnAwAAYK08RxvHkSz7cPN+oXd2cdQue1IuvXn1dJqkG2O+sPgkAADA54izAQAA8Ka+7/Mkrq7rvfsk4JEQghpdaNuWZiMn1zTNYpy9+RqqKhBv2zb9dRwnAACgCMTZAAAAeJn3frHtb9M0tCw4kPc+3R1SnU1MeXJd1y3G2U3T7Pp7VYzOmQsAAIpAnA0AAIDXPGqPUNc1yemxVJxd17Vzjp1ycqpKOt19u/5e4mwAAFAi4mwAAAC8IMb4aPE6ejQfbpomqrOLszjR4QvnlIrRvffzX23epxsAAGArxNkAAAB4wTAMeehmjBmGYfNWv3hVCGExziadPDM1CJGy1u73e/u+T38XS0ECAIAiEGcDAABgrRijtZa67FNJo2o12CDLclKdfXKLQ0TzHtxvKEL17E6rswEAAE6LOBsAAABrLXbNbtv26O3C/6l6W+lmzmDDyama+pQxRhVNb5hup0NTxhjibAAAUATibAAAALxA9dttmoZGFueh6m2ttX3fp9XZ7KwTetJsxBizXw+fdGjKObfTbwEAANgWcTYAAABeIP1GJAhzzoUQjt4i/Eet0lnXNUtBnt+T6uxqz5bWdV2n41I7/RYAAIBtEWcDAADgNd77vu9pTXA2MUYVZ1tru66j2cipLBbIL7ak37xuOv3VMca0OpuWQQAAoBTE2QAAAMBFqFYwzjmWgiyC2nGqxH6P3+i9V79ov64mAAAAGyLOBgAAAK4gr86WOLvruqM3DX9QTc9TO7UBGcdR/aK2bekdBAAAzo84GwAAALiCxTi77/uu61gB8uSerAa5U5ytDhVVoM0BAwAATos4GwAAALiIpmlUEtr3Pb2zzy8fitg1zpYFXfPfxaECAADOjzgbAAAAuAgVZ9M7uyB93z8q0E6XXd2kbjpvnE2cDQAASkGcDQAAAFzBo97Z4zimP3PgFuKJEMKjOHvz7ueLvU2stdv+FgAAgD0QZwMAAAAXkTcbUXE2TivGWNf1Ypxtrd18HCLvbUJpNgAAKAJxNgAAAHAFMca2bVV1dt/3aasKnJnafanNxyRUgfZOC04CAABsjjgbAAAAuIg8zu66jji7FI/ibGPMHiX24zhaa40xzrkQwuavDwAAsAfibAAAAOAi8t7ZVGcX5MlqkJu3z55N00SWDQAACkKcDQAAAFzE4lKQxNml8N4/irOdcyzjCQAA8EOcDQAAAJRuDjrVUpDOubZtibNLMY7jozi72qJ9NoE4AAC4AOJsAACAgqX51Pznxf+IO8h7ZxNnl6Wu60dx9jRNR28dAADA8YizAQAAgIvIq7NpNlIW1S4mtV/7bAAAgIIQZwMAAAAXQbOR0k3T9CjOpn02AADAD3E2AAAAcBmqtrdpmq7rQghHbxfWer4a5NFbBwAAcDzibAAAAOAiFuNsqrML8mQ1SGst1dkAAADE2QAAAMBFdF1HnF06Y8xinF3XNXE2AAAAcTYAAEBh8kjLe09kiZ+sVUXTNGnvbMLQItR1vRhnG2PYgwAAAMTZAAAAZRvHUfIvKcU9enNwJNWqwjlHdXZZYozW2kf9RqZpOnoDAQAADkacDQAAULAQQtqawBjT9/3RG4XDTNOUHg/WWuLs4rRt+yjOHobh6K0DAAA4GHE2AABAwfq+V+0I6rpOf4DuBJeX7uIQQno8WGv7vifOLsuT6mzibAAAAOJsAACAgqleyVVVUZ19Z6pa3znX9/04jkdvF16gOsak6CYEAABAnA0AAFCwGGMaX1K/eXPee9VspO97Gi4Xxzm3GGezKwEAAIizAQAAyqZaE1hrj94iHCaEIOuCirquu64jAy1OPutChBCO3jQAAICDEWcDAACUrWmaNPBSvbNxKyGEdHiDOLtQqgf6jDboAAAAxNkAAABlS/sSGGOstSz/eFuq+QxxdqFijMTZAAAAi4izAQAACqaW/qPZyM2pGNQYQ+/sQqVNY2Z0xgchBB12AAAgAElEQVQAACDOBgAAKFiMUcVezrmjNwqHUdXZxhiqswulmgjRSggAAEAQZwMAABRp7ijSti3V2XeW9pZRPZeNMW3bEmeXaJqmPM5u2/bo7QIAADgYcTYAAEDZ+r5PA6+maY7eIhzGe6+az6jqbPqqn5baNYvts9l9AAAAxNkAAABl67pOVWeTed2W915VZ9NspFyq3widRgAAAH6IswEAAEo3DANxNoSKs6Vanzi7UNZa4mwAAACFOBsAAKBsKs6m2cidhRBUs5G2bcdxPHq78A7VFt8YE0I4eqMAAAAORpwNAABQtnEcibMh8vUDibPLpfoIVVXV9/3RGwUAAHAw4mwAAICyqQSz67qjtwiHWYyzaTZSqDzO5uwGAAAgzgYAACibSjCttXQkuC3i7Cvp+17tzbquP9mbaVf9R38GAAA4OeJsAACAsqnMyzl39BbhMKrzjMTZ3vujtwvvUG3xJc5mbwIAgJsjzgYAAChb27bp6n/WWgKv21Jxdl3XVGeXazHO3ruSmkptAABwcsTZAAAARZpTJ9Vg11pLIHVbKgA1xhBnF0SduSGEdKRKDMOw4W8MIdCbCAAAlIU4GwAAoGyq2UjbtsTZt9X3fRqASnX2OI5HbxfeEWN0zu0UZ4cQuq6r65oSfgAAUBbibAAAgLKp/hJd1x29RTiMGtuQ6mzi7HKpuRefxNlqlEu9Ml25AQBAKYizAQAAyua9J86GGMdRVWd3XUecXS51dldV5ZzbZPpFXvfd9738FdM7AADAmRFnAwAAlG2aprqu50yqaZqjtwiH8d4TZ19JjDE9u8XnZdTe+/xlOU4AAEARiLMBAAAOo6og3yuKzAtyWdvttsZxTGPKOc6m3rZQMUZrrcqdN+lz3TTNHi8LAACwN+JsAACAb9s2W1Ttkuu6Jru8LbUUpDGm67qtFg/EIfL22Zvkzju9LAAAwN6IswEAAE4khPBqbfUwDKo6mzj7tlSpfh5nc2wUJ8+dN+mPn68aylKQAACgCMTZAAAApxBj7PveWuucm9dkWyOEoKqz99tInNw4jupg6PueqtuC5OMNqoFMVVXOuc9/kRr5qKqKJkUAAKAIxNkAAABf8qQwNsbYdd2cLj2Pq9TrDMPwKOqiFPdu8ji7bVvi7KKFEFTuvEl//GmanHPpy1KdDQAAikCcDQAAcLA8V3qp2bFKMK21+20qTk6NbRhj2rYdx/Ho7cL7vPcqzt6kkjpPyemxDgAAikCcDQAAcCTvvcqynXMvVVUTZ2OmDgbpnU2cXTTvfZX5fJ/mcfYmLbkBAAD2RpwNAABwJJVlV1X1UuPsn6wgl97Zd5avC9p1Hc1GSpevBvl5nJ0XfRNnAwCAIhBnAwAA7OV5kXWMUWXZxpimaV5teJ23S/5sq1GwaZrSjDKvzqadeonUOb5JnP3z85OuMGmMYdgDAAAUgTgbAADgADHGpmlURPVqmxHR9716kT02GEVQjSmMMX3f0xO5dGoGRlVVb1wo1D+JMVpr09dkKUgAAFAE4mwAAIBvCyGoIOmT6si2bYmzIUII6qCid/YFqHO8qrZ5iFMjalRnAwCAIhBnAwAA7C6tixzHMa/Lrl5vmT1T1dlt22601SiPaogsvbOJs0uXdgWRUYpNmsaoZkc0ogEAAEUgzgYAAPiefPm16rcjxPoXUamT6qtLdfad5c1G2rYlzi6dmsyxVZytxtVCCJ+/JgAAwN6IswEAAL5kGIbFHiMftjZW1dnW2q02GMXJ1wVt25YmEqXrum6PIStVnZ3G2VRqAwCA0yLOBgAA2EsaCfV9n9dlVx/0GElfWb0mVZa3tVidTZxdOhVnG2M2eVkVZ1PFDwAAikCcDQAAsLtpmvIsu67rTfIj1VeXOPvO8ji76zri7NLlszo22acqzuY4AQAARSDOBgAA2MziDP0QgoqNNsyyY4x5UP55xTcKpZqNEGdfQ34BWexQ9GqHkLZt09f03m+0vQAAADsizgYAAHjTmvBoHMfFuuwP+2XPpmmqMqwGeVvDMKg4u+97mkiULo+zNxmiUIMfzOoAAABFIM4GAADYyziOeSeQDbPsnwdxNtXZt6WOB+Lsa1C5c/VWn+t8+E213ac6GwAAFIE4GwAAYHsxxmEY8rps59y2JZB5nG2MocrytlTuWdc1zUYuQLVEr6qq67rPXzYt+ua6AQAASkGcDQAA8ClV9hhjbJomL5rePMv++fkJIeS/iCrL21KDKNI7m+rs0uVxdtu2n79s2jvbGMOwBwAAKAJxNgAAwMa6rssrpjeppsyFEFQ/k7quX10RDpehjj3i7GtQLdGrqmqaRv3MG2d9OupGnA0AAEpBnA0AALAl1Y52zp52iphjjGqZuLquaRpwW9M0qerstm2JKUuXT8Iwxnz+stba9DXpuQ8AAIpAnA0AALCNGONilr1JW4BHVHxZVZVzjursW0l3t+pKIb2zaT5TuhBC3oj/w1EKFZEzDAYAAEpBnA0AAPC3NQHxYo+RvQseY4yqxNI5R3x5W3lGyVKQ16AmYWxSTK2WgkyvGwyJAQCA0yLOBgAA+EiMcZqmfO3HL2TZ8tvbtjW/9i4Gx8l579My3rqu27ZleOMC8vbZb19eJKpWfYrquuY4AQAARSDOBgAAWGuxYjGEoOqjJcsehuE7WzUMg7XWOWettday7t+djeOojkPi7GtQAxVVVX14hYkxpqvIEmcDAIBSEGcDAAC8Q6LtcRzzJgB1Xe/d3kEF6977ruv6vifLvjlVw0vv7MvIF33tuu6TF8wL+TlOAABAEYizAQAA3pQ3y5Z6WDJlHCWPs9u2pXf2BeSLvqq2Qn92u1Y/EEJIq7OttfTLBgAARSDOBgAAeJl0rF7Msr/WY2QlIqpbUc1GrLUsBXkN3nt1tWma5pOzO4SQ5uMfvhoAAMDXEGcDAAC8bDHLds5Rl41jUZ19VXnvbOdcHkCvj6S992nT/7quQwhbbzUAAMD2iLMBAAD+oBKitm1VrlR93McW2ETf9yrOpjr7GlRvkCprNvIq1b3EObfVpgIAAOyKOBsAAOAFeb9s59zZGozgthaXgmTSwAXkzUY+jLN/fn6aptnw1QAAAL6DOBsAAOAfj2bre+/zHiN9339584AnVO9sqrMvI6/O/nxGSBpnU50NAABKQZwNAADwtxBCGv0IFk/D2VCdfVUhBOfcttXZae9say29swEAQBGIswEAAB6a0+q8LrttW7JsnA29s69KtbquPl68Ua0tmdZ6c2UDAABnRpwNAADwTIxxGAYVJFGXjXNSvd3rum7b1nt/9HbhUzHGtJh6sdnISxcllY83TbPp9gIAAOyFOBsAAOAh7721liwbpVDTCKy1XdelNbwcuoVSXdGrqvqw6D6EkF7ZrLUcGwAAoAjE2QAAAMsW+2XTYwRnRrORq9pkKUh17UrLvT/vxA0AAPAdxNkAAAALQghqar8xhsQHJ6cGYJxzxNnX4L1XQ2vOuQ9fM11bkosbAAAoBXE2AAC4o8UK6/k/juOosmwJj6jLxsnlzUb6vifOvoC8g78x5sMrUnqV+/zVAAAAvoM4GwAA4B/eexUbUbqIUuTNRoizryGEsHl1tnrBtMc6AADAaRFnAwAA/GeapnQCvgSCrP2IUgzDoAp4aTZyGWqYra7rD19QxdkcJwAAoAjE2QAAAP/nvVc9Ruq69t4fvV3AWotLQXIMX0Benf1hnJ2/4BtrSwIAAHwfcTYAALg7qbwOIdR1nVe2Hr11wAumaVKJZ9/3xNkXME2TukClzUbemz6iRu/GcdxuewEAAPZCnA0AAPATY1Rr6FVVNQzD0dsF/C2NMlV1tiwFSU/kC8jH2zbvnd33/SabCgAAsCvibAAAcEdpAjiOo6pSNMb8mWXTTRsnpHpnS5xNdfYFqIEKKb3Pr0Lrr0t5sxGqswEAQBGIswEAwH2FEPq+VzWP1GWjXHmcTe/sa1BtZKotloJUy95ynAAAgCIQZwMAgJuKMeZBdlVVbdsevWnAm8ZxVIln13VU3V5AHmdbazd52a7rpMf6568GAADwBcTZAADg4h7Nvs8n76/pMQKcmarOlphymqajtwufyuPspmneeB26JAEAgNIRZwMAgHuJMXrvu65T2ZBzjtQPpcurs4mzr0ENVLwdZwMAAJSOOBsAANzIOI6qXawUZdNgBNeQV2cPw0BP5AtQAxVVVXVdd/RGAQAAHIA4GwAA3MU4jsYYGozgwlQLHaqzLyNvjsQoBQAAuCfibAAAcH0xxrZtqyUsgIYrUdXZ1tq+71kK8gLyOHtxlILW2AAA4PKIswEAwGXNyU6eBAnn3LFbCGwrj7O7riPOvgA1ILfrtBIycQAAcGbE2QAA4OIeZdkSZ4cQjt5A4CNp+Jj3zibOvoAYo7VWXbsInQEAwD0RZwMAgOI9iXWmacr7Zc+6riMSwpV471Wc3bbtNE0c50WLMao1bK21R28UAADAMYizAQDAZXnvVUljWtvICpC4nhBCesxL72yWgryApmnSK1jTNEdvEQAAwDGIswEAwHWkJajjOD7Kstu2pccILimEkE5HqOuaOPsCQgh1XRNnAwAA/BBnAwCAS/Leq7n5M4qycWHTNKlmI33fe+/nH6DrSIm896ppEnE2AAC4LeJsAABwQYul2dZaylRxbeM4qmOe6uwLyKuzu647eqMAAACOQZwNAAAuaJom55wEQMYYCfWoS8XlqbVP67ruuo44u3TeexVn931/9EYBAAAcgzgbAABc0ziOzjnnnGq2AFxYHme3bTuO49HbhY9QnQ0AADAjzgYAAMV7VHbtvWfJR9zKMAyq2UjbtlRnX4BaDIA4GwAA3BZxNgAAwBVM0zSOo4rv6a9yN33fq6Ugu65j+dPSxRjVYgDE2QAA4LaIswEAAAoWY0zXvbTWUpB+Z23bqups4uwLyOPstm2P3igAAIBjEGcDAAAUbBzHtFeyLH1Jr/DbypuNdF03LxtItX6hQgjE2QAAAII4GwAAoGAq5BIUaN/WOI55sxGWgrwAVXffNM3RWwQAAHAM4mwAAICCqWpcQRHubalq/bqu27Ylzr6AruuozgYAAPghzgYAAChOmlbHGFWzkbquD9w2fF96PKjQk+rsyyDOBgAAEMTZAAAAZXPOqerso7cIh1EtKSTOZinIC1BxtnOOSRgAAOCeeNoBAAAom2qXbIw5eotwGBV6ylKQVGdfgBqosNYu/hgZNwAAuDzibAAAgLLFGFV1tvf+6I3CMfq+z+PsYRhIOUunFn01xrBPAQDAPRFnAwAAlC2EoOJscq7bUkuDznH20duFT6nq7Kqqpmk6eqMAAAAOQJwNAABQtmmaKNuEyOPsvu+Jsy8gb5HPJAwAAHBPxNkAAABl896nIVdd10dvEQ6jGqlba4dhoHf2BTRNo+Lso7cIAADgGNwGAQAAlC1f/S/9Wyq1b0VVZ9d13fc9cfYFPImzOccBAMCtEGcDAACUTTXVbZrm6C3CYdRSkBJn02T5Auq6Vj2Fjt4iAACAYxBnAwAAlE31zibOvrPF6mzi7AtQvbPpKQQAAG6LOBsAAKBsqnc2ZZt3pnpnS5zNmoEXYK0lzgYAAPghzgYAAChdnmAevUU4TAghPRicc13XhRDmH6DPcolijFVmcVe+un85HgAAQHGIswEAAMqThlCqv4RaChK3okr1nXN936dxNkoUYzTGqEkYbyfRj/4h0TYAACgCcTYAAEDZ8nbJxJe3pcp4rbX0zr4GtcjnJ3E2AABA0YizAQAAyqYKcq219Eq+LbUuqMTZDG9cQNu2qtkIuxUAANwTcTYAAEDZVIJpjKEa97byzjPDMJB7XoCKs40xjFoBAIB7Is4GAAAoW4zRWpsmmMSXt5XH2VRnX0CMsa5r1VPo82Yj3vu2bfu+Vy9FGxMAAHBmxNkAAABlU9XZzrmjtwiHyRupE2dfQ9M06WqQ753maU49TZMxpq7ruq6bpqHWGwAAlII4GwAAoGyqdzZx9p2pONsY03UdcXbpYoxN06R7tmmabV+w67qtthYAAGBXxNkAAOCrmNW+uRBC2ojAWnv0FuEw+VKQbdsSZ1+ASp/btt32BbluAACAUhBnAwCA3ZFZ7yqEkPbOds6lHzgf/q2M46gySpqNXECM0Tm3YZydv2Bd1xwnAACgCMTZAAAAZRuGIW2q+2EXAhQt753ddd3cFpmxjUKp5V6fnObrd3Hf9+kLGmOmadpukwEAAPZCnA0AAL4thLCYuZC1vcd7n8bZxhiqLG9LZZSyFCSr/JUuj7M/bzairht1XRNnAwCAIhBnAwCArxqGwTnXNA3RyVbyvgF8treSjgO1bZseCc65rus4HkqnRik2ibNVk6K6rhn2AAAARSDOBgAA35NmbdZayrG3ksbZdV3zwd6WirObpiHOLl2McRiGdLnXTU5ztYSsMYY4GwAAFIE4GwAAfEleYEjK9jaVZFGdDdF1XV6dPY7j0duFT6k9m/cGeTXdDiGkzUaqquI4AQAARSDOBgAA3+C9V71fKQbcivdeVW4SZ9+WGjSiOvsy8kU+P2yRn1dnc5wAAIAiEGcDAIDtqTrBvLlzVVXDMBy1edejPt6+74/eIhwjreE1xkh1NuNGFzCOo6q7/7DZSD7EmFZn07AIAACcFnE2AADYV4yxaRqVZTdNc/R2XYqKsz9fJg6FSntnS5zd9z1x9gV479PeIJ+f4zFGFWdTnQ0AAIpAnA0AAPaVt8w2xtCkdVvTNKWfcNd1R28RjqFON2st1dnXoHqDvLGUbv7zqkkRszoAAEARiLMBAMBmVFzive+6TiUm1lqy7M2pOJtP+LaGYUhreImzLyPGqK6ln+9WVZ1NnA0AAIpAnA0AAPaStvGd67Jpmb0HVZNLnH1b4zimcbbqnU1D5KKpnkKfn+bqEk0PKAAAUATibAAAsL1xHPN+2RU9nXczDEP6OTNmcFsqzm6aht7Zl6HS589bXRNnAwCAEhFnAwCAjXnv8yC7qqq6rkMIR2/dNanqbJoG3NY4jiqg7LqO8+4apmlKxyrmFvlvF90zDAYAAEpEnA0AALY0TZNq8FpVlTGmaRoytf2oHrifl22iUGpgQ5qNcOpdRnqmO+fU3/6Za6sfUHE2TYoAAEARdoyz6c0HAKfCZRnbWjyi8oUfpSibor9dxRjTmk1iqTtTASVLQV5M2sTJGPPhq3nv00tH2gyKewYAAHBaX6rO5n4IAL7v0bWXazJ2MgyDClWlfpBK4b3lS27SA/e2pmnKq7M5By+jbdsN52GowQ+GPQAAQBFoNgIA10FOjaPEGBfrsufWrthVvupmXddHbxSOoeptJc4mprwM1Vbow8V11eAH02gAAEARtoyz5xglxui9H8eRPn0AAFzeOI4qYaFA+MvyOJsP/7bUQqzE2Rejlvq01n7yamrwgyVkAQBAEbavzh7HsWkaeay11nL3DADAhYUQnHN5ll3XNaPaX5PvgnyNONzENE1pQNk0DXH2xajhw08a5atmI8TZAACgCBvH2eM4zhON5U6aOWsAAFzVk7pssuxvyquziaVuS7WPaJqm73t6Z19J3/dqF6d/+1LbMTUSxoMbAAAowpZx9jRNedNMdVdEX1cA+DJpADVNUwiBizA25L3Pv/eNMeuDVA7Iraj+A1VV8dnelmo2InE21dlXkp/v7w0fxhhVnP1JoTcAAMDXbBZnd12XTmwU1lqKQQDg+yTJ8t73fd80jTHGGFPXNQWb2IqqAJ2zbNKQQ3jv0zJ5GmffWd47u+97ZktcSQhBXXvfPuXbtv08FgcAAPiybeJs9RCVPtZSDAIAhwgh5P0H1GU5rd+klhOLFg+Mxbps5xxj2AeKMcrwFaNWN6eyTuLsS8rb5b93+VWF3twJAACAIrwfZ8+3O9M0SelfHmc3TcNdEQAcwnsvRdmbPPECIsYYQsjHsOu6pi4bOIO8OnsYBuLsi8mHq9u2feN11FKQPLgBAIAibFCdrSappXiyBYCvUU+hi/WzVVV1XXfUFuICHlX9840PnIRqBGStpTr7elQMLTv6jdfpui59EQa8AQBAET6Ns/OlSNKHW26dAeAoIYR8MjJjjfiE9z4/qKy1HFHfRxElHpGpOfMZKqsm0P3vYkIIavaVc+6N10kf5Xh2AwAApfgozl6cbjyj0wgAHGuapsUCbRY2wBumaVrsMdL3PV/3wHnEGNNTVaqz56pbztbLUIOLdV2/sXMfxdkcJwAA4Mw+irP7vn+UZVtruQ0CgMP1fb+4tsF7TTZxW13X5QeSLDHH1z1wKqpul+rsq1IPYu8NVKs4m+s5AAAowkdLQT6axl5V1TAMT/7h278UAPCSGONiEFk9aDnCJRq5fPTaGEOQXQp2092EENKzVeJseiJfj2qSXr21NobqwU3nKAAAUIR34mx5LnpSmt00zdbbCQB4X9/3edcR5xxdMvEntVDYHJoQkgLnpFLOuq67riPOvh41blGtm3elLt0qzuY4AQAARVgbZ6tbnxhj0zSP4mzuhADgbBYbH1truWLfUPqd/jyVzrNsYwxZNnBmap12ibNpNnI9MUY1UG2tffVF0sEPay2D3AAAoAhvNhtp23Zx6rrUBfCUCwAntNhHu+/7o7cLp5Bn3KpqjwMGKELeUpne2ZeUN358o312ep2v65o4GwAAFOGdOHuapsUs2xhjreV2GQBOKy+2bZqGMUgoMca8QY104D160wD8QQ1EUZ19DYvf1Plk2SfLFy1q2zZ9lKN3NgAAKMLLcXaMMZ+uPmfZTFoHgDPLr+FSuHf0duFEFvuJ8RUPnN/i8jbWWuLsq8rn0LyaR6tXeDUNBwAAOMTLcfbi1GNjTF3XPOgCwPkNw6Bm2DC/GDPvfZ5l13VNyR5QCjULxznX9z136ZfkvVdf6GtWg0ypTutc6gEAQBFei7NDCIttRuq6ZjAfAIqQd9usaIh8J096y4QQWC8UKN1inE119iV579VF+/lyjvn1nzgbAACU6LU4W93xCGNM13U7bR8AYHPjOKqxSeccHbRvbjHLds5RuQ+URTUbcc51XUdMeVVp82upMXpp6MJ7n/5z6pMAAEARXoizQwh5QZ+1lvseAChLfj1nAaiby0v8/qzyA3BOKt9smiaNsxm5vJh8heeX4mxVq8RULQAAUIQX4mx1cyzlHkxdxObyBy31X3gSK9qT3VfEnl3cyPX/8TymaarrOr2kv9pwE1ey2C+bHiNAiVS+KUtBUn1yVWq6lTHmpacz9XzHjFsAAFCEtXF23/f50mE86AJYtD7JPXnm+/PiFpaVa6uHWGvt4jPwabcfW8mL+xiuBsqlru3SbISb9qvy3qeD0y+t7Zx3HmuaZtetBQAA2MSqOHtxDjKj9wDWKyLgvltuO02Teo5llvENxRjVV3zXdfQYAcqlemerZiO4GBVnG2PWX8CHYVDztLgNAAAARVgVZy+2Gblb7oO9cUShLNc4Yuu6ThNtyrJuSDVO5RgASjcMgzqp+76nOvuq8pFpta+f3K547xnVBgAAJfo7zo4x5itAUuIB4G3XCIJzMcbi3lrXdemjbF3Xcnkv7o3gPeM4pqV5zrmjtwjAp1T7IImzaR90VTHGtyNp7716xKvrer4B4E4AAACc1t9xdgiBrmr4svhr8a++vz3Yiuy+ImLffK7u8/om55y1tu/7vu8LatSgJilXNJK6E5VlN01z/hMTwJ/SWZXGmKZphmEgzr6q/Elt/fe4KuTnHgAAAJTi7zhb3egYYyjNxt6GYbDWtm1LtnJmf+6d9AdijOM4tm3rfskD9s7b+D6pZXv0HtNEvu971XrYWqve+ze2+F1N08xPwsYYlvm9CTU/nSwbuIy0OlvibJqNXJu6CVlfnZ2vA0ycDQAAivBHnJ23Y2MmMnY1TVPbtnLUWWsZOylaCGEYhr7vu65LM9M09j1nIbNc+mRMZRiGaZrkjUzTNE1T3/dzIr/4vs72QPg8phzHMY2zq2wKDinnxXjv27ZVVflEXcBlLDYb4Ry/MLXKkbV25T/Mq7OZgwsAAIrwR5ytboiNMbddIYRA5wumaZKERTK1Ox9vp5Ie/N77YRjatm2aRiLdtm3HcZTAt23btm37vh+Goeu6vO1+TnbxseeX+u0yOeDPLX/u0cPkCau2Y4xN06hLPSNJV5I2Qu26TgXZTw5XACXq+z49wZ1zMi579HZhLyrOrut6Za1ACEH9Q779AQBAEZ7F2XO2mN4Qn7OUcj8v5U0nCadOTn1K8//Ne/gaY05V4oppmqy1dV3ncdh76ro+1YhFCEEtjfi2D4ODL19MpmmqfoeRKk69i/Leq3GL2Znb/gBYI/3WSEtujTEyzEzv7AtTcfZLV3V1R0ecDQAAivAszqaf2qJHaSw+ISvp5SHL4pxHPvNDSJYtcfaL0e5Dp2rT/Ogg/FMef7/XlOnAAzvG6JwzxszvRbX/RumeHNvsa+BiVHV2Hmdzyl9MPhKfP7I92umq3whxNgAAKMLDOHsYBnVjdNoutwei1GUTIYTF3g7OOT7hkwghzH1g0tDzQ8cOV6S/aBzHV7NsWTXRWpv+w6ZpxnEs8VIp8UdaoE3F7jXEGL33jw5jVtwFrieNs6U6exgGbqgubHFC7cp/OzccY2IWAAAoyHKcnd8VVa8sk30HcwfSpml4QvhE3rdXWGtJ084jhNA0jbV2znDn/uZrkl8p687/+0l2sRSeP38L8sbrupYlIud1INtfXddN07QyGQwhhBBijNJzfO83uEbe7YeFfy/jUZxNy2zgkvI4m2Yjl5c/uK3f4yGEcRwZ2gQAAAVZiLMXs+y6rrkPnvV9n6Z4zjluAd+W97SRj/Q8PSgw895P0yQ57DiOi2vKzbXbkv82TdN1nfxwflU5yYmzeBCm2ymxddd1fd/LQpey+mWMcX0htnxobds652RIoG1b+QC7rhuG4fBcO19LiknH17AYZ69fKwxAWVT7CKqz70CNyltE9Q8AACAASURBVBtjjt4iAACAHek423u/WKXI7LNZHvcbYwgF3jOOY17ea63loasUIYS+751zUn8tz8xz2jtN07wr1dN1dabi30fr41UbdbyZpkk+pefF7MaYY8ujVIG21PSdZMgBnwghqIONsQrgwsZxTM93qc6mSuDa1IA0k28AAMC1/T/OlhrDRzPujTF3vgmWxqPDMDRN86i7Li1H3rA4dkKWXSK5gMQYn0SfZ15adnFYRXxeMa1ihT8d+7Gkyb7U19Nm6hrSuRSnWoIVwObS8WNjTNM0NBu5PDUwX9f1o59klBoAAFxA9fPzE2OU+e+PAp1rx9lP7upCCJJir2kQvLioHR551DKb7Gwrjw7s/L9/58EmT3VPta9VWdPsw0vfmq7cuQMT7Xz2Sdu2R20MtjVNU9d11lrqsi9JXclJrO5M9RdqmmYYhgvfyeNn6TaGAQwAAHBh1c/PzzAMsr7Zo2zlDr2hZRWUYRikPe44jn3f5znU5T+lJ29h2xh0sVtx0zS0bVnjqEj6E/keP1Wmli+EKN6uzpbVYlculalYa9Md+ujPe5DRTbU2AGclABREjR9LnE24eW15nH2quywAAIBtVT8/PyGE501d71Cd96iLyEzm3VtrH0X/l2wyu9M7ykuzZTIsz1o7WdyPXz5c82L8sz1ojeOYJ9pvD1Mtvpo65q21j648pyrQPk9bGADAn9RiFRJnMzB5bX3fqxsJ6vEBAMCF/b93dgihbdumaWQm8slTp8+pfGqxUljUdd11nSxqF0Lw3j8q3C70UzokgpcJAemnRwXoGmt21mkLt1VuW9f1Cff44qXgjaYoT9YhcM7JJcV7H0KQjkZ58P2dz+fROIcq8rrkWB1wDZybyE3TlF7Dm6YZx5GKgWtTcfa1G0UCAABU+X/KiyivfQccY3xURNn3/aNEKcY4TZM8HozjOI4jj5Tr5RWpp2qjfH7puovyB/kvMuIiPXOappHFS621kp8euMHeezWn4QwJab4Bm7Qckfku+Ys45x5dUqZpyv/JgdNiVIE2KwcC5xdCkMv+CUcK8WWLvbOvfTOPfDxefXEfftMFAACwob/j7KZprn0DpGpY0jd+9KZdU95QuK5rnrLWCCH0fd80jTSpkBVcpQGO9MB50gTfGNO27VExh5r4XJ14AKPv+/wzVM2sn8sfKY0xT8bGhERR6l8ddV7EGFW8foeWU0DR5NolU8qufduGP6XfudLMjWYj15Z/axtjuA4AAIALW4iz1Rz5y3dNVQvmzN5eAu4CYozSU6XrOlkbU4p/fz4u7ogx5k0Y7vxRrydx53tLC86OauqSJ7yn3el5q42XroQhBFXfbYxZ2YloHEe1f/N/+LWnU7XLGHMCTm5uNaASbSKtG1qMs7mGX5uKs18ahgcAACiOjrOnafozT7mYxW65lw/xF8UYpXeKtVYdBlIOLI9Dn+ShbdvmTSc2fAtXFWN80uH9JYec0aru+JyNs2d5oXS1uuFGvhbT+iM8H1o7T78RKTA/amMA5FRWpcbhTjtkiC9Q30RN06gZQgSdFxNCUHfXzDEFAADXpuPsfCGRM6dOm8hTwrquj96ob0gfZmKMwzDkWfOiuq6f9Ap//oykCldf7cl72wewcRwfdXh/1fdDyRDCG3M+1L5Wh+v2W/mvxQ88r23Pt+STOvS8w/ixub/MBpD2BdVSu/Pbno/ACeUruB69RTiMavAlcTbV2RemuqVXxNkAAODq/oiz7/A4lK/AZq09eqM29iR1knbMzrmXulhII+aVc5nnv83TuudzIQnLZrKDXtpHMrl4/DWPVXw/zs6LjosoG8ybvFcrLol5Wff6cvgY40snyN6GYUiPOp6NgTNTcbZz7ugtwmHSm3lpNvLn+g0oWr5CyT2nmQIAgPvQcbYqLbzD7PI8zt7vIfDLFabPN+Dn58d7/0k75ldHO/K77TQgk1Yn0zSxYFFurpOVR9P5GdUYY61tmmZeE9IYI3/O67CkJXr+2e59KKpBsldL8kUI4ctHxaMGL883Pv8nL62me6quLHOcLYectZYTEzgt9Q3rnGNI+LbUNxFx9uXlN9iL9ypcEwAAwGXoOFv1BLh84+yfGzcbUb1x3/PS01G+wt48XjIMQ1oh3jQNz12pEELXdc65uq6ttdbaeaHOaZrir61W7NyW2u9vpKLDMEg/96Zp3ojC3xZCyIe7no/iLJ5WeZuOR9Tw0rH1ld57+UYgzgbOT82DucPsOjzyZ+9sXEy+evM3b5YAAAC+7584O8aYBjF1Xd+h0V6++mVVVZd/43NQtUhqfteE3etzup9ssKT6TcPzHgtVVTnn7jCa8pIQwjiOkl8fvS0vUBXHL1UrT9OUd8KRXiXf+RCkQjn97X9eGPMEvFo3QhNCyJvLH7uvZd/N0wKo9gJOa5qm9OpBmHVnamyjaZqu6y5/Z3tn6kbr0fc1AADAZfwTZ+dLxxy1WfvJk5d8NfDq6mVNT7JsKfv13kvrj2EYpKhnHEdV7DPfMa/8rNRgSZVUwecr2Mw/QDFRcfJTTO339aMUebybXp2+04A7xvhqgfZi0+0qS7TzZRXzvtuHX4jU8rCMMAGnlcbZtM29OXU/37btMAzE2Rem7h8Ov3kAAADY2z9xtpqqdp/HoTyuuvA0vcV4Tt7yn3NR824h1Sv9EFQ0Od9thxDylxVqk6gDLU4eSa+PoRdHUGZfKz7KlzB9PtASQkgfLNN/K2eZyhSkUUz+Zo0xh69e0Pe9NGSfT3bOQeC05u9ogsubW1wKkqPiwtSNfRELbgMAAHzinzhbRTCHJylfs5jS7lScfngYlC8XY4xZPws1/+fW2pW/WsWa6QH2pLGJtfbwD+16vvaR5qX36zPoxUZAhzyw5bMZnpc+ee/l2XJeRzE1h9rjOMoEiLyhSnWCTiM/yWqQ8l7OsEkAHpkjrauOx2MlemffjYqzLzm/FgAAIPVPnD3fDEl+8YV55Wkykqck8395/mOfW1zw7VFi9ckGSNmm9EmYpumQSpnPGxqoaO9R3Kz+o2rqYoxJy7qftJWoWBmyZOM4pnv21ZJq7/2j3h3VZ3H2NE2ywGbXdU+udfIz+a/+sxPOOI7PG9A/T+qrf8d7jqJWtjTG7BpnP/kWePQDa/6qCHt/zeHyYozzt7NzjkT7zlSc7ZyjOvva1FMMvbMBAMDl/RNnp7HFTiWxIYSXFrKLMY7j6Jxr23Ycx/XRxqtUarMysXqVesCo61py7Q1/xaL5g8rberyRT+WB+JpXyDs2WGvTj1eKVR819X5pzUmcxzAMn19YvPfe+2maJCCu69paa619+9yRTu7W2vmYbNu27/thGEIIMcZpmoZh6LruyYqpf8bN0zQ9f4VHpHz7vbe2LVUgT3U2cGbptzPNc+8sv3S3bUtZwIXlRTnqBmlN3ckPA6sAAKAc/8XZ6Up9cuOrfvTz25q2bSWNcs7JzEdZY1DyoxCC/CHNktI5+MYYa+0mT2iL70WVkYoN64JjjIv1mHl0td8dZN75YX2rkNk4jukrGGNWfkQq11scLXhUKX+r7jdFU0eveqj+8PyVAQ/nnNSaffJSj+qm67pumuZJVfWrB6TUd6fR+fOXlQ345K1tSCZVpF8N6pw96nH3Go/ZL43s7rolKJQ6MNJvTzrd35ma8SardlOdfWF510SWbgYAANf2X5wtscUcuGyYp8gDVV7SO99k28zzuGerDcst9pXeKkV9sq7dG5nye/I4u67rV18kr/p5O85efLgax7Hv+1utz3lh6rD/fIHZ6deHr/PoirSGtMp5tWvKOI5t2z4JyiXIPtUKTjKfIx1TJBD5DhnQ7fueix7WSy8vb3y54zLy+7Su66jOvrBxHNWQOSUgAADg2v6Ls+VOaL4Z+jx1SsmN9ZrixD81TbNrwVEeOjvnNnkGWOzAK74WZ+fNRqqqejWfUm9kfXV2nlA/KR7Jm5NUrNVeIDXBYtsLyyfyoZ2VpDz87bqnaZrGcWyaRi6JMoAn/ZSk1cm2b/ND8ik9qc7eWwih73vpby49Z2KM3nvpDPPNLfkmabFV17UcIWc7KnBO6vs9HfunTPtuVHGGtVat+M0hcT1qsPzJ7dafy1QAAACcn46z56egbZMCaU/xeZz9hdpA7726I6zrOo2u3r7n894/KjzfOySat3kxUl/f/0GiJbUf17fTzf/t8+KRfO4kxSbFSccwvrPA7Hp9369vbC29tiVX/fxslZZKs9PmlXLFkNNWLd/6HXMRvfk1L7Cprsw/V3kgT9teSacXKuKxhlpv+WvD5DghdbMnX16n/aLBJtTDy3m6lgEAAOzhS3G2916KND9JtL/WUnYYBrWdWxVoS09wueOUnGJe1+47lYaPIvU/Y2JZk3Px365PuEIIeb+RJ1Pp8zLw76dp+FDa02N9If/XSGNrKYN9dOWRU/We62jJCSsfziELVD5vYn69pSlliEWtGHGx94idqDj7jXWecRn57RNx9rXltTjrJ7PKjLG+77liAACAgvwTZ6cZwebpaggh70z9nES9suzbN6fhxxjzOuINmyR47yXXbttW3t3XluiJMS62DJahgnlZTlmZ8+fnR9bnHIZhcXnG6mlv8cXb4q7r1AcrUb73PvySz0dCRrWRrG1VnHQA47SjEelR17atNLmWP0s59jRNNzzwpNNIGq1+obhefc5/rskpi4IWvXfmjW/bVl0eNx9axoWpOJve2XemJrdJnM08jwuLMap6kfV3XMMwyDDqq4uCAAAAHOi/ODvtGZ1P4t6KBEbCOTc3jW3bVqaQy/9KcCnNZD+5/36ecTz52xhj/jCwR8T//aRsmqbni9FJyG6tnXfKox82xqxvVCLSefTqpaRC9kmRrMyW3eljOUS634vO455Id/fFdt/lqQHIvCfSFw7aRwNp+cVByuffvubnf7vru1tsXZpPf2G2OF6iloK86tcK/qQKF+Yr5NHbhR2pr8v1M3vSWn4WXQcAAKX4L85WycV3KsJUnCfFuTslvN77tm1lPt3zZrVSqpm3md6q5cjhXi2Tz8kU+K7rXt1NMk6wvu3M/GN1Xb/x6w53h8A6lQeCaRfga5w+V5Ufn+rZ+JDRiOfDb7k3Gjd97cR88otCCHlwf5lvHHxNOiLCJffOVJwtBSIcD9emvivz7vmPvoNoug0AAEq03Gykutyae6rJhqSxbdumubYsztY0Tdq6VLnGxyKfxtt9zOfOJI9e/M/f3nXdyiX45sXfrvHJ301acLr+yQpnoJYQOHBBQhlcfOl6JReNpmnk8n7mIy3GuNjNyRhDiRxepWIpDqHbypeClDveo7cLO1LfI8aYlf/wSZx95m9PAABwcw/j7C/0SP2mtJWKuttrmkaan6xJeNu2vca9XYzRey89gtfnRPJENAzD5x/CNE3OuSdL8EnnGedc13U8gxVqmqb03Dl6c6A9OpHTsno5Ew8/B6dpatv2pUptuWQ9WuHqDFdyGdtb3HLq4/AG9X16hoMch1Dt8mSNgYvd2ENRZSJ5DcGifL4md2sAAKAI/8XZ3vv0QehixbDq3b3tkrO/vfd93zdNk0dFsjKMrIm3SYqdkkUmpRxeIjPpBiPx04dt009Ixg8u9qaem4eR6MZYELVygMzGOEkuFmMcx1GuV7JKZ9/3stzC80u3XGFkMbTvX8MffXp93+eTgWRTb3WhwHvy44qlICFUsxG5rSLOvrY3VrCXyhL1dclgKgAAKMI/cfaTRdtOkmV84lGB9kqyVuEn3WNXfoZHfdRzvfY4jsMw9H0vDz97Rz/ySyWZusBhtijtr+Kcu/A7VaZpkhOHp+iCpLVaMqD1naUU3iZnkywv/OeVXGaE7DE+96pHX0lk2XhbegqsrM3EZaQXtDzOZqLbtcUY1VfJn/ddMm6d1/qwajcAACjCf3G2WorqPOV4b1PbH0JY2a95MQGRIuXSPxMcYpomqcGcHxvm8+vyR5T3nkfogsgXwXygGmPKerKV9YRV4+9HpF47X3n4C2eljPSo7ZHBg+tNAMLXpEUJxNl3pjpIUJ19ed579YXy562X6kgzu9j0XAAAcFX/xdkxxnPG2RtuhsQcaVjziJSUzn1X87wDWOlRe1x1inGA4XAhBLWEwKMvgvMfriGEaZqGYfizD8ncUukLk1F+ftccXhxbZYo3PkSzEQgVZ7MMyeXlcfafs2ynaVpcwIZvIgAAUIQq/T/njLM3J101pE2zrC0mnHNN0zjnpInzfTpCYG/jOC6mV13XUYmJr3l+QZMsu/qdemyMsdZeo5rPez8Mw5qVJKUPieTar5Zsr/m+CCE8Wn3XOUePEXxCdRtwzh29RTiM6mUkPaOucT3HI8/j7EUy7qu+GVkKEgAAFOFhnG2tvUnQJpPTY4xzGHGTN45v6rpucaXNpmk43nA4773qtWqtvd6M4xCC977rOlmB9nmuLfWMMjsnfZG3V0FQHb3SpImYCZ9TS17TbOTO1PVcLjIMmF2buslcv+iFmkFInA0AAIrwT5ydtlGr65qUDdhKjLHv+8UE7XqhIU5OJa3jOKaPwfOyt9eenuK9l472T0LtNAySbiRv/7q5+D1/ZTImbCLGmJ7INBu5szzOHoaBS82FxRjV19n6VFrdmp588WcAAADxT5zd9/18M1TXtbrxvXa0AXyBmv/LkwOOJaMsqqTrknXZi2RqzjiOTdP82Ydk/nCGYUjHetd8M3rv87rs4pbZxMmFENQxRq/k28pn2xBnX1t++q9vN5TG2cYYrhsAAKAI/8TZaY2eMYbpz8CGQgiL1dmcaDhEjDGvFzbG3HN8RdZU6LrOWmutTb8K83N2XihYRduLpAw8/5z7vmeQGBsKIajD9SbjUlDU0u4SZ3ddN8fZXHkuSX3R5O2GHu13tXDoPe8BAABAcf6Js7338yLXdV1zQwNsaBzHPBejEAaHiDGm3aXmp18GV2QdBe99Xrf+yFz5mIcFea4kX698ztic914dafTAva282UgaZ+N6VK+h6pU1kNTdKdcNAABQhH/i7LRYT3qnHrVZwPWoxXaq3wrNo7cLd6SqsaqqYlXS3DiObds659a02Jae41KyLbFRvsCm4KzHHvI4e323AVxJjFEV6krvbK7wF5ZPzli/GKzqg9c0za6bCgAAsIlK/f+u6+R+yBjjnGNCIrCJYRhU4YwxhhIYHCJvf8Hg5RMhhGEYhmFommbl0pHGmMXOQnzU2M80TcTZ+FlqJLWyMxLKtdhhZuW/VcUWfEkBAIAi6Dhb2mfP/UaYEA2slI79qHGgvFSqemUeKLCttDSbBQlfIk1I+r5v23b9ApLpWX+SQeKTbAY29DzOZo/fStpLyhgjcTadza5NjWHUdb3yrFfNRrglAAAARdBxdghhnlgtd8CHbBZwGSGEtm3T2EsqN+liiUOoDhhMEfhEjLHve+fcylxbVtpc7LL95Ffs/RZ2fX18jeoYUNHW5q4eVWdz13FheXW2MWblHlfNx4izAQBAEXSc/fNvTcf6sX0AKe+9NN611s4zHuQBQyKtozcQdzRNUzpRgGGVrcQYh2F4qRVJ3/eLX6+PvnP5LoaiDom8UTvVuPe0GGf3fc+EsGvLF2hZOaCl4uy01STfOwAA4LQW4uz5tkYWtiLsAP6k7vi994vVmhJj0ZUeXybHW9d16rBkWGVD0zS90Xtk7ml7eNLERaloIQTV0soYc/hBhUPEGNPClDnO5n7+2tRON8asHNBScTYTcwEAQBEW4mzp8zv3G2HSGfCSvu8fFWlKnJ0/YBAkYW/TNKWHpbWWLHtD4zgurv1Y17Vzzlr7aGXIVNu2XArwNhVm0WnkzlR1tnOOOPva8vHU9fNr1dHCyi4AAKAIC3H2z8/PHGdX/046A/An1b4wzarGceR5Eofw3kuiMZcDH71F1xFCWKzLnmf3xxhDCH3f/xlqyzDDS821ASF5lvSzIpC6OTW20bYtl/0LW5wbVNf14h7P1ypXd63pErIAAACntRxn930/3xgZY6jxAdbL2xdSCQtclYwTqFP+UX/8EELXdXlTiPl/q982X/LNO00TuTbWa9tWjh9u224urbc1xkiczWj6VeW3nU/i7Fxey7/3BgMAAHxuOc7++flxzqUF2tR0ACtN06SybAIp4JIWu+QbY8ZxfPKvYozjOEquLbW0eRJR/S4b65yTEGq/y4gUj+/04vgm2ZWsAHlz0jMwj7M5MK6q7/v8G2R9C2yVhrdtu+vWAgAAbOJhnD2OoxSIzTc3i/fB6QN2Pn9tww0FCiJNRaZpenTiAChdjFEVtUlB3Eun/DiO0zQ96lA0v6YE323bPsqdn3wXP/nJn58f7710Qem6josVcAFqmI3q7MsbxzH/4lifShNnAwCAEj2Ms39+Z63Oj9NN01DABQCAZNmqsPrPuuwnrzZNU9d1Xdc9KtYW1lrpfr7VgHGapK+v5gNwWqobssTZcyt/XI/3Pv/iyK/nj7418mYjFCQBAIDzexZnhxDSliNyb8TdMADg5tLh3g+zbMV7L7OjnoTa89fxytDh0Y/lU9Tz+k1yDaA4eZzddd0mFyic0GKcvX49WLVw6Pqm2wAAAAd6Fmf//PyM46gWrWqahvnIAID7UK082rZVcXNd/6+9uz1vVUmzAKoUSIEUSIEUSIEUSIEUSIEUSIEUSKFSOPODaTVdhWTZlszXWj/mudPX8uEeYWR2vezK3xsVdV03d4A8SbTnSe1hGH7WIbCagHjMHE4g6s5umqZtW3H2WUVt6ff3/WdxtulsAOAQvoiz//3713XdskR7voWeSzZDCH7jAeAipmlK+7KzLOu67hN/3LxpZJQ1pPI8n7Oqb30iR32p301AgN2KprPF2ae3Gme/uNIZfahZ1AQADuHrOPvfv3/zjFj6YHVZlvPTi+E/ot+chN1cjXMezmocxzQyePtc9qq5fuTLBpKyLOeV5lf+Wx6VdFdVJfaCQ1sGlHOcHW0F6XeVk0k/m4qiePFdjlZMbaIAABzCS3H2v3//+r4vyzIa055/S57v58uyLIoiz/OmaWyeDsCZhBDScea/ybJn4ziGEObx8Oe5dlmWX06Lj+P45DuIs+HQojh73grSL+cntvrY0ItxdvTRtoyzLXsAALv1apz979+/aZq6rquq6tFI1+pvQgBwaOM4Lh/ev2fZW+0kMU1T0zTPQ+26rudUejWPeB5nt2375/9NwNusbgWpR+jEVj8OXvyEappmeWf3oe4sAID3+kacPRvHseu6uq6rqpobSLIsW/4WlWVZ27bW8wE4gbZt06Rgwyz7bhiGuq6fLzA/mcps2/bRqzRow6FFy29lWZrOPrEQwmqc/WLfyDAMy88Ry5kAwCF8O86+m596HsdxfgJ6GIa+77uucw8MwLE8uucfhiGNCYqi2E8dR9d1ZVk+D7WzLEvD92EYnrzk0VNW1qph/5bVE3meV1Xl9/NzS7uzZ69csfu+X77EVpAAwCH8PM4GgPO53/+nWXaWZVVV7TAVGsdxGIZHicY9oY6OvG3bJzn4Dv8zgVcsp7OLopif0vATfWLRdo7firO7rhNnAwCHI84GgFjXdWnU2zTNnseT5/0qn3Rq53le1/Uy1er7/lGi7ZFzOKjlytY9zt76oPigaMI6jbOffHJFr3WqAACHIM4GgP+RTjrPc9lbH9dLxnF8PqY9bw03d+lO0/QoB8nzfD+dKsDrlmtU8yJW27ab1/3zOY92931lX8eoeEqcDQAcgjgbAP4rreCY89+tj+sbxnFsmuZ5qD0ry/LJQHee513X7XkgHZgt53Cjn+I5zrY6dWKP4uz0kyu9nuvOBgCOSJwNAP8v7RiZ57IPN9g4TdNyO7jfKMtyDsLk2rB/0zRFVzDT2acXvenfyqZ1ZwMARyTOBoB/IYTorn5Ogpqm2frQvm0YhrIsn2zz+ANN04zjKNGGnYuGbfM8b9u26zpbQZ5YCGH1gv9Kc0j0wfdKPwkAwObE2QBc2jRNbdums8zzVOM4jlsf4PdM0/TeIHuZi83hvlAbdiuqQi6Kom3buSt/60Pjg1Z3QXhlOTb67CvL8g+OFgDgl8TZAFzFMoed/zmE8KiU44hz2f/+/Wua5o0RdqQsS1k27FkUa1ZVZTr7CtKni26vZdPpLgt/cLQAAL/kVxYArqtt29Xctm3bg+a2j/6L3uWgKT9cRDSdPcfZy+nsg17ZeK6u6/RyXVXVly+M4uw8z//gaAEAfkmcDcBFPerlOPReWMMwfKhsZOZRdNizcRyjH1hlI1ew+lxOlmXPVy/S0u2iKJb/9vMHDgDwE+JsAC4qhJDneXT/n+f50e/hu67LsuxDobbpbNizaJVu7s5WNnJ6j1Znh2G4f0360RbN8s9e2UASAGBb4mwAristzj7HnXzXdVVV3Z8if2O6fY6/HzirdDq767q+74++SseXVvtG+r7/7ktc5AGA/RNnA3Bd4zjWdT1HvVmWNU1zmtCn67qiKPI877ouhDBNU9d1TdP8Mtfuum7r/zLgoWmaVuPsrY+Lj1vdOGE5nZ0KIUSvKorCID8AsH/ibACubpqmcRzPdw8/jmOazocQhmFomqaqqqZpxnHs+z4tXVmVZdn5/pbgBO4/6VHpRJ7nbds+zzQ5h67r0iv2lwu0IYSyLOevr6rKFR4AOARxNgBc3TiOc8Ytzj6Q0zxJwBul3dlN05jOvoLV6exXtgANITRNY80DADgQcTYA8P/atr03bqdOsE8mnFu0uV9ZlpLKi1idzn4lzgYAOBxxNgDwXyGEvu/vj58vnalbHE4p3QpSnH0RaZyd57k4GwA4JXE2ABALIXRdN3dqF0VRFIW+Ati/aZqWVfhVVenOvojXy0asSgIARyfOBgDW9X3f972+7D1bJlNSKpY7+92ns6O1KOfJKaVxtrIRAOCsxNkAAHAGq3H2MAwi7FNavq11XadlIxYjAYBTEmcDAMAZTNO03M31Pp0tzj69pmmiOLsoih/HgiQgfQAAIABJREFU2U4YAGDPxNkAAAc2DINyZGbDMCy7s8XZ11FVVRRn13W99UEBAHyEOBsAeA+R2d+7F+bOwWXXdfM8pvfimsZxzLJsOZ87l41sfVx83LJkZmb/XgDgrMTZAMBPCEz3IB3JzLJMYe5ljeMYTWe3bWs/wCuILgWKswGAExNnAwAcVVqYe7vdxJeXlXZnt21rOvsKlu+7phEA4NzE2QBwLX8wVW1w+89E8eXM3/9lTdO0nM4uiiKdznZ6nFJ0HWjbdusjAgD4FHE2AFza69lW3/d1Xdd13XWdRGw/QgjLuuQ8z+/vjrfpakIIyzg7z3Pd2RcRdWc3TbP8ty4FAMCZiLMBgK/VdR09yV5VlVx7D0IIy8HMKMbiUqJp/XkrSFsCnl60BejNPpAAwKmJswGAL7RtmxY0L8c/hdrbGoZBwwD/1kb1m6bpuk6d+rmlcXbXdVsfFADAp4izAeDqwn/c/3mapmmaxnGcC0YeZdnL1Kzv+2maolxbzP1n5h6YrY+CjU3TtBpn6xs5pfsF9r6gdVdV1bbHBgDwOeJsANipR1nwk8h49SVd19V13TRNVVVt2zZNM0efRVFUVVVVVZZlZVmWZdk0zfwPRVEsG3hfN3+ruq6f59pibviER93ZfuLObRzH6FJcFMXWBwUA8CnibAA4lXmkum3bOcVeFun+paIo2radpmnrv49rkVpe0/19X53OFmdfQXQFzrJs6yMCAPgUcTYA7N0rUdRcDzIMQ1mWfxtcP5NlWdM04ziu/iek/6PQ7Te6rpsH8P01XlbUnT1vBTkMw3JhyelxSlF39u12s5oIAJyVOBsAjupecl3XdZ7naZyxE48aSHijruuKoiiKoixLu8Bd1jRNyx+9+WQwnX0FaT1UtP+ncwAAOA1xNgDsyyuhQwhhHMeqquYE8w+j6V+Z67nnTSP/4G/yOubG5Hk9Y148WP6rDQ+MPxaVjZRl2batOPsK0jjbshYAcFbibADYtWXyOwzDXIq9q0aRH6iqqu/7cRzl2j+Tbq15DzHzPF/G2VzKNE3LWHOOs/2gnV40lT/r+37r4wIA+AhxNgDsUQhhGIZ5L8e5QaIsy7+pE8mybP5Dq6oahqHv+7quq6qqquqNB5Bl2TxH3Pe90dHfi0LMrQ+HzSzXuuYdWU1nX0F6cR6GYeuDAgD4CHE2AOzLOI5t26ZPjv84Mp5rKOah3bZtq6q6N+p2XTePe7dtW9d1Xddz+DVNUwghjcCmaZqD9aqquq5rmqZpmq7ruq7r+75t27ZtfxB5l2UZ1bzyXU3T3P8+i6LY+nDYTLQVpDj7ItLWKWUjAMBZibMB2Isngct1spi2bX8cXs/mkeeqquYY6x4Tf9k28N2/5EdfP47jD7L4LMuapnnyR1znHPiZuq6Xf5mWB65pWTtzu92KomiaRpx9BX3fRxdVcTYAcFbibAD4oBcD2RBC3/dVVf04xZ5DzLmT+k/+y54JIXRd991ykjzPhbA/E0JYVkxkWaZn4JqiDmVx9nUMwxBdUffwWQAA8AnibADYxtyOPY7jOI6/2dpxTrHn8pCt/5tic3HK3GHySlhfFMUO/ysOYTmd7a/xsqJMM8/zuQH/HmfLtc+q67roctq27f3fet8BgDMRZwOwL9M0zd3N6b86zQ15CGGapjl//Nb88rxJY1mWTdPMRdV933/ZIrIfr3SCZ1lW17Ux7e9admeXZXmgs4I3itqK5p8m09lXkBZVuQgAAGclzgZgR0IIdV3PE4Vd153ybnwYhrIsX0yx5/w6z/N7EfbRY6lxHJfB65P/8KZpTnkCfMhy+N3Wmpe1Op3ddd3Rrxt8Kb2uprsRAACcgzgbgB2Zpmk5vVvX9dZH9DYhhDnJfTHIzvN8HlKeR7m3Pvw367rule0iq6ra+kj3axlQRttvFkUhvrymaD/Aoijquu773vlwVvd3No2zXT8BgLMSZwOwF/P+gVGke44h03EcX9/msaqqE0xhf+mVv5O5KuH0fxVvsezOPs0PDt81jmMUZzdNI86+guitv51rPRgAYEmcDcAurFZwFEVx9MHkEELTNK9MIt9ut7IsL7WD3/yXUxTFl38tXddtfbB7t2zOFWdfVpRplmU59xSJs09vmiZxNgBwEeJsADZzT1jmLDu6Fc/zvO/7bY/wkS+zoRDCMAxd16X/Xavm7dr+5uD3Zg61v/wrqqoqXdsQ0t1Fo+67/dnho6Lu7Kqq5jj76OuCfCmEEF0zi6LY+qAAAD5CnA3AxkIIq1n2fuLd55lp9G/Hcey67suJ41mWZVVVSR5DCG3bfrlDZlmW8utVIQRxNv/WurPbtrUV5BVEKxnibADgxMTZAGwsyl/mm/D9ZNkvCiH0fV/X9YtB9hwzGZmMPN8iMssywdyqaZqiE28ZZ/sbu440zm6apuu65aXG+XBKaZyd57mPGADglMTZAGxmdZC5KIoD1f6O49g0TVVVL7Zjz5ls27YSpUf6vn++JJDnuSrt2bKuZznYnmXZgX6IeKNoN93VOJtTSreCzPPcBw0AcEribAC2sTqHe6At7IZheGUbwzTIlit9aRiG53+xZVke5Tz5G9Fg5gn2UOVnojg7z3Nx9kVM0xR9pLoOAABnJc4GYBtpX3aWZfvpGHky1Nb3fdRT/KWyLJum2c9/3SH0ff9k5r2qqq0PcEei6eyiKExlXtNqnN33vfPh9NKykbIsxdkAwCmJswH4a+M4tm0bbfqX5/n+N6/7bpA97/SoGePHuq57sjmkv9i7vu+Xf1FVVYkvr+lRd7bz4fRWt4L0FAsAcEribAD+1DiOaY/E/u+6+75vmuaVCDvP86qq2rZt29Y49u89KR7Z/2nzZ6KZ3LZttz4itrEaZ5vOvoLoIuA6AACcmDgbgE9ZBijzP4cQ0o6Roij2HPvOE9lPZoSXQbYpyA95lGg3TXP/mvRv/jrvRRRimlu/rLRF3XT2RaTT2cvLIwDAmYizAfg7aVNHnufblns+SXlCCG3bfpliz5mRzdY+Km2nuZ8/dV1vfXTbG8dx+ddiKvOylI1cyvJtXe3Ofv6SR/8MALBz4mwA/sI4jqut01uNkX6ZYrdtW9f1l0F2WZZt2woC/kBUDx2ltxd/C8ZxXG6baSrzsh7F2RbbTi9dfK3r+mcXxotfTgGA/RNnA/BxIYRl1nbPWfY2QzrvUfmo12Ipy7I8z/d2/KfXdd2jd+fHwc05TNO0zPqdmZcVxdllWZrOvoh0wdh1AAA4K3E2AJ81jmM65lxV1d7ilWmaXgmyb7fbPOpo2nETIYRHU/MXbx1Zxtm6sy9rGIbl2uFq2cjerr28Rfr59eKmFOM49n3vEw0AOBBxNgAfNE1TOjJWFMWu7pxDCMMwfJllz+PY4zhufbxXt7qh6Gz57lwhs7v/N4YQlnH2nvdW5aOiTp55Orvv+yv8OFxc+gjUK59W82dflmVlWe7qcxkA4AlxNgCfspoRV1W14T1zmulM0/RlR/ZckO1Wfz/GcVzt0b7sgPY0Tcu/B3H2ZXVdt/zRmKezxdmnFy1o3V7YZjmE0DTNMgQvy9J5AgAcgjgbgI9omiZNG/fTgTBNU9/30c38qrquBdk7tHqCZVnW9/3Wh7aBcRzF2Vd2TyGHYYims9u2FWef3jAM0cXwyzi7russy5ZnS5ZlLh0AwCGIswF4SZqGPMpHQght26Y5Y9M0nz/MZwe2/IK0AiVVFIV7+z1bHavP8/z5I/anzPXE2cyiTUHF2RcRlczMnl8Jd77kDADwhDgbgN9aBiXjOKZJ8X5mvvq+b9v2eZadZVlVVQKg/Xu0e+cFK0eiUzqKsZzJ19H3/fJMEGdfRPS+39b2qIjOgfn6GYXgO/mkBgB4TpwNwDulA19FUWw78DXfw0/TtDqMlvqzKXJ+L6pWuLvajGG0N2ZVVVsfEdvoui66/OrOvoL00+2Va2D6KJU4GwA4BHE2AN/zJBZp2zbKFnfSZTwMw5cd2VmWzZOMWx8s3/OociTtjT1xopeezFsfEduI0klx9kVEC1q3l9dlo/WPsiw/fagAAL8nzgbgPdK+7DzPN5907vu+ruvnWfY8Py7xOahHTehlWV5nD890RH3rI2Ib0erOHGcPw+Didm7p5++LT6hEcfbtdnOqAAD7524HgN8KITRNEwVqe9hHse/71W7lpbqu3b0f3XwGrr65Wx/aBy3P2+g8N519WdHSXVEUurOvIL0Avvj5G60FZlnmVAEA9k+cDcCvTNOUtj3keb5tefE0TW3bPhnKzvO8KIo9FKHwLqtvd/p8wCnDmqhqQJx9WdHCxhxnD8NwnScVrin9FH7x0y3NwU95hQQATkacDcDPDcOQVnZuGxPPWz6mR7UMsuu6nqbJTfvJPGpIv0IfehRmibMvK42zu64bx1GcfW5pKv1i01ff9y4dAMDhiLMB+KG+79PG3qqqPtcx8mUAPY7jao3yXV3X4zh+6PDY3GrlyOq2kCeThphbHxHbiM6Eqqq6rjOdfXppd/bP4mxbQQIAhyDOBmDFl8Fx13Vplv3HfdnRQT5vF8my7ApTuhf3aFvI07/1yxw/y7Jzl4bzRPRgSl3Xc5xtGe/colT69Tg72goyz/NPHyoAwO+JswH4tugG+J5lf6Jj5JVKkNW9KKNb9M33peRvTNO0eiZsW+b+aSGEsiyzLMuyrCgKo7iXtVzOmRc25u5scfa5TdMUXfFefMfTsW41XADA/omzAXjJ/RY3zbLzPG+aZpO4pO/7siyfD2VvdWxsJQ1obhfo35imqeu6pmnOHdzzXNSiLs6+iHEcoyvei2tawzBEn+afPlQAgN8TZwPwUDqllT7RvNXg8zyR/SjFnpVlaSj7guZR5fR8ePHpeziuaDq7qqq2befdIO9fY/z2fKJU+vby8yhRDp5lmWc7AID9E2cD8Kq+76M56K2y7HEcox3PIvNQttTmsoZhSCtHsiyzvMG5Rd3x83R23/ems88tXWle3TAg/UyM4mzT2QDAIYizAXhJ13VRgrzV5oqru1AuVVUlu2H1PKmqyuwhJxY9s1JVVdd1fd877c8tirNfX7qLSrfF2QDAIYizAfjCo1qPP65uCCF0XbdaIrG8FW/b1lA2/x5XjpRlealoz4/DpUTF8XVd933voYTTiz6j8zx/8SoXQlg+dJXnuSsGALB/4myA64ruWh/dxNZ1/aEp1/RPXD2GaZratn3eLjIHN5eKKflS3/erg/xVVYlsOKUozq6qao6znfDnFpXMfKsCe/nZes/BnTAAwJ6JswGILe9j67p+exr4rde2bft8Ivtmy0cea9t2tUS77/v71whuOI0ozm6axnT26YUQouXeL6ez7xe96CmWoij+5JABAH5FnA3AumEYooGvOQf8s2bqaZpWS06i49mkv5sDSU/j24OqHLk2R/eobMS5fWLRdo6373SGhBCWC35FUThVAID9E2cDsKLv+2Wf5v0OeTnT+jlzTfbzdpEsy8qytOUjXxrHcXVAu+u6rQ8N3qzruuV5Pm8F6Tp5btE+kLfbrSzLF18bReHibADgEMTZAPyPvu8flXv8zRz06lR4eq8uoOF10cjqPdH+m+UZ+DPLZHNe82vbVtnIuaVx9usbNUevLYrCFhQAwP6JswEuLZ3DWi3Lvt1uVVV9+kjGcVzddjKKIOu6Nj7Gd62e2M4lTibdCrJpGnH2uUUj+bfb7fV3PIqzX8/BAQA2JM4G4P9N09T3/Wqa/AcTW8MwPG8XmQ9DQQQ/M01T2p8zJ9pbHxq8TZRsrk5nW8I5mWiTibQ4+8k7PgyD6yEAcDjibAD+/XtQlj2rqurTWfaTP30ZyngImie+DOlWK0fyPFdcw2lEw7ZlWXZdZzr7xEII0Urwtx6litY/xNkAwCGIswH49+/fvydp8tvDvmXsGEJ4XjCS53nXdcYJeYtHlSOPvt6Jx7GsTmfriD+xEEL08V2W5esXrmiRT5wNAByCOBuAlfGuu49u//hk28nbf2qyTc7yXukpl2WZ04xziHonxNmnl9YofSuSjk4YcTYAcAjibAAedn0URfG56dSmaZ6MhM9D2R/6o7myKL65n2+qbDiB6PSuqkqcfW5Rvcztm9s5Rg+sfHrPZwCAtxBnA1zXPapumiaazs6y7FsPLD///pFhGJ4UjGRZVlWVslc+ZBiG1XMvivzUjHBEUXeE6ezTi+plbl89UxVd2aIT5ltROADAVsTZAPwbx7Esy3lWek6Tx3F8Y5y3/FZd1z0fyu77XpLIR602aP9+/QY2F01nF0Uhzj63KI/OsuxbD5o82QrS9RAA2C1xNgD//v37N01TXdd1XX8u+JiHstMYcR6VzbKs6zqFD/yBR2Xxngng6KJr7BxnO7FPLP1U/dZOAFEarmwEADgEcTYAHzeOY13XT4ay67oWuPCXohDnnv2tDiSaUuQoVqezo6ur8/lM0jj7vu3EK290dMIoGwEADkGcDcBnNU3zqCZ79rzoEz5kNdF2NnJoUbiZ57mykXNL4+xvvd3RTpJlWX7uUAEA3kWcDcBvPRkBW00Ml9Hhtx6LhvdKK0fyPPegAMclzr6asiyji9i3rmDTNC1fu+zOBgDYLXE2AB8RQoieYv7NLTd8wjAM6ZmpPZbj0p19Nel09qO3e3XhOboGuvoBAIcgzgbg/YZhWN1qb1aWpXiFnVjdntT5yUF1XbfcpaCqqq7rnM8n1nVddPn6VmPSMAzLNjBxNgBwCOJsAN5pmqa6rp+UZXvsnV1Jw6CbJ+45rGEY0jhbp9OJReXXt2/2X0cvv28jCQCwZ+JsAN5mHMeqqh4F2VmWybLZm3Ec09WXLMsMtHJE4zhGyWZUNvJkqwOOaJqm9Ar2+suj/S3E2QDAIYizAXiDEELXdU+GshWMsFurA9rfemAfdiIati2Komka194TCyGkl6/XFy2iLS6apvno0QIAvIU4G4DfGoahaZonWXZd19M0bX2Y8FBZlukCzNYHBd8mzr6a1Tj7Sb1MlHRHcbbrHgBwCOJsAH7leZCdZZmHl9m/6In72+2W5/nWBwXflpaN6M4+t+gdn7342mEYfvxaAIAN+ZUF4Ki+fJr4XR2pj75PCKFt2+W2Y9FUYNd1elo5hDQSyrJsHMdDnMCHOEj+zPKaXBRF27bi7HNLP39fvCakT6Xc1GcDAEcgzgY4j0/n10vDMDzZ9bGqKhEbBxJCSJOduq63Pq6HVn++hmFYrZXww3gdIYSiKO7ncJ7nprPPLYSQPiD14jseNY1867UAABsSZwPwDXMu1vf9810fNWVzOGnfSFmWRwmC73F8nud93299OGxpOZ2d53nbtrqzz225gDGLLgJPrmN1XS9fWBTF548XAOC3xNkAfMM4jnVdP9/18SgJIFeWnqXjOEYndp7nRxlU7LruiIfN20W1OaazT28YhvQT+fUFjGicv23bjx4tAMBbiLMBDu/P4uNxHFerNmdZlrkT5tCiQcUDhTvLOPtAh83bRZv75XneNM093LTWeD7TNKXT2d+6AoQQuq6r6/oouwUAAIizAU7rvfelXdel98x3ZVmqOODoVvtGtj6ol0RH7ofxsqI4e15lNJ19buk+Fnvu/QcA+D1xNsDxLHPqeajq04FF13XLPtY08hOXcALTNP3msf0NRdPZXddtfURsIyobybKsaRrX53P75XT2Iya1AYDdEmcDHNUwDFVV5XmeZVme5x8qrQ4hNE3zKMjOsqyuaxs/cg5RjeyeJ52jH/ZoJtds5mWl09nLshFOKW1JenIFEFIDACcgzgY4gNVt69Lc7Tcjmau3uHNi/ijLrqpqGAb3xpzJl4/t7/OEj4L4qqq2PiK2kW4FKc4+vb7vo6tW2pK0zwsXAMDPiLMBjmc1y77dbk3TvPFPGYbhUcFInufaDDiTe9YzDEPUN5Ln+aPnD/aTEEXbwR2l8pu3i+Lsoiiapun7fj/nKm8XjeS7AgAApyfOBjiYYRgebcn4lrrM2TiOT+ay35ubw36EEFYHtHeeBoYQyrJ8JYLn3KJk8z6dvfMTmN8IIURrz+JsAODcxNkAB/MoZa6qKgosvswvHn1B13WPEvOiKLquk4xwYumAdlEUOz/no+ns20F2sOTtok1B8zxv23YYBssbJxatZs3v+84vWQAAvyHOBjiSvu9XC0CyLBvH8S1/xPOOkXf9KbBb0zRFcXZZljvPhtJNLNUBXVPbtl/G2Ts/mfmBaDfIN/5KAACwQ+JsgMPoui5K2e6jo++axHwUl89/St/3X34HQQlHlxbRRrtB7lP03MYbq4c4kCjOLstyjrO3Pi4+K/rxF2cDAOcmzgbYtXs6/ChoLoriXXetXdc9yrLLshSIcBHppPNqnL23lZumaZbHnLYPcQV930eX7nkryK2Pi8+KfvyzLPORDQCcmDgb4ACi54iXWfa7blnbtl0d/Z5zMXNeXEo06njE6Wz7tV5T2p0tzr6CaCr/drstP7WtbAEAJyPOBti7KJ74fZad3tk2TfMoy67r2p0wVxONuO5/K8h///5Fe8EpG7mmaEr3Hmfv/wTmN9I4W3s+AHBi4myAXVhmDfd/nqbpUdBcVdVya68Xv/OqR39Enudm+rimdDfInT+gkBakmM6+pnQ6u65rvROnN45juhS99UEBAHyKOBtgp4ZhiMYtZ1mWvfE2tWmaR33ZsmyuLGr42Vs6nC5T7fyA+RtRnF0UhbKRKwghRB/l4mwA4MTE2QAbW52e7rpudWJ6Lhh5y2Pj4zg+msvOskxTARcXxYJVVW19RF+IDtiP8DVFZSPzVpCms6/glQ1sAQDOQZwNsDuPyrKzLHvXkF0UeUSJ+Ys1JnBiIYTlYk9RFKtf8/cH9og4m3/JUmhRFHVdm84+vRBC9DjX/lfgAAB+TJwNsC+PguayLN+SMocQHsXlsmy4m6Yp+unYeUAcXTpsBHdN0ZaAykYuIlp+u91uWZZF6227Wn4DAPgNcTbAjkRJxDKSeNdOdFHBriwbHknXlvb8AxIdre7sa4o+RMqybNt2ubYh0zyrqDs7z/M9X68AAH5DnA2wF33fp03WWZZVVfWbLPseXoQQHsXlt/dNf8NpHGtAO/rp3vOh8jnRaVBVVdd1prOvIPr9QdkIAHBi4myAXRiGIc2y8zxv2/Ytc9nTNFVV9STLftf0N5xJNPKcZdluV32iEiEJ5jVFazDi7IsIIUQf60VRhBAM4wMApyTOBthGNDSdZtlvLBgZxzF6DHn5pzRN444XVh1oQDsay9WdfU3jOKZx9jAMWx8XH7H87E67szc8MACAjxJnA/ypNDheHZp+47j0NE1lWa5m2XmeD8Ow22lT2IPox2e3A9q2guTfv3/DMERxdtu24uwrSBetoyuVdWsA4DTE2QBbSveau91uRVH8LH1Ib1anaSqKIv0jsiyr61rGAV+KSjxu+xjQTn/Yo9hdnH1NUZw9bwXpUn960zSlcfbWBwUA8Cl+0QHYTN/3b8yyU9M01XWd/hFzxvGWPwKuIMqJ7j+ku5p2FGfzL/lYKYpCnH0Fq79O7OoCBQDwRuJsgA086st+Y8dICGG1xiTLsqqqbPwIq1YDoPQpirqu//7YntOdzb9kOrsoCt3ZVxC977fbLc/zrQ8KAOBTxNkAfy2EsNoxUpblu0KH1T8iy7I5y95n8y/sVto3kuf53iYfo/FMcfY1RVtBms6+iDTOrqpq64MCAPgUcTbAnxrHcbUAZJ6he9cf8WQuW5YN3xVFhLO+77c+rv8RHWTTNFsfERtIy0a6rvM4zumJswGASxFnA3zE6uRmCCHqt70nDt+annsyFjqO45O9H/c2TwpHkf7kLvtG9vCTFe0FJ86+prRspG1bcfbpRV1DN2UjAMCpibMBPu4eda0WgPyyyXqZo43juBqX3+z9CL+T/vBuO/y4GqAvn/zwI39N0XR2nudN03go5/T2doECAPgocTbAX5j3fkyHp5qmeddcZ9d1q3PZt+9PfwOR9Fn+1bx42zHtKNIyk3tBr0xn7+FhAt4rLTFr23brgwIA+BRxNsDHTdO0Opf9xrvNvu+XPQNRnLG3kl84nBBClmXRctTWBxWLJnPlWReUxtlN01jYOL10vXzZhgQAcDLibIDPWt2Y8c+ybHs/wluEENIf5L099BBFmfKsC1otG9nbicrbdV0XXZ2sZgEAJybOBvigaZpWy6zfuEtb3/fR0Og9xWjb1kPl8C7pj3PXdVsf1P+IIq2yLF0Briaa0rUV5EWkcbbubADgxMTZAO83R0ir45zvTZnHcVzty87zXMEIvF2UFe4tL44mc/d2ePyBqNiqLMu2bU1nn170sy/OBgDOTZwN8Clpl2VRFG+ZkpsjqkcdI+/6U4DIss0jy7L3tgb93jiOy2c1iqLQNXQ1q9PZfd9b2Di3dK/atGvIOQAAnIY4G+Ajuq6LsuY8z9+YMj/KssuyFGDB59z7RuY4OyoO+svAKP2zpmlaXhbE2ReUTujrzr6CNM7+7nT28noi+AYAdk6cDfB+q1n2DwKF1VvKvu+rqlrty26axl0ofFRd17/JjD4qah8qy3LrI+KP3K/8aX960zRWNU4vLRv5cidYvy0AAMclzgb4leiGcJqmtm2jLLsoinc1Wbdtu1qWnWXZ3nalg1MahmG5mJRl2X66faJIK89zidXVRHF2URR1Xd8XU50PZzWOY/RbwevV+SGE/VzEAABeIc4GeJvVvR9vt9vrc9mPbj7n/72u69Wh7CzLbPwIf2Mcx2i9Kuob2co0TdFalzj7gqLSiaIolI1cQdSb/3qcPT/SMfcmmeIHAI5CnA3wHl3XpXPTeZ6/ZWh6HMe6rpch2v3G9Y2j38CX0tS4KIo9pMZp28DtdvPQxtVM0xRtB1rXtdnb04ve99trPUghhGV70rt+YwEA+DRxNsAbRFnze8c2h2FYLRi5KcuGLUR9DjvpG7nvUfn2SxAHEi23lGXZtq2p29MLIUS/J2RZ9uUhqumMAAAgAElEQVRUfnQpu32nogQAYEPibIDfSm8I5zvJ32fNq03cgirYVpocfbnr2ocOY/n/rsbZe8jZ+UvRySnOvo606+zLJ7fato1eUhTF/WyRawMAuyXOBviVYRhW4+ZfFoCEEJ4E2VvFZ8AsSo72MKDdNE10lXilbYCTWY2zNz85+QPRRSnP8y+XMdI423Q2AHAI4myAn5jv99IW3Xm4qW3bX37zZZ1lSscIbGs1O972p3Icx/RCseHxsJVlrJnnue7si0ins78sG/nxBpIAANsSZwN8Lb276/u+qqo0y66q6sXHuh/dMU7TlN6U3mVZ9susHPi9dOO1zQe00zjbdPY1LUduxdkXEUJI64a+jLPTJXkXDQDgEMTZAD+xujdjXde/rCh9PpddVVXf9yanYA/S5/S/DI8+bZqm+QKSZZkQ87KWZ2ZRFE3TbH5m8gd+0J39L9n8w3Q2AHAI4myAb0unILMse3Gm6cmNYgjhyVy2smzYm2hZayflHuM42vrvyvq+X3421XUtzr6CdDp7Nc6OfgmJ4uzlVpAAALslzgb4nnEc05vG38dY97HKVJZlO4nJgKWoQTvP8z/7o01Q8kgIYbmNcFmWAsor+EHZyL9//6JfPDYvTQIAeIU4G+BVIYS2bZcxwT0s+GW0NI7jantJlmVlWb5ybynbgr83DEP0Mys3ZA+Wn1NFUQgoz2r50Z/+FvHK+56uo7uIAQD7J84GeFValVsURdu2v7z3G4bhUZZd17WcGvYsWt+ykRp7sOytyvP8XjrhA+XE0rKyV6azo19slI0AAIcgzgZ4yTAMUW6V53nXdb/5niGEpmmyLEuz7GUAAexWGiH98rIAvxRCWC6R+jS5iKgF+/baVpDTNFmQAwAOR5wN8NB9kC0tA8myrG3bb32TyDRNjzZ+rKrKs+FwCMtt9+7jjcufevOw/IHlaTZN03KVNMsycfYV9H0frY6/suvGOI7LV9moAwA4BHE2wBdCCNEOS69n2aumaWqa5lHBiJtJOJAQQvqDbDmKDUUB5c0TA9eQ9qG9sowRdWdb+QAADkGcDfDMHD1HifNv9n58MpSd57ksGw4nWu4y4ci2pmmKqrFklFeQPimyXFd79EtLFGe7dgEAhyDOBviv6H4vhBDd6d1utx9vzziOY9/3afI1j9GpN4WDila8brdbWZZbHxTXFZVOZFlmOvsKopKZ2+32yqaO0QYerl0AwCGIswHWjeNY1/Vyxi3LsrquX7k/TIUQqqqKJuZm81C2dgI4qHEc0zWq1a/Uo80fSEsn6rre+qD4uDTOfmWNPJrpthUkAHAI4myA2DiObdtGt4Xzbd7raVS0MVc6v3nPsn9Tww3sQbpS9bN1L/i9KKCcF2ItpZzeMAzRVeiV3y6is2UYhvu/cs4AALslzgb4H8MwrM5Ql2X55QD16r3fOI5VVaXh+JyPL28dgYNK16vUO7CVNM6uquqVGmUOLX1M5JVR66hRzfo6AHAI4myA/xqGoSiKNHf+WcdICCFqpfz99wR2KN2ETb0DW4l2G87zvCxLezOcXgjhB1ehaD8PW0ECAIcgzgauaHU2LYSQ7tN4u93KsvxB7jwMQ1mWq1l2lmVt25qPgzNJM8Stj4iLij53iqKoqkqcfQXRs2XibADgrMTZAP/+/acSJI2eo2e0X9R13WpjyfzQt4IROJ90QNv+rmwiesaoLEtx9kVEv3islo1ES+nKRgCAIxJnAzycy87z/Lsz1CGEuq6jW8r7rFzTNIay4ZTS4tqyLLc+KK5oGWdnWVaWZdM0ytyv4JU4OxL98uM8AQAOQZwNXN00Tatz2T8YU5oLRla/1Vww8qH/BGAPoh//oiiW/9ZSFn8ghLAsG5nj7LZtxZSntLyqRG/9z+JsT48BAIcgzgaurmmaNH2ex9m+9X1CCI9i8TzPRQlwel3XRT/7imj5Y9F+gFmWFUXRtq2Y8vTSvqNXrj/R7y1+VwEADkGcDVzRPND0qC+7ruvvzlH2ff9oLrssSzkCXME0TWnRkB9//lJUenMvG9HkfnrRctqLz4S1bbt8lcfIAIBDEGcDFzVNUxpAz1Ns38qyQwhN0xRFET3kO7PxI1xKOqCtQZu/NAzD8vTL83yOs30SnV5aNvLKdLY4GwA4InE2cFF930c3fkVRfHd+7Unv9u12q+t6mqYPHT+wQ9M0LTfim+Nsrdl82v0ci9LJOc5WNnIF0UpGlmV933/5qmgFTj8SAHAI4mzgooZhyPP8nmiXZfndLHscxycbPzZNI8OCC0rr+CWJ/Jno9CvLsq7rtm2VjZzeNE3RIv0P4uy6rv/gUAEAfkmcDVxUCKGu6yzLsiyrquq7Y9RzGr6aZf8gGQdOI+0beSVUgreIprOrqmqapm1bjwqdXjSdHS2kPVpfF2cDAEckzgauK4TQdV3f998dox7HMeoTuPtBYwlwJuM4RjOSEiL+TJROlmU5J9o+mE6vruvoF5JXirD7vnexAgAOR5wN8JJ75D0Mw6MsO8syrQJAVENUFIXqIf5GFGcXRVFVlensK0h38ngUZy8vR7aCBACOSJwN8KoQQtu2q1n23Fgiywb+JblSnudmY/kb0bBtURRzd7Y4+/SiYPr26+5si3AAwG6JswFeEm38uCwTyPO86zphATDruu4He7LB7y0LlOd11rZtfUJdQVo28soSe7T+UVXVHxwqAMAvibMBvhYVjCyDqqIoBFXAUggheoyjLEujjvyBNJ1s2/YHW0RwOFGcnWXZKw+FNE2zfFXTNH9wqAAAvyTOBvhC3/dPCkZ0CACRaZqi6WzF+vyNKJ2sqqrrumEYxNmnF8XZeZ6/MpIf/XpjK0gA4BDE2cAVvX5j3/d9nudpll0URdd1Hz1I4Lii3SBvyR5r4kU+Ico05+ns5VKKE++s0sr+KM5O3/p04U3ZCABwCOJsgHUhhLQA955lG8oGnoiipTTOhk+IprPnfSA1Yl1BdM3JsuzL6eyomkacDQAchTgbYEUIoa7rLMvucfb8D1mWlWWpNAB4Lt2WbbWU1qgs75VOZ89lI1sfFx+Xdmd/+b53XRddpl6sKAEA2JY4G7i61cdvl0UBy0Rblg28Is2JjD3yB6IR3bIs+74XUF5B27bRNefLSrR0OrsoCmtsAMD+ibMB/sc4jlHp7dydPW/8KBQAXpQ++y8n4tNWp7N9cp3V8pIyDENUj/bKDh/RVpBW3QCAQxBnA/xX13X3jR+Xt4V5ntd1vfXRAUeSDmirMObTokWUqqpMZ19E3/dRnP1KX/+8hJ/neVEUVVXZFwQAOARxNsC/f2sbPy47Ruq6NlYJfFc0+ViWpSsJH5WWjZjOvoi0bGR11Hr1EhRCcGkCAA5EnA3w718SASxDbVk28DNRc9Ht5vcuPivKNOfpbB9hV5D+GlOW5dYHBQDwEW6rgGtZvatvmiaKsOf/WxSFjR+BH4uuLbfbzSWFjxrHcfmYkbKR60jj7KZptj4oAICPEGcDB/bLibP55WneNGvbVgQA/EaULd5uNy38fFRUoFyWpensi0jLRiyeAQBnJc4GjuRn9+RPXvUoyxY5Ab83TdO8u+yyi3/rg+LMlhsaP4qzpdunVNd19JuMvWcBgLMSZwNXFELo+76u62hwUpYNvFfXddEVpuu65RfIFnmj6HzTnX0dadnIOI5bHxQAwEeIs4FD+s3N+TRNTdMs59eWs5NlWbrzB94ovdq4yPAhaXd213XOtytIp7OjshGnAQBwGuJs4GBCCG3b/vgWfZqmsizTiez7nb+uSeC90k5bU5N8yDRNyzOtLEtx9kWkcbb3HQA4K3E2cCTTNN2DoTzP27b91stDCI/Ksufbfns/Am8XQoh6jaqq2vqgOKfoZCvL0rbGF5H+euN9BwDOSpwNHMA8YdQ0TVmW98f2syz7ViTU9330yP9SURQ2TQI+pCiK5QUnz3MXHD4hKhspiqJtW1O6V5DG2S4yAMBZibOB7T26017+79M0pWF00zSvf6t0l6Tl/Jq7PuBz0qQpvXzB74UQlp+VRVE0TWNK9wrSXWe/+wQbAMBRiLOBY0jLZ/M8/7Ln+p5upy+/fxMPYgOfNgxDuoq29UFxQmmcbTr7ItI4u67rrQ8KAOAjxNnA3s17P/74Uf25bjsqrr3f5xvKBv5AFDK+uCAH3zUMw5PubLn2ifV9/yTO9tYDAGcizgY288rN1aPNG7uue+WPeNSXnWVZ0zTjOP76PwLgJensZFmWMibeK8o0lY1cxzRN0e85ykYAgLMSZwP7sgx3hmGo6zpNolfv0NJU6FFftqFI4O+FEKKnTORNvN04jtE5Vte155AuIlq/d3kBAM5KnA3sVNd1UfQzJ9EvzmWP47iaZRdFIcsGNpGW+FdVtfVBcSpp40RVVT71LqIsy+Vbb79ZAOCsxNnAHnVdl7Zdv9iXPfeTrHaM3F5uKQF4u2maoitbnueKIHijdNNRu0RcRzQEYL9ZAOCsxNnAvswbP/44y/63Nv8481w/sK20ASnLMpOzvFG6ZCLOvojVt37rgwIA+AhxNvBx39rrLG0I+da2jeM4phUlWZbled62rV3XgG2lG0K+txCgbduu61zrriz6GFWxdRGrg/lbHxQAwEeIs4E/tRqyzP/jXBIS3YzVdf1ikP3vQZY9fxOP8wN7kFYb/6ZvZHlFnTcMyLIsyzKtSle23EJ5dStIqx2nFO0COl9bvNcAwCmJs4FdWN25saqqX0523263sixl2cBOjOOYNvtH6fMPEqhpmpYXwGiHSZHWdYQQlnF2URR1XRvYv4JpmqJri2p+AOCsxNnA9qZpKssyyneKonh9Lvvfv39N06SN29/9JgAfFUJIHyL5/apb9G3fW2DCgYQQlp+nZVk2TaNr6wqit/6mmh8AOC9xNrCx1VnF79aDdF2XZtm3283ej8DepK1Kt9vt96nTcjpbnH1ly+lscfalRNX84mwA4KzE2cDGiqKIkuiyLL91450+YHvPxD932AA/80rfyA8sU/KoK5lLWZ4JZVnaHfQ62raN4mwPqAEApyTOBj7u0V30vez1HmfPm1Z9ay47hPCoMttdHLBPad9I+ijJd/PH+0zud1cEOZnlZ+IcZ1veuIg0zr5PZ7smAABnIs4GtjEMQ1TymOf5d7tB0qbIWVEU7tyA3VrWQcx+/zTJvWfAgylXFrWoF0XRtq3F3Yvo+z66sPz+sQ8AgB0SZwMb6LruLc/aR4NI93Ekt+7AnqX12Xme/3I3yPtMbpZlMqwrW67yzuvECpTPKlq5H4YhurD8fptZAIAdEmcDf63v+yjLzrLsuxuXhRBWt3/M89xT1cDOrS7F/TKDXk58G9C+rHEcl9PZeZ43TWOJ9yLGcUx/L7KYAQCcjzgbeLPnLR9t2y7vtbIsW3Y7vmgcx9WOkSzLZNnA/q2uxv2yJWl5VYwWCJUvXce9c+Z+UtV1LdC8iNUGtu+OCwAA7J84G/gL0zQNw5Du2fjdYepxHOu6TmMgWTZwIKupU5Zlv8mdlzO5AqzL6vt++RE5l42Yzr6O6AS4eVYDADgjcTbwQeM4hhDGcUyD7J9l2Wnj9j0GMn0GHEh6Ncvz/B5n/yDXXl5mq6p69/FyDOl0tu7sq4mWyoqiUJ8NAJyMOBv4oKZpqqpazgze0+eyLL91gz0MQ/p97hmQe3XgWNILWp7nv/mGyz7usizfdZwcS9M00XR20zTLlWPNMyeTvqHLGv2ZvWEBgJMRZwOfsrrX2e0/Gz9+N4COpo3ut+tlWeoYAQ4njZx+WTbSNM3yW5nHvKa2bZeD/3me13Xdtq0U+zrSa0tVVU4AAOBMxNnARwzD8CjLfvEp+OVD94+S8bqu3aEBR7R6WftNx3HU6aQu+ZqiKDPLsrqudalfSlQ4M69qWN8CAM5EnA283+quj7OyLL97T/Vo78eyLGXZwEH1fZ9e1n7zrEl01bX/2zUth/Rv/1lCdjJcyjiO0YWlKAq/LwEAZyLOBt5p3vhxNX2etW37+nebpim6M18mNe7NgONajbO/dYWMRHtL2g3ymqKp/zzPq6oynX0p6a9hrgYAwMmIs4E3e1QMcvtmnWvXdVFf9t0PRrwBdmW1kek3qVPUMiHBvKaoaKIoiqZpfrNMwuGkS2VFUWx9UAAA7yTOBt5sNc7OsqwsyxfjlRDCoyB7jnt0wgJHtxpn53n+428YXXv1S1xTFGeXZdm2bdd1Wx8XH7H6mFoIIZrOdjUAAE5GnA282eoT9MMwhBBerAd5VDAyZ9k6RoATWI2zo0dYvnW5m6ZpmWEJsK4pWtW4x9k+Oq9jmqbowuJZDQDgZMTZwJtN01RV1T1VybKsaZoXb6T7vn+08eOczugYAU5jdcvcH+8GGUKIFv/ee7Ts2f1Ddtk5M+8D2bbtb7YY5XCiCX2LWwDA+Yizgfcbx7Gu6zzPsyx78S46hLCa7CxvxgyXAWeSDlHevrMbZHpJXO4GKc6+ptXp7GEYtj4u/k7625TydADgZMTZwEdM09R13esDQW3bzkPZ6Wh2WZZuxYFTSoOnH9ccR4W5ZVm+91A5hGWcPU9n933vM/RSol1hb7ebaQAA4GTE2cD2hmFYDhUub8UVjAAnlu6d++NagHEcl3F2URTvPVQOYbn5xFz21ff9OI4CzeuIFsnyPH/x3XeSAABHIc4GtjRNU9u2RVGkWXZVVeM4bn2AAB80TVNZllH29LM1vHEc3xKLc2jRdHbTNPNWzBaGT2k1gI4uKaazAYDzEWcDmxnHMb3pmjVN494buIJ037afFd0OwyDOZjmdPX+YznH2MtAUbp5bOiJwf8dff+udJADAnomzgb8TQhiGoWmaqqoeBdk/jnIAjijdEPJnSXT0fcTZ1xQ1d81lI/+kk1cSLWlkWfboWTdnBQBwUOJs4O9M07Takb1UlqX7K+BS0r6RV6qWokvlk7IRF9XrWJ5LeZ63bdv3fTSdzblFcfa8qvHoi+chA5uFAgDHIs4G/k7f90+C7PnG2y03cG7pVe4tfSPRBdZ09jUttwEsy7Jt2zmplGhfR/q71qOrQQihLMs8z4uieBJ5AwDsjTgb+AvTNDVNk2XZoyy7KArDQcA1hRCiutuqqr77TaLHX8TZ17SMs4uiaNt2HMfwH1sfHX8hhBD9upXn+aOvLIpi/uKiKJwhAMBRiLOBv9C27fO57FeerAc4pXlGMlrh++52uNE3EWdfUAhhGWfPzzzNW0FufWj8qeVpcLvdsix79JV93+d5nmXZD5bQAAC2Is4G/kJd10/i7HmjKoDLmpPo5Uzlowvjo2hymqbliLc4+4KmaYq6s+u6nruztz40/lTUX/RkN8h///kNrSzL5UNyzhkAYM/E2cBfiO6x7/dXVVXpGAFI626/W2Ub7f+mCfeCxNnXFL2/aXnR7XZ78rvWPMo9V9N8/mABAN5AnA38kWmaoqdf3TgB3EVrft999j96CKYsSyHmBS2rvYqiqOu667ppmu4ng7PiCtJH4rquW/3KcRzvD4VYAwMAjkKcDfypvu+LoijL0t6PAEvRgt8t6Rt5EkSm7dt5ngsuL2gZZ8/T2V3X2QfyaoZhiC4mq+1DUdl6WZY2MgEADkGcDWzArTVAJI2zsyx7fUPIKM7+1ms5jWVpcp7nVVW1betMuJqoemiOqtMvCyHkeb68aHhsDgA4BHE2AMA2lgt7Xdctt4JcHdB+9PJoH0hx9mUtc0xx9mWlcfZqTv37yn4AgE2IswEAtrcssf1uurSsmLhHmULMC0rLRsTZ57b6rFvanb1aNvIveSjku5X9AACbEGcDAGxvmqYfx9npMGZRFDqdLmh5JsxbQfZ9L86+mnR969EFIQq+xdkAwCGIswEAthf12D6fqYxM03RL2NXtgpbp5DydLc6+oHEco6tBnuerF4RoJawoCmcLALB/4mwAgO2tlo2UZfnikHUahQ/D8OljZm+WcXaWZXVdd10noLyaEEK0N+zqVpD/krIRJUUAwCGIswEAtjcMw2qc/eLLo60gb4ttJLWOXEc0nV1Vlensa4paRB6NXUdxdpZlnuoAAPZPnA0AsL1H09kvvjwaxmzbVop9QelWkMMwLM8EZ8VFpPXZXdd9+WWmswGAQxBnAwDsQppAZVmW5o+rieQ4jmVZZlmW5/l9LpurieLseTpbhH1B6cVkdV/ZYRiWX/NiWT8AwLbE2QAAu5Bu4FZV1be+g8nKi1vu7FcUhTj7srqueyXOjr6sbdu/P1QAgO8SZwMA7EI0KfkogYJHVstGtj4oNtD3/SsXk+jLvrt+BgCwCXE2AMAupHG2YUm+JS0bibqzuYh0a9nVi0kUZxdF4WwBAPZPnA0AsAtp2Yg4m29Zlo3McXbXdeM4Lr9GXnkF4zjmef7ldHb0Zatl/QAAeyPOBgDYhXQ626aOvOIeQbZtu5zJrapK38g1hRCiOHu1SGSapuUJI84GAA5BnA0AsAvLpohZNFf7z2gtT0UrImVZVlVlxv+Copx6ntZf/TLT2QDA4YizAQB2YdkUMZumaeuD4ki6rosGcue+ka2Pi78WQrgl0uWxqOAoy7JNjhYA4FvE2QAAuxBNZ4uW+K7likiWZXVd13WdhphcQTSdfbvd0tqZEMLyy4qi2ORQAQC+RZwNALAL0WjtajkAPFFV1fIUapqm6zoz/tcUdWff1rr4ozi7LMtNDhUA4FvE2QAAuxBNZ4uz+a6iKJanUF3X4uzLejHOXn7BcjpbiTYAsFvibACA7YUQoizypjubb4pWRObibGfRNb1SNhJ1ZysbAQAOQZwNALC9vu9vCUEk37JMJ4uiKIqiaRrd2Sf2ZIY6XR5r2zZ9+TL19kQIAHAI4mwAgO0tN/ETZ/Mzy+7soiiUjVzZD7aCFGcDAIcgzgYA2N5qnB3N1Wqz5YmoOCLLsq7rhmFYnjZOoRNbvrnRvrK3x9s8Liu2syz7q4MFAPg5cTYAwPai1uNZunUbPJImmFVV9X0vwr6aaZrS0eyu6778SnE2AHAI4mwAgO2tTmfXdb31cXEYaZz9KMTkxEIIy86ZL3PqsiyXE9wWPwCA/RNnAwBsbzWLrKpq6+PiMFZPIdPZV5Nm2c8Xxuq6vn9ZURSeCAEA9k+cDQCwvWEY0hCqaZqtj4vDUDbC6mUky7KohX+p7/sXg28AgJ0QZwMAbC/ax282DMPWx8VhRKdQWZZd13VdJ86+gnEc27ZNK7NvX1XwR6dNnud/dswAAD8jzgYA2N44jlEU9XymEiIhhLIs8zwviqJpmr7vu67r+36apq0Pjc9a3ftxVhTF8/WMEEKe51bRAIADEWcDAGwveuR/jrMFkXzLNE0hhDm+DCGM4zj/L1sfFx9xf2fbtl3Nsl8sD1nWbed53rbthw8cAOBXxNkAANtbDaRMZwPPTdO0GmTPzemvXEOi1nWV/QDAzomzAQC2l8bZprOBL63W7n9rR8doA8mu6z53tAAAvyfOBgDYXjQgOT/1n8bZiiP4MSfPWS3bQrIs+24evbz4ZFmmbAQA2DlxNgDA9pqmSeNs+SPwpb7v8zyf9//8QUPR8uIjzgYA9k+cDQCwPd3ZwI/9eOmrbdssy3RnAwAHIs4GANheCCHP8yjO1p0NfM44jullR5wNAOycOBsAYBfqun59Ons5jPnon9P/F+B+Wfj9NpIAAH9PnA0AsAtp30jf91sfFHBawzCkcbbpbABg58TZAAC7kEZLciXgc7quS+Psqqq2Pi4AgGfE2QAAu9D3fZQrFUWx/ALNIcAbpdccq2gAwP6JswEAdmG1x9ZukMCHrMbZOo4AgJ0TZwMA7EIIIc/zNz71b5obeCLt67893YEWAGAPxNkAAHtRluUyVyrL8sUXTtPUtm1d103TSLGBVHplSJ8IybJMnA0A7Jw4GwBgL5qmiaKlF19YVdX8kjzP67qWaAOviK45dV1vfUQAAF8QZwMA7MUwDNGw5DAMr7xw2VKSZZnGbeBFVVVlWZZlWVEURrMBgP0TZwMA7EX67H+6Ldvq5HXUUiKTAl4UQhjHcRgGy2AAwCGIswEA9qLv+yjO7rrulRfey0a+9SoAAIBjEWcDAOxFNGR9u92qqnrlhW3bLjeQNJ0NAACckjgbAGAviqKItoLM8/yVF07TdH+VxgAAAOCsxNkAAHuRTmcXRfHia+9ReFq3DQAAcA7ibACAvXglzl7dCjKEkOf5dxNwAACAYxFnAwDsxT2S/m539r9FFJ5l2UcPEgAAYCvibACAXQgh3BKvN4fUdX1/1UePEwAAYCvudgAAdmG5neMP9nVcTnYPw/DRQwUAANiEOBsAYC/SspFxHF987X0ryNvtVtf1R48TAABgE+JsAIBdWG7n+GXZSLQh5DRNWZaJswEAgHMTZwMA7MV9O8e7pmleeeE4jstXlWX56UMFAAD4e+JsAIBdCCFUVRXF2VVVvfLaKM4uiuLTRwsAAPD3xNkAALsQQkins5dz1lHByFJUNlKW5X0PySevAgAAOBZxNgDAXqTT2Xmev5JHj+O4jLOLorjH2QAAAKchzgYA2IumaZ5MZz8RQiiKQtkIAABwbuJsAICN3eev0zj7SXf2cmp7mqYoztYxAgAAnI84GwBgL4Zh+NlWkNF09osVJQAAAMcizgYA2ItoR8fb7ZZl2TiOX74w7c4WZwMAAOcjzgYA2JGyLKMB7bquv3xV27Y/CMEBAACORZwNALAXUQX266PWaen2MAx/c8wAAAB/RpwNALAj6XR2URTTNM3/9lGuXVVV9CrT2QAAwPmIswEAdqTv+yiYzvP8HmevivaB1J0NAACclTgbAGBHhmG4JZqmef6quq6XX1+W5T3OlmsDAACnIc4GANiRtAV79nxAu+u6aDr7zw4YAADgz4izAQB2ZBiGLMvSOPv51o7RTPdyOhsAAOA0xNkAADsyTdMP4uyobMR0NgAAcEribACAHVntzo7qs9PJ67IsozjbdDYAAHA+4mwAgCEO8FIAAAEmSURBVL2YpikKpu/qun7ywqg7u+u6PztmAACAPyPOBgDYi0f7QL7SH1IUxYvNJAAAAAclzgYA2IVxHB9l2bfbrW3b5y/vum5OtBVnAwAAZyXOBgDYhaqqnsTZy+7sR0IIbduO4/gHRwsAAPD3xNkAABubpul5ln273cqy3PowAQAANibOBgDYWAjh0Q6Qd1VVbX2YAAAAGxNnAwBsb5qm53F2XddbHyMAAMDGxNkAALuw2jcy/49ZlomzAQAAxNkAALvQ932e53meF//R9/2/f/+GYRjH8WcbPIYQ3n2YAAAAmxFnAwDsQghhHMdpmkIIYmgAAICUOBsA4Gyk4QAAwCmJswEAAAAAOABxNgAAAAAAByDOBgAAAADgAMTZAAAAAAAcwP8BFeo+RXprL10AAAAASUVORK5CYII=" alt><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>M1A1A1A1A1A1A1</em></strong></span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 29px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for both vertical asymptotes correct,</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>M1</em></strong> for recognizing that there are two turning points near the origin,</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>A1</em></strong> for both turning points near the origin correct, (only this <strong><em>A</em></strong> mark is dependent on the <strong><em>M</em></strong> mark)</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>A1</em></strong> for the other pair of turning points correct,</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>A1</em></strong> for correct positioning of the oblique asymptote,</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>A1</em></strong> for correct equation of the oblique asymptote,</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>A1</em></strong> for correct asymptotic behaviour in all sections.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well done, except for the behaviour near the origin. The questions alerted candidates to the existence of four turning points and an oblique asymptote, but not all reported back on this information.</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;">The graph of \(y = f(x){\text{ for }} - 2 \leqslant x \leqslant 8\) is shown.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 23px/normal Helvetica; text-align: center; margin: 0px;"><img 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" alt></p>
<p style="font: normal normal normal 23px/normal Helvetica; text-align: center; margin: 0px;"> </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;">On the set of axes provided, sketch the graph of \(y = \frac{1}{{f(x)}}\), clearly showing any asymptotes and indicating the coordinates of any local maxima or minima.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 23px/normal Helvetica; text-align: center; margin: 0px;"><img 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" alt></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="font: normal normal normal 23px/normal Helvetica; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"><img 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" alt> <strong><em>A1A1A1A1A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica; min-height: 28.0px;"> </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>Notes:</strong> Award <strong><em>A1</em></strong> for vertical asymptotes at <em>x</em> = −1, <em>x</em> = 2 and <em>x</em> = 5 .</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>A1</em></strong> for \(x \to - 2,{\text{ }}\frac{1}{{f(x)}} \to {0^ + }\)</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>A1</em></strong> for \(x \to 8,{\text{ }}\frac{1}{{f(x)}} \to - 1\)</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>A1</em></strong> for local maximum at \(\left( {0, - \frac{1}{2}} \right)\) (branch containing local max. must be present)</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>A1</em></strong> for local minimum at (3, 1) (branch containing local min. must be present)</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;">In each branch, correct asymptotic behaviour must be displayed to obtain the <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;">Disregard any stated horizontal asymptotes such as <em>y</em> = 0 or <em>y</em> = −1 .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A large number of candidates had difficulty graphing the reciprocal function. Most candidates were able to locate the vertical asymptotes but experienced difficulties graphing the four constituent branches. A common error was to specify incorrect coordinates of the local maximum <em>i.e.</em> (0,–1) or (0,–2) instead of \(\left( {0, - \frac{1}{2}} \right)\). A few candidates attempted to sketch the inverse while others had difficulty using the scaled grid.</span></p>
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