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</div><h2>SL Paper 2</h2><div class="specification">
<p>A particle P moves along a straight line. Its velocity \({v_{\text{P}}}{\text{ m}}\,{{\text{s}}^{ - 1}}\) after \(t\) seconds is given by \({v_{\text{P}}} = \sqrt t \sin \left( {\frac{\pi }{2}t} \right)\), for \(0 \leqslant t \leqslant 8\). The following diagram shows the graph of \({v_{\text{P}}}\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.04.21.png" alt="M17/5/MATME/SP2/ENG/TZ1/07"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the first value of \(t\) at which P changes direction.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <strong>total </strong>distance travelled by P, for \(0 \leqslant t \leqslant 8\).</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>A second particle Q also moves along a straight line. Its velocity, \({v_{\text{Q}}}{\text{ m}}\,{{\text{s}}^{ - 1}}\) after \(t\) seconds is given by \({v_{\text{Q}}} = \sqrt t \) for \(0 \leqslant t \leqslant 8\). After \(k\) seconds Q has travelled the same total distance as P.</p>
<p>Find \(k\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \frac{{20x}}{{{{\rm{e}}^{0.3x}}}}\) , for \(0 \le x \le 20\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of <em>f</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the <em>x</em>-coordinate of the maximum point on the graph of <em>f</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Write down the interval where <em>f</em> is increasing.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(f'(x) = \frac{{20 - 6x}}{{{{\rm{e}}^{0.3x}}}}\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the interval where the rate of change of <em>f</em> is increasing.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = {{\rm{e}}^{2x}}\cos x\) , \( - 1 \le x \le 2\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(f'(x) = {{\rm{e}}^{2x}}(2\cos x - \sin x)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Let the line <em>L</em> be the normal to the curve of <em>f</em> at \(x = 0\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the equation of <em>L</em> .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> and the line <em>L</em> intersect at the point (0, 1) and at a second point P.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find the <em>x</em>-coordinate of P.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the area of the region <strong>enclosed</strong> by the graph of <em>f</em> and the line <em>L</em> .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><span class="s1">A particle P </span>moves along a straight line so that its velocity, \(v\,{\text{m}}{{\text{s}}^{ - 1}}\), after \(t\) seconds, is given by \(v = \cos 3t - 2\sin t - 0.5\)<span class="s1">, for \(0 \leqslant t \leqslant 5\). The initial displacement of P from a fixed point O is 4 </span>metres.</p>
</div>
<div class="specification">
<p class="p1">The following sketch shows the graph of \(v\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-02-01_om_15.51.25.png" alt="M16/5/MATME/SP2/ENG/TZ1/09.b+c+d+e"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the displacement of <span class="s1">P </span>from <span class="s1">O </span>after <span class="s1">5 </span>seconds.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find when <span class="s1">P </span>is first at rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the number of times <span class="s1">P </span>changes direction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the acceleration of <span class="s1">P </span>after 3 seconds.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the maximum speed of <span class="s1">P</span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \sqrt[3]{{{x^4}}} - \frac{1}{2}\).</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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(f'(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 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">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows the graphs of \(f(x) = \ln (3x - 2) + 1\) and \(g(x) = - 4\cos (0.5x) + 2\) , for \(1 \le x \le 10\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/laurie.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>A</em> be the area of the region <strong>enclosed</strong> by the curves of <em>f</em> and <em>g</em>. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Find an expression for <em>A</em>. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> (ii) Calculate the value of <em>A</em>.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Find \(f'(x)\) . </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> (ii) Find \(g'(x)\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There are two values of <em>x</em> for which the gradient of <em>f</em> is equal to the gradient </span><span style="font-family: times new roman,times; font-size: medium;">of <em>g</em>. Find both these values of <em>x</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = {x^2} - 4x + 1\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of <em>f</em> , for \( - 1 \le x \le 5\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This function can also be written as \(f(x) = {(x - p)^2} - 3\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the value of <em>p </em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>g</em> is obtained by reflecting the graph of <em>f</em> in the <em>x</em>-axis, followed by a </span><span style="font-family: times new roman,times; font-size: medium;">translation of \(\left( {\begin{array}{*{20}{c}}<br>0\\<br>6<br>\end{array}} \right)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(g(x) = - {x^2} + 4x + 5\) .</span> </p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>g </em>is obtained by reflecting the graph of <em>f </em>in the <em>x</em>-axis, followed by a translation of \(\left( {\begin{array}{*{20}{c}}<br>0\\<br>6<br>\end{array}} \right)\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graphs of <em>f</em> and <em>g</em> intersect at two points.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the <em>x</em>-coordinates of these two points.</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><span style="font-family: times new roman,times; font-size: medium;">The graph of \(g\) is obtained by reflecting the graph of \(f\) in the <em>x</em>-axis, followed by a translation of \(\left( {\begin{array}{*{20}{c}}<br> 0 \\ <br> 6 <br>\end{array}} \right)\) .<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>R</em> be the region enclosed by the graphs of <em>f</em> and <em>g</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the area of <em>R</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \cos 2x\) and \(g(x) = \ln (3x - 5)\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(f'(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(g'(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(h(x) = f(x) \times g(x)\) . Find \(h'(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = x{(x - 5)^2}\) , for \(0 \le x \le 6\) . The following diagram shows the graph of <em>f</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/sully.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let R be the region enclosed by the <em>x</em>-axis and the curve of <em>f</em> .</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 area of <em>R</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find the volume of the solid formed when <em>R</em> is rotated through \({360^ \circ }\) about the </span><span style="font-family: times new roman,times; font-size: medium;"><em>x</em>-axis.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows a part of the graph of a quadratic function </span><span style="font-family: times new roman,times; font-size: medium;">\(g(x) = x(a - x)\) . The graph of <em>g</em> crosses the <em>x</em>-axis when \(x = a\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/555.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The area of the shaded region is equal to the area of <em>R</em>. Find the value of <em>a</em>.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The velocity <em>v</em> ms<sup>−1</sup> of an object after <em>t</em> seconds is given by \(v(t) = 15\sqrt t - 3t\) , </span><span style="font-family: times new roman,times; font-size: medium;">for \(0 \le t \le 25\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the grid below, sketch the graph of <em>v</em> , clearly indicating the maximum point.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br></span><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down an expression for <em>d</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Hence, write down the value of <em>d</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<br><hr><br><div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A gradient function is given by </span><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{d}}y}}{{{\rm{d}}x}} = 10{{\rm{e}}^{2x}} - 5\) . When \(x = 0\) , \(y = 8\) . Find the value </span><span style="font-family: times new roman,times; font-size: medium;">of <em>y</em> when \(x = 1\) .</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;">A particle moves in a straight line. Its velocity, \(v{\text{ m}}{{\text{s}}^{ - 1}}\), at time \(t\) seconds, is given by</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;">\[v = {\left( {{t^2} - 4} \right)^3},{\text{ for }}0 \leqslant t \leqslant 3.\]</span></p>
<div> </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 velocity of the particle when \(t = 1\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \(t\) for which the particle is at rest.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the total distance the particle travels during the first three seconds.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Show that the acceleration of the particle is given by \(a = 6t{({t^2} - 4)^2}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find all possible values of \(t\) for which the velocity and acceleration are both positive or</span><span style="font-family: 'times new roman', times; font-size: medium;"> both negative.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows the graph of \(f(x) = {{\rm{e}}^{ - {x^2}}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/berlin.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The points A, B, C, D and E lie on the graph of <em>f</em> . Two of these are points of inflexion.</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;">Identify the <strong>two</strong> points of inflexion.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find \(f'(x)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Show that \(f''(x) = (4{x^2} - 2){{\rm{e}}^{ - {x^2}}}\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the <em>x</em>-coordinate of each point of inflexion.</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><span style="font-family: times new roman,times; font-size: medium;">Use the second derivative to show that one of these points is a point of inflexion.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f(x) = - 0.5{x^4} + 3{x^2} + 2x\). The following diagram shows part of the graph of \(f\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.09.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/08"></p>
<p> </p>
<p>There are \(x\)-intercepts at \(x = 0\) and at \(x = p\). There is a maximum at A where \(x = a\), and a point of inflexion at B where \(x = b\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(p\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the rate of change of \(f\) at A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the the rate of change of \(f\) at B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let \(R\) be the region enclosed by the graph of \(f\) , the \(x\)-axis, the line \(x = b\) and the line \(x = a\). The region \(R\) is rotated 360° about the \(x\)-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p><strong>Note:</strong> <strong>In this question, distance is in metres and time is in seconds.</strong></p>
<p> </p>
<p>A particle moves along a horizontal line starting at a fixed point A. The velocity \(v\) of the particle, at time \(t\), is given by \(v(t) = \frac{{2{t^2} - 4t}}{{{t^2} - 2t + 2}}\), for \(0 \leqslant t \leqslant 5\). The following diagram shows the graph of \(v\)</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_08.18.11.png" alt="M17/5/MATME/SP2/ENG/TZ2/07"></p>
<p>There are \(t\)-intercepts at \((0,{\text{ }}0)\) and \((2,{\text{ }}0)\).</p>
<p>Find the maximum distance of the particle from A during the time \(0 \leqslant t \leqslant 5\) and justify your answer.</p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = x\cos x\) , for \(0 \le x \le 6\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(f'(x)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the grid below, sketch the graph of \(y = f'(x)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/bbc.png" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">The acceleration, \(a{\text{ m}}{{\text{s}}^{ - 2}}\), of a particle at time <em>t</em> seconds is given by \[a = \frac{1}{t} + 3\sin 2t {\text{, for }} t \ge 1.\]<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The particle is at rest when \(t = 1\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the velocity of the particle when \(t = 5\) .</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A particle <span class="s1">P </span>starts from a point <span class="s1">A </span>and moves along a horizontal straight line. Its velocity \(v{\text{ cm}}\,{{\text{s}}^{ - 1}}\) after \(t\) <span class="s2">seconds is given by</span></p>
<p class="p2">\[v(t) = \left\{ {\begin{array}{*{20}{l}} { - 2t + 2,}&{{\text{for }}0 \leqslant t \leqslant 1} \\ {3\sqrt t + \frac{4}{{{t^2}}} - 7,}&{{\text{for }}1 \leqslant t \leqslant 12} \end{array}} \right.\]</p>
<p class="p1">The following diagram shows the graph of \(v\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.40.29.png" alt="N16/5/MATME/SP2/ENG/TZ0/09"></p>
</div>
<div class="specification">
<p class="p1"><span class="s1">P </span>is at rest when \(t = 1\) and \(t = p\).</p>
</div>
<div class="specification">
<p class="p1">When \(t = q\), the acceleration of <span class="s1">P </span>is zero.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the initial velocity of \(P\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(p\).</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">(i) <span class="Apple-converted-space"> </span>Find the value of \(q\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Hence, find the <strong>speed </strong>of <span class="s1">P </span>when \(t = q\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the total distance travelled by <span class="s1">P </span>between \(t = 1\) and \(t = p\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Hence or otherwise, find the displacement of <span class="s1">P </span>from <span class="s1">A </span>when \(t = p\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = {{\rm{e}}^x}(1 - {x^2})\) .</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Part of the graph of \(y = f(x)\), for \( - 6 \le x \le 2\) , is shown below. The <em>x</em>-coordinates of the local minimum and maximum points are <em>r</em> and <em>s</em> respectively. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/aching.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(f'(x) = {{\rm{e}}^x}(1 - 2x - {x^2})\) . </span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the <strong>equation</strong> of the horizontal asymptote.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the value of <em>r</em> and of <em>s</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>L</em> be the normal to the curve of <em>f</em> at \({\text{P}}(0{\text{, }}1)\) . Show that <em>L</em> has equation \(x + y = 1\) .</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><span style="font-family: times new roman,times; font-size: medium;">Let <em>R</em> be the region enclosed by the curve \(y = f(x)\) and the line <em>L</em>. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Find an expression for the area of <em>R</em>. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> (ii) Calculate the area of <em>R</em>.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">e(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A particle’s displacement, in metres, is given by \(s(t) = 2t\cos t\) , for \(0 \le t \le 6\) , </span><span style="font-family: times new roman,times; font-size: medium;">where <em>t</em> is the time in seconds.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the grid below, sketch the graph of \(s\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/N12P2Q7.jpg" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the maximum velocity of the particle.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = a{x^3} + b{x^2} + c\) , where <em>a</em> , <em>b</em> and <em>c</em> are real numbers. The graph of <em>f</em> passes </span><span style="font-family: times new roman,times; font-size: medium;">through the point (2, 9) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(8a + 4b + c = 9\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> has a local minimum at \((1{\text{, }}4)\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find two other equations in <em>a</em> , <em>b</em> and <em>c</em> , giving your answers in a similar form to </span><span style="font-family: times new roman,times; font-size: medium;">part (a).</span></p>
<p> </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><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>a</em> , of <em>b</em> and of <em>c</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f'(x) = - 24{x^3} + 9{x^2} + 3x + 1\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">There are two points of inflexion on the graph of <em>f</em> . Write down the <em>x</em>-coordinates </span><span style="font-family: times new roman,times; font-size: medium;">of these points.</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;">Let \(g(x) = f''(x)\) . Explain why the graph of <em>g</em> has no points of inflexion.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = {x^2}\) and \(g(x) = 3\ln (x + 1)\), for \(x > - 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Solve \(f(x) = g(x)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the area of the region enclosed by the graphs of \(f\) and \(g\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the graph of the semicircle given by \(f(x) = \sqrt {6x - {x^2}} \), for \(0 \leqslant x \leqslant 6\). A rectangle \(\rm{PQRS}\) is drawn with upper vertices \(\rm{R}\) and \(\rm{S}\) on the graph of \(f\), and \(\rm{PQ}\) on the \(x\)-axis, as shown in the following diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><img src="images/maths_7.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \({\text{OP}} = x\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find \({\text{PQ}}\), giving your answer in terms of \(x\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence, write down an expression for the area of the rectangle, giving your answer in terms of \(x\).</span></p>
<div class="marks">[[N/A]]</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 rate of change of area when \(x = 2\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The area is decreasing for \(a < x < b\). Find the value of \(a\) and of \(b\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows a plan for a window in the shape of a trapezium.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/tpc.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Three sides of the window are \(2{\text{ m}}\) long. The angle between the sloping sides of the </span><span style="font-family: times new roman,times; font-size: medium;">window and the base is \(\theta \) , where \(0 < \theta < \frac{\pi }{2}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that the area of the window is given by \(y = 4\sin \theta + 2\sin 2\theta \) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Zoe wants a window to have an area of \(5{\text{ }}{{\text{m}}^2}\). Find the two possible values of \(\theta \) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">John wants two windows which have the same area <em>A</em> but different values of \(\theta \) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find all possible values for <em>A</em> .</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: TimesNewRomanPSMT;">Consider </span><span style="font-family: TimesNewRomanPS-ItalicMT;">\(f(x) = x\ln (4 - {x^2})\)</span><span style="font-family: TimesNewRomanPSMT;"> , for </span><span style="font-family: Times New Roman;" lang="JA">\( - 2 < x < 2\)</span><span style="font-family: TimesNewRomanPSMT;"> . The graph of </span><em><span style="font-family: TimesNewRomanPS-ItalicMT;">f </span></em><span style="font-family: TimesNewRomanPSMT;">is given below.</span></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: TimesNewRomanPSMT;"><br><img src="images/witch.png" alt></span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let P and Q be points on the curve of <em>f</em> where the tangent to the graph of <em>f</em> is </span><span style="font-family: times new roman,times; font-size: medium;">parallel to the <em>x</em>-axis.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find the <em>x</em>-coordinate of P and of Q.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Consider \(f(x) = k\) . Write down all values of <em>k</em> for which there are </span><span style="font-family: times new roman,times; font-size: medium;">exactly two solutions.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Show that \(g'(x) = \frac{{ - 2{x^4}}}{{4 - {x^2}}} + 3{x^2}\ln (4 - {x^2})\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) .</span></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of \(g'\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) .</span></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider \(g'(x) = w\) . Write down all values of <em>w</em> for which there are exactly </span><span style="font-family: times new roman,times; font-size: medium;">two solutions.</span></p>
<p align="LEFT"> </p>
<p align="LEFT"> </p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A particle starts from point \(A\) and moves along a straight line. Its velocity, \(v\;{\text{m}}{{\text{s}}^{ - 1}}\), after \(t\) seconds is given by \(v(t) = {{\text{e}}^{\frac{1}{2}\cos t}} - 1\), for \(0 \le t \le 4\). The particle is at rest when \(t = \frac{\pi }{2}\).</p>
<p class="p1">The following diagram shows the graph of \(v\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-14_om_09.53.11.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the distance travelled by the particle for \(0 \le t \le\ \frac{\pi }{2}\).</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">Explain why the particle passes through \(A\) again.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f(x) = \ln x\) and \(g(x) = 3 + \ln \left( {\frac{x}{2}} \right)\), for \(x > 0\).</p>
<p>The graph of \(g\) can be obtained from the graph of \(f\) by two transformations:</p>
<p>\[\begin{array}{*{20}{l}} {{\text{a horizontal stretch of scale factor }}q{\text{ followed by}}} \\ {{\text{a translation of }}\left( {\begin{array}{*{20}{c}} h \\ k \end{array}} \right).} \end{array}\]</p>
</div>
<div class="specification">
<p>Let \(h(x) = g(x) \times \cos (0.1x)\), for \(0 < x < 4\). The following diagram shows the graph of \(h\) and the line \(y = x\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.34.27.png" alt="M17/5/MATME/SP2/ENG/TZ1/10.b.c"></p>
<p>The graph of \(h\) intersects the graph of \({h^{ - 1}}\) at two points. These points have \(x\) coordinates 0.111 and 3.31 correct to three significant figures.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(q\);</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(h\);</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(k\).</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>Find \(\int_{0.111}^{3.31} {\left( {h(x) - x} \right){\text{d}}x} \).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area of the region enclosed by the graphs of \(h\) and \({h^{ - 1}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let \(d\) be the vertical distance from a point on the graph of \(h\) to the line \(y = x\). There is a point \({\text{P}}(a,{\text{ }}b)\) on the graph of \(h\) where \(d\) is a maximum.</p>
<p>Find the coordinates of P, where \(0.111 < a < 3.31\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = x\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . The graph of <em>f</em> is shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/troy.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> crosses the <em>x</em>-axis at \(x = a\) , \(x = 0\) and \(x = b\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>a</em> and of <em>b</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> has a maximum value when \(x = c\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>c</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The region under the graph of <em>f</em> from \(x = 0\) to \(x = c\) is rotated \({360^ \circ }\) about </span><span style="font-family: times new roman,times; font-size: medium;">the <em>x</em>-axis. Find the volume of the solid formed.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let <em>R</em> be the region enclosed by the curve, the <em>x</em>-axis and the line \(x = c\) , </span><span style="font-family: times new roman,times; font-size: medium;">between \(x = a\) and \(x = c\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the area of <em>R</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A farmer wishes to create a rectangular enclosure, ABCD, of area 525 m<sup>2</sup>, as shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/friends.png" alt></span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">The fencing used for side AB costs \(\$ 11\) per metre. The fencing for the other three sides </span><span style="font-family: times new roman,times; font-size: medium;">costs \(\$ 3\) per metre. The farmer creates an enclosure so that the cost is a minimum. Find this minimum cost.</span></p>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = {{\rm{e}}^{\frac{x}{4}}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> and \(g(x) = mx\) , where \(m \ge 0\) , and \( - 5 \le x \le 5\) . Let \(R\) be the region </span><span style="font-family: times new roman,times; font-size: medium;">enclosed by the \(y\)-axis, the graph of \(f\) , and the graph of \(g\) .</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(m = 1\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Sketch the graphs of \(f\) and \(g\) on the same axes.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the area of \(R\) .</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><span style="font-family: times new roman,times; font-size: medium;">Find the area of \(R\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider all values of \(m\) such that the graphs of \(f\) and \(g\) intersect. Find the </span><span style="font-family: times new roman,times; font-size: medium;">value of \(m\) that gives the greatest value for the area of \(R\) .</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \frac{{3x}}{{x - q}}\), where \(x \ne q\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the equations of the vertical and horizontal asymptotes of the graph of \(f\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The vertical and horizontal asymptotes to the graph of \(f\) intersect at the point \({\text{Q}}(1,3)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \(q\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The vertical and horizontal asymptotes to the graph of \(f\) intersect at the point \({\text{Q}}(1,3)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The point \({\text{P}}(x,{\text{ }}y)\) lies on the graph of \(f\). Show that \({\text{PQ}} = \sqrt {{{(x - 1)}^2} + {{\left( {\frac{3}{{x - 1}}} \right)}^2}} \).</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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The vertical and horizontal asymptotes to the graph of \(f\) intersect at the point \({\text{Q}}(1,3)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Hence find the coordinates of the points on the graph of \(f\) that are closest to \((1,3)\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The velocity \(v{\text{ m}}{{\text{s}}^{ - 1}}\) of a particle after \(t\) seconds is given by</p>
<p class="p1">\(v(t) = {(0.3t + 0.1)^t} - 4\), for \(0 \le t \le 5\)</p>
<p class="p1">The following diagram shows the graph of \(v\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-25_om_06.42.03.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(t\) when the particle is at rest.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(t\) when the acceleration of the particle is \(0\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = A{{\rm{e}}^{kx}} + 3\) . Part of the graph of <em>f</em> is shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/ryan.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The <em>y</em>-intercept is at (0, 13) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(A = 10\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(f(15) = 3.49\) (correct to 3 significant figures), find the value of <em>k</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Using your value of <em>k</em> , find \(f'(x)\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Hence, explain why <em>f</em> is a decreasing function.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) Write down the equation of the horizontal asymptote of the graph <em>f</em> .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = - {x^2} + 12x - 24\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the area enclosed by the graphs of <em>f</em> and <em>g</em> .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(f(t) = 2{t^2} + 7\) , where \(t > 0\) . The function <em>v</em> is obtained when the graph of <em>f</em> is </span><span style="font-family: times new roman,times; font-size: medium;">transformed by</span></p>
<p style="margin-left: 60px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">a stretch by a scale factor of \(\frac{1}{3}\) </span><span style="font-family: times new roman,times; font-size: medium;">parallel to the <em>y</em>-axis,</span></p>
<p style="margin-left: 60px;"><span style="font-family: times new roman,times; font-size: medium;">followed by a translation by the vector \(\left( {\begin{array}{*{20}{c}}<br>2\\<br>{ - 4}<br>\end{array}} \right)\) .</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 \(v(t)\) , giving your answer in the form \(a{(t - b)^2} + c\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A particle moves along a straight line so that its velocity in ms<sup>−1</sup> , at </span><span style="font-family: times new roman,times; font-size: medium;">time <em>t </em>seconds, is given by<em> v</em> . Find the distance the particle travels between </span><span style="font-family: times new roman,times; font-size: medium;">\(t = 5.0\) and \(t = 6.8\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = 2\ln (x - 3)\), for \(x > 3\). The following diagram shows part of the graph of \(f\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-22_om_17.05.00.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the equation of the vertical asymptote to the graph of \(f\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the \(x\)-intercept of the graph 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">The region enclosed by the graph of \(f\), the \(x\)-axis and the line \(x = 10\) <span class="s1">is rotated \(360\)° </span>about the \(x\)-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f(x) = - {x^4} + 2{x^3} - 1\), for \(0 \le x \le 2\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of \(f\) on the following grid.</p>
<p style="text-align: center;"><img src="image_1.html" alt></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">Solve \(f(x) = 0\).</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">The region enclosed by the graph of \(f\) and the \(x\)-axis is rotated \(360°\) about the <em>\(x\)</em>-axis.</p>
<p class="p1">Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows part of the graph of the gradient function, \(y = f'(x)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/bed.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the grid below, sketch a graph of \(y = f''(x)\) , clearly indicating the <em>x</em>-intercept.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="images/hsm2.png" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Complete the table, for the graph of \(y = f(x)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="images/abacus.png" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Justify your answer to part (b) (ii).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A particle moves along a straight line such that its velocity, \(v{\text{ m}}{{\text{s}}^{ - 1}}\), is given by \(v(t) = 10t{{\text{e}}^{ - 1.7t}}\), for \(t \geqslant 0\).</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: 17.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">On the grid below, sketch the graph of \(v\), for \(0 \leqslant t \leqslant 4\).</span></p>
<p style="font: normal normal normal 17px/normal 'Times New Roman'; text-align: center; margin: 0px;"><img src="images/maths_5a.png" alt></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 distance travelled by the particle in the first three seconds.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the velocity of the particle when its acceleration is zero.</span></p>
<div class="marks">[3]</div>
<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 population of deer in an enclosed game reserve is modelled by the function \(P(t) = 210\sin (0.5t - 2.6) + 990\), where \(t\) is in months, and \(t = 1\) corresponds to 1 January 2014.</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 number of deer in the reserve on 1 May 2014.</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 rate of change of the deer population on 1 May 2014.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Interpret the answer to part (i) with reference to the deer population size on 1 May 2014.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph of \(y = (x - 1)\sin x\) , for \(0 \le x \le \frac{{5\pi }}{2}\)</span><span style="font-family: times new roman,times; font-size: medium;"> , is shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/exhausted.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The graph has \(x\)-intercepts at \(0\), \(1\), \( \pi\) and \(k\) .</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 <em>k</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The shaded region is rotated \(360^\circ \) about the <em>x</em>-axis. Let <em>V</em> be the volume of the </span><span style="font-family: times new roman,times; font-size: medium;">solid formed.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Write down an expression for <em>V</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The shaded region is rotated \(360^\circ \) about the <em>x</em>-axis. Let <em>V</em> be the volume of the </span><span style="font-family: times new roman,times; font-size: medium;">solid formed.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find <em>V</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Let \(f(x) = {({x^2} + 3)^7}\). Find the term in \({x^5}\) in the expansion of the derivative, \(f’(x)\).</p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(h(x) = \frac{{2x - 1}}{{x + 1}}\) , \(x \ne - 1\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({h^{ - 1}}(x)\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Sketch the graph of <em>h</em> for \( - 4 \le x \le 4\) and \( - 5 \le y \le 8\) , including any </span><span style="font-family: times new roman,times; font-size: medium;">asymptotes.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Write down the equations of the asymptotes.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) Write down the <em>x</em>-intercept of the graph of <em>h</em> .</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let <em>R</em> be the region in the first quadrant enclosed by the graph of <em>h</em> , the <em>x</em>-axis </span><span style="font-family: times new roman,times; font-size: medium;">and the line \(x = 3\).</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find the area of <em>R</em>.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Write down an expression for the volume obtained when <em>R</em> is revolved </span><span style="font-family: times new roman,times; font-size: medium;">through \({360^ \circ }\) about the <em>x</em>-axis.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = \frac{1}{{x - 1}} + 2\), for \(x > 1\).</p>
</div>
<div class="specification">
<p class="p1">Let \(g(x) = a{e^{ - x}} + b\), for \(x \geqslant 1\). The graphs of \(f\) and \(g\) have the same horizontal asymptote.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the equation of the horizontal asymptote of the graph of \(f\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(f'(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the value of \(b\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that \(g'(1) = - e\), find the value of \(a\).</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">There is a value of \(x\)<span class="s1">, for \(1 < x < 4\)</span>, for which the graphs of \(f\) and \(g\) have the same gradient. Find this gradient.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = 0.225{x^3} - 2.7x\), for \( - 3 \leqslant x \leqslant 3\). There is a local minimum point at <span class="s1">A</span>.</p>
</div>
<div class="specification">
<p class="p1">On the following grid,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the coordinates of <span class="s1">A</span><span class="s2">.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>sketch the graph of \(f\), clearly indicating the point <span class="s1">A</span><span class="s2">;</span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>sketch the tangent to the graph of \(f\) at <span class="s1">A</span>.</p>
<p class="p1" style="text-align: left;"><img src="images/Schermafbeelding_2017-03-03_om_17.19.46.png" alt="N16/5/MATME/SP2/ENG/TZ0/02.b"></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f(x) = 6 - \ln ({x^2} + 2)\), for \(x \in \mathbb{R}\). The graph of \(f\) passes through the point \((p,{\text{ }}4)\), where \(p > 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(p\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following diagram shows part of the graph of \(f\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_13.30.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/05.b"></p>
<p>The region enclosed by the graph of \(f\), the \(x\)-axis and the lines \(x = - p\) and \(x = p\) is rotated 360° about the \(x\)-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A particle moves in a straight line with velocity \(v = 12t - 2{t^3} - 1\) , for \(t \ge 0\) , where <em>v</em> is </span><span style="font-family: times new roman,times; font-size: medium;">in centimetres per second and <em>t</em> is in seconds.</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 acceleration of the particle after 2.7 seconds.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the displacement of the particle after 1.3 seconds.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">Let \(f(x) = \frac{{\ln (4x)}}{x}\) for \(0 < x \le 5\).</p>
<p class="p1">Points \({\text{P}}(0.25,{\text{ }}0)\) and \(Q\) are on the curve of \(f\). The tangent to the curve of \(f\) at \(P\) is perpendicular to the tangent at \(Q\). Find the coordinates of \(Q\).</p>
</div>
<br><hr><br><div class="specification">
<p>Let \(f\left( x \right) = 12\,\,{\text{cos}}\,x - 5\,\,{\text{sin}}\,x,\,\, - \pi \leqslant x \leqslant 2\pi \), be a periodic function with \(f\left( x \right) = f\left( {x + 2\pi } \right)\)</p>
<p>The following diagram shows the graph of \(f\).</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">There is a maximum point at A. The minimum value of \(f\) is −13 .</p>
</div>
<div class="specification">
<p>A ball on a spring is attached to a fixed point O. The ball is then pulled down and released, so that it moves back and forth vertically.</p>
<p style="text-align: center;"><img 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"></p>
<p>The distance, <em>d</em> centimetres, of the centre of the ball from O at time <em>t</em> seconds, is given by</p>
<p style="padding-left: 90px;">\(d\left( t \right) = f\left( t \right) + 17,\,\,0 \leqslant t \leqslant 5.\)</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of \(f\), write down the amplitude.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of \(f\), write down the period.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write \(f\left( x \right)\) in the form \(p\,\,{\text{cos}}\,\left( {x + r} \right)\).</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 maximum speed of the ball.</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>Find the first time when the ball’s speed is changing at a rate of 2 cm s<sup>−2</sup>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f\left( x \right) = \,\,{\text{sin}}\,\left( {{e^x}} \right)\) for 0 ≤ \(x\) ≤ 1.5. The following diagram shows the graph of \(f\).</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <em>x</em>-intercept of the graph of \(f\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The region enclosed by the graph of \(f\), the<em> y</em>-axis and the <em>x</em>-axis is rotated 360° about the <em>x</em>-axis.</p>
<p>Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = (x - 1)(x - 4)\).</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 \(x\)-intercepts of the graph of \(f\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The region enclosed by the graph of \(f\) and the \(x\)-axis is rotated \(360^\circ\) about the \(x\)-axis.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the volume of the solid formed.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \cos ({{\rm{e}}^x})\) , for \( - 2 \le x \le 2\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(f'(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the grid below, sketch the graph of \(f'(x)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P2TZ2Q2.png" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows a waterwheel with a bucket. The wheel rotates at a </span><span style="font-family: times new roman,times; font-size: medium;">constant rate in an anticlockwise (counter-clockwise) direction.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/bucket.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The diameter of the wheel is 8 metres. The centre of the wheel, A, is 2 metres </span><span style="font-family: times new roman,times; font-size: medium;">above the water level. After <em>t</em> seconds, the height of the bucket above the water level </span><span style="font-family: times new roman,times; font-size: medium;">is given by \(h = a\sin bt + 2\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(a = 4\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The wheel turns at a rate of one rotation every 30 seconds.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Show that \(b = \frac{\pi }{{15}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">In the first rotation, there are two values of <em>t</em> when the bucket is <strong>descending</strong> at a rate </span><span style="font-family: times new roman,times; font-size: medium;">of \(0.5{\text{ m}}{{\text{s}}^{ - 1}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find these values of <em>t</em> .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">In the first rotation, there are two values of <em>t</em> when the bucket is <strong>descending</strong> at a rate </span><span style="font-family: times new roman,times; font-size: medium;">of \(0.5{\text{ m}}{{\text{s}}^{ - 1}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Determine whether the bucket is underwater at the second value of <em>t</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \frac{{g(x)}}{{h(x)}}\), where \(g(2) = 18,{\text{ }}h(2) = 6,{\text{ }}g'(2) = 5\), and \(h'(2) = 2\). Find the equation of the normal to the graph of \(f\) at \(x = 2\).</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = {{\rm{e}}^x}\sin 2x + 10\) , for \(0 \le x \le 4\) . Part of the graph of <em>f</em> is given below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/apple.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">There is an <em>x</em>-intercept at the point A, a local maximum point at M, where \(x = p\) and </span><span style="font-size: medium;"><span style="font-family: times new roman,times;">a local minimum point at N, where \(x = q\)</span><span style="font-family: times new roman,times;"> .</span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the <em>x</em>-coordinate of A.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find the value of</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) <em>p</em> ;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) <em>q</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find \(\int_p^q {f(x){\rm{d}}x} \)</span><span style="font-family: times new roman,times; font-size: medium;"> . Explain why this is not the area of the shaded region.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = 5\cos \frac{\pi }{4}x\) and \(g(x) = - 0.5{x^2} + 5x - 8\) for \(0 \le x \le 9\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the same diagram, sketch the graphs of <em>f</em> and <em>g</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider the graph of \(f\) . Write down</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) the <em>x</em>-intercept that lies between \(x = 0\) and \(x = 3\) ;</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) the period;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) the amplitude.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider the graph of <em>g</em> . Write down</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) the two <em>x</em>-intercepts;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) the equation of the axis of symmetry.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>R</em> be the region enclosed by the graphs of <em>f</em> and <em>g</em> . Find the area of <em>R</em>.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = x\cos (x - \sin x)\) , \(0 \le x \le 3\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of <em>f</em> on the following set of axes.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="images/marvin.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> intersects the <em>x</em>-axis when \(x = a\) , \(a \ne 0\) . Write down the </span><span style="font-family: times new roman,times; font-size: medium;">value of <em>a</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> is revolved \(360^\circ \) about the <em>x</em>-axis from \(x = 0\) to \(x = a\) . </span><span style="font-family: times new roman,times; font-size: medium;">Find the volume of the solid formed.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <em>f</em>(<em>x</em>) = ln <em>x</em> − 5<em>x</em> , for <em>x</em> > 0 .</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>f '</em>(<em>x</em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>f "</em>(<em>x</em>).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve<em> f '</em>(<em>x</em>)<em> = f "</em>(<em>x</em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = {x^3} - 4x + 1\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Expand \({(x + h)^3}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Use the formula \(f'(x) = \mathop {\lim }\limits_{h \to 0} \frac{{f(x + h) - f(x)}}{h}\) </span><span style="font-family: times new roman,times; font-size: medium;">to show that </span><span style="font-family: times new roman,times; font-size: medium;">the derivative of \(f(x)\) is \(3{x^2} - 4\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The tangent to the curve of f at the point \({\text{P}}(1{\text{, }} - 2)\) is parallel to the tangent at </span><span style="font-family: times new roman,times; font-size: medium;">a point Q. Find the coordinates of Q.</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><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> is decreasing for \(p < x < q\) . Find the value of <em>p</em> and of <em>q</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><span style="font-family: times new roman,times; font-size: medium;">Write down the range of values for the gradient of \(f\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider a function \(f\), for \(0 \le x \le 10\). The following diagram shows the graph of \(f'\), the derivative of \(f\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-14_om_07.44.17.png" alt></p>
<p class="p1">The graph of \(f'\) passes through \((2,{\text{ }} - 2)\) and \((5,{\text{ }}1)\), and has \(x\)-intercepts at \(0\), \(4\) and \(6\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(f\) has a local maximum point when \(x = p\). State the value of \(p\), and justify your answer.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down \(f'(2)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Let \(g(x) = \ln \left( {f(x)} \right)\) and \(f(2) = 3\).</p>
<p class="p1">Find \(g'(2)\).</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">Verify that \(\ln 3 + \int_2^a {g'(x){\text{d}}x = g(a)} \), where \(0 \le a \le 10\).</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">The following diagram shows the graph of \(g'\), the derivative of \(g\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-14_om_07.59.38.png" alt></p>
<p class="p1">The shaded region \(A\) is enclosed by the curve, the <em>\(x\)</em>-axis and the line \(x = 2\), and has area \({\text{0.66 unit}}{{\text{s}}^{\text{2}}}\).</p>
<p class="p1">The shaded region \(B\) is enclosed by the curve, the \(x\)-axis and the line \(x = 5\), and has area \({\text{0.21 unit}}{{\text{s}}^{\text{2}}}\)<span class="s1">.</span></p>
<p class="p2">Find \(g(5)\)<span class="s2">.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Note: In this question, distance is in metres and time is in seconds.</strong></p>
<p>A particle P moves in a straight line for five seconds. Its acceleration at time \(t\) is given by \(a = 3{t^2} - 14t + 8\), for \(0 \leqslant t \leqslant 5\).</p>
</div>
<div class="specification">
<p>When \(t = 0\), the velocity of P is \(3{\text{ m}}\,{{\text{s}}^{ - 1}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the values of \(t\) when \(a = 0\).</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>Hence or otherwise, find all possible values of \(t\) for which the velocity of P is decreasing.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity of P at time \(t\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by P when its velocity is increasing.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows the graph of \(f(x) = a\sin bx + c\), for \(0 \leqslant x \leqslant 12\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.53.31.png" alt="N16/5/MATME/SP2/ENG/TZ0/10"></p>
<p class="p1" style="text-align: center;">The graph of \(f\) has a minimum point at \((3,{\text{ }}5)\) and a maximum point at \((9,{\text{ }}17)\).</p>
</div>
<div class="specification">
<p class="p1">The graph of \(g\) is obtained from the graph of \(f\) by a translation of \(\left( {\begin{array}{*{20}{c}} k \\ 0 \end{array}} \right)\). The maximum point on the graph of \(g\) has coordinates \((11.5,{\text{ }}17)\).</p>
</div>
<div class="specification">
<p class="p1">The graph of \(g\) changes from concave-up to concave-down when \(x = w\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the value of \(c\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Show that \(b = \frac{\pi }{6}\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Find the value of \(a\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the value of \(k\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find \(g(x)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find \(w\).</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Hence or otherwise, find the maximum positive rate of change of \(g\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = x{{\text{e}}^{ - x}}\) and \(g(x) = - 3f(x) + 1\).</p>
<p class="p1">The graphs of \(f\) and \(g\) intersect at \(x = p\) and \(x = q\), where \(p < q\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(p\) <span class="s1">and of \(q\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence, find the area of the region enclosed by the graphs of \(f\) <span class="s1">and \(g\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><strong>All lengths in this question are in metres.</strong></p>
<p class="p1">Let \(f(x) = - 0.8{x^2} + 0.5\), for \( - 0.5 \leqslant x \leqslant 0.5\). Mark uses \(f(x)\) as a model to create a barrel. The region enclosed by the graph of \(f\), the \(x\)-axis, the line \(x = - 0.5\) and the line \(x = 0.5\) is rotated <span class="s1">360°</span> about the \(x\)-axis. This is shown in the following diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_15.49.19.png" alt="N16/5/MATME/SP2/ENG/TZ0/06"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the model to find the volume of the barrel.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">The empty barrel is being filled with water. The volume \(V{\text{ }}{{\text{m}}^3}\) </span>of water in the barrel after \(t\) minutes is given by \(V = 0.8(1 - {{\text{e}}^{ - 0.1t}})\). How long will it take for the barrel to be half-full?</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider the curve with equation \(f(x) = p{x^2} + qx\) , where <em>p</em> and <em>q</em> are constants. </span><span style="font-family: times new roman,times; font-size: medium;">The point \({\text{A}}(1{\text{, }}3)\) lies on the curve. The tangent to the curve at A has gradient \(8\). </span><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>p</em> and of <em>q</em> .</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the curve \(y = \ln (3x - 1)\) . Let P be the point on the curve where \(x = 2\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the gradient of the curve at P.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The normal to the curve at P cuts the <em>x</em>-axis at R. Find the coordinates of R.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">A particle moves in a straight line. Its velocity \(v{\text{ m}}\,{{\text{s}}^{ - 1}}\) after \(t\) seconds is given by</p>
<p class="p1">\[v = 6t - 6,{\text{ for }}0 \leqslant t \leqslant 2.\]</p>
<p class="p1">After \(p\) <span class="s1">seconds, the particle is 2 m </span>from its initial position. Find the possible values of \(p\).</p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = 4x - {{\rm{e}}^{x - 2}} - 3\) , for \(0 \le x \le 5\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the <em>x</em>-intercepts of the graph of <em>f</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the grid below, sketch the graph of <em>f</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/chops.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the gradient of the graph of <em>f</em> at \(x = 3\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Ramiro and Lautaro are travelling from Buenos Aires to El Moro.</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;">Ramiro travels in a vehicle whose velocity in \({\text{m}}{{\text{s}}^{ - 1}}\) is given by \({V_R} = 40 - {t^2}\), where \(t\) is in seconds.</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;">Lautaro travels in a vehicle whose displacement from Buenos Aires in metres is given by \({S_L} = 2{t^2} + 60\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">When \(t = 0\), both vehicles are at the same point.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find Ramiro’s displacement from Buenos Aires when \(t = 10\).</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;">Let \(f(x) = 5 - {x^2}\). Part of the graph of \(f\)is shown in the following diagram.</span></p>
<p style="margin: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 21px; line-height: normal; font-family: 'Times New Roman'; text-align: center;"><img src="images/maths_2.png" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The graph crosses the \(x\)-axis at the points \(\rm{A}\) and \(\rm{B}\).</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 \(x\)-coordinate of \({\text{A}}\) and of \({\text{B}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The region enclosed by the graph of \(f\) and the \(x\)-axis is revolved \(360^\circ \) about the \(x\)-axis.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the volume of the solid formed.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = 3\sin x + 4\cos x\) , for \( - 2\pi \le x \le 2\pi \) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of <em>f</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Write down</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) the amplitude;</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) the period;</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(iii) the <em>x</em>-intercept that lies between \( - \frac{\pi }{2}\) </span><span style="font-family: times new roman,times; font-size: medium;">and 0.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Hence write \(f(x)\) in the form \(p\sin (qx + r)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down one value of <em>x</em> such that \(f'(x) = 0\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Write down the two values of <em>k</em> for which the equation \(f(x) = k\) has exactly </span><span style="font-family: times new roman,times; font-size: medium;">two solutions.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = \ln (x + 1)\) , for \(0 \le x \le \pi \) . There is a value of <em>x</em>, between \(0\) and \(1\), </span><span style="font-family: times new roman,times; font-size: medium;">for which the gradient of <em>f</em> is equal to the gradient of <em>g</em>. Find this value of <em>x</em>.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \cos ({x^2})\) and \(g(x) = {{\rm{e}}^x}\) , for \( - 1.5 \le x \le 0.5\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the area of the region enclosed by the graphs of <em>f</em> and <em>g</em> .</span></p>
</div>
<br><hr><br><div class="specification">
<p>A particle P moves along a straight line. The velocity <em>v</em> m s<sup>−1</sup> of P after <em>t</em> seconds is given by <em>v</em> (<em>t</em>) = 7 cos <em>t</em> − 5<em>t </em><sup>cos <em>t</em></sup>, for 0 ≤ <em>t</em> ≤ 7.</p>
<p>The following diagram shows the graph of <em>v</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial velocity of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum speed of P.</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>Write down the number of times that the acceleration of P is 0 m s<sup>−2</sup> .</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 P when it changes direction.</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>Find the total distance travelled by P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The velocity of a particle in ms<sup>−1</sup> is given by \(v = {{\rm{e}}^{\sin t}} - 1\) , for \(0 \le t \le 5\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the grid below, sketch the graph of \(v\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/ronan.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the total distance travelled by the particle in the first five seconds.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the positive \(t\)-intercept.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \frac{{100}}{{(1 + 50{{\rm{e}}^{ - 0.2x}})}}\) . Part of the graph of \(f\) is shown below.</span></p>
<p><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down \(f(0)\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Solve \(f(x) = 95\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the range of \(f\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(f'(x) = \frac{{1000{{\rm{e}}^{ - 0.2x}}}}{{{{(1 + 50{{\rm{e}}^{ - 0.2x}})}^2}}}\) .</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><span style="font-family: times new roman,times; font-size: medium;">Find the maximum rate of change of \(f\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <em>g</em>(<em>x</em>) = −(<em>x</em> − 1)<sup>2</sup> + 5.</p>
</div>
<div class="specification">
<p>Let <em>f</em>(<em>x</em>) = x<sup>2</sup>. The following diagram shows part of the graph of <em>f</em>.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxcAAAJWCAYAAAAqU3pBAAAgAElEQVR4AezdD3gV1b3o/d9GH5VexJ5gn9sAWqreBHxVQELKLfiIoFF7quGFo209FRSxx0vRFm8BBRsNFYrg1dY/PbYCFTzaUyh5QttTCgciFGgVEoN/DpActSqQ+FyBVzFXWm7JvM/asMPO7Jnsf/NnrZnvPI9mz+w1a36/zxr2zsrMmpWwLMsSFgQQQAABBBBAAAEEEECgSIFeRe7P7ggggAACCCCAAAIIIIBAUoDOBScCAggggAACCCCAAAIIeCJwulstiUTC7S22I4AAAggggAACCCCAQMwFnEZXuHYulJXTDjE3JH0EEEAAAQQQQAABBGIv4HYhgtuiYn9qAIAAAggggAACCCCAgDcCdC68caQWBBBAAAEEEEAAAQRiL0DnIvanAAAIIIAAAggggAACCHgjQOfCG0dqQQABBBBAAAEEEEAg9gJ0LmJ/CgCAAAIIIIAAAggggIA3AnQuvHGkFgQQQAABBBBAAAEEYi9A5yL2pwAACCCAAAIIIIAAAgh4I0DnwhtHakEAAQQQQAABBBBAIPYCdC5ifwoAgAACCCCAAAIIIICANwJ0LrxxpBYEEEAAAQQQQAABBGIvQOci9qcAAAgggAACCCCAAAIIeCNA58IbR2pBAAEEEEAAAQQQQCD2AnQuYn8KAIAAAggggAACCCCAgDcCdC68caQWBBBAAAEEEEAAAQRiL0DnIvanAAAIIIAAAggggAACCHgjQOfCG0dqQQABBBBAAAEEEEAg9gJ0LmJ/CgCAAAIIIIAAAggggIA3AnQuvHGkFgQQQAABBBBAAAEEYi9A5yL2pwAACCCAAAIIIIAAAgh4I0DnwhtHakEAAQQQQAABBBBAIPYCdC5ifwoAgAAC0RLYJ3VTLpJEIiGJxFfl0aaPTqZ3UBrmVEj/O+rkQGe0MiYbBBBAAAF9BOhc6NMWRIIAAgh4IHCeTFzxlhxvWSZV8qr8+2sfyIm+RF8Zcu0NUr7/I/k/HhyFKhBAAAEEEHASoHPhpMI2BBBAwHCBXhcMlWsubJe3D/+fk52LM+S/DhwkF1xzifTnk9/w1iV8BBBAQF8BvmL0bRsiQwABBAoX6PVfpOTCUnn7jffkQ1VL53tS/9hu+ftvDJM+hdfKnggggAACCPQoQOeiRx7eRAABBAwV6PVf5LOf/8zJ4Dulo3mdNFZNlwkDznBMaNeuXaL+Y0EAAQQQQKAYAToXxeixLwIIIKCtQG/57Oc/K7L9Hdm3b5MsXlMq357wBXH60D98+LB861vfkuHDh8v+/fu1zYjAEEAAAQT0F3D6ntE/aiJEAAEEEMgicJac87mzRT7dLk//6DUZe/f1MsDlE/+ZZ57pqqu2trbrNS8QQAABBBDIV8DlqybfaiiPAAIIIKCXwOlydsnnRKRErrzzWzKu1P12qHnz5snDDz+cDH/p0qWyYcMGvVIhGgQQQAABYwToXBjTVASKAAII5Ctwntz/L/PltsF9HXc8evRo8naoWbNmSVVVVbLMggUL5IEHHhB1qxQLAggggAAC+QrQuchXjPIIIICA9gKd0tH0nCyT22XuuAGO4yxUCqtXr5adO3fKPffc05XRzJkzk68XLVrUtY0XCCCAAAII5CqQsCzLciqsZnd1ecupONsQQAABBEIVUB2KH8sNN7wnt/78v0nL7pHy/ZmVro+dbW1tlfLyclmzZo1MnDgxGXnqc1/dFnXttddKc3OzDBs2LNSsODgCCCCAgJ4Cqe8Me3R0LuwirCOAAAJGCnTKkYYHZPD4Jrn1uR/Id2+tlNIerk1PmDAhmWV9fX1XtulfFLNnz5bNmzfLli1bpHfv3l1leIEAAggggIASSP/OSBehc5GuwWsEEEAgBgJ1dXUyadIkaWlpkbKysq6M078o1JiLfv36yZNPPikzZszoKsMLBBBAAAEElED6d0a6SA9/10ovxmsEEEAAgagIdHR0JG+HSu9Y2HMrKSmR9evXy2uvvWZ/i3UEEEAAAQRcBbhy4UrDGwgggEC8BNz+ChUvBbJFAAEEEMhFwO07gysXuehRBgEEEEAAAQQQQAABBLIK0LnISkQBBBBAAAEEEEAAAQQQyEWAzkUuSpRBAAEEEEAAAQQQQACBrAJ0LrISUQABBBBAAAEEEEAAAQRyEaBzkYsSZRBAAAHNBTrbm2Ttrx6VKf0Tkug/VxqOdGoeMeEhgAACCERRgM5FFFuVnBBAIEYCx6R9x9Ny+4jbpO7d82TK5o/Falso4/ry8R6jk4BUEUAAAW0ETtcmEgJBAAEEEMhToFM6mp6WWybskhvrN8h3KkuFLkWehBRHAAEEEPBUgM6Fp5xUhgACCAQo0NEoz3zvBbngqTV0LAJk51AIIIAAAu4C/JHL3YZ3EEAAAY0F/iKtqx6VWTJeRneultvVWIvEpTLl0fXS2sF4C40bjtAQQACBSAvQuYh085IcAghEVqDzXdn2y1dlbOUlMnT0PbKi7bh8sud7Io/dLv/0TKN0RDZxEkMAAQQQ0FmA26J0bh1i6ybw4IMPJtdra2sl9VptsK932+nkir2MfZ19nAQybQtxu++++2Tu3LnSt29f54M4tGEhx4ndPn/9s/zljc/Ksf/6uvz6mbfk10nH++XsisWyedbtcsu7E2R4v8yPeLuTfT3931aqwexl7Oupcuk/7WXs6+llU6/tZezrqXLpP+1l7OvpZVOv7WXs66ly6T/tZezr6WVTr+1l7Oupcuk/7WXs60ePHk0W7927d9du9jL29a6CaS/sZbKtq12zlbG/H8V90giTL51y7qmMKs+CQOQFLJdFRFzeYTMC4QjU1NSEc+ACjkqsp9DWrFljzZo169SGIl9hewLweMsyq0pGWLM3fdhN1Gm7+jzP9b9ulWm8EtfzYMWKFZ7+e7I3cVxd7Q5+rJtk60f+1Bk9Abe+ArdFRb77SIIIhCtwwQUXyJIlS8INIoJH7/X5QTKstE12vXtQMkdYXCDlA/t0ZW1ZlvprUY//1dTUdJXnhb4CW7dulVGjRukbIJEhgEDsBRKqH+WkkEgkkl9ETu+xDQEEEMhV4PDhw9KvXz/Zt2+fDBw4MNfdKJdV4KA0zLlOvnlwrux8dqIMSP6pqFOONDwggx+5SDavmyplef75iM/9rOihF1Bt1NzcLMOGDQs9FgJAAIF4C7h9Z+T51RNvRLIPV8DpXvBwI3I/OrGesikpKZGRI0fK7t27T20s4hW2KbxzZew9c+X6dQ/K3OfeTA7g7mz/kyxb8Z7cu3Bi3h0Lk1yVgEnxehVra2trsvHPP//81Eng+U+vYvU8MIcKTYpVhW9avA7kbEIgJwE6FzkxUQgBBIoRmDBhgqR+MSqmHvbtLtBrwAT58eZH5dIt35CzEwk57ZZfS8k9j8q9Iz7bvSBrkRB49913pbq6WlSHnQUBBBDQVYDOha4tQ1wIREhg8ODBsnHjxghlpEsqvaRP2bXyvRVvnBhP8dIjMmUEs3Tr0jpex9HY2CiVlZVeV0t9CCCAgKcCjLnwlJPKEEDASUBdtSgvL5dPP/1U0h+h6VSWbeEJuN0/G15EHDldQF0BnD59ulRVVaVv5jUCCCAQioDbdwZXLkJpDg5aiIBJ96sSa/cWLisrS25Qg7qLXbAtVtB5f5NcVQYmxetFrOrBCGvXrpVBgwY5N6BHW72I1aNQslZjUqwqGdPizdoAFEDARYDOhQsMmxFAwFuBadOmyZtvvultpdSGQEwE3n///WSmqY56TNImTQQQMFCAzoWBjUbICJgoMHToUNm7d6+JoRMzAqELvPPOO6I66CwIIICA7gJ0LnRvIeJDICIC6i+uO3bsiEg2pIFAsAIvv/yyqA46i7kCtbW15gZP5AjkIUDnIg8siiKAQOEC6l5xdc/40aNHC6+EPRGIqYB6KAK3RJnd+Iy5MLv9iD53AToXuVtREgEEihBI/WLkxaDuIsJgVwSME1Ad8iAGcxsHQ8AIIKClAJ0LLZuFoBCIpgCDuqPZrmTlr0CqQ57qoPt7NGpHAAEEihOgc1GcH3sjgEAeAl/84hcZ1J2HF0URUALqKWsM5uZcQAABUwToXJjSUsSJQAQE1EzdDOqOQEOSQqAC6ilrDOYOlJyDIYBAEQJ0LorAY1cEEMhP4JJLLmFQd35klEYg2SHnlihOBAQQMEWAzoUpLUWcCERAIPULUktLSwSyIQUE/BcIamZu/zPhCAggEBcBOhdxaWnyREATAXXvuJoQjAUBBLILMDN3diNKIICAXgIJy7Isp5ASiYS4vOVUnG0IIIBATgIrV65MDlBdvHhxTuUpFJwAn/vBWed6JP695CpFOQQQCFrA7TuDKxdBtwTHK1jApAmIiNW9mS+88EJZsmSJe4Es72CbBajAt01yVSmaFG8xsaonRamxSkEtxcQaVIyp45gUq4rZtHhTzvxEIF8BOhf5ilEeAQSKEhgyZEhy//379xdVDzsjEAcB1RG/7LLL4pAqOSKAQEQE6FxEpCFJAwFTBEpKSmTkyJGye/duU0ImTgRCEWhtbU0et7y8PJTjc1AEEECgEAHGXBSixj4IIFCUwMKFC6Vv374yY8aMouphZ28F3O6f9fYo1JarQF1dnagxF/X19bnuQjkEEEAgMAG37wyuXATWBByoWAGT7lcl1p5bW02mt3Hjxp4LubyLrQtMkZtNclWpmhRvobGqyfMqKyuLbNn8di801vyO4k1pk2JVGZsWrzetRC1xFKBzEcdWJ2cEQhZgMr2QG4DDGyGgZrOvqKgwIlaCRAABBFICdC5SEvxEAIHABM4777zksfbt2xfYMTkQAiYJHD16NDmb/aBBg0wKm1gRQAABoXPBSYAAAoEL9O7dW6qrq5PzXQR+cA6IgAECqY53alZ7A0ImRAQQQCApwIBuTgQEEAhF4KmnnpIjR47I3LlzQzk+B80UcBucl1mSLX4LqMHc69atk2effdbvQ1F/QAJqzEVtbW1AR+MwCPgv4PadwZUL/+05gkcCJg2GI9bsja7+IlvIU3CwzW5bSAmTXFV+JsVbSKwvv/yyDB06tJCmLGqfQmIt6oBF7GxSrEWkya4IGCdA58K4JiNgBKIhcPHFF8vOnTvl8OHD0UiILBDwUGDz5s0yfPhwD2ukKgQQQCAYAToXwThzFAQQsAkMHDgwuWXPnj22d1hFIN4CavZ61fFOzWYfbw2yRwAB0wQYc2FaixEvAhESmD17tqjH0k6ePDlCWZmbitv9s+ZmZGbk27dvl5kzZ4p6FC0LAgggoKuA23cGVy50bTHiyhAw6f5aYs1oPscNo0aNyvuJUdg6Uha90SRXlaxJ8eYb69tvvy1jx44tuk0LqSDfWAs5hlf7mBSrytm0eL1qJ+qJnwCdi/i1ORkjoI3ABRdcIEuWLNEmHgJBQAeBN998U1THmwUBBBAwUYDOhYmtRswIRETg/PPPT2ai7jFnQQCBEwKqw6063iwIIICAiQJ0LkxsNWJGICICJSUlMnLkSNm9e3dEMgojjYPSMKdC1L2vJ/7rL9cu3yudYYTCMYsWaG1tTdZRXl5edF1UoJcAc1zo1R5E458AnQv/bKkZAQRyEJgwYYI0NjbmUJIiTgKdB/4gLzzflPbWGPnamEHCh3saiUEv1S1RavZ6NYs9S7QEGHMRrfYkG3cBvn/cbXgHAQQCEKioqOCpOAU7fyTNv1gr5/7Lh2JZ1sn/VsnUsrMKrpEdwxVQk+ddffXV4QbB0RFAAIEiBOhcFIHHrgggULyAmkxv7dq1TKZXCOWRV2XVYytl8Q+WyPK6zdLawc1QhTDqtA+T5+nUGsSCAAKFCNC5KESNfRBAwDOB1GR677//vmd1xqOiv0jrr56Rxe0isnmx3DHpKim/4QGpaz0Sj/QjmKWarV5NnveFL3whgtmREgIIxEWAzkVcWpo8EdBYYNasWfLOO+9oHKGOoZ0lZVNXiWX9VdoafyPLZleJbP6hTPqnZdLEFQwdGyxrTKnZ6lMd7qw7UAABBBDQUIDOhYaNQkgIxE1AzdKt7jVnKUTgDCkd8VWZ+shvpG3TQzJ28wuyasfhQipin5AF1OR5qqPNggACCJgskLDUKECHxW1Kb4eibEIgEIHUkzbU4/xSr9WB7etOwdjL2NfZx0kg09Yvt6qqKhkzZozU1NQkA/HrOPZ67etOCvYy9nW99rlbJo++TOrlapl+9RflzLTg5s+fn7bm/jLVBukl7Dnb19PLpl7by9jXU+XSf9rL2NfTy6Ze28vY11Pl0n/ay9jX08umXtvL2NdT5dJ/2svY19PLqte/+c1v5Lvf/a6oTkZqybaPKmcvY19P1ZX+014m23oux7HXEcV90g0LyU8ZsSAQFQHXvoLqXDgtIurBIywI6CNQU1OjTzBZIiHWLEC2tw8dOqT+yGHt27fP9k7mKraZJqe2HLValt1iVS3bYx0/tTGnV8rVpM/9KJ4Hyr+5uTmn9vKrUBRd/bLKt16TbPPNjfLxFHD7zuDKRVS6j+SBgOECar6L6dOni7qKwVKowEFpmLtU5L7ZMq5v/ne9uv4VqtBw2C9nATV5npo479NPP2WOi5zVKIgAAmEKuH1n5P/tE2YWHDvWAum3QukOQaz5t5B6tn8uk+lhe9K2s12a1v5OmtqPndjQ2S47Hn9MNl99q4wtoGNhkqtK2KR4c4lVTZ43bdq00DsWucSa/79uf/YwKVbTzll/Woxa4yJA5yIuLU2eCGguUFZWxmR6ebVRp3z8yo+lov+ZkkhcKlMe+4N0/P19Mn/cAGbnzstRj8LqgQZDhw7VIxiiQAABBIoQOL2IfdkVAQQQ8Exg0KBBXZPplZSUeFZvZCvqNUDGLVwv1sLIZhirxNTkeY8//nisciZZBBCIpgBjLqLZrmSFgJEC6v7N5uZmGTZsmJHxmx602/2zpuele/xq8rx+/frJvn37hDkudG8t4kMAgZSA23cGt0WlhPipvYBJ99cSa2Gnk3rG/+uvv97jztj2yFPwmya5qiRNijdbrDpNnpct1oJPMB92NClW085ZH5qLKmMkQOciRo1NqgjoLqAm01MDW1kQiJMAk+fFqbXJFYHoC9C5iH4bkyECxghcdtllsmTJEmPiJVAEvBDYunWrjBo1youqqAMBBBAIXYDORehNQAAIIJASUM/5V4t65j8LAnEQOHr0qCxdulTUVTsWBBBAIAoCDOiOQiuSAwIRElCT6U2ePFkmTpwYoazMSMVtcJ4Z0ZsZ5a5du2T48OFiWWqCdJYoC6gxIrW1tVFOkdxiJuD2ncGVi5idCCana9LgPWIt/ExTk+nt3bvXtQJsXWmKesMkV5WoSfH2FOs777yTnDyvqMbzcOeeYvXwMJ5UZVKsniRMJQgYIkDnwpCGIkwE4iKgJtOrr6+PS7rkGXMBJs+L+QlA+ghEUIDORQQblZQQMFng4osvlp07d4p69j8LAlEXUJPnqduiWBBAAIGoCDDmIiotSR4IREhA3ce5bds2GT16dISy0j8Vt/tn9Y/czAj3798v5513nhw6dEiYld7MNiRqBOIs4PadwZWLOJ8VhuVu0v21xFrcyaUm01MzdTst2DqpFL/NJFeVrUnxusW6e/duqa6u1qpj4RZr8WeY9zWYFKtp56z3rUWNcRKgcxGn1iZXBAwRUM/837hxoyHREiYChQk0NjZKZWVlYTuzFwIIIKCpAJ0LTRuGsBCIs4B65v/atWsZdxHnkyAGuasHF1RUVMQgU1JEAIE4CdC5iFNrkysChgioJ0ap5f333zckYsJEID8B9cAC9eAC9QADlngIMMdFPNqZLEXoXHAWIICAlgJq3MXrr7+uZWwEhUCxAnv27ElWMXDgwGKrYn9DBEwbI2IIK2FqKEDnQsNGISQEEBBRt0a9+eabUCAQSYG3335bVAeaBQEEEIiaAJ2LqLUo+SAQEYHLLrtMlixZEpFsSAOB7gJbt24V9eACFgQQQCBqAnQuotai5INARATKy8uTmbS2tkYkI9JA4ITA0aNHZenSpcmrc5gggAACUROgcxG1FiUfBCIi0Lt3b5k2bRq3RkWkPUnjlEBLS0tyJfXgglPv8AoBBBAwX4DOhfltSAYIRFbgiiuukJdffjmy+ZFYPAXUgwoYbxHPtidrBOIgQOciDq1MjggYKnDhhRcy7sLQtiNsdwH1oAL1wAIWBBBAIIoCdC6i2KrkhEBEBIYMGZLMZP/+/RHJiDQQkGSHWT2wgAUBBBCIokDCsizLKbFEIiEubzkVZxsCCCDgi0BlZaU8/PDDUlVV5Uv9VHpKgM/9UxZ+vVIPKFAPK/j0009FjStiQQABBEwVcPvO4MqFqS0aw7hNmoCIWL07QSdMmCCNjY1dFWLbReHpC5NcVeImxZseq7olqrq6WtuORXqsnp5gPlRmUqymnbM+NBdVxkiAzkWMGptUETBRoKKiQurr600MnZgRyBBQDyi4+uqrM7azAQEEEIiKAJ2LqLQkeSAQUYGLL75Ydu7cKYy7iGgDxywtNTHk8OHDY5Y16SKAQJwEGHMRp9YmVwQMFWDcRTAN53b/bDBHj/5RUuMtDh06JCUlJdFPmAwRQCDSAm7fGVy5iHSzRys5k+6vJVZvzz017iI1Uze23tqmajPJVcVsUrypWFPjLXTuWKRiTZ0XOv80KVbTzlmd253Y9Begc6F/GxEhArEXUOMuNm7cGHsHAMwW2Lt3L+MtzG5CokcAgRwE6FzkgEQRBBAIV2DQoEGydu1aOXz4cLiBcHQEihBQDyYoKysrogZ2RQABBPQXoHOhfxsRIQKxF0j9QrZnz57YW7gDHJMDdTOk/7XLpbXTvRTvhCOgHkigHkygHlDAggACCERZgAHdUW5dckMgQgILFy6Uvn37yowZMyKUlXepdB6okztHTpLlly6TlnVTpayAPx25Dc7zLsr41rRhwwb5yU9+wmOV43sKJMcJ1dbWxliA1KMm4PadUcDXT9RoyMcUAZMG7xGr92dVatwFtg62HTvksbl/kHOvucThzdw2meSqMjIpXhWrmgjShPktTHPN7eymFAIIBClA5yJIbY6FAAIFC6jbSdS4i6NHjxZcRzR3/EiannlR5J7pcu3nz4xmihHISo23YH6LCDQkKSCAQFYBOhdZiSiAAAI6CAwcOFBGjhwpBw8e1CEcTWLolI6mlfKE3CJ3jWDeBE0aJSOMI0eOJMdbDBkyJOM9NiCAAAJRE6BzEbUWJR8EIiyg5rt47733Ipxhnql1NMozT4jcc1eF9MlzV4oHJ9DW1ibV1dVMnBccuZZHYryFls1CUD4I0LnwAZUqEUDAHwE17kLNFcCiBD6Spmcb5IKFd8mIPnyU63xOqCdFmTDeQmfDKMRm0niWKHiTQ3gCPC0qPHuOnKdA6oNZ/fUn9VpVYV93qtZexr7OPk4CmbZhu6nbS370ox/Jd7/7XXn88cdjfB5Ycqy9SRLX/UROf225JJLN96lc+ZeXZPya/vLtW4ZLvxMbk+/Mnz/fuYEdttbU1GRstbe7fT1jB4d/l3HeR/nffvvtsnz58m7nrM5uTu1l35ZtXeWXrYz9fd33sbeZPf5c1u11sI6AqQJuT4sSy2URcX3LZQ82I+CvQE1Njb8H8LB2YvUQ01ZV//79rW3bttm26rnq33nwobVp9ghLfU47/1dqVS3bYx3Pg0XFatLnvn+2eaDlUHTfvn1J10OHDuVQOvwiprgqKZNiNTHe8M9GItBdwO07g2vppnYXiRuBmAoMHjxYmpubY5p9Ku1zZdwjjeovQGn/fSibZo8QqVomLcfbZP3UwcIHfMorvJ+7d++W8vJyxluE1wTaHFld1WBBIA4CfPfEoZXJEYEICZx77rmycePGCGVEKlEWUPNbDBgwIMopkluOAum38+a4C8UQMFKAzoWRzUbQCMRX4HOf+1xyvovDhw/HF4HMjRFQ81uUlpYaEy+BIoAAAsUK0LkoVpD9EUAgUIF+/folj7dnz55Aj6v/wU7eKrV+qpTxya5Fc6mnRO3cuVNUh5gFAQQQiIsAX0FxaWnyRCBCArNmzWLcRYTaM6qpqPEWauLHvn37RjVF8kIAAQQyBOhcZJCwAQEEdBcYNWoU4y50byTiEzXeQk38yIIAAgjESYDORZxam1wRiIhAZWUl4y4i0pZRTkONt7jyyiujnCK5IYAAAhkCdC4ySNiAAAK6CwwcODB5uwnjLnRvqfjGlxpvMWTIkPgikDkCCMRSgM5FLJudpBEwX0DdbrJlyxbzEyGDSArs2LFDqqurmd8ikq1LUggg0JNAQs3+51TAdUpvp8JsQwABBAIW2L59u8ycOVPUL3Es3gjwue+No6pl9uzZcv7558uMGTO8q5SaEEAAAY0E3L4zuHKhUSMRSs8CJk1ARKw9t2Ux76Zs1e0m6jGf6vYTXZdUrLrGlx6XSbGquHWO9+jRo7JkyRIZM2ZMkljnWNPPAd1dTY7VNFu7NesI5CNA5yIfLcoigIA2AiUlJcnbTrhyoU2TEMhJgZaWluSr8vJyTBBAAIHYCdC5iF2TkzAC0RG4+uqrZe/evdFJiEwiIfDOO+/ItGnTpHfv3pHIhyQQQACBfAQYc5GPFmURQEArAcZdeNscbvfPenuU6NemxltccsklMnny5OgnS4YIIBBbAbfvDK5cxPaUMC9x7lv2p81MclUC6fHqPu4iPVZ/Ws+7Wk2K1X4eeKfgTU1qvMVll13WVZlJtsTa1WyevzDJ1vPkqTBWAnQuYtXcJItAtARS4y52794drcTIxliB1tbWZOyMtzC2CQkcAQSKFKBzUSQguyOAQLgCatxFY2NjuEFwdAROCrz55puMt+BsQACBWAvQuYh185M8AuYLDB8+XOrr681PhAwiIbBu3Tq54oorIpELSSCAAAKFCDCguxA19kEAAW0EDh8+LP369RP1+M+ysjJt4jIxELfBeSbmEkbMan6Lz3zmM9Lc3CzDhg0LIwSOqaqFwkMAACAASURBVLGAGnNRW1urcYSEhkB+Am7fGVy5yM+R0iEKmDQYjlj9O1HstmrchXrs58svv+zfQQus2R5rgdUEsptJsSoQHeN1m99Cx1jdTipidZNhOwII5CpA5yJXKcohgIC2Auo2lK1bt2obH4HFQ2Dbtm0ya9Ys5reIR3OTJQIIuAjQuXCBYTMCCJgjoB77uXTpUlG3SLEgEJbAxo0bRT1ggAUBBBCIswCdizi3PrkjEBGB1P3te/bsiUhGpGGawP79+2Xt2rVy8cUXmxY68QYkwHiLgKA5TOgCdC5CbwICQAABLwQWLFiQHEjrRV3UgUC+Amqulerqahk4cGC+u1I+JgImjWeJSZOQpk8CdC58gqVaBBAIVqCiokLUbSksCIQhoOZa4ZaoMOQ5JgII6CZA50K3FiEeBBAoSEDdjqJuS2HcRUF87FSkwLx580TNucKCAAIIxF2AzkXczwDyRyAiAup2lJEjRzJbd0Ta06Q0Wltbk+EOGTLEpLCJNWABxlwEDM7hQhOgcxEaPQdGAAGvBSZMmEDnwmtU6ssq8OabbybHW6g5V1gQcBNgzIWbDNujJkDnImotSj4IxFjgyiuvlPr6+hgLkHoYAuvWrZOJEyeGcWiOiQACCGgnQOdCuyYhIAQQKFRA3Zayc+dOSd2mUmg97IdArgJHjx5NzrGi5lphQQABBBAQoXPBWYAAApERULelTJs2TV5++eXI5EQiegu8+uqryQBTc63oHS3RIYAAAv4L0Lnw35gjIIBAgAJXXHGFbN26NcAjcqg4CzQ3N8usWbPiTEDuCCCAQDcBOhfdOFhBAAHTBdTtKUuXLhV1uwoLAn4LqLlVmN/Cb2XqRwABkwToXJjUWsSKAAJZBVK3p6RuV8m6AwUQKFBg//79yblV1BwrLAgggAACJwToXHAmIIBA5AQWLFgg6nYVFgT8FNi9e3fyEbRqjhUWBBBAAIETAgnLsiwnjEQiIS5vORVnGwIIIKCNwPbt22XmzJmyY8cObWLyJ5Bj0r7jWblvwgxZ2V4qY2c/JT/9/gQp61PY34343M+vlWbPni3nn3++zJgxI78dKY0AAghEQMDtO6Owb6AIgJCCeQImTUBErP6dX7nYph5Jq25bCXPJJdbC4+uUjuZ1skEmys/bLDnetlpu/OBBGfuDzXKkgEr9jbWAgLLsEna8akzPkiVLZMyYMVkiFQk71qwBphUg1jQMj1+aZOtx6lQXMwE6FzFrcNJFIA4C6pG01dXV0b5y0fmeNH58udxaWZp8pniv0v8ud0y5QeT5jdJ4pDMOzRxqji0tLcnjl5eXhxoHB0cAAQR0E6BzoVuLEA8CCHgioJ7gE+n5Lnp9UcaOPS9tsqJj8sG770n5vROksi8f7Z6cRD1U8vrrryfnVOndu3cPpXgLAQQQiJ8AYy7i1+ZkjEAsBHbt2iXDhw+XTz/9VCL/C2BHqzSsek5WvHWVLHr4GiktsG/hdv9sLE6YPJOcMGGCTJ48WSZOnJjnnhRHAAEEoiHg9p1R4FdQNFDIwiwBk+5XJVb/zq1cbXV4JG2usRau1SlHGuZK/7PLZfwdP5SVf3pJ/vRWISMuzBoXoLz8t3VvldQjaCsrK90Lpb0TZqxpYeT0klhzYiqokEm2BSXITgicFODKBaeCMQKpD+ba2tpuv1jY150Sspexr7OPk4CI3cm+7rSXvYx9Pch9tm3bJmeeeaaMHDkyeVh7LPb1IGOzH8sei33dXl6tnypzXDra/0NO/89XZHHTQLl5WpUMPvs0p13S9jnx9qk6RObPny81NTUZ+6WX6X7cjKJdG6K8z9tvvy0dHR0ydOjQrnydXphsYI9d5Wfflm09ivvY2zmbgdP79jpYR8BUAbcrF+pxs46LiOtbjuXZiIDfAjU1NX4fwrP6idUzyoyK8rFdv369NXLkyIw6gtqQT6xexHS8ZZlVJSOs2Zs+7Fad+jzP9b9uO2q8ErRtOsWsWbOsJ598Mn1Tj6/DjLXHwBzeJFYHFI82mWTrUcpUE3EBt74Ct0WZ2l0kbgQQyCqgZk7euXOnhP1I2qyBelSg10Vflq9VnZlRm5qzKNt/TlcsMipiQ1JAPYJWjedhQQABBBDIFOC2qEwTtiCAQIQE1MDb6dOnS1VVVYSycknlSIPMubxOvrTlMZk44AyXQu6bXS9xu+8Su3di9aCA2LWuvwmrW3vVbVIsCERFwO07gysXUWnhGOSRGnNhQqrE6l8r5WurHkm7evVq/wLqoeZ8Y+2hqoy3Og/UyR39r5U5K3ZIu5rWovOANCx6Rj6Ye5dUFdCx8DPWjOA92BBWvGocz7Rp0/J6AllYsRbCTKyFqLEPAgikC9C5SNfgNQIIRE5AzaC8dOlSOXz4cKRy63VOmYy+pk0W3/Yl6X9aQvrf/gv5aNKP5edTL5E+kcpUr2Q2btwoN910k15BEQ0CCCCgkQCdC40ag1AQQMB7AfVIWvW0qD179nhfeZg19rlEpq54o2ssRduK78nEESdm6w4zrCgfO/UI2oqKiiinSW4IIIBAUQJ0LoriY2cEEDBBQI272LJliwmhEqPGAjt27JDq6mopKSnROEpC01WA8Ra6tgxxeS1A58JrUepDAAHtBNRfmuvr67WLi4DMEnj55ZdFjeFhQaAQAZPGsxSSH/sgkBKgc5GS4CcCCERWQHUu1CNpW1tbI5sjifkrcPToUVGPoFVjeFgQQAABBNwF6Fy42/AOAghEREDdxqKe8KP+8syCQCECr776anI3NYaHBQEEEEDAXYDOhbsN7yCAQIQErr/+eqmrq4tQRqQSpIAas7NgwYIgD8mxIibAmIuINSjpuArQuXCl4Q0EEIiSQGVlpaxduzY2s3VHqe10yEWN2bnyyit1CIUYDBVgzIWhDUfYeQvQucibjB0QQMBEgYEDByYfSbt7924TwyfmEAXUWB01ZmfIkCEhRsGhEUAAATME6FyY0U5EiQACHghMnjxZGhsbPaiJKuIkoMbqqDE7PII2Tq1OrgggUKgAnYtC5dgPAQSME1BP+pk3b56oJ/+wIJCrgBqrc8UVV+RanHIIIIBArAXoXMS6+UkegXgJpGbrTj35J17Zk20hAqlZuceNG1fI7uyDAAIIxE6AzkXsmpyEEYi3gLo1itm6430O5JN9Q0NDclZuNWaHBQEEEEAguwCdi+xGlEAAgQgJDB8+PHlrVIRSIhUfBbZu3SoTJ0708QhUjQACCERLgM5FtNqTbBBAIIvA5Zdfniyxa9euLCV5O+4Chw8flqVLl8qoUaPiTkH+CCCAQM4CCcuyLKfSiURCXN5yKs42BBBAwBiBO++8U4YOHSozZswwJuYgAuVzv7vyhg0b5IEHHpAdO3Z0f4M1BBBAAAFx+87gygUnhzECJk1ARKz+nVZe2N50002ycuVK/4I8WbMXsfoepIGxqpCDsF29erWoMTrFLkHEWmyMqf2JNSXh/U+TbL3PnhrjJEDnIk6tTa4IIJAUqKioSE6KpiZHY0HASUA9rljdEqUeX8yCAAIIIJC7AJ2L3K0oiQACERFQk6GpSdHU5GgsCDgJpB5XrB5fzIIAAgggkLsAYy5yt6IkAghESEBNjKZujaqvr49QVsWl4nb/bHG1mrn3woULk4HPnTvXzASIGgEEEPBZwO07gysXPsNTvXcCJt2vSqzetbu9Jq9sKysrZe3ataImSfNr8SpWv+JLr9ekWFXcfserOp1XXnllOlHBr/2OteDAHHYkVgcUjzaZZOtRylQTUwE6FzFteNJGIO4CalK06upqUZOksSCQLqAeU7xz505JPbY4/T1eI4AAAgj0LEDnomcf3kUAgQgLqMnR1O1RLAikC/zud7+TBQsWSO/evdM38xoBBBBAIAcBOhc5IFEEAQSiKTBu3Djfb42Kplx0s1JPiZo3b55nt0RFV4rMEEAAAWcBOhfOLmxFAIEYCHBrVAwaOc8UU0+J4paoPOEojgACCJwUoHPBqYAAArEW4NaoWDd/RvJbtmzhlqgMFTYggAACuQvQucjdipIIIBBBAW6NimCjFpESt0QVgceuCCCAgIjQueA0QACBWAukbo3asWNHrB1IXkQ9JUot3BLF2YAAAggULkDnonA79kQAgYgIqFuj1q1bF5FsSKNQgW3btnFLVKF47JdVoLa2NmsZCiAQBQE6F1FoRXJAAIGiBEaNGiVLly6Vw4cPF1UPO5stoGZsr6ioMDsJotdWgEn0tG0aAvNYgM6Fx6BUhwAC5gmUlZXJyJEjpbGx0bzgidgTgdTEeXQuPOGkEgQQiLEAnYsYNz6pI4DAKYHJkyfL6tWrT23gVawE1C1R06ZNk5KSkljlTbIIIICA1wJ0LrwWpT4EEDBSYMKECebdGtXRKv/+6BTpn0hIItFfrprzvDS1HzPSP+yg1S1Rt912W9hhcPwICzDmIsKNS2rdBOhcdONgBQEE4iqQemrUb3/7WzMIOt+Ttc82iNz4pLRZlhxvWy03frBYKm55Wpo6Os3IQZMot2/fLjt37uQpUZq0R1TDYMxFVFuWvOwCdC7sIqwjgEBsBUyaUK/zz/vlnJunyjVlfZPt1at0tHxn3kyp2vyCrNrBwPR8TmImzstHi7IIIIBAzwJ0Lnr24V0EEIiRwFe/+lVZu3at7N+/X/use104WsYOOKNbnL0+P0iGlXbbxEoWgaNHjwoT52VB4m0EEEAgDwE6F3lgURQBBKItoAbzqkG9DQ0N5ib6mVHypfITVzPMTSK4yF999dXkwZg4LzhzjoQAAtEWoHMR7fYlOwQQyFPgpptukrq6ujz30qF4pxxp3Cy77posVbYrGjpEp2sM3BKla8sQFwIImCpA58LUliNuBBDwReDiiy825taobgAdjfKzFefKwrsqpE+3N1hxE+CWKDcZtiOAAAKFCyQsy7Kcdk8kEuLyllNxtiHgu0DqSRvqcX6p1+qg9nWnQOxl7Ovs4ySQaRsXt1/+8pcyePBgGTp0aMb5pafBX6T95Vdk1I9/Le/94n85Nub8+fMdt9s31tTU2DcZYnAi7HzaZ9++ffLzn/9cPv30U1m0aFFG3ukb7PXa19PLpl7by9jXU+XSf9rL2NfTy6Ze28vY11Pl0n/ay2RbV/tmK2N/P4r7pBsWkp8yYkEgKgKufQXVuXBaRFTfggUBfQRqamr0CSZLJMSaBaiIt4OwXbNmjVVdXV1ElCd2DSJWy/qrtb/+n63n9nxcVLwqVpM+972wXbBggaX+83vxIla/Y0zVT6wpCe9/mmTrffbUGEUBt+8MrlxEpftIHggg4JnA4cOHpV+/ftLc3CzDhg3zrF7vKzom7Q3L5V/lBvnOuAFy4j7XI7J3xVr54P/9RxnbN787X13/CuV94KHXaE4bh05FAAgggICjgNt3Rn7fPI5VsxGBYATSb4UK5oiFH4VYC7fLtmcQtuqpUbNmzZJt27ZlC6fH9/2N9Yi01j0kt4z/H3Lv+IFyWnKWbjVT9zky5MX/K/375Pfx7m+sPTIV9Gax8W7evFlGjhwZSOex2FgLAipwJ2ItEC6H3UyyzSEdiiDgKpDft49rNbyBAAIIREugurpa7r77blGDfvVbjsmBurkydtIPZXNGcKVS9bUvy0V8umfIpG9YuXKlzJgxI30TrxFAAAEEPBDg68cDRKpAAIHoCYwePTr5l+2tW7dqmNwZMmDiU9JmWckHb6iHb5z6r03WTx188hYpDUPXIKTW1tbkE8HUpIksCCCAAALeCjDmwltPakMAgQgJPPXUU/Laa6/Js88+G6Gs3FNxu3/WfQ8z34lbu5rZSkSNAAK6C7h9Z3DlQveWI74uAZPuVyXWrmbz/EWQtmPGjJGlS5eKGvxbyBJkrIXEl76PSbGquIuJV90SpSZLDGopJtagYkwdh1hTEt7/NMnW++ypMU4CdC7i1NrkigACeQmoJ0WpQb9q8C9LNAR27dolO3fulIqKimgkRBYIIICAZgJ0LjRrEMJBAAG9BNSgX/WXbpZoCPzud7+TBQsWiHoiGAsCCCCAgPcCdC68N6VGBBCIkIAa9Lt27VpRf/FmMVtA3d42b948+cpXvmJ2IkSPAAIIaCxA50LjxiE0BBAIX0D9hXvatGlFz3kRfiZE0NjYGNjcFmgjgAACcRWgcxHXlidvBBDIWeC2225L3hql55wXOacR+4KrV6+WyZMnx94BAAQQQMBPAToXfupSNwIIRELg8ssvT+bx6quvRiKfOCaxf//+5JO/JkyYEMf0yRkBBBAITIDORWDUHAgBBEwV6N27d/Iv3s8995ypKcQ+7vr6+uTtbQMHDoy9BQAIIICAnwJ0LvzUpW4EEIiMQFVVVfIv3+ov4CxmCajb2dQTv9TtbSwIhCVQW1sb1qE5LgKBCtC5CJSbgyGAgKkCZWVlUl1dLQ0NDaamENu41e1sam6L1O1tsYUg8VAFmEQvVH4OHqAAnYsAsTkUAgiYLaAGAz/11FNmJxHD6NWjhJ988klRt7exIIAAAgj4K0Dnwl9fakcAgQgJXH/99cm/gG/fvj1CWUU7FXUb25IlS0Td1saCAAIIIOC/AJ0L/405AgIIRERA/eVb/QVc/SWcxQwBdRubup1N3dbGgkCYAoy5CFOfYwcpQOciSG2OhQACxguMGTMm+ZdwNdszi/4C6ja26dOn6x8oEUZegDEXkW9iEjwpQOeCUwEBBBDIQ2DYsGHJv4Rv3rw5j70oGoaAun1NDeSuqKgI4/AcEwEEEIilAJ2LWDY7SSOAQDECamD3okWLiqmCfQMQSA3kLikpCeBoHAIBBBBAQAnQueA8QAABBPIUYGB3nmAhFGcgdwjoHBIBBBCgc8E5gAACCOQvwMDu/M2C3oOB3EGLczwEEEDghABXLjgTEEAAgQIE1KNN1SNOGdhdAJ7Pu6gZuRnI7TMy1SOAAAIuAnQuXGDYjAACCPQkkJqx+8UXX+ypGO+FILB169bkUa+44ooQjs4hEUAAgXgL0LmId/uTPQIIFCEwa9Ysufvuu0X9pZxFH4Gf/OQnogbdMyO3Pm1CJAggEB+BhGVZllO6iURCXN5yKs42BBBAIHYCqlNx5ZVXysMPPxyJGaCj8Lnf2toq5eXlsm/fPhk4cGDszkkSRgABBIIScPvO4MpFUC3AcYoWMGkCImIturldK9DJVv1lXP2FXP2l3GnRKVan+NK3mRSritst3l/96leirijp1LFwizXdX5fXxOpfS5hk658CNcdBgM5FHFqZHBFAwDeBW265RdR8CmrCNpZwBdTg+nnz5olqExYEEEAAgXAE6FyE485REUAgIgJqgrYnn3wy2cGISErGpqEG11dXV4uaRZ0FAQQQQCAcAcZchOPOURFAIEICUbnP3+3+WROaKmrjX0wwJ0YEEIi3gNt3Blcu4n1eGJW9SferEqt/p5aOtqnH0tbX13dLXMdYuwWYtmJSrCpse7zr1q1LZqPj42ftsaaxa/eSWP1rEpNs/VOg5jgI0LmIQyuTIwII+C6Qeiwtk+r5Tu14gEWLFsl9993H42cdddiIAAIIBCdA5yI4a46EAAIRFhg9enTyfn8m1Qu+kdVg+p07d8r1118f/ME5IgIIIIBANwE6F904WEEAAQQKF5g+fbqsXLky2En1Olqloe5FeXTKtTKn4WDhwRu855IlS5KD6pk0z+BGJHQEEIiMAJ2LyDQliSCAQNgCqfv9U/f/+x5P515Z/vUHZMWaH8qslYd8P5yOB1BXLdSjgHn8rI6tQ0wIIBBHAToXcWx1ckYAAV8E1F/O1X3/6v5/9fQi35deg2Xqb1fJzx+cKVW+H0zPA6SuWqhHArMggAACCIQvQOci/DYgAgQQiJBA6r7/wK5eRMgu31S4apGvGOURQAAB/wXoXPhvzBEQQCBGAulXL/72t7/FKPPgU1W3Q6kJDLlqEbw9R0QAAQTcBOhcuMmwHQEEEChQIHX1or29vcAa2C2bwKFDh0TdElVVFdcbwrIJ8b5uArW1tbqFRDwI+CJA58IXVipFAIE4C6irF5MnT5Y//vGPcWbwNffm5mZRc4uoCQxZEDBBgEn0TGglYvRCIGFZluVUkduU3k5l2YZAEAKpD2b115/Ua3Vc+7pTLPYy9nX2cRLItMUt08RJTjnNnj07+Zf122+/XZYvX97tnHXbp9Dz2jrULC8+3SiTNr0uZ215MqP6+fPnZ2xz21BTU5Pxlr3d7esZOzj8u/RyH3XV4umnn5Zvf/vb8tRTT3Wz9fI46XnZ67Wvp5dNvbaXsa+nyqX/tJexr6eXTb22l7Gvp8ql/7SXybau9s1Wxv5+FPdJNywkP2XEgkBUBFz7Cqpz4bSIiNNmtiEQmkBNTU1ox873wMSar1ju5U2yvf76663q6urckyuw5PGWZVaVjLBmb/qwwBosS7ma8rk/a9Ys68tf/nLBuQa9o0nnLLH6d3aYZOufAjVHScDtO4PboqLSfSQPBBDQTuCSSy6RtrY2qaur0y42UwNqbW1NXhEaPny4qSkQd0wFuGoR04aPYdp0LmLY6KSMAALBCKQ/OSqQeS+CSSvUoyxdujQ51qJfv36hxsHBEchXIP22x3z3pTwCJgnQuTCptYgVAQSME0g9OcqfeS8OSsOcCjmt/A7ZIE2yePznJHHtcmntNI4pp4BTVy2mTZuWU3kKIYAAAggEL0DnInhzjogAAjES8Pfqxbky7pFGNUDu1H/rp0pZRD/ZU1cteEJUjP4BkSoCCBgnENGvIOPagYARQCDCAv5evYgwXFpqXLVIw+AlAgggoLEAnQuNG4fQEEAgGgL+Xr2IhlG2LNSEecxrkU2J9xFAAIHwBehchN8GRIAAAjEQUFcv+vfvL8uWLYtBtt6muGHDBlG3RN13333eVkxtCCCAAAKeC9C58JyUChFAAIFMAXX14qGHHpK7775b1C0+LLkJqKdsPfDAA7JmzRopKSnJbSdKIYAAAgiEJkDnIjR6DowAAnETGDZsWPLWHvVXeJbcBNSVHnXFJzVuJbe9KIUAAgggEJZAQs0U6HRw1ym9nQqzDQEEEEAgJwF11aK8vFyam5tFdTZ0WnT73D98+LCo+Sy2bdsmo0eP1omKWBBAAIHYC7h9Z3DlIvanhjkAJk1ARKz+nVem26rHqC5YsCB5i5ROE+vp6Lpo0SJRc1o4dSx0jNftrCdWN5nitpvkqjI1Ld7iWoe94yxA5yLOrU/uCCAQisDMmTOlra1N/JlYL5SUPD9o6tGz6glRLAgggAAC5gjQuTCnrYgUAQQiIpD+aFp16w9LdwF1RWf27NnJKzxMmNfdhjUEEEBAdwHGXOjeQsSHAAKRFFC/QH/jG98Q9cvz4sWLtcjR7f7ZoIOrq6sTdUvU73//e54QFTQ+x0MAAQRyFHD7zuDKRY6AFAtfwKT7VYnVv/MlKrbq6oXqVKjJ4Xbt2uUfWI416+K6f/9+mTRpkjz88MM9dix0iTcXXmLNRSn/Mia5quxMizf/FmEPBE4I0LngTEAAAQRCElBXLZ588kn51re+JToN7g6JI3nYJ554IjmIu6qqKswwODYCCCCAQIECdC4KhGM3BBBAwAuBO+64I1nN6tWrvajO6DrUTNzqSg5/4TW6GQkeAQRiLkDnIuYnAOkjgEC4Aur2qJ/97GcyZcqUWM/crQa2p2biHjhwYLiNwtERQAABBAoWoHNRMB07IoAAAt4IqMn01NwX6glJcb09Sg3gHjp0qEycONEbVGpBAAEEEAhFgM5FKOwcFAEEEOgukJr7YtmyZd3fiMEat0PFoJFJEQEEYiNwemwyJVEEEEBAY4HU7VHDhw8X9Z/TrNQah19waOrpUNdee62sWbNGuB2qYEZ2RAABBLQR4MqFNk1BIAggEHcBdXvUihUrRF3FiMPkeuoWsBkzZoiahZvboeJ+9pM/AghERYDORVRakjwQQCASAjfddFNy7MGcOXMikU9PSahbwNra2uS+++7rqRjvIRAJgdra2kjkQRIIZBOgc5FNiPcRQACBAAXU7VHqUayvvfaaPPXUUwEeOdhDbd++Xe6+++7kk7JKSkqCPThHQyAEAR6xHAI6hwxFgDEXobBzUAQQQMBdQI09UI+nVWMv1ER7UZtQrrW1VcaMGZMcZ6FuBWNBAAEEEIiOAFcuotOWZIIAAhESUL90q0HOau4HNeg5KosaZ/HNb34z+ehdxllEpVXJAwEEEDglQOfilAWvEEAAAa0E1C/fau4Hda92VOa/SN0aogatsyAQJwHGXMSpteOdK52LeLc/2SOAgOYCTzzxhHz44Ydyzz33GN/BUGNINm/eLHV1daLGlrAgECeBVMc6TjmTazwF6FzEs93JGgEEDBFQv4SrX8rVAG/VwTB1UTmoAdyqY8F8Fqa2InEjgAAC2QXoXGQ3ogQCCCAQqoD6ZVz9Um7qE6TUDNyqY7Ft2zY6FqGeSRwcAQQQ8F+Ap0X5b8wREEAAgaIF0p8gpSpTk8+ZsKhHzqoZuNevXx+bWcdNaBdiRAABBPwSoHPhlyz1IoAAAh4LqCdIqb/+q8e4qkX3Doa6YqE6Firm0aNHe6xBdQgggAACOgrQudCxVYgJAQQQcBFQv6Tv27dPUo9x1bWDQcfCpQHZjAACCERcgDEXEW9g0kMAgegJpG6RWrlypdx5553aPUVKDd7mikX0zjsyQgABBHIRoHORixJlEEAAAc0E1C1SqUHe6ilSOky0p+bimD17tqhOD7dCaXbCEA4CCCAQkEDCsizL6ViJREJc3nIqzjYEEEAAgRAE1C/0qnOhniT1+OOPFzW2oZjP/dbW1mTHoq2tjcfNhnAecEgEEEAgaAG37wyuXATdEhyvYAGTJiAi1oKbOeuO2HYnUvNgqIn21NgLNdBb3ZJUyGzexbiqKyjl5eVSWVkpW7ZsCeRxs8XE213Q/zVi9cfYJFclUEi86t+zeuIaCwImCdC5MKm1iBUBBBBwEFAd1ZhjcwAAIABJREFUjMmTJ0tzc3PylqRvfOMbgfxCoq5WqDEfixYtSj5qdu7cucy87dA+bEKgUIH3338/+UcDdbvh4cOHC62G/RAIVIDORaDcHAwBBBDwT0CNw/j9738vV199ta+/kKhfctRfVNXVir/7u79L3gZVVVXlX2LUjEBMBRYvXpzsuG/evFmuu+665L+1mFKQtkECjLkwqLEIFQEEEMhVQF1VWLJkiSxdulQWLFggX/nKV0R1Pnpa3O6fTe2jBo3X19cnZ9uurq6Whx56KGudqX35iQAChQuoWx3VmKp58+bJtGnTkrdYqafGsSAQpoDbdwZXLsJsFY6dl0Ah96vmdQAPCxOrh5i2qrC1gbislpWVybPPPpu8Veqjjz6S4cOHy4QJE5K3Te3atStjLzdX1aFQT39S+5533nnJgePqSVCqk5Gts5JxEA83uMXr4SE8q4pYPaPsVpFJrirwYuJVtz6q2w7VrY8ffvhh8t+i+ndZyPiqboisIOCDAFcufEClSn8EUh/MtbW13T6k7etOR7eXsa+zj5OAiN3Jvu60l72MfZ19nAT8t1a/hKgnOalfUtTVDLWoDsc//MM/JDsMan3VqlVy8803yyeffCIff/yx/PGPf0yWU1cp1PLFL35R+vbtm3FeJN+0/c/e7vZ1W/Hkqr2MfZ19nAT8OXec7O3bsq2raLOVsb+v+z72FrDHn8u6vY5819W/5dWrV8uUKVNE/dtcvny5lJSU5FsN5REoWsDtygWdi6JpqSAoAXUSsyCAAAIIIIDAKYGWlhZRVypZEAhawK1zwW1RQbcExytKQM29YsJ/KkkT4lQx1tTUJNvElHhNsjUpVs4D/z5bOA/8sY3jOXvo0CGZNWtW8jNb/VTrdCySHPxPI4HTNYqFUBBAAAEEEEAAAQQcBNR8Muqxz2pZv3698IQ2ByQ2aSHAlQstmoEgEEAAAQQQQACBTAH1UAU1n8ykSZOSD1ZQE1XSsch0Yos+AnQu9GkLIkEAAQS8Eehsl6YVc+SqREIS/afI4zvapdObmqkFAQQCFFBPhFJPaVNPiFJPimKiygDxOVTBAnQuCqZjRwQQQEBHgY+k6bHp8r2Wq+XF45Ycb/qmfDhnujzW9JGOwRITAgj0IKAmq1yxYoX84he/CPXRzz2EyFsIZAgw5iKDhA0IIICAuQKdrXUy97Eh8v2946VU/fmodLzc9/2XZPDcOrlx3VQp409K5jYukcdOYMeOHbHLmYTNF+Brxvw2JAMEEEDgpMBf5K1tv5cNl14kA/ukPt57Sd+Kq+XWN34v2976C1IIIIAAAgj4KpD69vH1IFSOAAIIIBCAQOe7su2X26R02CD5fMan+zb55bZ3GXsRQDNwCAQQQCDOAhlfP3HGIHcE4iqg5rhgiYBAR5u0vCFyaXl/6ROBdEgBAQTcBP4m7XV3iZrELJHoL1c9ukM65Ji073hapvRPSOKiR6Xpb277sh0BfwUYc+GvL7V7KJCaMMnDKn2ryqRYfUPwqWKTbE2K1afm8q1ak2xNilU1mEl/bIhvrKdL6cRnxDp+v9Td+VWZ9Nga2TB0p7yy70p5us2SFb79y6NiBLILcOUiuxElEEAAATME+vSX8ktF3mhpkw4zIiZKBGIj8OCDD3qfa6/z5Op/vEFK2xfLjH8tlXtuu4Srlt4rU2OeAnQu8gSjOAKFCxyTA3UzpP+1y6VVw0kHOtu3y+NTLj1xmf2quVLXeqTwVP3c89gh+fdHp0j/1O0Ac56XpvZjfh6xwLqPyKE/t8ivHp0iF81pkEA0ew2SMV8bkxFv5wfvyq72MfK1MYPE/A/9Tulo3Sx7d/9Rplw0VxqOaPiPKdUCHa3Jc/Xx+fNP3Lqi7bkqIp3tsuPxKXIi1mtlTt1eczqone9J3R0Vcu3yvfqOKTrSIBsfV+eBuo1J/XezLG/14gELJx/YUFoql46++MQT4lLnHz8RCEnA/O+ZkOA4bJgCnXKkYe7JXy5PflBr+gt7ulLngd9KzYynpT19oy6vO16T+g2nydd//oZYx9vklRsPyIyxi/T7xa3zPWl59c8iNz4pbZYlx9tWy40fLJaKW56Wpg6dfsn8i7QunylbXntN7pm1Uj4NrJ3PkovGXCeXPr9RGrt+6e6Ujv1vyRtV18mYi84KLBK/DtTZ+px8vfbnsnv9RlkZHGz+6XS+J2ufbUieqzNrajQ+V1VqH0lz/XaRrz8rM2vmSdsrN8oHM74pP2g4mH/ege9xTA7UL5EZy9sCP3LuBzwmBzbWyRufpO3h4b/Hzk8+koPSLht++Ud5S6ePwbR0eRkvAToX8WrvaGTbuU82vvCbtF/SS6Xqa1+Wi3Q+mzt2yGNz/yDnXnOJhm3wN3m78ah86dZRJ/7q1atUKu+YIrfKBlnfeFireDv/vF/O+n+GyzVlfZNx9SodLd+ZN1OqNr8gq3boFOtZUjZ1mUysHicPV5UGatirbKIsvHeP/GDRJmnvVH+Q3iSLfrBH7l04MRJzXPQqmyq/feGncuXYiwN1zfdg6lw95+apBpyrIp1v/4d8/KUbpbL0DBE5TUorvyZTbhV5fv3rwVxxyxe3q7wlHU3PyNztZ8o1wf4z64ogpxcdu+QXPy2RCXO+nxzPosaJWOs9mnOm8z2p/8EGOfcbVSJvvCX7tfojS046FIqggM6/jkWQm5SKF+iUjuY6+em5P5aP1Qd08r82WT91sMa3e3wkTc+8KHLPdLn282cWT+B5DafLhWNHyYC0T4PkbTTl/yg3V5Z4frRiKux14Wj5wtmndaui1+cHyTCdf7HoFm0QK5+VEff+RB753L/IiNMSctotG6X80Z/IvSM+G8TBOcZJAXWujh2gflk/teh6rmbE2nlQ3t11ntx78+Vyoht/KgetXh1rk2eeELnn3uvk81oFlh5MpxzZUS+PbVgqf9jaLHUNrR7ebqau2vxENlTdLwv+6WtS1a7+IPSWND2+SOoO6HiraLoLr6MskPbrRJTTJLfoCByWHatekA2LH5EFy+ukQddxAV3gndLRtFKekFvkrhF6/aLeFWK3F0ektWG53L+gXea8+G0Z0TURW7dC+q18ZpR8qVzrX4OCNVNXn2auSN46Zr30iEwZUapx5ztYmtCPpvW52inHDv1Zlt//I3lrzlOad0g/kvbGN0XumSwjbH9wCL2N0wPobJVfPfKctEu7vPfH38qk8WPlhjl10lrUFYYOaXr0KkkkbpAn5HZ5dOIX5PT+l8g1Y9tk8Q+ek/f+frpMtHVs00PiNQJ+C9C58FuY+j0V6Gz9tTyyuElENsjiOybJ+PKb9B542NF44i9rd1Xo/wSPIw0yp/85Uj7+Dlm88g+y/k/vePgXNk9Pg7TKOuVI42bZdddkqeLLNM2Fl/oJ6H6uHpSGOZWy6Onn5Y7Fv5Y/rX9F3irqF2A/W+DEH21ekUvkLt2vyPUaLFPXtyXHst35ta/K7LEimxfPkH96prGIz9c+MuJ7L4llrZdHJg4+8d3Sp1K+91KbWC8tlIknbxv1swWoG4GeBOhc9KTDe9oJqPut1ycH8jZK/bLZMlZ1MiZ9T55p+ki7WNUgyaZnG+SChXeZcQWg7zh5pE0Nkn5FnpstsnjSTfKduvf0ffqKavGORvnZinNloQmdNw3PUEIKUED7c/VcGfdIo9R8/15pfO5W9QEgY79TLwd0HCDc0SjPrvmCjP/vA/T/o03qFOtVKqXll8sjm3bKpvsvlc2P1cuOrocupArxE4GICFguy4l5dFzeZDMCmggcb9tg3T+21Cqdvcn6OJCYjloty25S01n3/F/VT63GV/7Zun/Nu9bxrrg+tDbNHmFJ1TKr5dTGrne9fnG8ZZlVlS1Oucla1nI089DH91jLqoJyzdXU7vb/WY2PPWQt2xNMy1snTXpu+1KratmeU20eqGNmM+a7xZzP/ZPnTOn91qaPA/jHlC9kRvmAz9WM4+e7QWdfZflDa83+v55K6uNN1uxS27+9U+/q9yoZ7whr9qYP9YuNiBDIQ8DtO4MrFxHpJJqcRmfrcrm269nfqWeA23/eLDfOmJeRZq/S8XLf928T6fbozYxiHm5QTwFadeqJH12DylODy0/8rBn1n/LxmqXyw0mD5LSu3D4n49UtXRvukPLT+vv+TPbUVZ4Tg967x3dq2yp574UfZvq4zJeQWdCLLbmZpp6ucmIiqmNyYO2/ypvXz5SpgwMaa5G6vcGlzZ0eLvDgQ096ARRIHb5M8OVj5E/U/4ePtXtZ9TG59+v/GOy5WkT4J86DE480riqiHt92PfKqrFpyv0waeOapOSPOGS+L29tlwx1D5DTP5o/wPoOuf2PJyS7LpXxgH+8PQo0IaCBA50KDRoh7CLn+Ejy83+kOVL2kz8CL5NJLL5KBWg0+/kzyFoNTv8SrX+4/lE2zR4hULZOW47o/4apD9rd8LNd/6UINbzs4Lu0Ny2XV2TfIrV0diyOyd8XzspnbDBz+jbApPIFjyXP1P84oN+xcPTE3ytvXV0i5Vp+rInLy9k312VpTU3PiDz0fb5LZpaVStWyPHLdWydQyzedz6WiTt0bcIf+ge5zh/cPhyIYL0LkwvAEJX30J/m8ZMefGSDzDP5T2tD5Ozm57VdfsweoXoqflkQ9ukVlV52n2lKEjcmjvFrll/P+Qe8cPTLsqdI4MefH/Sn/dfhEKpUE5qB4CR6S17qHkubrh+cc1PlePyYG6GdL/qjmyoqk9eb9ncm6URw7L3FlXd3tEtR6uZkXR2d4ka9c2JeecUZF3tm+Xxxe8KlffPUbvx/yaxUy0ugm43Vrldh+VW3m2I+C/wF+ttsZ/s+ob207e0/5Xq+2Vf7Zmf3+D1WbCbddWsGMucm+Pj609y6ZapanxGaWTrSVrGjU0/au1f823T8WZijf5U7f7rY9bH2+63xary/iW3BvK95JGfO4n71dPH/OkW9urZjLrXP1kz3PW5NKU6SXW5CVrrMa2tDENvp95RR5A4zEXqXGB6t+WqM/W1S9ZLZ8Y8YVVZKOwexwE3L4z1CVFx8VtB8fCbEQgAIGamnlW26aHrLEnf6ksnbzEWr2pxfokgGPne4iampp8dwmtvEmxKiST4jUtVpM+902zDe0feJ4HxjVPsDyKm2SbR1oUjbGA23eG003sul1cIR4ETgqcJqXjHpSXrAcRQQABBBBAAAEEENBQgDEXGjYKISGAAAIIIIAAAgggYKIAnQsTW42YEUAAAQQQQAABBBDQUIDOhYaNQkgIIIAAAggggAACCJgoQOfCxFYjZgQQQAABBBBAAAEENBSgc6FhoxASAggggAACCCCAAAImCtC5MLHViBkBBBBAAAEEEEAAAQ0F6Fxo2CiEhAACCCCAAALREqitrY1WQmSDgIsAnQsXGDYjgAACCCCAAAJeCTz4IHM0eWVJPXoL0LnQu32IDgEEEEAAAQQQQAABYwToXBjTVASKAAIIIIAAAggggIDeAnQu9G4fokMAAQSyCByR1oa18qtHp8hFcxrkSJbSvI0AAuEIMOYiHHeOGrwAnYvgzTkiAggg4JHAX6R1+UypXfGc3DNrpXzqUa1UgwAC3gsw5sJ7U2rUU4DOhZ7tQlQIIIBADgJnSdnUZfLCz38oD1eV5lCeIggggAACCPgrQOfCX19qRwABBBBAAAEEEEAgNgIJy7Isp2wTiYS4vOVUnG0IIIAAAmEJdO6V5dePkweG/YvsfWSc9C0wDj73C4RjNwRyEFC3RTHuIgcoihgj4PadwZULY5qQQE26X5VY/TtfsfXH1iRXJWBSvMTKOeuPALUioKcAnQs924WoEEAAAQQQQAABBBAwToDbooxrsvgGnPrrn7qsnHqtNOzrTkL2MvZ19nESyLTFLdPESc7uZF/vcR/roDS/+Lz85u1PnIqd3Ha2XHjDrdL666elVs36e3Kfxkn1MvmsLXKmw57z58932Jq5qaamJmOjPX77esYODv8u2SeAc+dkQ3hh7VSHfVu2dRVOtjL293Xfx36u2+PPZd1eB+sImCrgdluUGlfhuIi4vuVYno0I+C1QU1Pj9yE8q59YPaPMqAjbDBLLOr7HWlZVapXO3mR97PB2LpuUq0mf+5wHubRq/mVwzd8s1z1Mss01J8rFW8DtO4MrF6Z2F4kbAQQQSAkwoDslwU8EEEAAgYAE3K5cMOYioAbgMMULpN8KVXxt/tZArP75YuuPrUmuSsCkeImVc9a0c9afFqPWuAjQuYhLS5MnAghEUKBTjjTMlf6nDZE7NrRL++Lxck7iZlne+pcI5kpKCCCAAAImCJxuQpDEiAACCCDgJNBL+o5bKG3WQqc32YYAAggggEDgAoy5CJycAyKAAAJ6CrjdP6tntESFAAIIIBCmgNt3BrdFhdkqHDsvAe5bzosr58ImuaqkTIqXWHM+DfMuiG3eZDntgGtOTAUVMsm2oATZCYGTAnQuOBUQQAABBBBAAAEEEEDAEwE6F54wUgkCCCCAAAIIIIAAAgjQueAcQAABBBBAAAEEEEAAAU8E6Fx4wkglCCCAAAIIIIAAAgggQOeCcwABBBBAAAEEEEAAAQQ8EaBz4QkjlSCAAAIIIIAAAggggACdC84BBBBAAAEEEEAAAQQQ8ESAzoUnjFSCAAIIIIAAAgi4C9TW1rq/yTsIREiAzkWEGpNUEEAAAQQQQEBPASbR07NdiMp7AToX3ptSIwIIIIAAAggggAACsRSgcxHLZidpBBBAAAEEEEAAAQS8F6Bz4b0pNSKAAAIIIIAAAt0EGHPRjYOVCAvQuYhw45IaAggggAACCOghwJgLPdqBKPwXoHPhvzFHQAABBBBAAAEEEEAgFgJ0LmLRzCSJAAIIIIAAAggggID/AgnLsiynwyQSCXF5y6k42xBAAAEEDBfgc9/wBiR8rQXUbVGMu9C6iQguTwG37wyuXOQJSfHwBEy6X5VY/TtPsPXH1iRXJWBSvMTKOeuPALUioKcAnQs924WoEEAAAQQQQAABBBAwToDOhXFNRsAIIIAAAggggAACCOgpQOdCz3YhKgQQQAABBBBAAAEEjBNgQLdxTUbACCCAgD8CboPz/DkatSKAAAIImCzg9p3BlQuTWzVmsTMo0p8GN8lVCZgUL7H6c85yHuBq2jlgYrz+nWXUHHUBOhdRb2HyQwABBBBAAAEEEEAgIAE6FwFBcxgEEEAAAQQQQAABBKIuwJiLqLcw+SGAAAI5CrjdP5vj7hRDAAEEEIiRgNt3BlcuYnQSmJ4q96/704ImuSoBk+IlVn/OWc4DXE07B0yM17+zjJqjLkDnIuotTH4IIIAAAggggAACCAQkQOciIGgOgwACCCCAAAIIIIBA1AXoXES9hckPAQQiLHBEWv/9cZnSPyHq3tfEVXNkRVO7dEY4Y1JDAAEEENBbgM6F3u1DdAgggICLwDE5sPZ5+Tf5e3m6zRLreJu8cuMHcn/FnfJY00cu+7AZAQQQQAABfwXoXPjrS+0IIICAPwKdB+Q/z7lRvnNNmfRRR+hVKpXfuV8ernpVHlv1qhzx56jUigACCCCAQI8Cp/f4Lm8igAACCOgp0OuLMnasLbRe58qgYf1tG1lFAAEEEEAgOAGuXARnzZEQQACBAAT6yfVfuvDE1YwAjsYhEEAAAQQQSBegc5GuwWsEEEDAZIEjr8v6XdfJ9KrzhA93kxuS2KMoUFtbG8W0yAmBDAG+fzJI2IAAAgiYKPCRNP3s1/K5hbfLiD58tJvYgsQcbQGTJtWMdkuQnd8CCcuyLKeDuE3p7VSWbQgEIZD6YFZ//Um9Vse1rzvFYi9jX2cfJ4FMW9wyTZzk7E729R73sQ5K84vPy2/e/sSp2MltZ8uFN9wqrb9+WmoffFBELDnW3iSdox6RXu+tljMc9pw/f77D1sxNNTU1GRvt8dvXM3Zw+HfJPgGcOycbwgtrpzrs27Ktq3CylbG/r/s+9nPdHn8u6/Y6WEfAVAHXvoLqXDgt6tuKBQGdBGpqanQKp8dYiLVHnqLexDaT7/j+f7Mee+4N65PMt3LeolxN+tznPMi5afMqiGteXHkVNsk2r8QoHFsBt+8Mrp2b2l0kbgQQQEBEOtsb5MerzpKv33rJyUHcndKx91eyfPNBfBBAQCMBdVWDBYE4CNC5iEMrkyMCCERQoFM6Wuvk/lu+KffeO176n3Zylu7EaXL2kFUi/ZOzX0Qwb1JCwEyB9Nt5zcyAqBHITYB5LnJzohQCCCCglUDngXr5zthJsrzdIayq62TMRWc5vMEmBBBAAAEE/BWgc+GvL7UjgAACvgj0GjBRlrVZssyX2qkUAQQQQACBwgS4LaowN/ZCAAEEEEAAAQQQQAABmwCdCxsIqwgggAACCCCAAAIIIFCYAJ2LwtzYCwEEEEAAAQQQQAABBGwCdC5sIKwigAACCCCAAAIIIIBAYQJ0LgpzYy8EEEAAAQQQQAABBBCwCSTUtIK2bclV1ym9nQqzDQEEEEDAeAE+941vQhJAAAEEAhNw+87gykVgTcCBihUwaQIiYi22td33x9bdpph3THJVeZoUL7EWc2a672uSq2nnrLs67yCQXYDORXYjSiCAAAIIIIAAAggggEAOAnQuckCiCAIIIIAAAggggAACCGQXYMxFdiNKIIAAArEQcLt/NhbJkyQCCCCAQF4Cbt8ZXLnIi5HCYQqYdH8tsfp3pmDrj61JrkrApHiJlXPWtHPWnxaj1rgI0LmIS0uTJwIIIIAAAggggAACPgvQufAZmOoRQAABBBBAAAEEEIiLAJ2LuLQ0eSKAAAIIIIAAAggg4LMAnQufgakeAQQQQAABBBBAAIG4CNC5iEtLkycCCCCAAAIIIIAAAj4L0LnwGZjqEUAAAQQQQAABBBCIiwCdi7i0NHkigAACCCCAAAIIIOCzAJ0Ln4GpHgEEEEAAAQQQqK2tBQGBWAjQuYhFM5MkAggggAACCIQpYNJkimE6cWzzBehcmN+GZIAAAggggAACCCCAgBYCdC60aAaCQAABBBBAAAEEEEDAfAE6F+a3IRkggAACCCCAgOYCjLnQvIEIzzMBOheeUVIRAggggAACCCDgLMCYC2cXtkZPgM5F9NqUjBBAAAEEEEAAAQQQCEWAzkUo7BwUAQQQQAABBBBAAIHoCSQsy7Kc0kokEuLyllNxtiGAAAIIGC7A577hDUj4Wguo26IYd6F1ExFcngJu3xlcucgTkuLhCZh0vyqx+neeYOuPrUmuSsCkeImVc9YfAWpFQE8BOhd6tgtRIYAAAggggAACCCBgnACdC+OajIARQAABBBBAAAEEENBTgM6Fnu1CVAgggAACCCCAAAIIGCfAgG7jmoyAEUAAARHpbJcdP75PJty7UtqlSmav+bF8f+Jg6VMEjtvgvCKqZFcEEEAAgYgKuH1ncOUiog0exbQYFOlPq5rkqgRMite/WD+S5vrtIl9/Vtqsv0rbKzfKBzO+KT9oOFjwSeJfrAWH1OOOJsVLrD02ZcFvmuSqkjQt3oIbhh1jL0DnIvanAAAIIGCaQOfb/yEff+lGqSw9Q0TOkNLKr8mUW0WeX/+6HDEtGeJFAAEEEIiUAJ2LSDUnySCAQBwEel04WsYOUB2Lk0vnQXl313ly782XS9/UNn4igAACCCAQggBjLkJA55AIIICANwKd0tG6WVYtWyVvXft9eXjcACnmL0Zu9896Eyu1IIAAAghEScDtO6OY76Eo+ZCLAQIm3a9KrP6dUNimbA9Kw5xKObt8vNyx+Nfyp/WvyFsdnak38/5pkqtKzqR4iTXv0zGnHUxyNe2czakBKISAiwBXLlxg2KyfQOqLpLa2ttsvFvZ1p8jtZezr7OMkIGJ3sq877WUvY19nHyeBIqxr/qe0v/6ybFj7Rzk2dY18fcBrcnYi8xjz58/P3OiwpaamJmOrvQ3t6xk7SBH5PPhgV3UcJ9OxCyfthd3Jvp5WtOulvUy2dbVjtjL296O4TxfgyRf2nHNZt9fBOgKmCrhduRDLZRFxfctlDzYj4K9ATU2NvwfwsHZi9RDTVlV0bY9aLctustRnb4//VS2zWo7bUKyT+5beb236OONNe2HHdeVq0ud+dM8Dx+YJbCOu/lGbZOufAjVHScDtO+N0U3tLxI0AAghES+AsKZu6SqyphWR1llw05jqpkrcK2Zl9EEAAAQQQ8EyAMReeUVIRAgggEJZAp3Tsf0vevr5CyvvwsR5WK3BcBBBAAAEp6sEi+CGAAAIIBC5wTA7UzZD+V82RFU3tooZwd7ZvkkWPHJa5s66WAfQtAm8RDogAAgggcEqAr6FTFrxCAAEEDBA4Xc65eKRc07JYbqvoL6clLpXbX/hEJj33hEwdzCwXBjQgISKAAAKRFmDMRaSbl+QQQCB6Ar2kz+ApsqJtiqyIXnJkhAACCCBguABXLgxvQMJHAAEEEEAAAf0F1GNqWRCIgwCdizi0MjkigAACCCCAQKgCqbmaQg2CgyMQgACdiwCQOQQCCCCAAAIIIIAAAnEQoHMRh1YmRwQQQAABBBBAAAEEAhCgcxEAModAAAEEEEAAgXgLMOYi3u0fp+zpXMSptckVAQQQQAABBEIRYMxFKOwcNAQBOhchoHNIBBBAAAEEEEAAAQSiKEDnIoqtSk4IIIAAAggggAACCIQgkLAsy3I6biKREJe3nIqzDQEEEEDAcAE+9w1vQMLXWkDdFsW4C62biODyFHD7zuDKRZ6QFA9PwKT7VYnVv/MEW39sTXJVAibFS6ycs/4IUCsCegrQudCzXYgKAQQQQAABBBBAAAHjBOhcGNdkBIwAAggggAACCCCAgJ4CdC70bBeiQgABBBBAAAEEEEDAOAEGdBvXZASMAAII+CPgNjjPn6NRKwIIIICAyQJu3xlcuTC5VWMWO4Mi/Wlwk1yVgEnxEqs/5yznAa6mnQMmxuvfWUbNURegcxH1FiY/BBBAAAEEEEAAAQQCEqBNOmDjAAAR2klEQVRzERA0h0EAAQQQQAABBBBAIOoCjLmIeguTHwIIIJCjgNv9sznuTjEEEEAAgRgJuH1ncOUiRieB6aly/7o/LWiSqxIwKV5i9eec5TzA1bRzwMR4/TvLqDnqAnQuot7C5IcAAggggAACCCCAQEACdC4CguYwCCCAAAIIIIAAAghEXYDORdRbmPwQQAABBBBAAAEEEAhIgM5FQNAcBgEEEEAAAQQQQACBqAvQuYh6C5MfAggggAACCCCAAAIBCdC5CAiawyCAAAIIIIAAAgggEHUBOhdRb2HyQwABBBBAAAEEEEAgIAE6FwFBcxgEEEAAAQQQiK9AbW1tfJMn81gJ0LmIVXOTLAIIIIAAAgiEIWDSpJph+HDM6AjQuYhOW5IJAggggAACCCCAAAKhCtC5CJWfgyOAAAIIIIAAAgggEB2BhGVZllM6iURCXN5yKs42BBBAAIHQBI7Jgbp7ZeRPL5fN66ZKWYF/NuJzP7QG5MAIIICAcQJu3xkFfgUZlz8BR0DApPtVidW/Ew7bTNvOA7+VmhlPS3vmWzlvMclVJWVSvMSa82mYV0GTXE07Z/NqCAojYBOgc2EDYRUBBBAwSqBjhzw29w9y7jWXGBU2wSKAAAIIRFOAzkU025WsEEAgFgIfSdMzL4rcM12u/fyZsciYJBFAAAEE9BZgzIXe7UN0CCCAgItAp3Q0PSXffmmUPP29C2THnOtk/K7p0sKYCxcvNiMQroC6jYu5LsJtA47urQBjLrz1pLYQBEy6v5ZY/TtBsD1p29Eozzwhcs9dFdLHA26TXFW6JsVLrB6coA5VmOTqED6bEIisALdFRbZpSQwBBKIr8JE0PdsgFyy8S0b04WM8uu1MZggggIB5AtwWZV6bxTbi1F+p1GXl1GuFYV93ArKXsa+zj5NApi1umSZOcnYn+7rzPvfLjBtHyNO/2e309qltF35V7hzbKXs++W+y5Zc/ktoHHxSRT+XPG1+Q5/s8LN/+0nvSL3GqeOrV/PnzUy97/FlTU5Pxvj1++3rGDg7/LtnHz3PH+89Ep/ayb8u2rs6LbGXs7+u+j/1ct8efy7q9DtYRMFXA7bYoNZeF4yLi+pZjeTYi4LdATU2N34fwrH5i9YwyoyJsP7Q2zR6h5idy+a/Uqlq2xzqeIdfzBuVq0uc+50HP7Vnou7gWKpd9P5Nss2dDCQSS8+Q5MnDlwtTuInEjgAACXQIHpYEB3V0avEAAAQQQ8F/A7coFN+v6b88RPBJIvxXKoyp9q4ZYfaPtdkucf0fxpmbOA28cnWrB1kml+G24Fm/oVoNJtm45sB2BXAToXOSiRBkEEEAAAQQQQAABBBDIKnB61hIUQAABBBDQXOBcGfdIY3IQhuaBEh4CCCCAQMQFGHMR8QYmPQQQQCBXAbf7Z3Pdn3IIIIAAAvERcPvO4Lao+JwDxmdq0v2qxOrf6YatP7YmuSoBk+IlVs5Z085Zf1qMWuMiQOciLi1NnggggAACCCCAAAII+CxA58JnYKpHAAEEEEAAAQQQQCAuAnQu4tLS5IkAAggggAACCCCAgM8CdC58BqZ6BBBAAAEEEEAAAQTiIkDnIi4tTZ4IIIAAAggggAACCPgsQOfCZ2CqRwABBBBAAAEEEEAgLgJ0LuLS0uSJAAIIIIAAAggggIDPAnQufAamegQQQAABBBBAoLa2FgQEYiFA5yIWzUySCCCAAAIIIBCmgEmTKYbpxLHNF6BzYX4bkgECCCCAAAIIIIAAAloI0LnQohkIAgEEEEAAAQQQQAAB8wUSlmVZTmkkEglxecupONsQQAABBAwX4HPf8AYkfAQQQCBAAbfvDK5cBNgIHKo4AZPuVyXW4tq6p72x7Umn8PdMclVZmhQvsRZ+Xva0p0mupp2zPbnzHgLZBOhcZBPifQQQQAABBBBAAAEEEMhJgM5FTkwU+v/bu98Qy8oyAODPNSmRTSSEcg3Kihk/tBWs+MUl1GS3JRTJYklbFrcPQsQGi/8yGZlBCmTZkDIWYi01iTaLTMgMXFZRItm1yLB2ESow54N90G0gE7w3rjbbdOaeuXfu3vfe+573t7DsnHvOed/n+T3v3sMz95wZAgQIECBAgAABAgT6CXjmop+Q/QQIEChEoO7+2ULSlyaBpALd27j8roukxAYfs0DdNcMnF2MuhOmGF8jp/lqxDl/nfmey7Sc03P6cXLsZ5hSvWIdbk/3Oysm1Xy72E2iSgOaiSdWUCwECBAgQIECAAIEJCmguJohvagIECBAgQIAAAQJNEtBcNKmaciFAgAABAgQIECAwQQEPdE8Q39QECBCYJoG6h/OmKUaxECBAgMB0CNRdM3xyMR31EcUAAjk9vCfWAQo65CFsh4Trc1pOrt1UcopXrH0W35C7c3LNbc0OWRKnEXhLQHNhIRAgQIAAAQIECBAgMBIBzcVIGA1CgAABAgQIECBAgIBnLqwBAgQIEHhLoO7+WTwECBAgQKAqUHfN8MlFVcr21ArkdH+tWNMtI7ZpbHNy7QrkFK9Yrdnc1myaihm1FAHNRSmVlicBAgQIECBAgACBxAKai8TAhidAgAABAgQIECBQioDmopRKy5MAAQIECBAgQIBAYgHNRWJgwxMgQCCdwD/i8K0XR/ehurf/boxt9/052ukmNDIBAgQIEFhTQHOxJo+dBAgQmF6B9t+fiocePLYiwC2xY8sHwxv7ChJfEiBAgMBYBc4c62wmI0CAAIERCbwav/vRI3HeD1+JzhXnjWhMwxAgQIAAgdMT0Fycnp+zCRAgMBmBk8/Fof0PxN2z74vZV7fHlq2fjJkNPrOYTDHMSoAAAQLLAq5EyxL+JUCAQDYCr8eJhw/E3YsRceTu+NK1l8fsVXfEz06czCYDgRIoTWB+fr60lOVbqIDmotDCS5sAgZwFzoqZ3Yei0/l3vHz00Th4y9aII9+Ma288GMeWPM6dc2XF3lyBnH6ZYnOrILNxCLQ6nU6n10R1v9K717FeIzAOgeU35u53f5a/7s5b3e4VS/WY6rZzegmstuW22qSXXNWpuj36c96Mpb88Hc89uBRv7Lw8rrzw7FVTLCwsrHqt1wtzc3OrXq7GX91edUKP/5fOmda183b1qvWpbnePqr7Wb7uJ51TXej+DXvurY9gmkKtAba/QbS56/YmIXi97jcDEBObm5iY293onFut6xQY/vrm2/+ocP/j57jd71v679WDn+Ju9vF7pPHHL5s75tzzRea3X7j6vdV1zet9v7jroU6jEu7mmA87JNp2CkZskUHfN8EB3ru2iuAkQaJjAf2912j1sWhvi/bOzsSk2xoZhh3AeAQLJBLqfYvhDoAQBz1yUUGU5EiBQgMBSvPTiprj1czN+z0UB1ZZifgIrb+fNL3oRExhcQHMxuJUjCRAgMB0C7cU49sgv49jiG2/H016MZ7+1P45cuTMuO8fb+nQUSRQECBAoU8BVqMy6y5oAgawF2vHab++Jize+K1qtTbFr/1Ox9JnbYuGKC3xqkXVdBU+AAIH8Bfy0qPxrKAMCBAiMRKD2J3+MZHSDECBAgECTBOquGT65aFKVG55LTverijXdYmSbxjYn165ATvGK1ZrNbc2mqZhRSxHQXJRSaXkSIECAAAECBAgQSCyguUgMbHgCBAgQIECAAAECpQhoLkqptDwJECBAgAABAgQIJBbwQHdiYMMTIEAgF4G6h/NyiV+cBAgQIDA+gbprhk8uxlcDM52mgIciTxOw5vScXLsp5BSvWGsW3QheZjsCxB5DcO2BMqKXcrIdUcqGKVRAc1Fo4aVNgAABAgQIECBAYNQCmotRixqPAAECBAgQIECAQKECnrkotPDSJkCAQFWg7v7Z6nG2CRAgQIBA3TXDJxfWRjYCOd2vKtZ0y4ptGtucXLsCOcUrVms2tzWbpmJGLUVAc1FKpeVJgAABAgQIECBAILGA5iIxsOEJECBAgAABAgQIlCKguSil0vIkQIAAAQIEJiYwPz8/sblNTGCcApqLcWqbiwABAgQIEChSIKdnb4oskKRHJqC5GBmlgQgQIECAAAECBAiULaC5KLv+sidAgAABAgQIECAwMgHNxcgoDUSAAAECBAgQIECgbAHNRdn1lz0BAgQIECAwBgEPdI8B2RRTIaC5mIoyCIIAAQIECBBosoAHuptcXbmtFNBcrNTwNQECBAgQIECAAAECQwtoLoamcyIBAgQIECBAgAABAisFWp1Op7PyheWvW61W1OxaPsS/BAgQINAgAe/7DSqmVAgQIJBYoO6a4ZOLxPCGH51ATverinV0da+OxLYqMprtnFy7GecUr1hHs0aro+TkmtuarVrbJrAeAc3FerQcS4AAAQIECBAgQIBArYDmopbGDgIECBAgQIAAAQIE1iPgmYv1aDmWAAECDRaou3+2wSlLjQABAgSGFKi7ZvjkYkhQp41fIKf7a8Wabn2wTWObk2tXIKd4xWrN5rZm01TMqKUIaC5KqbQ8CRAgQIAAAQIECCQW0FwkBjY8AQIECBAgQIAAgVIENBelVFqeBAg0VqC9eCweeXhf7NrYitbG2+PwyXZjc5UYAQIECEy3gAe6p7s+oiNAgMAaAm/E4rPfi9uuORCx947YdfX2uGLmnDWOX3tX3cN5a59lLwECBAiUKFB3zfDJRYmrIdOcPRSZpnA5uXYFcoo3baztWDp2b1x3zbPxiZ//Or5/047TaizSxjr6tZtTvGIdff1zey/IMd40VTNqCQJnlpCkHAkQINA4gaWjceCmh+JD3/lpfPWS88N3ihpXYQkRIEAgSwHXoyzLJmgCBMoWeD1OHNoXN8en4tL2T+KG7rMWrU2xa9/jcWLJ8xZlrw3ZEyBAYLICmovJ+pudAAEC6xdo/zWe/vFzcdklH42PX7on7n/5zfjnn26K2H9D3HjgaCytf0RnECCQWGB+fj7xDIYnMB0CmovpqIMoCBAgMLjA0stx/Plz45Jt22Pz+e+MiDNiw0U74ut3bYkjN++LQydeH3wsRxIgMBaBnJ69GQuISRor4KdFNba0zUts+Y25+92f5a+7WVa3e2VePaa67ZxeAqttua026SVXdapu9z7na/GVqzfHvY++0Gv3/1778FXx5W0Rj3/3aFz7xB/irCe/fWrfndd/IGZm74j37rw+rrzw7FOvd79YWFj4v+26jbm5uVW7qvFXt1ed0OP/pXNSrp3Rvyf2qlf1tX7b3XXR75jq/mk/p7rWq/EPsl0dwzaBXAXqflqU5iLXioqbAIFyBU4ejlsv+mL8/q7D8djui049zN0+cV9sn/1V7Dj+QOyeOatcH5kTIECAQHKBuubCbVHJ6U1AgACBEQuc87HYtnNjPP/MC7F46vntdiy99GI8v/XTseUjGosRixuOAAECBAYU0FwMCOUwAgQITI/AeXHZnttj+2N3xu0/+ONbD3C3F38TB+//W+z9xmdjxjv79JRKJAQIEChMwCWosIJLlwCBZgicccE1cc+RfbHpyS/Eu1uteMd1v4j37NkXezef24wEZUGAAAECWQp45iLLsgmaAAECBAgQIECAwOQEPHMxOXszEyBAgAABAgQIEChCwG1RRZRZkgQIECBAgAABAgTSC2gu0hubgQABAgQIECBAgEARApqLIsosSQIECBAgQIAAAQLpBTQX6Y3NQIAAAQIECBAgQKAIAc1FEWWWJAECBAgQIECAAIH0ApqL9MZmIECAAAECBAgQIFCEgOaiiDJLkgABAgQIECBAgEB6Ac1FemMzECBAgAABAgQIEChCQHNRRJklSYAAAQIECBAgQCC9gOYivbEZCBAgQIAAAQIECBQhoLkoosySJECAAAECBAgQIJBeQHOR3tgMBAgQIECAAAECBIoQ0FwUUWZJEiBAgAABAgQIEEgvoLlIb2wGAgQIECBAgAABAkUIaC6KKLMkCRAgQIAAAQIECKQX0FykNzYDAQIECBAgQIAAgSIEzlwry1artdZu+wgQIECAAAECBAgQIHBKoLa56HQ6pw7yBQECBAgQIECAAAECBPoJuC2qn5D9BAgQIECAAAECBAgMJKC5GIjJQQQIECBAgAABAgQI9BPQXPQTsp8AAQIECBAgQIAAgYEE/gM/4Zz7W0NuCAAAAABJRU5ErkJggg=="></p>
<p>The graph of <em>g</em> intersects the graph of <em>f</em> at <em>x</em> = −1 and <em>x</em> = 2.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the vertex of the graph of <em>g</em>.</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>On the grid above, sketch the graph of g for −2 ≤ <em>x</em> ≤ 4.</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 area of the region enclosed by the graphs of <em>f</em> and <em>g</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br>