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<h2>SL Paper 2</h2><div class="specification">
<p>The height of water, in metres, in Dungeness harbour is modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mi>sin</mi><mo>(</mo><mi>b</mi><mo>(</mo><mi>t</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>+</mo><mi>d</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the number of hours after midnight, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>c</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> are constants, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>></mo><mn>0</mn><mo>,</mo><mo> </mo><mi>b</mi><mo>></mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>></mo><mn>0</mn></math>.</p>
<p>The following graph shows the height of the water for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math> hours, starting at midnight.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXAAAAE3CAYAAACzRBrrAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABVTSURBVHhe7d1PU1PZusfx5Z0LL0DAuRZMm1hhKto4VM9tvCPBqsYzuYRBS0+Mk8YeCKOGrmp0dOSU4OzCUZxCGZxC2XMDzht8Ad78FnvhBkPLvyTr2fv7qUol2UFUwv7l2c9ae+1zn2scAMCc/0ruAQDGEOAAYBQBDgBGEeAAYBQBDgBGEeAAYBQBDgBGEeAAYBQBDgBGRR/gc3PP3cjIj8mz/bR9dXUleQYA+dLwU+kfPPjJh3Da6upb19XVVbt1JFt2aZteC2Zmpv39yMh9f1+Pvn9PT48bHLyTbAGAfGh4Bf748a9ufPxn/1j31eqWD2rR4+7uHtfe3u6Wlv6zL7yXlhbdyspK3fBWsOt10fecnv7NbWys++cAkBdNaaH89ddfPqTrhXG1+sEVi30+yNMmJn5xN27cSJ59oWper+nPiL7vnTv/U9s24Z8DQF40JcBVLYfATVP/ent7+6ug1tdXq1U3MLB/+8DA975lIt3dl/daM8Vi0X8v3QAgLxoe4GptKIzVpz5ocXG3DXIw3NfX131lrVua2izaFloxoe/d1XXR36vlAgB50fAAX11d9fdqe2jQMn1TBR164GkbGxtfbRN9GKhiV8WdFr5WHxQAkBcND3BV2QppVczpm6ppORjGor54PfowUFgf7JeLBkYV7gCQFw0NcFXEqprrhXSozPv6vu6Nh5bIQWqt1Ouli8K7XtUOAFnV0AAPU/3q9b9Dn7teIHd3d9etpldXV+p+L32tbmF6IgDkQcMCXIH6/Pm//OODs0lUlR82M0UU0vrz6bndof+t7zU4+EOydVdoudSr5gEgqxoS4DrRRtP8wqCiBizDY4WvpgPKbohf8Y/TFNK7Z2Xutlkk/HlNI9TJQWn6On0YHPaBsLW1mTwCgOyI9qr0CnfNXEmfnXkYfQjMzPxed3CzUqm44eG7tft3rq2tLdkKAPZFG+CiaYYfPnzYOxW/HoX8xYsXD10L5fbtm25tbc3dvHnLTU5OJVsBwL6GTyM8DYWy+tp/txqhXj8svBcW5n14y8uXC+79+/f+MQBkQdQV+Gns7Oy4/v6r7uPHrWSLc729vW5+/mXyDABsi7oCP42nT2f3hbeoGl9efp08AwDbMlmBa9aJqu9Pnz4lW764cKHDVSq7bRUAsCyzLZS03WmM+6txALAusy0UAMg6AhwAjCLAAcAoAhwAjCLAAcAoAhwAjCLAAcAoAhwAjCLAAcAoAhwAjCLAAcAoAhwAjCLAAcAoAhwAjCLAAcAoAhwAjCLAAcAoAhwAjCLAAcAoAhwAjCLAAcAoAhwAjCLAAcAoAhwAjIoqwKvVqpuY+MV1dXW47e3tZOsX2jY4+IN/vbv7spube568AgD5E1WADw7+99+G8sjIj669vb0W9Fu1r/u3D/vV1ZXkVQDIl6gCfHX1rbt//5/Js/2WlhZ9WI+P/+yfd3f31AL/jnvw4Cf/HADyxkwPfGVlxXV1dflb0NPT49suugFA3pgJ8I2NjVp4X0ye7QphvrGx7u8BIE/MBHi1+sH3v49Cg5zp22HbAMAyMwF+sPqWejNVRIOc6dth2wDAMjMB3t3d/VWrJPS+NaAJAHljJsDrDViur6/78E4PbAJAXkQb4AfbI5oyqLDW3G/RtELdxsfH/XMAyJuoAnxg4Pu9gC4Wr7iZmWn/ONDJOwp2DULq6x4//rX2dX3JqwCQL+c+1ySPM0uBz8AlgKwx0wMHAOxHgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4Tuz9+/fJIwCtcO5zTfI4s7q6Oly1upU8w3FUKhW3tlbxYb21ten+/PPP5JWvXbjQ4To7O1yhcMVdunTJ37e1tSWvAjhrBDj22dnZccvLr2u3ZffmzXKydX84Bx0dHbVQ//JzrRfyCvJbt267/v7+2td3JlsBnAUCHJ5Ce2FhYS+0FdiFQsEH70kq6VC56/uGQFeYDw0N177nNSpz4AwQ4DmmanthYd7Nzs66jx+33Pnz5324KmQvX76cfNXpqSrXh8P8/Pze3zM8fK9Wmd+iKgdOgQDPIQX306ezteD+w3369MlX26VSybc6Gk0Vuf7utbU1//zmzVv+7ybIgeMjwHNGFXe5/NAHd29vrxsdHfOtkmZTv1xB/vLlwl5Frsqf1gpwdAR4Tqgn/ejRQ9+PVsVdLpd9u6TV9O+amnriK3IFebn8qClHAkAWEOAZp3aJKu5Q6ZZKY77SjY1aK/pQUY9cRwaTk1O0VYBv4ESeDFMoFgrf+fBWr7lSeRdleIuOBiqVNTc6WvLV+JUrhVplPpm8CqAeKvAMUtVdKo36KYFql6iabUWf+6TUH1e7R0GuqYezs0+pxoE6qMAzRj1lVd0K77t3h2pV+BtT4S2awjg//9JX4+rZ9/df9YOvAPajAs8QtRx0U69bVXcMg5SnpWp8bGzUB/nVq/3+/8VMFWAXFXgGqGVy+/ZNH94aAFSvOwvhLaEaVw9fRxWqxhXqAAhw8xRmapmoX6yWg8IuaxWq/j+qvJ88max9WG37DytaKgABbppC7Pr1fv/4xYsFH+BZpvnh+oDq7Ox0Y2MlPz0SyDMC3CiFl0JMszQsDlSeVGipqB/+7NlTX42rhQTkEQFujMJqeHjIh5dCTGGWtyl2aqloamGYM64Qpy+OPGIWiiFhsFIzMjSop75w3oW1XUQfZme5iiIQOypwI1RhagaGwluDeYT3rtAXF40HMLiJPCHADVB47/Z6t314s9jTfqEvrvEAjQsQ4sgLWiiRC+EttAj+Hi0m5A0VeMTS0wQJ72/T4KZ+Thrc1QJeWg8GyDICPFIKb7UDtBgV4X10YYaKKvAQ4kwzRFYR4BEK4R3meBPex6f2SQjx3fEDQhzZQ4BHJh3eqryzdlp8MynEHz4s+544IY4sIsAjQnifPV3AQjN3CHFkEQEeCcK7cTTtkhBHFhHgESC8G48QRxYR4C1GeDcPIY6sIcBbSJc/I7ybixBHlhDgLaIzLIeH7/rLn2neMuHdPIQ4soIAb4GDp8dzxfXmI8SRBeYCfGLiF7+2SbiNjPyYvGIDa5vEgxCHdaYWs9re3nbF4hW3tPSqFt5dydZvi2UxKwWEgkKB8erVMuEdCQaSYZWpCnx6+jc3OHjnWOEdi3R4q+ojvONBJQ6rzFTgGxvrbmDge/+4WOxzN27c8GF+FDFU4AoGXf5LQaHAQHyoxGGNufXAFeTT09NuaWnRB/jjx78mr3yhwP6WZga6VsTTokq6hmPWrxxvHSEOUxTgFi0u/t/nzs4L/v5b9HWtMjn5xP/9o6P/m2xB7ObnX/j3bGjobrIFiJPZaYQDAzf8bXFxMdkSH1VzU1OTrre3l6vDGKIWl46U3rxZ5qIQiJrpeeA9PT3Jo/ikz7KcnX2WbIUVCvD0RSGAGJkO8PX19ShDPH2WJX1Uu9IXhSDEESMzAT4399zfgpmZaX8/MnLf38dCU9CGh4f8Y8LbPkIcMTMT4DqJ58GDn/wME53MIzMzv/v7mGi64MePW37HZ653NqRD/OnT2WQr0HrmphGeRLPmgYfpgsz1zqZr167unYjF+4sYmO6Bx0SzTRTeqtTYubNJLTENSmtwWjOMgFYjwM8A0wXzQeMZhDhiQgvllMLqgp2dnQxa5kR6XZsXLxZcoVBIXgGaiwr8FNIzTp48mSK8c0Lvsy7CoWmimi6qD3GgFQjwUwgzTnSiDjNO8kUX4dARl+j3gBBHKxDgJ6QZJzqEfviwzCF0TulDmxBHKxHgJ6DBqzDjZGhoONmKPDoY4qwljmYiwI8pvcYJM04gCnG10T59+kSIo6kI8GPY2trct8YJEKiNxlV9bNB+rEIsCwjwIwozTlRlMV0Q9egELkI8fpOTk+4f/7jlg9w6AvyIyuWHe6dRM+MEhzkY4oiLKu8wfqWZRNYR4EegBYw4TR5HlQ5xVjCMy9TUE98CLZWycWlDAvwb9In96FGZQUsci0I8rGBIiMdBs8d0YfHh4XuZqL6FU+n/hnpk/f1X/eNK5R19bxxbWKFSYU4B0DoajygUvqvtw+1ueflNZvZlKvBDMGiJs5BeS5xKvHUmJ5/4fblcLmdqXybAD8GgJc4KId5aaoM+e/bUXb3aXzuivpZszQYCvI4waHn37hCDljgThHhr6EhaP28NXKr6zhoC/IDl5dd+0FJre5fLj5KtwOmlQ5xLszWHWidacK5UGsvMwGUag5gpYW3vrA10IC5cmq051DrRCTsqxrJ65jQVeEKHWmNju4e2WuuZ8EajKEy4qk9jpVsnWZ79Q4An9GarKlLbhEFLNJKKA0K8sTQJQa0T7c9ZbJ0EBHiNrmf55s2yGx0tcUiLpiDEGycs96xZJ1nfn3PfA9ebrR1Ib7ZaJ0Az6VBf4y70xM9G3saxch3g4c3mgsRopXSI6yhQNxxf+uf46tVyLlqhuW2hhPAWBi3RSul2itp5zBM/mXDynS5zmJdxrFwGeJhxEk6Tz/IgB2wIIc7JPicTTr5TKzRPlznMXYAf7Dky4wSxUIhzxubx5XnF0FwFOANGsIAQPzq1QsNlDvPYCs1NgKfDmzVOELt0iOvMTf3+Yj/9TNIrhuaxFZqbANe63mGAgzVOYIFCXDNS9Hur4oMQ/yIUZDpZJ8+t0Fy1UP74YzZXAxywTwGugAohrpYBnG+bhIIsz0fTLGYFGKATzjRNTtQuyPPgu8YF1FpSiylvg5YH5W4WCmCRqkwFt6gSz+up94T3fgQ4YISqboW4zhzW8g866SdPCO+vEeCAISHE02dt5mFwk/CujwAHjNFc59ev3+xNM1RLZWtrM3k1W/ThpGmUhHd9BDhglMIszFDRNFldDjBLwlRB/f8I7/oIcMAwDW5q5T25d284M31xTZcsFL7z4a0PKcK7PgIcME598Urlnb/2owJcLQfLLRXNsFHlLTp3g7OmD0eAAxkQVjMMZ26qpWJtqqFaJhqs1AybsEZ/f/+15FXUw4k8QMbsLvA05E8z1/Kqaj/EvsiT/s1a4lkfPlb+zTGgAgcyRi0VXU5Mi7bpWq/qJWu97Fip7XP9er/b3Nz0p8ZzgZWjowIHMmx3rezdK9WoRz46OlYL9ELyamsd/Lep6ubiKsdDgAM5oCp3dvYPv/SqpuSVSqWWhaUGWMvlsj860DrepdIYi8ydEAEO5IQGCbUglk6KkWYHuYJ7cnJy7+9Xi0fhTbvk5AhwIGcOBmm4jmSjWis6wWhhYcFX3NLqI4AsIcCBnApBroBVa+XChQ7X39/v512fdrlafU/1uDWVUd9brRJ93+HhYYL7DBHgQM6ptaLA1UwVDSiKwlwVuYL80qXL/v6wVoeCemdn2//ZSuWtW1tbS17Zre7DhwLOHgEOYI+q8uXlZR/KCmNVz8ehVRJ7ews+/AuFK/S3G4wAB3AoBfrm5latqq4kW76m0G5ra49memKeEOAAYBRnYgKAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgAOAUQQ4ABhFgANABGZmpt3S0mLy7GgIcABosbm5525i4hdXLPYlW46GAAeAFhoY+N49ePCTf9zdfdmH+VGd+1yTPM6srq4OV61uJc8AIC4K7vv3/+lGRu4nW46GChwAWmhjY91tb2+7YrGYbDk6AhwAWmh1ddW1t7fXqvCeZMvREeAA0ELr6+vHHrwMCHAAaKHV1RXX03P86lsIcABokdD/Hhi44QYHf0i2Hh0BDgAtUq1W/b2mET5+/Kt/fBxMIwQAo6jAAcAoAhwtoaMixIP3o3G2tjaTR2ePAAeABlpYWHCFQq9bXn6dbDk7BDgANNjHj1vu3r1hd/v2Tff+/ftk6+kR4ADQJGtra+769X5XKo26nZ2dZOvJnXoWCr0zADi+3t5eNz//Mnl2MkwjREvwnsSF96NxpqYm/S04f/68K5cfuVu3bidbTo4WCgA0yehoyVUq784kvIUAB4AGU7vk7duKD/C2trZk6+nRQkFL8J7EhffDJipwtARhERfeD5sIcAAwigAHAKMIcAAwylSAa+FzLXquAZfjXn4fcZiY+MW/f+E2MvJj8gqaYWZm2u9Deh/q0T6lfUvvjb5O+xziZSrAtbPr4p8acJmb+7f/JdTliGCDwkABsbr61r+Hus3M/J68ikZTeD9//q9D9xlt1z6lfUvvjfY1PmDjZibAl5YW/S/Y+PjP/rmu4Dw4eMdfyQI2TE//5t+zrq6uZAuaaWTkvv/wVDDXMzEx4S/tFa6OrivE6JJfHOnGy0yAr6ys+B0/vfPrQqC6JFG4LBHipSBQBRgO4QmFuGgf0nuUvriugr6r66K/ajriZCbANzY2/C9TWghz/eIhbqrqdFi+tPQfHww6cuLoKR5hHzp4dKTn2vcQJzMBXq1+OPTQD3YoyNX31k1VuFpjaL1wFMs+ZouZAD9YfQsj5Hap16rb4iIBHoODlXfAPhY3MwHe3d39VaskVA1h0AW2pPutaK2wDx1sl+jIV/se4mQmwOsNWGpwRb94h1UPiJveP0I8DtqHdEsPWIb9ra+vL9mC2JgJcE0/U1iHExDUO9VtfHzcP0fc1O9OzzzRbBTR1DY0X73WiKboap8KR7oaZC4W+3yrC3EyE+CiEwz0i6ezxBTkmqeqXzDET++bAkHvXbF4xW/jJJ7mUjjr56/3Qh+mOuMyTUGtEA9nO2tAU/sc4sV64ABglKkKHADwBQEOAEYR4ABgFAEOAEYR4ABgFAEOAEYR4ABgFAEOAEYR4ABgFAEOAEYR4ABgFAEOAEYR4ABgFAEOAEYR4ABgFAEOAEYR4ABgFAEOAEYR4ABgFAEOAEYR4ABgFAEOAEYR4ABgFAEOAEad+1yTPAYAGEIFDgBGEeAAYBQBDgBGEeAAYBQBDgBGEeAAYJJz/w9PMjVju40zHwAAAABJRU5ErkJggg=="></p>
<p>The first high tide occurs at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>04</mn><mo>:</mo><mn>30</mn></math> and the next high tide occurs <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> hours later. Throughout the day, the height of the water fluctuates between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>2</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>8</mn><mo> </mo><mtext>m</mtext></math>.</p>
<p>All heights are given correct to one decimal place.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</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 the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</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>Find the smallest possible value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</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 height of the water at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>:</mo><mn>00</mn></math>.</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>Determine the number of hours, over a 24-hour period, for which the tide is higher than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> metres.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>OAB is a sector of the circle with centre O and radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAiQAAAEiCAYAAADJQsnwAAAgAElEQVR4Ae2dDXQV5bX3/0m9LqGIGGDVEwPlIjeht9hAE9Qr8XJAG6rWwkoKLtsaXICtH0l84wsB/Fjc3GupJVlwm2Cl1ZNCsKhg8mKlKhEwtsEqJECEW00upVhjTllAFEiptSTnXXuSSYbk5OR8zJz5+s9arDOZeeZ59v7tIfmf/XwlBAKBAHiQAAmQAAmQAAmQgIkEEk1sm02TAAmQAAmQAAmQgEKAgoQvAgmQAAmQAAmQgOkEKEhMDwENIAESIAESIAESoCDhO0ACJEACbiJwoRFlkxKQkDALZY0dAC7AX3MfEhISkLCwBn43sdDN1y50tNThpbLlWKcwDVFxRwv2vFSG+9Y14kKIYta8Zey7QkFizajTKhIgARIgAbsQuHAQG26bhfnL9qEzpM0daNzwQ9w8fxl2hS4Yshan3rzEqY7RLxIgARIggXAIXAJPzgYEAhvCKcwyJGAYAWZIDEPLikmABEjAbAJn0fLGOixMli6aBCQvXIc3Wtr7GTVYGv7iZ7ufL0NNox9dvTVIV8VOlC28trvLZ9ZybGpswb6yWcrPk8p6uiX8NVgoXUKTSlCzswSz5DxhASpbPgPQrw65l7wQZTWN8Pc0dKGxDJOU55/Enj9o23sENS1ngY4WvFG2EMlKvXOwfNO+3md7Te09+Qg1CychIWESFr70DhpryjR8nsI+/+e9JZWTni4WlWFCwhwsr9yDlo4e48S3f8rEsj9K6Tosy7wcCZPK0DigP0banYrMZXVKtX9clol/6u02k0tn0bLnxT6WCcmYtbwSe8S/UIfYV7m8h6lwHeS5Lv9FviYkXIuFZTv7/FDaCCfmwYyRGO5B5fI53e/BYDYEe1R7TdYh4UECJEACJOA0An8PtFY/GPAAstZUkH/eQGnDuUAg8I9AW/UPu+/nVQfaFAwhnvU8GKhu/btSqrO1OrDI069uz7xA3nenKPVdU9oQ+IeUbKsO5PW3wbMysPtMZyBoHUrZKYFF1ccDnWJhQ2ngmv7Pqz97HwwU53W31+dnRqB498lBAvrnQHXeNUF49PiR7Qs0S6NynDsc8A2ou6ecd22g4VxncN+uKQ00KI731KN8BGtXjcGZwPu+RYPE6vZAacMn2oo0558EGkpvD+6Lap9SevBynkXVgVbF33BiHuxdCQweQ8+igO/9Mxp7Q58yQ6JVZzwnARIgAacQOFuP8vyn4IcH3pW1aOsMINDZhnfX5sEzlI9dx7Dz5zLA9XaUNnwCWT+zs7Uai+RB///g2F8ki/AZju58AZUyCtb7H9jd9ncEAn9H23NT8ectRwZpwQNv6bs4J/W1PIIbRn7eU0ff9UDncVQvmgLgCN46dkqTjZEqpyDPdxjnAp0417AWXrlU9xQ2YyneP9eJwLl3UeoVIxtRfeDDoQeNeleiuvmMYndr9YPdXGr34cgJSW98hpat/4nFVUcAzyL43pdyAXS21WKltFFXiqUbGtDhycGmfzSg9BoxxovShnMIHF2KjAEDIsYhZ9MhNJQqVuOa0gb8I/AmlmaMQFfLS3hocSX8vf5JrFqxe2U2gN9g2dJfolHNyGjJXvgj3tzwGwAZKN59UrGvl0FdKR7Z2qLw62qpwSPLpFw2Vu5uRafGD3/lapTXnQLCirm2cfX8FOrKV6PSr8YmgEDgDN73LYLHX4nHftmAIXI8akWgIOlFwRMSIAEScA6Brr8cxyFlysy3UVAwCx75bZ/owXWLF+LuoRRJ4mQs2tmGQOczmNW6BzU1z2Dl9/O7xQfO4eSZz4Cu46h/sR6AB9l33wmv51IAl8Iz+0E8XpwxCMgs3P3tr2GEmDJiBIbjMqQu2opA4Di2zDqF2pqXULnyB8it7BY050+ewXltTZ47sPA7/4oRSMSI9H/H7YoIyMDdC2/H5BGJwIh/xazb07RPhDgXu/MwL3WkYvfV/zYb39CW1vr3xDLcM1nKCcKbseLxe+CBH3UbfovmAV0z2krCOf8MR+tfR60UzS7Co/dMUfgg8WrMXrEcxRKrul/jzeaLSHRXnDgGE2eKeGvEmptnYWHZFtTUtuJfyhrRGWjDzkWTkYgLOHFkX3f9eT9EweyrlT/8iZ5vYPWbbQgEGvCT2WOAcGIezJ0LH+JAdaMiIKsWX4vLlW6zK/AVRWAB/s270HC2r5MvWBXqtQEaTr3BTxIgARIgAfsS6DrXDmVYgycJo76o+e45/AqMHT6UX2fxQWURZvf8Ubm49OUYe8VlQNdf0f5HUTwZmDphjObb7WW4YuzlFz+i/uSZhAlXiXBRjy50fLAZD86+B1VB5hsPH3sFLjJ1eBKuGK7xRammxx61yrA/h+OqUV/ss3vsl3GtCBwFmgxtUf3z4hvpKX3lkIjhVyR12/XHo/jw5AVkjA270SAFL+Bc+0nl+jXfSMdErXu9sfoIhz/8BMgQKac5Er+MeU/4sHHM47hnTS2qln0PVeptyf78fAVyUhPRdqxZvRriM4yYB3v65Ic4rDILdt/fjk//2gWM1DoWrCA0jIPf51USIAESIAEbEki8PAlKAsF/FMeVLpYeJ86fwckgX7a1LvZ1IWSj2LcN2xva0NnbLdFTMvGLSLpGvr634dBxbdfKZzhz8py2ur7z/oKiqwVbH1qJKr8H3uJfoHp7A9o6z/V2a/Q9aMJZr3/NeKOpVdN11IXzZ9q7MzfXTMKXx8b6vf4SXJ7UrWj++EYTjmmTCb2xGodrv3xlUAiJnuuw8Cc7lW6S5t3bUV39K5TmTQHqfozcgpfQ0nUZkif2ZI3+8inOaevX1BhWzDXle0+/OApXKRm3nu6qgHTZaP9tQI4nPEZDS5beVnlCAiRAAiRgFwKJk27Endnyl6Iemzf+rnvWSZcf+3ybsDlINqLPry50tB7FYbng+RdcP+fbmJsxGid+uwO/0X4TTpyArDuzZFAJaje/iDpldsrn8O95Cv+1RlL4YRwdbWg+LMaMxsTrszFvbga+dOL3qP5NON/ow6g/liJa/x4rxcYPukdCdPl348n/2tg9Nue+f0daeH9rQ1hyGSZlfRMyWgS16/CjjUcgy9Wh62PsefInWCN4vN/GrLSLckVKfV0f12CxMoNqDh7Zcw6TZs9FTs53cNfcmZpxQpfgS1Ou66n/RWys+7hbXHUcQaUyOyoZcyr/gDPhxDyYFyO/hjl3SxddHdaWV+MDGesitj/SPeMmefmesMeQiJLhQQIkQAIk4DgCIWZNKDNU1BkeA2dOBJ/5khHwemV2St8MlqDlQs2y6T/7pPN4oHpR/xkynsCN3huVGSee4t0BmaPRO8tG+/w/GgKl18iMF9UPCeC5QEOp9+IZPgPiqs52uSaQV/3nvru99f0wUN3WM0Xm3LuBUq9n6Fksne8HfNmaclo7+1oIBAJ/CzT75mvqU20ffBYMEOUsG/TNUgoEQtTv/Y/A7ra/DzJTpn/MB74rgUBn4Nz7GwN5/WdbyTvGWTbBJByvkQAJkIDbCFyKq3NWo652LfKUlDrgyVuL2v+p7ZkRMjiPxKu/hSdeqUKxMmNFvqEXY2PD/8NzBbcoAyg373xP+dabePU8/LTu9e4uAkmoSP1161E4bczglWvvqGMgipX8gDILpHjjdrz03P9VBphGMiBSW61u5yOuw9JX6rB7W2kvQ5mpUuzbjeZXHkKGDKSVI3Eibv2vR/vKjPsC8FmwvpHLMOnWh7BWulSU44vK0v3AKGQs3YLm3S/0spTBwt5iH3Y3b8HSjFE95ft/qM/5+mIlRbzF8O2uxk9zvtwzLmMUMh5+Bg3VWj+mIK+0Gg1bVmK251KEG/P+FsjIjxGT78ZTdbvh642j+i6sw6KewcADnxt4JUHE28DLvEICJEACJEACoQh0oLHsju6FvjwPonr/WuRcfSnQsQ9ld8zDsrrhyKt+E5tyxoWqhPdIoJcABUkvCp6QAAmQAAmET6ALHY0/xR2ZD6N77dF+T2pFSr9b/JEEghHgoNZgVHiNBEiABEhgCAKJGJHxILY0VGu6GeSRnq6GutXdGZMhauFtElAJMEOikuAnCZAACZAACZCAaQSYITENPRsmARIgARIgARJQCVCQqCT4SQIkQAIkQAIkYBoBChLT0LNhEogzgbN7sLxnG3rZSr7/v+SFZXhpT0v3okxxNo3NkQAJkAAFCd8BEnALgZGz8ZO2TpzZvRIezIev+W+9Szx3tr2LH1/1BubfnIsHK3tWinQLF/pJAiRgCQIUJJYIA40gAXMJKPth/Pin8GWfRtVjW7AvzN05zbWarZMACTiJAAWJk6JJX0iABEiABEjApgRi3hbIpn7TbBIgAS2BLj8aN/8Sm2tHI8/3XVwXxlbh2sd5TgIkQAKxEqAgiZUgnycBWxLYhsVp27C4n+2e4t14edEUjOh3nT+SAAmQgNEE2GVjNGHWTwKWJNB/UGsDqkvzgDU3Y/LCTd1biFvSbhpFAiTgVAIUJE6NLP0igQgIJHoykLP056jzzYe/aiUe2tqCYHuVRlAli5IACZBARAQoSCLCxcIk4GQCl+KqCZPggR+Hm9u4HomTQ03fSMCCBChILBgUmkQC5hC4gHOfnlU2R7s2LZnjSMwJAlslAdcS4KBW14aejpOAhoDMstn+K5TnPwW/9z/w3K0TwW8rGj48JQESMJwAd/s1HDEbIAGLEJCl4yffjDX+wezJRrGvAAtuzUaG59LBCvE6CZAACRhCgILEEKyslARIgARIgARIIBICzMpGQotlSYAESIAESIAEDCFAQWIIVlZKAiRAAiRAAiQQCQEKkkhosSwJOIjA3/72N6xfv95BHtEVEiABOxPgLBs7R4+2k0CUBESMFBYW4tlnn1VqyM/Pj7ImPkYCJEAC+hBghkQfjqyFBGxDQBUjTU1Nis1VVVXMlNgmejSUBJxLgILEubGlZyQQlIDP54OIkZqaGuW+fFKUBEXFiyRAAnEkwC6bOMJmUyRgNgEZMyLiQ0RISkqKYo58ys85OTnKz+y+MTtKbJ8E3EmAgsSdcafXLiQgYqSgoADNzc29YkTFoIqScePGKZcoSlQy/CQBEogXAQqSeJFmOyRgIgFVjNTX1yM1NTWoJSJK5H5WVpZyn6IkKCZeJAESMIgABYlBYFktCViFgHTHSGZExMaMGTNCmiX3KUpCIuJNEiABgwhQkBgEltWSgBUI7N27F7m5uWGJEdVerSgZOXIk8vLy1Fv8JAESIAHDCHAvG8PQsmISMJeAiBHpfgmVGUlISEAgEAhqaDjPB32QF0mABEggCgKc9hsFND5CAlYnoIqJioqKIbtpBvNFmymR+niQAAmQgJEEKEiMpMu6ScAEAloxEuvAVBElmzZtUjItFCUmBJNNkoCLCHAMiYuCTVedT6C1tRVFRUWQzEisYkSlJWNIzp49q4iSgwcPYurUqeotfpIACZCAbgQ4hkQ3lKyIBMwlIGJEFjcTARGuGAk1hqS/N8EWVetfhj+TAAmQQLQE2GUTLTk+RwIWIqCKEa/XG7YYidR8ETnz5s1TRI+0x4MESIAE9CRAQaInTdZFAiYQUMVIeno6SkpKDLVAuoOkHcnEUJQYipqVk4DrCLDLxnUhp8NOIiA7986cOVMRCeXl5Rg2bFhE7kXSZaNWrO4WLD9H06ZaDz9JgARIQEuAgkRLg+ckYCMCegiDaASJIJK277rrLowdO5aixEbvDE0lASsTYJeNlaND20hgEAJ6iJFBqg7rsmRiZJBrU1MTVq1aFdYzLEQCJEACoQhQkISiw3skYEECqhhRxUCk3TR6uaTuEFxXV6eIE73qZT0kQALuJMB1SNwZd3ptUwJaMSKb5okoMPOQ9n/xi19g2rRpihnhTjc202a2TQIkYE0CzJBYMy60igSCEvD5fEo3iRXEiGqgLJQm++XIjsJczVWlwk8SIIFICVCQREqM5UnAJAJWXphMlpivrq7mEvMmvRtslgScQICzbJwQRfrgeAIiRiQD0dzcjNTUVN38jXaWzWAGWFk0DWYzr5MACViDADMk1ogDrSCBQQmoYkS6RfQUI4M2GMMNGUMiq8XKwmnt7e0x1MRHSYAE3EaAGRK3RZz+2oqAjBXJzc1VxmhIt4jeh94ZErFPHXgr51w4Te+IsT4ScC4BChLnxpae2ZyADBDNysoyTIwIHiMEidQr2ZFvfvObygqyzzzzjM0jQfNJgATiQYBdNvGgzDZIIEIC8RAjEZoUUfGkpCRIdkfWSpEuJx4kQAIkMBQBrkMyFCHeJ4E4E1DFSEVFBYzopomXO7JGybp165Qsj4x9yc7OjlfTbIcESMCGBNhlY8Og0WTnEtCKkXgsMmZUl402QrW1tZgzZw4OHjwIWbOEBwmQAAkEI0BBEowKr5GACQRaW1uV2Sl5eXmIhxgRF+MhSKQdTgc24YVikyRgMwIUJDYLGM11JgEzxIiQjJcgkbbuvfdenDx5Es8//zzM2n/HmW8PvSIBZxDgoFZnxJFe2JiAKkZk/Y54ZUbMwCVTgOUoLCw0o3m2SQIkYHECFCQWDxDNczYBVYykp6ejpKTE0c5KVkS6bjjzxtFhpnMkEDUBdtlEjY4PkkBsBGQBsZkzZyprdZi1gFg8u2xUWurAXVl51s6ziFR/+EkCJKAPAQoSfTiyFhKIiIBVVjM1Q5AIKHUFWr335okoCCxMAiRgKQIUJJYKB41xAwGriBFhbZYgkbZXr16N7du34/XXX4cspMaDBEjA3QQoSNwdf3ofZwKqGJFxFJIlkMXDzDzMFCQqC/Gfy8ub+RawbRKwBgEOarVGHGiFCwiof4CtIkbMRi6DXFetWsVBrmYHgu2TgEUIMENikUDQDOcTsOLiYGZmSNSIHzp0CNOmTTN0E0G1LX6SAAlYlwAzJNaNDS1zEAErihGr4JXl5Ddt2qTseSPToHmQAAm4kwAzJO6MO72OIwERIwUFBbDijBIrZEjUUBQXF6OlpYUruapA+EkCLiPADInLAk5340tAFSOy5obseMtjcAKyMFxbW5uyQ/DgpXiHBEjAqQSYIXFqZOmX6QTUtTasvACYlTIkEjDJkKSlpWHnzp3Izs42PYY0gARIIH4EKEjix5otuYiAXVYjtZogkVdEFXIfffSR6dOiXfTK0lUSMJ0ABYnpIaABTiNgFzEi3K0oSMQujidx2v8K+kMCQxPgGJKhGbEECYRNQBUjFRUV3KclbGoDC3I8yUAmvEICTifADInTI0z/4kZAK0by8/Pj1m4sDVk1QyI+cTxJLJHlsyRgPwIUJPaLGS22IAFZPyMnJwd5eXmwixgRjFYWJGIfx5NY8GWnSSRgEAEKEoPAslr3ELCrGJEIWV2QiI0ynuSTTz5BeXk5ZLl5HiRAAs4kwDEkzowrvYoTAVWMeL1eW2VG4oRHl2ZWrFih7Hfj8/l0qY+VkAAJWJMAMyTWjAutsgEBVYykp6fb9tu7HTIk8iqo+90cPHgQstQ8DxIgAecRoCBxXkzpURwIyM69M2fOhJ3FiGCyiyARW9X9gN566y123cThHWcTJBBvAhQk8SbO9mxPQMRIYWGh4ofdxzXYSZAI97vuuktZgn/NmjW2f4/oAAmQwMUEKEgu5sGfSCAkASeJEXHUToJE7OVU4JCvJ2+SgK0JcFCrrcNH4+NJQBUjTU1NWLVqFbsN4gm/py3ZoLC6uhqPPfYY2tvbTbCATZIACRhFgBkSo8iyXkcR0IoRWRsjJSXFEf7ZLUOiQr/33nuV02eeeUa9xE8SIAGbE6AgsXkAaX58CKgDKp0kRoScXQWJzHAaN26cki2RBel4kAAJ2J8Au2zsH0N6YDABp4oRg7EZWr1kqKTrJjc3FyJOeJAACdifADMk9o8hPTCQgIiRgoICNDc3K7M7DGzKlKrtmiFRYbHrRiXBTxKwPwEKEvvHkB4YREAVI/X19Y7dudfugoRdNwa9/KyWBEwgQEFiAnQ2aX0C6qZuThYjEgW7CxLxQY3V6dOnkZSUZP2XixaSAAkEJUBBEhQLL7qZwN69e5GVlQWnixGJsRMEifghXTdXXnkluGCam//n0ne7E6AgsXsEab+uBNwkRgScUwSJ2nWzc+dOZGdn6/pOsDISIIH4EOAsm/hwZis2IKCKkYqKCseOGbFBGKIyUZ11wwXTosLHh0jAEgQoSCwRBhphNgGtGMnPzzfbHLYfBYFbb70VycnJ2LBhQxRP8xESIAGzCbDLxuwIsH3TCUi6XxbXysvLg9vEiFO6bNSXSN3r5uDBg5g6dap6mZ8kQAI2IEBBYoMg0UTjCLhZjAhVpwkS8Wn16tXYt28fnn/+ee43ZNx/HdZMAroTYJeN7khZoV0IqGLE6/W6LjNilxhFY2dRURHa2trw2muvRfM4nyEBEjCJADMkJoFns+YSUMVIeno6ysvLXftN2okZEnmzamtrMWfOHHBtEnP/n7F1EoiEAAVJJLRY1hEEZOfemTNnwu1iRILpVEEivnFtEkf8d6UTLiJAQeKiYNNVQMRIYWGhgsLNmRH1XXCyIOEAVzXK/CQBexCgILFHnGilDgQoRgZCdLIgEW9lP6Jdu3ZxgOvA0PMKCViOAAe1Wi4kNMgIAqoYaWpqwqpVq1w7ZsQItlauc/HixRzgauUA0TYS0BCgINHA4KkzCWjFiGzEJqt68nAHgWHDhmHFihV48skn0d7e7g6n6SUJ2JQABYlNA0ezwyfg8/kgmRGKkfCZOamkLHrHFVydFFH64lQCHEPi1MjSL4WAjCGoqqqiGBnkfXD6GBLV7UOHDmHatGlobm5GamqqepmfJEACFiJAQWKhYNAUfQmIGCkoKOAfoRBY3SJIBEFxcbFCYs2aNSGI8BYJkIBZBChIzCLPdg0loIqR+vp67twbgrSbBIkshjdu3DjwnQjxQvAWCZhIgILERPhs2hgCMlYkNzeXf3jCwOsmQSI41GnA27dvD4MOi5AACcSTAAe1xpM22zKcwN69eylGDKds3wa++93vKtOARbTyIAESsBYBChJrxYPWxEBAxEhWVhYzIzEwdPqjSUlJvdOAZTo4DxIgAesQoCCxTixoSQwEVDFSUVHBMSMxcHTDo7feeqviJncDdkO06aOdCFCQ2ClatDUoAa0Yyc/PD1qGF0lAJaBdLI1ZEpUKP0nAfAIUJObHgBbEQEBmThQVFUEyIxQjMYB02aOSJZHF0rZt2+Yyz+kuCViXAGfZWDc2tGwIAiJGZBXOvLw8ipEhWA12222zbLQc1Mza6dOnIWNLeJAACZhLgBkSc/mz9SgJqGLE6/VSjETJ0O2PzZgxA3PnzsWWLVvcjoL+k4AlCDBDYokw0IhICKhiJD09HeXl5dy5NxJ4/cq6OUMiKJgl6fdC8EcSMJEAMyQmwmfTkROQQYjSTUMxEjk7PjGQALMkA5nwCgmYRYAZErPIs92ICYgYKSwsVJ5jZiRifEEfcHuGRKAwSxL01eBFEog7AWZI4o6cDUZDgGIkGmp8JhwCzJKEQ4llSMB4AsyQGM+YLcRIQBUjTU1NkCW/U1JSYqyRj6sEmCHpJsEsifpG8JMEzCPADIl57NlyGAQoRsKAxCIxE1CzJDt27Ii5LlZAAiQQHQEKkui48ak4EfD5fGBmJE6wXd7MAw88oOwGLCKYBwmQQPwJUJDEnzlbDJOAbBVfVVXFbpowebFYbARuuukmpQLucRMbRz5NAtES4BiSaMnxOUMJiBgpKChAc3MzUlNTDW3LzZVzDMnF0ZcxSk8++STeeustrm9zMRr+RAKGE2CGxHDEbCBSAqoYqa+vpxiJFB7Lx0RA3Qn4wIEDMdXDh0mABCInQEESOTM+YSAB+YYqmRERIzLQkAcJxJOA7AQseyOVlpbGs1m2RQIkAIBdNnwNLENAnXpJMRK/kLDLZiDr9vZ2jB49mqJ4IBpeIQFDCTBDYiheh1fur8HChATIH7Xk5XtwtsuPxk3LMSshE8v3nIrIeYqRiHCxsIEEZOffiooKvPzyywa2wqpJgAT6E7ik/wX+TAJhE/DkYNOZ3bhqcjEwJwX/u3EH2ieMx6WeG3B92siwq1HFiPwRYDdN2NhY0EAC2dnZSEtLw5IlSziOyUDOrJoEtAQoSLQ0eB4hgS6cbdiFzf7RuGvnRvx2QTGKMkbhG23hV6MVI/n5+eE/yJIkYCABmdklYqS2tpaCxEDOrJoEtATYZaOlwfMICXyOvxw/Cj8O48DYebg3Y1REz7e2tqKoqEhJj1OMRISOheNA4J577lEGWMuYEh4kQALGE6AgMZ6xc1voOo76F+sBzz14/AeZGBGBpyJGcnJylBkNFCMRgGPRuBGQ7sPp06ejrq4ubm2yIRJwMwEKEjdHP1bfO9rQfBjIfiIP3pHhv0qqGPF6vaAYiTUIfN5IAitWrFBWCzayDdZNAiTQTSD8vyIkRgIXEVDHj2ThzqwJCPdFUsVIeno6SkpKLqqRP5CA1QiIaJbZNjLWiQcJkICxBML9O2KsFazdhgR6xo94JmHCVZeGZb9sWibdNCJGysvLuTR3WNRYyEwCMgX4Rz/6EacAmxkEtu0aAlwYzTWhNtdRESOFhYWKERQj5sZC2zoXRtPSCH7e0tKiTAE+ffo0RKDwIAESMIYAMyTGcGWtGgIUIxoYPLUdAZkCPHfuXOzYscN2ttNgErATAQoSO0XLhraqYqSpqQmrVq1iN40NY0iTgQceeACy6SMPEiAB4wiwy8Y4tq6vWStGZNO8lJQU1zOxGgB22YQXEXmXhw8fzv1twsPFUiQQFQFmSKLCxofCIeDz+SCZEYqRcGixjJUJyC7AMrj1rbfesrKZtI0EbE2AGRJbh8+6xkt6u6qqimLEuiFSLGOGJPwAHTp0CNOmTQMHt4bPjCVJIBICzJBEQotlwyIgYqSgoADPPfccu2nCIsZCdiAwdepUZXArV261Q7Roox0JUJDYMWoWtlkVI/X19dyUzMJxomnREZB1dCTzx4MESEB/AtDfXBUAABjoSURBVOyy0Z+pa2uUsSK5ubkc+GejN4BdNpEFS1YaHjduHD766CNm/yJDx9IkMCQBZkiGRMQC4RCQpbUpRsIhxTJ2JiAzxZYsWYLt27fb2Q3aTgKWJEBBYsmw2MsoESNZWVnMjNgrbLQ2SgLz589nt02U7PgYCYQiQEESig7vDUlAFSMVFRWQ7dp5kIDTCWRmZmL//v2QWTc8SIAE9CNAQaIfS9fVpBUj+fn5rvOfDruTgLrhngzc5kECJKAfAQ5q1Y+lq2qSwX0y4yAvLw8UI/YNPQe1Rhc7VYyfP3+e2yFEh5BPkcAAAsyQDEDCC0MRoBgZihDvO53A17/+dcXFAwcOON1V+kcCcSNAQRI31M5oSBUjXq+XmRFnhJReREGAS8lHAY2PkMAQBNhlMwQg3u4joIqR9PR0lJeXM1Xdh8a2Z+yyiT507LaJnh2fJIFgBJghCUaF1wYQkN1OZcwIxcgANLzgUgLstnFp4Om2YQQoSAxD65yKRYwUFhZSjDgnpPREBwLsttEBIqsgAQ0BdtloYPB0IAFVjMgddtMM5GP3K+yyiS2CardNIBCIrSI+TQIkAAoSvgSDElDFSFNTE2SfGlk2m4ezCFCQxBZP+T8yfPhwHDx4ELIbMA8SIIHoCbDLJnp2jn6SYsTR4aVzOhGQbptly5Yp2yboVCWrIQHXEqAgcW3oQzvu8/nAzEhoRrxLAkLglltu4d42fBVIQAcC7LLRAaLTqli/fr3yC5bdNE6L7EB/2GUzkEmkV9rb2zF69Gg0NzcjNTU10sdZngRIoIfAJSRBAloCIkYKCgqUX64cM6Ilw3MSCE5A9rZZsmQJ3nnnHQqS4Ih4lQTCIsAum7AwuaOQKkZk0zB+03NHzOmlPgRuuukmZeC3PrWxFhJwJwF22bgz7gO8lu6Z3NxcZXDejBkzBtznBWcSYJeNPnGVVYzHjRuH06dPQzImPEiABCInwAxJ5Mwc94SspUAx4riw0qE4EpDuzenTp6OhoSGOrbIpEnAWAQoSZ8UzYm/UhZ2km4aZkYjx8QES6CWQl5dHQdJLgyckEDkBCpLImTnmCVWMVFRUUIw4Jqp0xCwC06ZNw6OPPmpW82yXBGxPgILE9iGMzgGtGMnPz4+uEj5FAiTQS0DdbK+lpaX3Gk9IgATCJ0BBEj4rx5SUAXhFRUWQzAjFiGPCSkdMJiCrtqrTf002hc2TgC0JUJDYMmzRGy1iJCcnB9LfTTESPUc+SQLBCMj039/97nfBbvEaCZDAEAQ47XcIQE66rYoRr9eLNWvWOMk1+hIlAU77jRLcII9Jd01aWhrOnz8PyZjwIAESCJ8AMyThs7J1SVWMpKeno6SkxNa+0HgSsCoBdUHBAwcOWNVE2kUCliVAQWLZ0OhnmOzcK900IkbKy8v5zU0/tKyJBAYQkN1/Dx48OOA6L5AACYQmQEESmo/t74oYKSwspBixfSTpgF0I3HDDDdi1a5ddzKWdJGAZAhxDYplQ6G+IKkakZmZG9OfrhBo5hkT/KKrjSLiMvP5sWaOzCTBD4tD4qmKkqakJq1atYjeNQ+NMt6xHQB1H8v7771vPOFpEAhYmQEFi4eBEa5pWjMimebLPBg8SIIH4EeA4kvixZkvOIUBB4pxY9nri8/kgmRGKkV4kPCGBuBLgOJK44mZjDiHAMSQOCaTqxvr161FVVUUxogLhZ0gCHEMSEk/UN9VxJFyPJGqEfNCFBChIHBR0ESMFBQVobm6G2o/tIPfoigEEKEgMgNpTpbCV6b9Tp041rhHWTAIOIsAuG4cEUxUj9fX1FCMOiSndsDcBGUfy3nvv2dsJWk8CcSRAQRJH2EY1JWNFJDMiYmTGjBlGNcN6SYAEIiAwZcoUHDlyJIInWJQE3E2AXTY2j//evXuRlZVFMWLzOJplPrtsjCN/6NAhTJs2DYFAwLhGWDMJOIgAMyQ2DibFiI2DR9MdT2D8+PGKjzLAlQcJkMDQBChIhmZkyRKqGKmoqGA3jSUjRKPcTiApKQlz587F8ePH3Y6C/pNAWAQoSMLCZK1CWjGSn59vLeNoDQmQQC+B6667Dg0NDb0/84QESGBwAhQkg7Ox5J3W1lYUFRVBMiMUI5YMEY0igV4CmZmZ2LdvX+/PPCEBEhicAAe1Ds7GcndEjOTk5CAvL49ixHLRsadBHNRqbNy4QJqxfFm7swgwQ2KTeKpixOv1UozYJGY0kwTUBQplsUIeJEACoQlQkITmY4m7qhhJT09HSUmJJWyiESRAAuERWLJkCY4dOxZeYZYiARcToCCxePBl517pphExUl5ejmHDhlncYppHAiSgJSD/d9955x3tJZ6TAAkEIUBBEgSKVS6JGCksLKQYsUpAaAcJREFAum3q6uqieJKPkIC7CFCQWDTeqhgR85gZsWiQaBYJhEFgwoQJ2L9/P+T/NA8SIIHBCXCWzeBsTLujipGmpibIPjUpKSmm2cKGnU2As2ziE1/hzF2448OardiXADMkFosdxYjFAkJzSEAHAjKwlRvt6QCSVTiaAAWJxcLr8/nAzIjFgkJzSCBGAv/8z/+MDz74IMZa+DgJOJsABYmF4rt+/XpUVVWxm8ZCMaEpJKAHgcmTJ+NPf/qTHlWxDhJwLAGOIbFIaEWMFBQUsJ/ZIvFwixkcQxKfSKsrtgYCgfg0yFZIwIYEmCGxQNBUMVJfXw91ZUcLmEUTSIAEdCIwZswYpSYRJjxIgASCE6AgCc4lbldlFo1kRkSMzJgxI27tsiESIIH4EUhKSsL06dNx8uTJ+DXKlkjAZgQoSEwM2N69e5Gbm0sxYmIM2DQJxIuA7EN14sSJeDXHdkjAdgQoSEwKmYiRrKwsihGT+LNZEog3gSlTpnAJ+XhDZ3u2IkBBYkK4VDFSUVHBbhoT+LNJEjCDwFVXXQWOITGDPNu0CwHOsolzpLRiJD8/P86tszkSuJgAZ9lczMPInzjTxki6rNsJBChI4hjF1tZWZefevLw8UIzEETybGpQABcmgaHS/IaswDx8+nFP7dSfLCp1CgF02cYokxUicQLMZErAogWHDhnGmjUVjQ7OsQYCCJA5xUMWIjLJnZiQOwNkECViUAGfaWDQwNMsSBChIDA6DKkbS09NRUlJicGusngRIwMoExo8fz5k2Vg4QbTOVAAWJgfilzzgnJwciRsrLyyEpWx4kQALuJZCcnIxPPvnEvQDoOQmEIMBBrSHgxHJLxEhhYaFSBcVILCT5rJEEOKjVSLoD6+ZMm4FMeIUEVALMkKgkdPykGNERJqsiAQcRkFk2crS3tzvIK7pCAvoQuESfaliLSkAVI01NTZB9athNo5LhJwmQQEpKigLh1KlTkP1teJAACfQRYIakj0XMZ/3FiPrLJ+aKWQEJkIBjCMydOxfHjx93jD90hAT0IsAMiV4kATz66KM4ePAgtm/fDooRHcGyKhJwEIHU1FR0dHQ4yCO6QgL6EGCGRB+OWLBgAdatWwf5ZTN69GidamU1JEACTiPATfacFlH6oxcBChIdSIoY2bZtG3w+H44eParMrpHuGx4kQAIk0J/AiBEjOPW3PxT+TAIAKEhifA1UMfL0009j0aJFykBWGdAq2RIeJEACJNCfwMSJE/Hss8/2v8yfScD1BChIYngFiouLlcyIiJH77rtPqUnGjsjsGhlHsn79+hhq56MkQAJOJKBO/WUW1YnRpU+xEODCaFHS27BhA+6//35oxYi2qkOHDmHatGnYtGkTZHdfHiRgRQJcGC3+UREhwl1/48+dLVqfADMkUcRoKDEiVU6dOhX19fVYuHAh9u7dG0UrfIQESMCJBNS1ic6fP+9E9+gTCURNgIIkQnSqGJk/f35vN81gVcyYMUPJkGRlZUE22eNBAiRAAkJgyZIlOHbsGGGQAAloCFCQaGAMdaoVI1u3bh2quHJfumuWLVuG/Px8sM84LGQsRAKOJ3DllVdyLRLHR5kORkqAgiRMYvv378fSpUshmZFwxYhadUlJCdra2jjzRgXCTxJwOQFZi+TIkSMup0D3SeBiAlyp9WIeQX8SMTJr1izcdtttEYsRqVD6jJ977jmkpaUhMzMT2dnZQdvhRRIgAXcQkLVIeJAACVxMgLNsLuYx4CdVjHz1q1/Fu+++O+B+JBeqqqqUqcCvv/46N9aKBBzLGkaAs2wMQxuyYnUWXiAQCFmON0nATQTYZRMi2qoYkbVFXnvttRAlw7sl40nS09Px5JNPhvcAS5EACTiSgLoWiSOdo1MkECUBZkgGAdfe3o7x48crm+S9/fbbumU0WlpalK4bmRIss3B4kICZBJghMYe+/H6RPa8++ugjbsRpTgjYqgUJMEMSJCjyy+LGG2/UXYxIU7L5niyWVlRUxFk3QdjzEgm4gUBSUpLiJtcicUO06WO4BChI+pFSxYhc1jMzom1GZurIIRvy8SABEnAvgZMnT7rXeXpOAv0IUJBogKhiRBYx27x5s27dNJomlFOZdSOb78kqrtImDxIgAfcRkPWJTpw44T7H6TEJDEKAgqQHjFaMvPnmm5g+ffogyPS5LONH5s6diy1btuhTIWshARIgARIgARsToCDpCZ7s1iuZkXiIEfV9kW9IBQUFzJKoQPhJAi4iIIujvfPOOy7ymK6SQGgCFCQAFixYgFdffTWuYkTCwixJ6JeTd0nAyQS4OJqTo0vfoiHgekEiYkQGl9bU1BjeTRMsQMySBKPCayTgDgKyDAAPEiCBbgKuFiSqGHn66adNW85dzZLs2LGD7yQJkICLCEiXzcsvv+wij+kqCYQm4FpBUlxcrGRGRIzI+BEzjwceeEBZUp67AZsZBbZNAiRAAiRgJgFXCpINGzagtLQU0YmRLnS07ETZwmshq1wmJC/Eun1+dMUQxZtuugmyTP2BAwdiqIWPkgAJ2InAmDFjFHNlMD0PEiABwHWCRMTI/fffH70Y+WAzHvQuxeGpG9DW+QkaHj6Nh5e/gIMd0UsSWZekoqICGzdu5DtJAiTgEgJcrdUlgaabYRNwlSBRxYislBpVN01HAzbcvxJv3FqC1Q/NgCdxFNJneXFN3e/R1PZ52NCDFczOzsazzz7LKcDB4PAaCZAACZCA4wm4RpBoxcjWrVujCOynaNzwn1hWl4Unlt+GqxVyXTh/ph3ncRLt5y5EUWffI7LHjSyU1tDQ0HeRZyRAAo4mIP/njxw54mgf6RwJhEvAFYJExmcsXboUkhmJTowAXR/vwc/W/gae4vvwndTLevh+jr8cPwo/xiLp8kvCZT5ouZycHO5vMygd3lAJKGOXZPySDv/UOvlpDgH5IsKDBEigm4DjBYmIkVmzZuG2226LWowAn+HozhdQ6c/A3XO+hpG9b08HWpuPAZ5JmHDVpb1Xoz254YYb2G0TLTyXPRcIBKDHP5dho7skQAIWJuBoQaKKka9+9asxiBEAXcdR/2I9gEasuXms5pvpWNy8phGeu29B5sjYUcq3JdlDh902Fv4fQ9NIQEcC48ePxwcffKBjjayKBOxLIPa/ohb1XRUjKSkpeO2112KzsqMNzYf9QLYPzZ1930w7m33IRv+sSWxNzZs3j4IkNoR8mgRsQyA5ORmffvqpbeyloSRgJAFHChLZuVe6aUSMvP3221Cn10UL8sL/HkC134PsO2/EpF5ip1Dn+xlqPdmYk5kUbdUDnps5cya2b98+4DovkAAJkAAJkICTCfT+eXWKkyJGbrzxRt3ECKDOpEnDN9JTehdu6fr4t/jV5jZ4H56H63TorlH5f+UrX1EWSeNiSSoRfpKAcwnIBnvcz8a58aVnkRFwlCBRxYgg0CMz0o0yEcOvSMLwi2bSfIqDz1eiMm0Zyu7LxIjImIcsLdkcGUfyhz/8IWQ53iQBErA/gQkTJnA/G/uHkR7oRMAxgkQVI5JZ2Lx5c8zdNFq+l/zL15HrqcfmX7+HDpxFS80aLF37JfieXoyMEfoj9Hq9/NakDQDPSYAESIAEHE9A/7+mJiDTipE333xTyTDoasZILx7f82OMX3s9Lk+4At6Xx+KRunVYNLlvArCe7cn03z//+c96Vsm6SIAESIAESMDSBBICspiBzY8FCxbg1VdfhSFixAQ2hw4dwrRp05R1Jkxonk1anIAsiKbXf1s967I4NkuaJzt8Dx8+HM3NzeAiaZYMEY2KIwHbZ0icJkYk9vILSg7J/PAgARJwLgHZWJMHCZBANwFbCxIRI9u2bUNNTY3+3TQmviHqN6VTp06ZaAWbJgESIAESIIH4EbCtIFHFyNNPPw3ZKddph8y0OXnypNPcoj8kQAJBCJw/fz7IVV4iAXcRsKUgKS4uVjIjIkbuu+8+R0ZMZtqcOHHCkb7RKRIggT4CS5YswbFjx/ou8IwEXErAdoJkw4YNKC0thZPFiEvfRbpNAq4kcOWVV7rSbzpNAv0J2EqQiBi5//77XSFGuOlW/1eVP5MACZAACTiZgG0EiSpG5s+f79huGu2Lxk23tDR4TgIkQAIk4HQCthAkWjGydetWp8eE/pEACbiIALOhLgo2XQ1JwPKCZP/+/Vi6dCkkM0IxEjKWvEkCJGBDAsyG2jBoNNkQApcYUqtOlYoYmTVrFv7617/iww8/xPXXX69TzdavRhZFk432ZEYRDxLoT0DP90LPuvrbyZ+HJiC7/aprDw1dmiVIwLkELL10vHTVuHk63KhRozB58mTnvn30jARIQCEwceJETJ06lTRIwNUE4iJIuvyNeOW1rfjvxWtQp+CegrzSEhR+71vI8Fzq6gDQeRIgARIYikDXxzW4d/oLmFFXhUWplw1VnPdJwJYEDB5D8jn8e0pwc/IjePsLudjSGVA2BQucq8bCpHexNPkOPLLnY3TZEh2NJgESIIF4EPgMR3e+gEp/PV6sP87fl/FAzjZMIWBghqQLHY0/xR2ZlZhYvQPP5HwZF6ufT9FY9n1kLgNKG57D0oxRpgBgoyRAAiRgaQId+1D20GvAqFew7MgDaH5tEVIv/mVqafNpHAmES8C417qrBVsfKUWd5w5875Zx/cSImDcKGT94GMWe32Dtz/bgY6ZJwo0Zy5EACbiGQBfO7tuBuhnzseT2bHhqfwZfHTfddE34XeaoYYKk6+jbeLHWD8/dtyBz5CDNjEhG2rUe+CtfwM6jn7kMPd0lARIggSEIdLXgpbXAw9+ZjFGZt+BuTyM273wPZ4d4jLdJwI4EBlEKsbrShY7Wozg8VDWJYzBhajKAY2hu7RiqNO+TAAnoQuBz+BtfxUtlC5GckIAE+TdrOSpfboT/QgtefrmF4xR04Rx7JV1H38Ve77dwnXypG3kjFj8xH/7Nu9Bwlinl2OmyBqsRMEiQWM1N2kMCJKAQ6PJj37p7kXHHizg+sRCN6kDz3f8H6Z1vYsV4L352mn/srPG2nEKd7/eY8e2vYYRi0GWYlPVNZPtfwa92fUTRaI0g0QodCRgkSBIxImUSrh3K0K5TOH6oDfBkY05m0lCleZ8ESCAmAp/j4+0/wryHT+PhV36KpTkZ8Ki/ARI9yMh5GE+9sgxobgPzlTGB1ufhs+9h5+afY3HasO4sVkICvpC2GLU4gsqf78ZR6kZ9OLMWyxBQfx3pblDipBtxZ7YndHqxow3Nh4cYZ6K7ZayQBFxK4Gw9yvOfAoofxg+CzmpLxIiMu7Hy+uEuBWQltz9Dy0tbgedOdi+VEOhZMiHwd7RWPwhP7euo57g7KwWMtuhAwDBBgsRULFi9DN5B04uf4+NdNdiMB7G+MAsjdXCGVZAACQxGQP7AbcAavwfXpiX3dAEEKzsG3pwb+P8xGJp4Xut4D7/e+29Y7B3Tr9VLcfUtObjbwzVJ+oHhjw4gYJwggXzbWoyfV9+BY7k/wMpN++BXU4wdLXij7F5Mzz+HZdsfxbyruVqrA94lumBpAh1obT4GIBlTJ4wJMg3f0sa7y7iuj7Fn9eNYO2Ycrgr2G1qZnQjULn4Ij3FhSXe9Gw73NtjrrqPLI5Ga8wReaV6J6SefQsYXekb0X16AXUnz8UrjMyi6zsNfjjoSZ1UkQAI2JtD1ASpvnY6bf1wL/5qbccWcSrSoX+TELeX+bCyu9QOoxY9vTkHK8j2cBmzjkNP0PgIGrtTa1wjPSIAEzCbwGVoq85C2+BiKd7+On8zu3xVgtn1snwRIwO0EDM6QuB0v/ScBqxDomTIKLqxllYjQDhIggYsJUJBczIM/kYBjCSSmfhvLizPgX7MWv2j8NLifXX401rVw2m9wOrxKAiRgIAEKEgPhsmoSsBaBMZj9+Eb48j7Essw7sbxyD1o61AEKXeho2YNNGxvxxcxJIWbhWMsjWkMCJOAcAhQkzoklPSGBoQmMmIJFv6xFw/bvAJu/j7TLv9CzdPxKbH3/CmTf8y1MHsFfC0ODZAkSIAG9CXBQq95EWR8JkAAJkAAJkEDEBPhVKGJkfIAESIAESIAESEBvAhQkehNlfSRAAiRAAiRAAhEToCCJGBkfIAESIAESIAES0JsABYneRFkfCZAACZAACZBAxAT+Py3Axv2/tF4lAAAAAElFTkSuQmCC"></p>
<p>The angle AOB is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ<!-- θ --></mi>
</math></span> radians, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < \theta < \frac{\pi }{2}">
<mn>0</mn>
<mo><</mo>
<mi>θ<!-- θ --></mi>
<mo><</mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
</math></span>.</p>
<p>The point C lies on OA and OA is perpendicular to BC.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{OC}} = r\,{\text{cos}}\,\theta "> <mrow> <mtext>OC</mtext> </mrow> <mo>=</mo> <mi>r</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></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>Find the area of triangle OBC in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <em>θ</em>.</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>Given that the area of triangle OBC is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{5}"> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> </math></span> of the area of sector OAB, find <em>θ</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider a function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 5, 8\,{\text{sin}}\left( {\frac{\pi }{6}\left( {x + 1} \right)} \right) + b"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>5</mn><mo>.</mo><mn>8</mn><mspace width="thinmathspace"></mspace><mtext>sin</mtext><mrow><mo>(</mo><mfrac><mi>π</mi><mn>6</mn></mfrac><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>)</mo></mrow><mo>+</mo><mi>b</mi></math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> ≤ 10, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b \in \mathbb{R}"> <mi>b</mi> <mo>∈<!-- ∈ --></mo> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> </math></span>.</p>
</div>
<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> has a local maximum at the point (2, 21.8) , and a local minimum at (8, 10.2).</p>
</div>
<div class="specification">
<p>A second function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = p\,{\text{sin}}\left( {\frac{{2\pi }}{9}\left( {x - 3.75} \right)} \right) + q">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>p</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π<!-- π --></mi>
</mrow>
<mn>9</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3.75</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>q</mi>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 10; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q \in \mathbb{R}">
<mi>q</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> passes through the points (3, 2.5) and (6, 15.1).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the period of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></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>Hence, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>(6).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for which the functions have the greatest difference.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
<mn>0.5</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
<mn>2000</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</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>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></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>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></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>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = a\sin bx + c">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mi>sin</mi>
<mo><!-- --></mo>
<mi>b</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 12">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>12</mn>
</math></span>.</p>
<p 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 style="text-align: center;">The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> has a minimum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(3,{\text{ }}5)">
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span> and a maximum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(9,{\text{ }}17)">
<mo stretchy="false">(</mo>
<mn>9</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>17</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is obtained from the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> by a translation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} k \\ 0 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. The maximum point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> has coordinates <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(11.5,{\text{ }}17)">
<mo stretchy="false">(</mo>
<mn>11.5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>17</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> changes from concave-up to concave-down when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = w">
<mi>x</mi>
<mo>=</mo>
<mi>w</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span>.</p>
<p>(ii) Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = \frac{\pi }{6}"> <mi>b</mi> <mo>=</mo> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </math></span>.</p>
<p>(iii) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<p>(ii) Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x)"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></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>(i) Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w"> <mi>w</mi> </math></span>.</p>
<p>(ii) Hence or otherwise, find the maximum positive rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AB}}} = \left( {\begin{array}{*{20}{c}} 4 \\ 1 \\ 2 \end{array}} \right)">
<mover>
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\overrightarrow {{\text{AB}}} } \right|">
<mrow>
<mo>|</mo>
<mrow>
<mover>
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>→</mo>
</mover>
</mrow>
<mo>|</mo>
</mrow>
</math></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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AC}}} = \left( {\begin{array}{*{20}{c}} 3 \\ 0 \\ 0 \end{array}} \right)">
<mover>
<mrow>
<mtext>AC</mtext>
</mrow>
<mo>→</mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat AC}}">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">A</mi>
<mo stretchy="false">^</mo>
</mover>
</mrow>
<mi mathvariant="normal">C</mi>
</mrow>
</mrow>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Olivia’s house consists of four vertical walls and a sloping roof made from two rectangles. The height, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{CD}}">
<mrow>
<mtext>CD</mtext>
</mrow>
</math></span>, from the ground to the base of the roof is 4.5 m.</p>
<p>The base angles of the roof are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{B}}\limits^ \wedge {\text{C}} = 27^\circ ">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>=</mo>
<msup>
<mn>27</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{B}} = 26^\circ ">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>=</mo>
<msup>
<mn>26</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The house is 10 m long and 5 m wide.</p>
</div>
<div class="specification">
<p>The length <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AC}}">
<mrow>
<mtext>AC</mtext>
</mrow>
</math></span> is approximately 2.84 m.</p>
</div>
<div class="specification">
<p>Olivia decides to put solar panels on the roof. The solar panels are fitted to both sides of the roof.</p>
<p style="text-align: center;"><img 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AESIIEMAvRUZOBIz5cPPvhAXnjhBZkxY4Z88YtflH//93/vqvyBAwfkww8/NGMsfvWrX8nOnTvNc7Nnz5Y77rhDBg8eLDfffLP069ev6xp+IAESIAESIAEaFSm8BzDkgdiJlpYW2bBhg4wcOdI0IPr06SPPPvus7NixQ2BYXH311SYdGCBNTU1y8uRJeeWVV6S2ttY8Tm9GCm8eVpkESIAEchCgUZEDTrGdgnGwZs0aWbJkiSxfvlwWLlzYZTiouiLP1KlTBcMdq1atUod7/D1z5oy89tpr9Gb0IMMDJEACJJBeAjQqUtL2R48elblz55q1Vd6JbFWHwTB58mSZN2+eTJ8+PVu2jOP0ZmTg4BcSIAESSCUBGhVF3uznzp2T9evXm96JLVu2yH333dfDO+GE4OWXX5Zx48bJkSNHzOERpzz5jtGbkY8Qz5MACZBAcRGgUVFc7ZlRmz179shjjz0mpaWl5lCG1xkcTz/9tBljsWvXLi1BmfRmZDQPv5AACZBA0RGgUVF0TSoC78STTz5pBlR68U7YUcAIWLBggXl448aN9tNavtOboQUjhZAACZBALAjQqIhFM+hTQnknRowYIVVVVWbAZRDpfuIrgpRHb0YQeryWBEiABApLgEZFYflrKx2d/7Jly2TTpk1SX19vBlrqEq4jviKILvRmBKHHa0mABEggOgI0KqJjHVpJ27dvlylTpggWp1q6dKn0799fe1m64yuCKEhvRhB6vJYESIAEwiNAoyI8tqFLVt6JY8eOyaOPPqrVO2FX3hpfsXbtWlczSOwywvxOb0aYdCmbBEiABNwRoFHhjlOscqGDV0tsI24CBkUUS2aj48b6FVi7AmtYxDnRmxHn1qFuJEACxUqARkXCWta6xPYTTzwhFRUVkdYAi2iNGjVKGhoaZOzYsZGWHbQwejOCEuT1JEACJJCbAI2K3Hxic9bqncAS2w899FAk3gknANgfBDEWiOUII37DqcwwjtGbEQZVyiQBEkgzARoVCWh9eAcef/zxjA3ACq32nDlzTBXiGF8RhA29GUHo8VoSIIG0E6BREeM7AG/S+TYAK5T6WGBr4sSJiYivCMKI3owg9HgtCZBA2gjQqIhpi6sNwLDENrwU2J48binJ8RVBWNKbEYQeryUBEihmAjQqYta6fjcAK1Q1iiW+Igi/bN4MrBsS1vLmQfTltSRAAiQQFgEaFWGR9SFXLbHtdwMwH0VquaRY4yuCwDl06JA8+OCD8u1vf9v19vFByuO1JEACJBAHAjQqYtAKujYAK1RV8KY+fvx4mTRpkixevLhQasSu3EIvbx47IFSIBEig6An0LvoaxryCmJaJgMf33ntPTp8+bb7VXn311THXOlM96Lt161ZZsmSJwNvC1EEA63isW7dO5s6da+4cSy4kQAIkUOwE6KkoUAsj2C+sDcAKVCVz3QrsQQLjKMnrV+jkBy+O2j6+2Kbf6uREWSRAAsVBgJ6KArQjvBMDBgwwS0YHjKWviyGhHlg2HEt4ozNlEnOPlJUrVwr2Z6mrqyMSEiABEihqAvRURNi8WGK7trbW7GAKscR2FFVlfIUz5bROv3WmwaMkQALFSoCeighaFh0tpl6WlZXJZz7zGdm1a1fke3ZEUE2zCMZXOJPGOiNbtmyRhQsXCoa+mEiABEigGAnQUxFyqxZ6A7CQq5dVPIZ4GF/REw+n3/ZkwiMkQALFQ4CeipDa0uqdGDNmTFF7J5wQqvgK/GV8RTchxld0s+AnEiCB4iNAT0UIbaqW2IboDRs2xHKJ7RCq3UMkjImpU6fK0KFDZdWqVT3Op/UA4yvS2vKsNwkUPwF6KjS2MTrRFStWyKhRo8yFoA4cOJBagwJYEV+BLdIRnIrhEKYOAoyv4J1AAiRQrAToqdDUsso7kbQltjVVP6cYLIhVWVkpTU1NptciZ+YUnUR8xdmzZ2Xbtm2mAZaiqrOqJEACRUqAnoqADYsltqurq03vBNZnQAcBdz9TN4GKigpZvny5TJs2jfEV3VgEi2G1tLSY29tbDvMjCZAACSSWAD0VAZouqRuABaiy70sZX+GMDrODMNV49+7dRTvN2LnmPEoCJFCMBGhU+GhV6wZg9fX1cvfdd9N97YIj1mfASqJgViyriLqodt4snH6bFxEzkAAJJIQAhz88NhQ6AOsGYOgck7YBmMcqa8uO/UDwRo71K/CGztRBQE2/5fLmvCNIgASSToCeCpctWIwbgLmsuvZsmBGCFUaxsmi/fv20y0+iQAwPcfv4JLYcdSYBErASoKfCSiPLZ3gn4LbHEtvFtAFYluqGfnjWrFkyYsQIqampCb2spBTA5c2T0lLUkwRIIBcBeipy0EnrEts5kGg7Bc8P3P5w+U+fPl2b3KQLUvEVnH6b9Jak/iSQTgL0VDi0O1zRagMwTA8t5g3AHKofySHEV6xZs0ZmzJghWOODqYMADC1Ov+XdQAIkkFQC9FTYWo7eCRuQkL8yvqInYE6/7cmER0iABJJBgEZFZzvhQV5XVyfz58833xSxRTVndYR/E4P7ggULzII2btwYfoEJKYHTbxPSUFSTBEgggwCNChHT/T537lwTTJo3AMu4MyL8wvgKZ9hc3tyZC4+SAAnEl0CqYyrwlswNwAp/c1rjK15++eXCKxQTDbi8eUwagmqQAAm4JpBaowKdF9YFOHjwoLnR1eLFiznc4fq20Z9x7Nixsm7dOsGwEzwXTB0EwAOb1C1dupRISIAESCD2BFI3/GFdYnvLli1y33330ZiI0W2KnTuRsNkWY1o6GobxFTG6QakKCZBATgKp8lRgjBpLbGOGB9YBwPoI7Lhy3h+Rn1y5cqUcO3bMDJqNvPCYFojhoYaGBnN5c06/jWkjUS0SIAGTQCo8FVbvBDeziv+dj45z1KhRZkeKYRGmDgKcfss7gQRIIO4Eit5TgRUKP/vZz8p7773HJbbjfjd26jdy5EjB0BTjKzIbjMubZ/LgNxIggfgRKFpPBcahly1bJps2beJW2/G771xpxPiKnpg4/bYnEx4hARKID4Gi9FRYNwB79913zT0m4oOcmrglwPiKnqSs028ZX9GTD4+QAAkUlkBReSq4xHZhb6YwSlfxFbt37xas28DUQYDxFbwTSIAE4kigaDwV3AAsjrdXcJ0QX4Hg2srKSq5fYcHJ+AoLDH4kARKIDYGi8FRgdseIESOktrZWvv71r8cGLhXRR6C6utqcCrxt2zZOA+7EquIrMDUaW8gzkQAJkEChCcTSqMAwxvHjxz3FQvTq1Utuu+02c5vyfv36FZory9dMAEuqYwXUSZMmCVY/ZeoggJVhx40bx+m3vCFIgARiQSCWwx+YsfHkk08KPBBeErwVNTU1Xi5h3oQQwCJlW7dulSVLlggWMWPqIIB1PDj9lncDCZBAXAjEzqjAmxeGMQ4dOiTPP/+8J07YHwGrMSK+gqn4CAwdOpTxFQ7NiuEPGNSYQg2PDhMJkAAJFIpArIY/8ECcOnWq7Ny5s4sHltNGZ5IvYfjDMAxR7uAjR44IgvyYio8A4yt6tim8eliCnvEVPdnwCAmQQHQEYuWpePHFFzMMCmDAUIiXpHa7nDt3rufhEy/lMG/hCOCNvKWlRdasWVM4JWJWMuKINmzYIPPnzzcN65ipR3VIgARSQiA2ngq8aWE5baeEzZTy7QGhPBW4Hh6PBQsWmKI2btzoJJLHEk6AO3c6NyCG/rCGBRaAw0JZTCRAAiQQJYHYeCrWr1+ftd7YA8LLWDGC+hhfkRVnUZxAh4kFsaZMmWJONS2KSmmoBOMrNECkCBIgAd8EYuGpwBTSsrKynJXIt7uo1VOhBKn4CjeeDnUN/yaLwIoVK2THjh1y4MABrl/R2XSMr0jWPUxtSaCYCMTCqMDGUW5iJ7CPR7Y1KJyMCjSUWs6Y7uBium2766KCexHMu2rVqu4TKf+kDHUub57yG4HVJ4GICRTcqFDeBDf1Xr58edaFj7IZFZDL3S7d0E1uHsZXOLcdDGkMD50+fZrxFc6IeJQESEAzgYIbFegQLl++3KNaGA7BdFJ7yja9NJdRQXewnWLxfceCWNgfxO0U5OIj4FwjTr915sKjJEAC4RAouFGRrVq5jASna/LlV7tdMr7CiV5xHGN8Rc92xPAQlzfvyYVHSIAEwiGQGqMC+DjdLpybKC5SVXzF9ddfL5xK3N0qjK/oZsFPJEAC4RKIzZTScKvZIZ3T7aKgXLgyMJUYgblcqj2zDbi8eSYPfiMBEgiPQKo8FcDI+Irwbqa4SFbBv1yqPbNFGF+RyYPfSIAE9BNInVEBhIyv0H8jxU2imkq8a9eurNOQ46Zz2Pqo+Iry8nJOvw0bNuWTQEoJpNKoQFtzul1x3/HoQLlUe8825vTbnkx4hARIQB+B1BoVQEh3sL4bKY6S0IFOnjxZ5s2bZ+7eGUcdC6ETp98WgjrLJIF0EEhVoKa9SZO12+WH0rz5q9KrcrM0t9trUqTf20/I5sohUrn5hPipMvYHwU6mM2bMMIe8ipSS52pVVFQIFpKbNm2apz11PBfEC0iABFJHINVGBWYLbN26VZYsWSJ4e2MqPgLY3XbdunUyd+5cM0i3+Gror0bYpK+0tNTceM+fBF5FAiRAAj0JpNqoAA5Ot+t5UxTbkVmzZsmIESOkpqaGb+adjaum39bW1prxRcXW5qwPCZBAYQik3qgAdoy7V1VVmWPvCPDTny5I877NUjOhVLDyZ69epTKhZrPsa75gKcqep1JqNu+T5ks5HP/trXJ4+2qZUQqZTnLfkX01t0qvCTWycfUMKUWe0sWy74JdZrtc2LdYSnt9VTbu+6WsmXFLp7xKqdlyUFqt2d2WWfkj2Xfwue46l86Q1b9slkuWGgtkbamRCabuvUw9N++z5bHmFzsjJ44ZF5hf0IGuXLnSXL+irq6uZ4aUHuH28SlteFabBEIkQKOiE2548RXtculwnTw47WUp+7sTYhiGGG2H5LtX/FTumv/zzviIC3Ji80Ipn3ZAPr/ysLQZhrS1fE8+f+BbUnbPD+Wwo2Hxvhx+ao7cs/NqefjwR5lyH6zLvGb//ycN/aqk2fhIWvY/KGOuzdbsL8jcaVtFHt4jbUabXGx6UOSZb8g3njrYaQx4KHPPcvl+/Sdl1i/OiIFyt94k/1zxHVl/+P0O4u1vyfY5FXLPvhtlZQv0b5OLf/cFOTBtinxr+1sOMRRuOGb/pWB32w0bNsj8+fMF61gwdRBgfAXvBBIgAa0EjJgmEfST7pPX/E6Sm5qaDMipr693Ou3z2AdGU919hlTUGU1tWUSc32tUlww3ZtafMjKymMdLjIq61402wybHPDfaqN57NkNoW1OdUSH3GXVNHxiGcdbYWz3akJJFxt7zGZIzrjGMNuP83kVGidh16Dyurg9SZkZdVHlKT6WOrby21426isHO9VeXePy7ZcsW47bbbjNOnz7t8crizX758mVj9uzZ5r/irSVrRgIkEAWBbK+sWg2XpAhDfMXu3bvN7aKxX4KedKWUjvjvUr7nx1K34yXZt32/bUijXS40/kqea71Zxg7/nGQ0SN9SKbtF5NWmlsxhAyh27Z2ysqVRVo45J/u2bzfHxbdvrpG7ymaJ/5BTuw69pW//IXJL6x7Z3XguWJkZdTknjbv3SGvJEBn0+SstmG3lWc6I5OOYkTnrFy7V3hMNhoeWLl3K5c17ouEREiABjwQy+jCP1xZldv3u4N7Sd/S35BdNq+XP3/8n+f6UCVJ2zRWW+IGP5Xen3pDWHDRbj56S31njGsy8GDKZJaXXlMld634j5qDCp++Wv2vcIBVyUprOZEQv5JDu5lSLHD31jrSL5jJbfyB3feqKzviNjriQK7IaRfk4uqlHRx7GV/Rkxem3PZnwCAmQgHcCNCocmOmfbtdb+g4tl8kzV8qvzXiJRqn/yu/ksbu+Id/fd0E+P2iIlDjooQ6VjBwkn7e1VHvzz+Vbsw7K3fWnpO3XK2Xm5MkyefJfSun5/5RX1YXa/pbKyAJaA7MAACAASURBVEHXiegus6JOmtqMjngQxJp0/WuUlXde56B9Lo7vOOR3PsT4CmcunH7rzIVHSYAE3BOwdVXuLyzmnGFPt+tdMlomz50h95fAA3BO+t76Jbm/5HV5+fjvMwMUL7VI06sit5SVSt8M4O1y6cwb8qrYhyv+JBfft84oybjIxRe7h6OznJIKqbz10xrL7Ce3VlZIyav/JsdbP7bohWDMNTKh11dlc/OHluPOHzM5wpPiPo0cOVK2bNkiMCCx8iZTBwHr9FsyIQESIAGvBGhUZCGmb7pd50qYExbL9q4ppBek+Ve/koMyWR6svEl6X3ur/M0TY+TFed+THx5s7egcLx2XzfO/JavKqmTFV4dmxlpIb7nWNEQa5LlnXuqc8vmxtB7cKIvn/SjnUEqW6nYePiyrvv9Up57tcunEczJ/2i/k7qcflPJrP6GxzN5ybfmD8vTdB2Te4o1y0DQs2uVS8w75/iM/Eql9RL469Cqbqi442q7I91XFV2AZ73CmEufTIH7nGV8RvzahRiSQJAI0KnK0lp74iqtk6AM/lMb5/WRn+ac64wc+JeU7+8n8XyyRSTcgUPFaGTZzjezfOl5+VzNarsC6Ddf8L2ka/0Np+sW3ZHRfh2a6dpx8+xcrZcy/zpDSKxCPMFoe/ZfrZMaOF6Q611hKjvqKVEj1/TfLyeVjpVevK+SaO/fJLVvq5YeTB3YYNTrL7D1QJv+wXraOf1tqSv9rR3nlO+X6+T+V578zxuaZgdJuOOasnOPJtWvXSktLi7mct2OGFB5kfEUKG51VJgFNBFK9oZgbhniDnTp1qrny5qpVq9xcksA8WPzqMRl21xvyRNOzMrOHlyCBVfKgMmb6lJWVmTN/YEgydRBQ28djR18YGkwkQAIkkI+AwytwvkvSdV7FV+zfv1+effbZdFU+JbXlUu3ODa3iK7AwHIeHnBnxKAmQQCYBGhWZPBy/0R3siKWoDoa/VHvycMGg5vTb5LUbNSaBQhLg8IcH+sodvGvXLsG0RKbiIoC38fHjx8ukSZNk8eLFxVW5ALU5evSojBo1ShoaGgTTTplIgARIIBsBGhXZyDgcR6ezYMEC88zGjRsdcvBQ0gkwvsK5BTH0B6Oa8RXOfHiUBEiggwCNCo93AtY0gKsc0xAxJbEYE3Y8xUJUaU3oOKdMmSKnT59mgKLlJpgzZ475DTNmMDTCRAIkQAJ2AjQq7ERcfMcul+PGjZMjR44IFlEqtpR2owLtuWLFCtmxY4ccOHCAHWjnDX7u3DmZOHGiaUzDqGYiARIgATsBGhV2Ii6/F3N8BY0KMWc7FP9UYpc3uyUb4yssMPiRBEigBwEaFT2QuDtgja8oNncwjYqOewBDXQMGDJD6+npzyMvdnVH8uRBfMWPGDA4PFX9Ts4Yk4JkAjQrPyLovUPEViK0oJncwjYruNt6zZ49UVlZKU1OTuQBa95l0f6qurhYEtW7bto3DQ+m+FVh7EsggQKMiA4f3L8XoDqZRkXkfML4ikwe+cfptTyY8QgIkIEKjQsNdUGzT7WhUZN4U6EAZX5HJBN84/bYnEx4hgbQToFGh6Q4opul2NCp63hSMr+jJBEc4/daZC4+SQFoJ0KjQ1PLFNN2ORoXzTaHiK4p1KrFzrfMfZXxFfkbMQQJpIUCjQmNLF0t8BY2K7DdFMU8lzl7r3GcYX5GbD8+SQJoI0KjQ3NrFEF9BoyL7TWGdSsyl2rs5Mb6imwU/kUCaCXCXUs2tj+mlI0aMMKeYogNiKi4CWJ566dKlcuzYMYEBydRBANvH796925x+CwODiQRIIJ0EfBoVH8tvt8+T0srN0tzuAtyFfVJT2kvwBtzx76uyuflDFxcmMwsWw2ppaZE1a9YkswLUOieB/v37m22LBaAw5MXUQaCiokKWL18u06ZNM6eckgsJkED6CPgyKtp/+0/yvXk/klZXvD6W3/5quzxnzVwxUcYNucrV1UnMhLfZrVu3ypIlSwTBfUzFRwBbgK9bt07mzp0rCNJl6iCwcOFCKS0tNb05ZEICJJA+At6NiksH5anF/yLXfXm4O1qXjsq2v+8nW8+3mTtfYvdLY/dMGeq9ZHflxSQX3MFY3hmrMWI6IlPxEZg1a5Y51FVTU1N8lfNZIxjUCGatra01p5v6FMPLSIAEEkrAY9f+vhxe/7zIgm9K5ef/q4sqt8uFgzvkqT2b5PvL62T7vma55OKqYsmCLdKrqqoYX1EsDWqrhzW+Ah0pUwcBDA8hvgLbxzO+gncFCaSLgAejol0uHX5W1so35KHR/dxRam+Wn698RlqlVfavmitT7iqXe2q2S/MlN4EY7oqIe65ly5YxviLujRRAPxVfMX/+fHn55ZcDSCquSxlfUVztydqQgFsC7o2KS42yfq3Igodulb6upQ+TmbtbxGhrkcYdG6S6XGT/qnny4PrG1HgsGF/h9mZJbj7EV2zZskUQT8Chru52ZHxFNwt+IoG0EHBpVLwvhzfuk5tWPCSj+7q8xEqwd4mMvneOrNx7SPYuukX2P7VDDl5Ij7eC8RXWm6E4P6upxPBMcSpxRxtb4ys4/bY473vWigTsBFxYCBj2+EepHzhVJt1wpf16b9973yB3Ploj1bJHdjemK2Ie8RWYboe/7HS83TZJyb1y5Upz/Yq6urqkqBy6nhgeamhoEE6/DR01CyCBWBBwYVSck4M/2yQ/mDJIruhaZ+J6uWvVYZE9s6TsilKp3HxCXPsd+pZK2S1lUtbf9SBKLEDpUILuYB0U4yujX79+smHDBmF8RWYbcfptJg9+I4FiJuBzme53ZF/NRLnr6Del6UWP00Mv7JPFT4o8uuJOuTYHWa9LRXvNn6PoUE8lYbfLpLAMtaECCC+GpdoDVN/xUi5v7oiFB0mg6Ai48FS4rfP7cnj1/5RepfNk+28/Ni9qbz0sO3celtZON0Z768uyZvm/yZfmj8tpULgtMYn5ON0uia3mTWfGV/TkZZ1+y/iKnnx4hASKhYBGo8IJyTn5zf++R0qv6CW9SmfIUy//Ub7y3e/InSUBYzOcikrQsThNt/OyGiRjQdzfZIyv6MlKTb9lfEVPNjxCAsVCwOfwR/jV9+qC95o//BrkLgEd9NSpUwUzQ1atWpU7c4hnJ02aJGPGjJHFixd3leLEsrq62jxfSF27FEzIB+wLMmrUKHMhKBiSTB0EuH087wQSKF4CNCoK2LZxiK/Yvn27ufLhkSNHZOTIkSYNu1GB/Uuw3Lg1TwGxJapoxff06dOCN3UmMWc/LViwwETB7eN5R5BAcRGgUVHg9oxDhz1nzhw5e/asbNu2TTD2bTUqMDwyceJEKS8vL6hHpcDNFKh4eHmwXLXiG0hYkVwMgxrTqxF/Mm/evCKpFatBAiRAoyIG90Ch3cHKY4JVIfGQtxoVK1askB07dsiuXbsEUyaZvBPAUNf48eMFQ03WYSbvkorrCjU8hHUsMO2UiQRIIPkEUmlUqIcZdkyNQ4rDdDtE5COArqmpScrKyswdZRUnbA7FmIBgdwo8FeBKlpkcOf02kwe/kUDSCaTSqEAn3qdPn1g94JU7GK5geAuiTipw9Prrr5dNmzbJ5cuXzbfrESNGCMe99bQG4yucOWL4DWnt2rXm8JtzLh4lARJIAoFUGhVoGLj4keIUQIddLseNG1ewgEj1Ng0uGAqB5yJOfMwGS/h/jK/o2YAqbofxFT3Z8AgJJI1AyOtUxBsHXNHwDOAtPQ6p0MsZY3or9idBgkFRX1/PGQuabwxsONbS0iJLly7VLDm54ri8eXLbjpqTgJ1Aqj0ViKlAICJSXALoCh1foYaG7r33Xs5WsP9aNH1XgbEw2jADgqmDAOMreCeQQPIJpN6oULEE3/zmN2MTjFjo+AoMDb377ruuZ3uA4QsvvCAXLlzg9ECXzwQ1lRiBsfAQMXUQYHwF7wQSSDaB1BsVaD715hin+AEVXxH36XaIw0CcwM6dO81fQtz1jdPPVU3XPXDgAAMUOxtGxVdw+m2c7lTqQgLuCdCo6GSFN8cf//jHsXL5x9kdrLwTiL2wpttuu00wy4GrR1qpOH9WXrJCL9XurF3hjqqAYU6/LVwbsGQS8EuARoWFHN4c33///VitHBlHdzDWr3j88ce7vBMWhObH2bNnc3qgHUqW78pLxviKTECcfpvJg99IICkEUj37w95ICxculPfee89807afK9T3OO12iTdrGF7YJEsNdzhxwToXa9ascTrFYzYC8OjgjXzKlCnmUt6207H+CoMIw3T4qzshgLWqqipWs7N015HySKAYCdBTYWtVPCDxQNu6dWtsAujUypaFjFeADnPnzpVDhw7ZiGX/Svd1djb2M0mMr4CRiY3BYERi2Av7w9x+++0yfPhwGTBgQOA4Ecjn8ub2O4XfSSDeBGhUOLQP3r7gtYhTAF2h4ivwYIfXYcmSJQ6k8h+KU/Brfm0Ll0N10NAgSSuYKiPcydjEMBhWZIVna+DAgb7ibBhfUbh7kiWTgB8CNCqyUMMmX2+//Xaq4yv8eCfsOLnehZ1I9u+qgy7UUu3ZNct9Rs1Uyp1LfHszGF+RjyzPk0B8CNCoyNIW6s3x7rvvjs0CRWq6XdjLGaOc9evX+/ZO2JFilc64LC5m1y1u31UHfeTIERk5cmTc1MuqD4zw+fPnZz2f7YRbbwaXN89GkMdJIGYEjJgmEWyU6T6Fkf/06dPGbbfdZjQ1NblXJOScR44cwdaqxu7du0MpCXJRZ5Sh819Y+oYCocBC161bZ7bBu+++W2BN3Bd/+fJlY/bs2YHvGdx7VVVVRn19vfm7g1wk/L333nvNc+61Yk4SIIGoCXjruSPULgwjwaq+W/kNDQ3mA1493KwyCvUZD1zoD6NHV0IHhoe5TkPCLkunvrrqHUc5qoNGJ52kpIxwe7sH/Q4OuD8hH7Jw/zORAAnEkwCNChftgjfHuD3gYQDgzU2HsROWd8LemejS10WTJT6L6qC3bNmSqLrACLe3u47v6veHexXy4uQ9TFQDUVkSCJkAjQqXgPFQi9MDHsYEXMXLly93WYOe2aLwTtg7FBhDTO4IqA4aQ15JSjDC7e2u47v6/eGex72vw6BOElfqSgJJIECjwmUroQPGgyxOD3i8reFh7SdeISrvhFNnQve1y5vOMAwVX5GkoSM1fOPU9kGP4fcH+YyvcH8PMScJREmAsz88BM6qKZa7du1yvYOnB/G+snqdbodpi2vXrpXa2lpf5em6iLtzuiOpZiEhN9rt6quvdndhgXOp6bFO61cEUQ2LbOH3d/nyZXOBLS5vHoQmryWBEAhEacF4KQtvNF5S2PmVLnDBqvFddazQf93GV6gAz6Bvizqup/va/V2jvGTwWiQpqeEbHfeLVYb6/TG+Ikl3A3VNCwFvPXeEVPAQ8ZLCzm/VJWnxFXCdQ2frgzkOnxlfYb2rcn9WU4nRUScpRRVfAcOLiQRIoPAEvPXcEeobtpHgVb616urNMU7xFdmm26m4izgYEU46ML7Cemfl/gwvGTw8jK/oWENFxVfAYFbei9wEeZYESCBsAjQqfBLGAy1uD/hs7uA4eimsBganB7q/CVUHmqSZDzCC8FuxtrmOz5AJA1/JV7ND3NNkThIgAd0EaFQEIKriK+L0gHeabqc8Kzoe5GHIUJ1DgKZIzaWqLRlf0eGtUB4KFb8RJ+9ham5KVpQELAR6hxD7mRqR2IPjM5/5jNTV1cWmzthdtbS0VJYuXdqlU79+/WTDhg1d3+P2ATMEampq4qZWLPVRbYl9NrBPSFLS2LFjZd26ddrVxbbr2MFXyZ87d65g7xomEiCBAhGwGBix+og3Yi8p7PzZdIGXAm/acQqgyxZfAc9KGJ4GXTLpvs52l/U8Dla47xhfwfiKnncHj5BA4QhwnQoNxhzm5A8YMABWkAZpekTs2bNHKisrxb4exJw5cwRvd3FNSduds5Ack7hzZxTrV0yePFmStn18Ie8jlk0COgnQqNBEs1evXrEyKlCtFStWyI4dO+TAgQNdiyap7dN1L0qkCaOoxY3g5mfKTQALY40fP14mTZqUqK3l1fbuuWvn/Sy2Ud+4caM5LDRu3DhpaGgwh0W8S+IVJEACfgnQqPBLznZdHI0KdDpTp06V66+/3nzYKpWxMuioUaPU19j9VZ1D7BSLoULNzc1SVlYmu3fvloqKihhq6KzS008/LYgL0Z22bNkiiHWCfMRaYMXZ/v376y6G8kiABLIQoFGRBYzXw3E0KlAH5W62u4PV8t5e6xlVftU5RFVekstRbXn69OnEdKBq+fEwhuLUEBqG+pCStLx5ku9D6k4CIECjQtN9EFejAtVT7mb1sFVVxph8ofcAUbpY/1ZVVcmjjz4am/1VrLrF9TPjK7pbRg2h4cjEiRNNzwWMaiYSIIEICBQuRjR3yWHP5vAqP7e2ZoRmviwFPa92u8Q6ByqpmSu6Zm8ElYPZDGqdAcxqwJobVn2V3vzbk4BqSzBLUlLrSwS9d+zXq/UrcD/hXJxmZyWpfagrCXglUHBPBcb3T5482cN8mjJlimAHQmvq27dv1nFjr54Cr/mtejh91i3PqYwgx5S7GTIQzKaSGpNX3wv1d/ny5YI1NrALp3LnQxfGV7hvEdWWjK/oYKaG0BBbgRgLxle4v5eYkwR8E/BqhejO72Vvilz7ROBtxEvymj+fbN3y8pXn53y25YwLuXup3TvhtKQ4169w39qqLZO09Dm8LE7tjt9U0H/K8wX5+IeymEiABMIj4K0nDkkPNzsZ3nvvvTkfCF47da/581Vdt7x85fk9r9zN6mGr5GDH0KAPcK/Xw1WPhzz+qc4wmwy7vkpv/u1JwGmp9p654nUEBi+MR93GBYxWDKEldXnzeLUStSGB/ARiYVSoH3y2DgXH83UqyOMlec2fT7ZuefnKC3JexVdYV2NEx44HMOoR9j+rdwJv1DAY85WpOocg9U7LtWhLME3y1vK4L2BoKgMp3/2R6zwMFSQ8Q5CP8RVp+SWwnoUg4K0nDlHDXG+qbh6OeFh4SSo/OlbIx8PL2sl6kYW8Sp7X6wqRH52OkzvYy1AU6uvnHwwalI9/eDP1IoPua/d3C+5lsMXvKkkJ+uK+QMdvDdLFZxzz683AdUjqngvyW08ST+pKAlET8NYTh6xdtjdWNw8APEC9JJXfaszgbdhNWU7lKHlO5+J4THmH0Mlbk9o+HfXR+Q9tq8b53XonnMq362vVnZ8zCai2VNwzz8bzG4xNq8cMn2Hw43dqrwe+47hbb4byduIlAvcjymIiARLQS8BbT6y37B7SlHvS2pm47URwjZek8luNChxz4xVxKkfJczoX12OKt90djIc06qPrH94O/XonnHSw6xtXvnHQS3W4SepAYSw4tbs6Bo8V7imv3gw1hKYMF7BhIgES0EvAW0+st2xHaejU1cMDDwG3D0Nc4yWp/HhjV+Wpv1a3q1uZSp7b/HHJh4czOFs9NGCezWukGLn5q8s7YS/Lrm9cWMZRD9WWfo3lQtXJbuzb7wHrd9wPMBBwTT5vhoqvUIYLvDlMJEAC+gh464n1lZtVEjo39cDAQ8JtwjVekjU/3nhUmfjr1pCxlmeVZz2ehM9O8RXWdrCycfvZ6p2At8ntdW7zMb7C/Z2l2tLL78m99PByWl8w3N4XKl8ub4b6fSvDxWpQh1cbSiaBdBDw1hNHxAQdEt5yvSQ8TLwke354J/CQUeOuXmQhr12e1+vd5leeFfVgdHtdrnyQibc9+1CTGpNXD2o3f63eCbCEXDfX+clj1zdXHdN+ThnOfu/vQvDDPa7r/snmzYDhgntW5++pEKxYJgnEhYC3njgirfED9/L2oGIDvDwY0InpTLrl5dINZenuUBVDe7yCl/gK9SaMdvBynR+DQl1j1zcXt7Sfwz2DztXP8F6h2KlhCtXeuv4qQwL3qjI4ClVHlksCxURAb89aIDJ4MOAh4WXcGA8nnUm3vFy6oSw8CHV3qH7jK+BqVkZg2N4Je6cCDqrsXMx4zjDfxtVQV5J4qGEKe9sH/a4CNZXhooziJLGhriQQNwJ6e9YC1g4dCx4ybh8MyKsz6ZaXSzeUhQdhGB2qkzsYbFEWyrX/U7yj9E7YdVBvnbmY8VwHAdWWMCCTlILEV9jvF+t3Faiphvrwu2IiARLwT0Bvz+pfDy1Xenkw4MGiM+mWl0s3VRY6dN0Bi9ncwWpMXj2Qrd4JnMtmdKj8Yf9Vb525uPFcBwHVlmmNr7Dfi8rThXsI9zF+A0wkQAL+COjtWf3poPUqtw8GPFh0Jt3yculmLQtvcLrjK5Q7WL3FKV1QDspW3gmMzYf1BolyvP6z66v05t+eBBhf0X1/KU+Xn2HUnmR5hATSTUBvzxoDlm4fDNaOWYfauuXl0slalvIs6I6vgOGActRbHPRBWSrIDx14ob0T0M/+z6pvLoZpP4e2ZHxF9/2jPF24f3BPKcM57fcJ608CXgkUnVEBAHgwoMPLNW6MB4fOpFteLt3sZakHoe4O1Sm+AnrFyTsBFtZ/6q0zFz+e6yCgfie6PV1h8w3r/lOeLvzFPcX4irBbkvKLkYDenjVGhPKNG9s75qCq65aXSx+nsvAg1N2hKi+IeotTOim20COO/+z6Kr35tycB1Za6PV09S9J3RN2XYdx7yjB3O4yqr1aURALFQaBojQo0T65xY6eOOUiT6paXS5dsZeFBqLtDzRdfEcaDXYdM9daZiyPPdRBwmkocdzbqvtRxr1hlKMMchgs+wyvCRAIk4J5AURsVucaN8SDRmXTLy6VbtrLUg1B3h6riK6zuYMXW+kCO22ervrl48pxhTJ061SgrKzM9T+hI0b5xT+q+1H3fKcNcDQ/lGkaNOyPqRwJRE9Dbs0atvYvysj0YsnXMLkQ6ZtEtz7GQzoO5ykJ9cV65cXPJ8XLOyR2s2KK8OP7j9ED3LfzYY49ltGFSOtKw4yvU8FCSpt+6b3XmJAH9BGJvVODhhh92kDcnpwdDro7ZD2bd8nLpkK+ssOIrnNzBim0cjQroRPd1rjup+9wtt9ySYVQMGTLEHD7EvaTbQO0uNfgnPBfCmoWk6p1rGDV4DSiBBIqLQOyNCuXiVLM51JRGr81gfzDk65i9ytctL1f5bsoKI74CD1mUbZ9uB7Y4Htd/dn1zsU3bOXTKMNztbafuH2uHDQMNLPHWHsTI1804iviKJE6/1c2Z8kjADYHEGBXWhx4ebl7dkXgIqgcDPkOezqRbXi7d3JSFOsKzoLtDxZsryrfGKyi2OB7Xf1Z9c7FN0zn8hmA04B8+o21xv8D7ZE0w5HEMxgd+Q6qN8RkGJc6pt3rrdVF+ht5KL51/GV8RZSuyrGIgoLdnDYFIrrcQdJp4EKJTc5Pw4MMDVL1Zu7nGbR48yKJKbstSngXdHSrjK6Jq6XDKwe8FbYj7CH/d/n6s2uCeQkeu7gXIwm9LeTNw3o9caxleP6Ns6KH7H54xSGqoz+sLjdd6MD8JJJlAdD2hT0qqY8z3oICh4CbhgaBkucnvNg9kRpW8lIW8eNjrfMBDVtLiK3R7bKJqa93lKO8E2k+nsYnfKTpd/A6zeTP8Dl26ZYD7Eve6+n3r/Iv6IaF+KCPsuritM/ORQNwIRNcTBqh5vocDfuRe3h7UGLJ6UARQretS6BhV8lIW8uJBiLc4nUkZe/bOWrHN12ZRnUe9VTvjjVO9depkkQRZ6ATVmzzayJWR2XbKqJ852qioe91o81hJyFfeDJSrOnv8hXcD941Oo0apZ31p0HmPwQhDnfDPOoyqyuVfEiCBDgLR9YQBiKsHktNDAj9w1Wl4KUL3gwG6RZW8lIW86kFoNwCC6pvNHWx9U3VqsyiO4Z5RBoS1Q0XZYXRmQVmGeT04gIdX70RbU51RgeGEijqjyatV4VAh/E6VNwO6qPsA9wsMHZzT4QEIy7CFMYSEeoCnW++oAwoeIoGiJRBdTxgAoXrDUg8h9Rc/anSYfhIeXjofDNApquSlLJVXPQh1d6hO7mDFVrVT1H9xv6jOSXWoVh3Q7n7vm6jaWEc5YKB+OzAovdX5PaOx9jvGD2ofNkrkPqOu6QMdKmXIgD7wLEA3pSfaCe2DDhxt5/d+DcuwVYaq8ojAEGIiARLoJhBdT9hdpudPeMBYO4URI0aY34O+eet8MEC/qJKXsqx58QDU3aGiY1BeH2v9FVtru4X9GXVTD31rh+pULjqxYk74baDeaBs/njzj/F6j+it1RtN7e43qEjFKqvca5yMABl3RhjBWrd4MtBc8ELivlMGYSx3kwf3g1PZBjyme0AdlqO+59OE5EkgLgeh6wgBE1QPS+pDEgwff/b7JKHV0PRigS1TJS1n2vHhY6+5Q8VDFwxUsrQnfUX4U/1An1dlY75dcZQc1Sq11jctntIV6S/dfvw+MproHjeq9Zw3DOGvsrR5tSMkiY+95DWMgHkGhTWFI4F5CG6v2hMGRz5uBa9Vwi2Kirg/yF2Urr48yqNV3j9UzjLYWo3HHPxi104d31q3EKK/eYOxobDH+2LTL2BGCh8izjryABDwQiK4n9KCUPasyIOzDHXiooDPz/YPuLCjwg8EwzAeCXe+wvuOB6DbZ8yrPgt0AcCsvWz48vFEWOgBr0vkwd+oI0P7KO2HtUJ3yOh0LapRa61rIz2hXZUxZDSxfOrW9btTN/KHReLHDiOiIrRjdaWT4kqj1IrQZ2hy/f7s3AwxwDzo9E3AM1yIPGOHecbon3BxD2UjKI4Jnk9fU1tJgPDV9uFEyvdaob2zpCoZta2k06munhzbs5FVP5icBLwTc905epGrOi87CaewSDwk8VPCACJIgBw8Y9aDwIwsPoqiSl7Kc8qoHod0ACKo/HqzgCPkqqbLcPKi95kF7qc5DdaheZdj1VXon6S86SvwOUBdlYPnXv804v/e7xlesMz5gZFSUGCUz640z0Tsr8lYF95jyZliNAzU9RAAAIABJREFUWDDBPQkmeIY4JfVsQT7rtW7uI8UaZSO/0zPKqUzzmDmzZrgh5U91GW+ZeRHTMj02hlymbvxGAtkJRNcTZtch0Bk8FPCDRqcSJOHBDDnqQeFVFq6NKnkpK1tePAh1d6jo4JXXx8pCsYUuOv5Bb2UQof29dgZ2HXB9EhN4qyGmwN6JLgCdwx2ObRVOwGZX0Ro/KI8EDE/cL6rNwUmnN0MZK2gHlKO+564KDLdFRonk8f6c/1ej/tcYgmIigeQQiK4nDJEJDAE8NFRH47co9bbr7sGQWQrKjyp5KStXXjwIdXeoYIeHq90drNhCnyD/dHgnnMrXPRwU9r2Ae115J4Le91ZdMdTxFYegzLYz9cbMkhJfa1ZY5RfqM7wZ8CSoe17dA7j/ca/iXLbfPY7jvJM3A22gvGWQhX/qe9a6dnp+JKRZNVnL5QkSiIBAdD1hyJXBDx6dmdX17qdIvMlYHxRuZeAhFVXyUla+vHgI6u5Q8QBGufhrTWCL437+oW1V54m3UOjtR06ua5R8q85x+4wOC4YV6mE1sPToCZd7dZbpo50eDE1rVujRN5gU5c3AfYn7C0zxV3kzcN7JQMAx67Xq94PjuB7tkjNhZk2JFCz4NaduPEkCAQlE1xMGVDTf5fhBqzeFfHlznXf9YLAJwQMpigT9UBb+ukn59FIxD7o7VDxo8YC1vv0pttDJyz/VeeJ6yPVyrZe80DeoUeqmTfzmQRtBRxi9utvLMD4yWvY+bpRnneWBGSH3GSIlRvmiPUZLDGMr/HJV12XzSOC5orwZ+e4PGBu453IOo9KoUMj5twgJRNMTRgQODwU8dNWbg99iXT0YbMLxIIkqoSy8TblJbvRSnVW+B6ab8qx5lJFnNYAUW+iV75+188R1+J7vmqDnoXPcEtpFeXlwb1t56tFVGQyqTeyxE/bz6XjLBmfcdxi6s3szYOjiOM7bkxrqsxrUGXnU8EdWAy4jN7+QQKIIRNcTRoRFud6DvsnlfTDY6oPOLKqEstD5Qcd8ya1e6KwgU2eHhc4QRh7e8qxJsc1lAKjOE/rgc668us+hvLgkvPEq74RTBxYXPdOiBwwFtAnuaauRi98O7hs8f3DfP/TQQ8anP/1p877t+btSRlqeQM20QGU9i4pAdD1hhNh0xlfgge6mo3XbeevAgLKUVyZfR+NFL7yN6e5QYdxBB7fxFXhQqzrhr/XBDTlR/bPrq6PdvMiweidghLm5B73IZ149BNAuuMfRRsqbhHv0uuuuy7hX7Ya1uWIp4iqyTinFulj/Zvy6KYp1TPWwoBQSAIGiNCrwQ8fbAf4FSZCDTg0Pi3wJD5KokioLHV8+o0fldaMb6uslvxuZyANDBXpa3cGKLcpT/5APx/EPn9XxQvy16+u2rjryKU8O7l8rMx2yKSN8AmizoUOHZty/PYM324yLrz9jTDcNi2qjbm+TcbFLtfNG095/MOrq/8NyrOskP5BArAlE1xNGjEG9yQd984YcdGp40OdKyBNVspaFN6BcRo81rxv9vOZ3IxN5lJEHg0ElxdbqncBbX6G8E6i79R90tuqr9A7rL3igTOiQ734LSwfK1UPAbhRnG47F6pk76qqN8q57r3uZ7iKMhdUDl1JiTSC6nrAAGPAmjwd0UFe2WgdDueWdqoJyokrWstDpoSPK1glZ87rRz2t+NzKRJ1t8BZiiDviHtzmUH6d/PdzWbivsIR/qrrwTMBDBiin5BNTQX67nRvJryRqQQCaB6HrCzHIj+4Y3Bh2ubHR4uYYawuqMnUDZy1JeGae3IXteJ3nWY17zW6/N9xkPV8i3T7fDcbDFuTj+C2qU5uKCusMzg/rbueS6jueSQSDM31MyCFDLtBHoLUWepk+fLiNGjJBly5bJBx984Lu2CxculNLSUlm6dKlvGWFd2L9/f9mwYYPMnTtXzp07F1YxgeUOHTpU6uvrpbKyUs6cOdMlb8CAAV2f4/gBbW/VV4eOuBefffZZKSsrE3DZtWuXVFRU6BBNGSRAAiRQMAK9YEUVrPSICkZHO3HiRIGBMW/ePN+lomNBB4iOcfLkyRlyevXqBa9PxrGwvmQrC53USy+9JBs3buwqOlvergy2D17z2y539bW6ulqam5tl27ZtcvXVV5vXKLauBBQg0+zZs2Xt2rVd+gZR4ejRo/L4449LS0uLaQyOHDkyiDheG2MCUfyeYlx9qpZCAkXvqUCb9uvXz3x4z58/X15++WXfzQyPwO7du2XKlCmCjiFuCUYTEoyLOCd4jdChrlmzpktNxbbrQMw+bNq0Serq6gJpBe/EihUrZNSoUTJmzBg5cOCA0KAIhJQXkwAJxI1AmsZ7dMVXOK2DEeXYaa6yVECkiq/Ildep7b3md5Lh5li2+Io4BmuCifrnN74C7YG4CcRPqLZxw4l5kk0gqt9TsilR+2IikIrhD6shN2fOHPNrEFc23jgXLFhgylFDDVG6OfOVBS8K4iswTv/Zz37W07BMPtlWlkE/b9++3fT6nD59WuCpQALbqVOnys6dO4OKD+16q775CsHQ25NPPim1tbWyZcsWue+++7QMoeQrl+fjQSDK31M8akwt0k4gFcMf1kZeuXKlHDt2LJArG3EACNiEnDgONcCljtiRmpoaa9Vj9xlxKVVVVaauMCaQwPbpp5+Ona5WhcBW6Ws9bv+8Z88eM5YH8SNNTU1mTI+KIbHn5XcSIAESKAoCxeR2cVsXuJ/hlgw6hU+tg6HkuS0/aD63LlW1kJKX8tzK9iIzV16s0YBhAfsCXmptEOgTx389V0jsriWX2O5mkfZPUf+e0s6b9S88gaJfpyIbYrXYENZ4CJJUfEWUDw+3ZaHDRl4vcQBuZQdhZr9WraxpX8Ar7vEVTkapuq9g0AW9t+yc+D15BArxe0oeJWpcTARSN/yh3EtOrnd1zsvfWbNmmetgeLkmqrzK1R7GOgs666BmfmBWDYYKVILe9957r/oaq7/Qa9CgQV06YUos4nVQB0w5RqyNihPpysQPJEACJFDkBFJrVKBdnaY2em1vFV+B6+IYXwG9Hn300cCLf3nl4jU/Fn5avny5TJs2rSteQcVX3HbbbV7FhZofAZdYYwOLViG2AgGnWL/kM5/5jLz77rs91jAJVRkKJwESIIEYEUjd7A87e7wZY1VDrD8RZEVDrH8xbtw4aWhokLFjx9qL0frdS0S5yosFp2688ca8i3+p/FoVdilMzfxAZ71q1aquqxTbrgMF+oAFsBCgqzwQuHfAFWtuPPHEE4HunwJVicWGTKCQv6eQq0bxJOBMoJjGcvzWRY2DBx0D17UORr56eBmnVXlVQGS++AqVP58OYZ3PFl+B2BXoVqh/1ngPsFS7UHIDsLDuhOKQW+jfU3FQZC2SRCD1ngplajktHa3OefmrYx2MfOV5efux5sWbNYYX4K5Xb9v2sqz57eei+o6pmNgfBNMw4bVAghcDa4NgZcsok907wSW2o6Sf/LLi8HtKPkXWIFEEkmQBhamrepPPNVXQTflqRcswt8z28vZjz4s3bsxMQH2dkj2/U54ojqEdMNXUug04vBg4Bh2j+Gf3TqjZKPibjV8UbFhGcgjE5feUHGLUNOkE6KmwmIBqUyunDcMs2fJ+xNss9ncIK74Cbz+XL192tTKj05tSrvgKp/x5KxxCBuWZgGi1aik+RxFf4eSdwAql2KUWG4Fxv44QGrxIRcbl91SkeFmtOBJIulWkW3+16BL2pgiSwoyvgBfEvlhUNl2d3pTwlo09KJzWWXDKn0122MeVZwIsrSms+Ap4QazeCesiVtCB3glrK/CzGwJx+j250Zd5SCAogdQufpULnHK9B+1EMMyQa6ghlw65zkEvyLV3tk7XZHuoqYBI/LWmbPmteaL8bF21VJWr6g9ddf2zB1zC4IKRAeMrqIGp9Obf9BGI2+8pfS3AGkdNgEaFA3F0WuhM3HoDHESYh8KMr1Bv8fl2vMz1UEPHiXpajadc+bPVM+zj8EzY4ysU26BGBeRaPTZW7wS8FlY2YdeT8ouPQBx/T8VHmTWKEwEaFVlaQ73JW93hWbLmPKz2BbF2XDkv8HASsu2drf3yfA81eGXwT6V8+VW+KP8qzwS8M9ak2Po1LOzeCbQ1ZKEcuwfHWi4/k4BbAnH8PbnVnflIwA8BGhU5qMEQwEMhqPtbdVZhdFQYArF3ttYq5XuoKa+MMnry5bfKjvKz8szYh3zwHTp7+Wf3TkA2GEJGUCMySiYsK/4E4vp7ij85aphUAjQq8rScrvgKvBXbhxryFO36NDpEe2erLnbzUEOninzqr7o2bn+d4iugozIIUId8/6zeCRhUyuCzHo9bvalPvAjgd+J2WMzN7y9etaM2JBCMAKeU5pmSo5aOvv766zOmNua5rMdpyBk/frxMmjRJFi9e3ON8kAPnzp2TiRMnyoYNG3pMd3Q7pQ0LTv34xz+WnTt3wtAMok6o1z799NPmHivWBbxU/Q8dOpS1bOwfYuXDJbazouIJCwHcW2+//bacPHlSXnnlFdm/f795Fveam9+J29+fpUh+JIFEE6BR4aL5sH4FdjWdN2+eTJ8+3cUVzll07TPiJB1rY2AthV27dkm/fv26snh5qKHDnj9/vquHZVcBEX+wrl+xdu3arrU61NogTupgozLseIoNynD9Cy+8IDNmzJCqqipzszUrL6freSwdBLIZEOXl5XL77bfLTTfdZO6fg/vF7e/Kbb50EGYt00CARoXLVlaLLh05cqSHN8ClCDMb3rCxPfbp06ezLpXtRZ41L3ZJfemllzI8Kl4eauhw+/TpY+60GeeOVnkmYODB0FMJ9YexoJLdO8ElthUZ/sW9jmXg7R4IJwPCiZbb35XbfE5l8BgJJJJAsNGTdF3tNLXRD4Gw4yugp0pex3S95lflRP1Xzfywb5Cm4isQC6PGvfEX31E36/GodWZ5hSGA9kewNeJnlixZ0hV3g98hYpFwDyFOwkty+ztxm89L2cxLAnEmQE+FB1PQ6nq3Lh3tQYSZFXLCiq9QstesWWNuwe71Tclrfq9115kfngkM2VjjK9QbqFpKWw0LcYltneTjKwvtDy/g8ePH5cSJE3Lw4EEzTghDXcOHD5fBgwfLuHHjAg/xuf2duM0XX6LUjAQ8EoizxRNH3fBGgymJ2WZbuNVZzbQIYwoj3sqgoyrDrU7IV7g3qzbj/N5FRknWGRzDjem1/2jsbTqfUR14JvBPeSXUSesiVmgr+3mVj3+TTQD3OqZDwwOF2VW4f3E/5PJA6LjH3cpwmy/ZrUDtSaCbAD0VHo0wZNcVX+G0xbcPdRwvwdv7iy++aG4V7iZKXQkp/JvVO7KvZqLcdfSb0vTiTBnaG5p9LK2Hfyr/+5EaWdV0t9TtWyMzh11rqqziK/D2iX+f+9zn5A9/+IM89thj5gZgq1at6to+XdWRf5NJAF4IxAwh4PnYsWPmvY3N30aMGGG28aBBg1y1tY573K0Mt/mS2SLUmgQcCHTbF/zkhYCKr/A6FmsvA29Y8CqE8SaNMWOvb0pe89vrE/z7WWNv9WhDKuqMprZMaW1NdUaFiFFSvdew+it+8pOfdI2TQ3/8gwcoDKaZGvFblATQrvjdwTMRZEE6Hfe4Wxlu80XJkWWRQJgEzPdAB1uDh/IQmDVrlvmGtGzZMnOaYp7sWU9jqiPG+5cuXZo1j98T0A0JnpViTq+99lpG9R566CFzCjCmkDIVFwHM9qmoqHDlkSiumrM2JJAMAjQqfLYTOqyVK1eabti6ujqfUsRcOwHBhrW1tWbAoW9BDhdCR0ybg+GCtTaSnNpbD8pzdT+VPSUz5Ym/uVU6Bj86anTjjTdmVG3AgAEZ3/mFBEiABEggIgJhukHSIDvb1Eavdde1z4hTuRgKcApmdMpbeHdt5/CHY8DmaKN679keamOYQw31IFgv6JBUjwJ4IBYEdN2bOuS4leE2XywAUwkS0ECAnoqAxhumLm7ZsiWwNwAuXaz8OG3atEDDKU7VwWqgf/ZnfyaYZpqYVFEnTW2GOfXPMD6SlsZ6qZ3+kay6a4LM2HxcLlkqAo8MAjKRduzYoX1RMUtR/EgCJEACJJCDAI2KHHDcnsLKjohA1xVfsWDBArdFu86HIRDM2ceMk+SlK6Vk9GR55CcvSF3Fu/LsrL+VnzV/mLxqUGMSIAESKHICNCo0NbDO+ApMl8PCTjoT3uYRu1FZWZnc+Ire18mgkaUiclKazlh9FTpJURYJkAAJkIBfAjQq/JKzXYe9MrALJjbkCjLbon///uYwBfawwGqQOhNk796929wvA3P+E5fa/yDvv/ORiNwkZf37Jk59KkwCJEACxU6ARoXGFtYVXzF27FhZt26duesoFnfSmRC7MWbMmGTFV4hIe+th2f7U92Te5nelfNEcuXvIVTqxUBYJkAAJkIAGAlxRUwNEu4jq6mpz1b9t27Z1bc1tz5PvOzwJKrYiyD4jTuVA9tSpU+Wb3/ymOeffmqdwKwC2y4V9j8mwu34grVaFrJ/Lq6Xu21+Vu+8ZLSUO5nDhdLcqyc9hEdDVvjrkuJXhNl9YzCiXBKImQKMiBOLotHVsGIa1JTBzAwv+IBhUZ4JsrOdg34I9yQ/BJOuus22LVZau9tUhx60Mt/mKtc1Yr/QRoFERUptjf4KysjIzhgFDDn6Trn1GnMrHTJAf//jHYvWoJPkhmGTdndqHxzIJ6GpfHXLcynCbL7Om/EYCySXg4ERObmXipPnQoUOlvr4+8GyLsOMrvvSlL4WyRHic2oK6kAAJkAAJREOARkWInDF0UVVVFXi2hdpnpKamRvvCWJD93nvvaV8iPESsqRCN4Sl4qfCmy0QCJEACSSFAoyLklsKCWC0tLYFmW+jaZ8SpqpCNzcyefPJJM7jUKQ+PhUtAGRBYmwRBvjAkEEdz4MCBcAumdBIgARLQTIAxFZqBOonTFV+BdStGjRolDQ0NgmERnQlvxVh189ChQ+bS2DplRyUrCePXmCL89ttvy8mTJ+WVV16R/fv3m3jKy8vl9ttvl5tuusmMxYGxh5SEOiWtff0yhfH31ltvyZtvvilYR8YwjLxV91tWXsHMQAIxJUCjIqKG2b59u0yZMsXcNRTxFn4T3maxMibkYTErnQlysXiXm4elznJ1yYrbA9yNAYEdVrFwWrYUtzpl0zOK47pYuJGTr+3wW3bzO3FTVhTsWAYJREWARkVUpEVkxYoV5oZXcGurN1E/xc+ZM8e8bO3atYHk2MvGVNg+ffrIu+++m7Ojs18Xl++FfICDHbaZhycJcTROHoh8BoQTx0LWyUmfQh7TxcIuJ58BAe+Rve3sMrJxcZsv2/U8TgJJI0CjIsIWU4tOwVOhdtX0UzweghMnTjTXrsDYO1MHgage4GhHrO9x/PhxOXHihLlR286dO01jora21hyeGjhwoBZPUlR1SsI9pIOFMpwxMyvb8JPdgHBi41YXt/mcyuAxEkgiARoVEbeaWnQKDzXMDvGbwoyv8KtToa8L4wGey4AYPny4DB48WKwGhG4ddMsrdBsFKd8ri2xtBx22bNnSo+286OZWF7f5vJTNvCQQZwI0KgrQOlh0CruFwl0e1/iKAmAJXKSOBziCak+dOiWNjY1dHojZs2fLHXfc4aoT0qGDFYRueVbZSfuci0U2AwJDUXbjL5cct0zcynCbz225zEcCcSdAo6JALaQzvuLs2bMZq2IWqEoFL9bvAxzXwXDYtGmT+XfEiBGmsTdo0CDPRp9fHbLB0y0vWzlJOG5lEcT4s8rxW2+3Mtzm86sHryOBuBGgUVGgFsGbFTb1ChpfATk69hkpEAatxfp9gOO6oF4jVRG/Oqjr7X91y7PLT9J3sNBh/Olg6laG23xJagfqSgK5CNCoyEUn5HO64it0rYMRcnVDF+/3Ae73OqcK6ZQF+brlOemclGNgocP408HUrQy3+ZLSBtSTBPIRoFGRj1DI53VtGKbWwbDvOhqy+rES7/cB7vc6p8rrlAX5uuU56ZyUY7pY6JDjVobbfElpA+pJAvkI0KjIRyiC81h0Cota7dq1K9D6EFjiGV4L666jEagfmyL8PsD9XudUcZ2yIF+3PCedk3JMFwsdctzKcJsvKW1APUkgHwEaFfkIRXAecRELFiwwS9q4caPvEtMeX+H3Ae73OqeG0ikL8nXLc9I5Kcd0sdAhx60Mt/mS0gbUkwTyEaBRkY9QROcRX4F1K7CY1fTp032Xmub4Cr8PcL/XOTWSTlmQr1uek85JOaaLhQ45bmW4zZeUNqCeJJCPAI2KfIQiPK87vkJHUFuE1Q9clN8HuN/rnBTWKQvydctz0jkpx3Sx0CHHrQy3+ZLSBtSTBPIRoFGRj1DE53XFV+haByPi6gcqzu8D3O91TsrqlAX5uuU56ZyUY7pY6JDjVobbfElpA+pJAvkI0KjIRyji8zrjK3SsgxFx9QMV5/cB7vc6J2V1yoJ83fKcdE7KMV0sdMhxK8NtvqS0AfUkgXwEaFTkI1SA8yq+ArEVQTYM07UORgEQ+CrS7wPc73VOSuqUBfm65TnpnJRjuljokONWhtt8SWkD6kkC+QjQqMhHqEDnVXxFQ0ODjB071rcWuvYZ8a1AhBf6fYD7vc6pajplQb5ueU46J+WYLhY65LiV4TZfUtqAepJAPgK982XgeS8ELkjzvp3y89UzZEjNPrngeOnH0nr4OamZUCq9et0iM9a8LK3tPTPCkMBOigsXLhR4HPymiooKWb58uUybNk0wtMJEAiRAAiRAAmERoFGhjeyH0rx5oSzb8owsqHpWLjvKbZdLh38k33jkpFQ+f0qMtl0y4+wP5BtPHZRLDvkx/IHNrZYtWxbIIIBhUlpaKkuXLnUohYdIgAS8EDh37pyX7MxLAqkiwOEP3c3dfkI2332nPDZyq5xYeadca5VvnpslTTU7ZeWd13WcubBPaoatl7L9z8rMoVdZc5uf8QCbOHGiuXYF4yt64Mk44NfV7Pe6jMI7v+iUBZG65TnpnJRjulh4kQPvHpa+P378uJw4cUJ27Nghhw4dMpEZhpEXnZey8gpjBhJIAIFPJEDHolGx/Y3/Iz/dc4N8bV3f7jpd+0WpvP+3srLhlDwwdJjYXUf9+vWTDRs2yKhRo8x/fuMr+vfvL7t375bKyko5cuSIjBw5slsHfooNAQx1vfXWW/Lmm2+aHVlsFEuBInYD4uDBg7Jz506pqqqS4cOHm7sBw3uI3xITCZCAMwF7H+aci0c1EPhQ3mjYJXtKhsigz19pk/eR7Pnp/5E3HGIrkBEGgK74inXr1sncuXOFLlxbExTgKwwIBORi3xfs24K3WnijDhw4IH379jW3+S6AWqkoEgYEVp/FRnxY02XSpEnSp08f2bRpk1y6dMk0ILBmDLwRq1atMj2FMOhpUKTi9mAlAxCgpyIAPG+XXpIzTSdFbpko/ft6t+XwhvTSSy+Z8RVr166Vq6++2lvxnblnzZolx44dk5qaGgmyz4ivwlN8EYy4t99+W06ePCmvvPKK7N+/36RRXl4ut99+u3zjG98w29Zvu6YYrauqw4A4deqUaUjgAhgQs2fPNmOWbr31VtNowNAGEwmQQDACNCqC8Yv06pUrV5rxFXV1db7Xr0CnhYBN7DOCN2QYK0x6CbgxIB599NFAO9Lq1bi4pFkNCBjQ8D4oA2Lo0KGStuXri6t1WZu4E6BREVkL9ZX+ZTeJPPeGnLnULkOv9e6tQHzF1q1bpaysTPBwxHRRPwku3DVr1si4cePki1/8IuMr/EDsvAZudHRSygOBwwistXogaEAEAJznUgwhvfbaa6YHwsmAwG+EHrk8EHmaBDQSoFGhEWZuUVfJkHETpULeyMzW/o6cOvq+VHztL2SICzsDxkR9fb0ZcImodL9jvBgfVvEVu3bt4ltzZqs4fssXyHfvvfdKbW2tIMCPKRwCiEFRQaxgDeZjxoyRYcOGmUZ2kKHBcDSmVBJIFwFOKdXd3pqnlGZTD4F9cPNu27bNd3wFOskFCxaYRRTD25zf6XtO1+UzIAYPHiwDBw7sYdQ5ycrWhm6O65bnpsy45gELLOQGAwKzMQYMGOD73o+qjmy/qEiznLgQoFGhuyVyGRWCxa9+KPc8ckG++/wiufNzZ2XfYw/K9/t9T37xyBixTDTNqxU6vfHjx5tR64sXL86bP1sGuI8RX4HYiiDrYGSTH+Vxvw9wXIchDATyNTY2mp4GTCXEOPwdd9wh2QwIp7r51cFJFo7plpetHB4PhwDbLxyulBpfAjQqtLVNu1zY95gMu+sH0tol8z6pa7IvavWxtB7cKI9OmifPtlZI9TPfl2/fP0ZKXAx9dInt/ABPBeIrsP6E3/gKiNK1z4hdv6i/+32A4zprIN+gQYPMmBU/+vvVIVtZuuVlKyeq4whifeedd3zzjUpPXeUUW/vp4kI5xUuARkXC2xbz7KdMmWKu+uc3vgIIMBME8/IhL4icQuL0+wD3e51TXXXKgnzd8px0DutYtlkwWJHSzWqUYekVpdwkt1+UnFhW8RCgUVEEbakjvgIY5syZY9JIarCb3we43+ucbh2dsiBftzwnnXUcs8egqOWs1WqUmGV04403mgHBSamTDi5pqqsOXpSRfAI0KpLfhuZmY4ivwDRGrP7nN+HNUsc+I37LD3qd3we43+uc9NUpC/J1y3PS2esxuwFhX846XwxKHOvklYHb/Gmqq1smzFfcBGhUFEn7IuAS0fCYborAS7/p6NGj5h4jDQ0N4nefEb9lB73O7wPc73VO+uqUBfm65TnpnOtYUAPCSXah6+SkU1jH0lTXsBhSbrII0KhIVnvl1HbPnj3m+hVBVwxManyF3we43+ucGkOnLMjXLc9JZ+uxfKtRfuELXwgccxN1naz1i/pzmuoaNVuWF08CNCri2S6+tcLmSBjPxqZUQfaRSGJ8hd8HuN/rnBpJpyzXNIhHAAAUJElEQVTI1y3PqnM+AyLILBhrOfbPYdbJXlahv6eproVmzfLjQYBGRTzaQZsWcFdPnTrVnLKXtvgKvw9wv9c5NZpOWZCvS16+5azDMiCiYORURlyO6Wq/uNSHepBAPgI0KvIRSuB5XfEVutbBiAqh3we43+uc6qVTFuT7kYf2f+utt7IuZ13o1Sj91MmJdRKOpamuSWgP6hg+ARoV4TMuSAm64it0rYMRBQS/D3C/1znVSacsyPcqD/mt+2EU2oCIgpFTGXE55rX94qI39SABvwRoVPgll4DrdMVX6FoHI2xkfh/gfq9zqo9OWZDvVZ7X/E51CPtYEnTUxSBNddXFjHKSTcDH4tDJrnCatF+4cKGMGDGia9Mwv3VftmyZtLS0mNul+5XB67wRwJohmN7LRAIkQAJJIkBPRZJay4euGF/HuhXYLAybhvlNSYiv8PtW6Pc6J5Z+ZGVbzhqLmWF7by9LWvsp36keYR5Lgo666p+muupiRjnJJkCjItnt50p7tWHYkSNHZOTIka6uccoU9/gKvw9wv9c5Mcony76YVK7lrJ3k5zuWr/x810dxPgk66uKQprrqYkY5ySZAoyLZ7edae2wWhkWtdu3aZe6/4PpCW8Y4x1f4fYD7vc6GxvxqlWU3ILwuZ+0kP98xa/n58hbqfBJ01MUmTXXVxYxykk2ARkWy28+19ujgFixYYObfuHGj6+vsGSFHxz4jdrk6vvt9gPu9zqqzMiCwFf3y5cslCgPCWr76rKMuSlZYf5Ogo666p6muuphRTrIJ0KhIdvt50l5XfIWudTA8Ke8is98HuJ/rsq1GuWnTJtm9e7foWM7aRZV7ZPFTlx5CQj6QBB11IUhTXXUxo5xkE6BRkez286y9rvgKXetgeK5Ajgv8PsDzXZfNgMDMmqFDh0qUq1HmqL55Kl9d8l0fxfkk6KiLQ5rqqosZ5SSbAI2KZLefL+1VfAUCL/v37+9LBi7StQ6GbwVsF/p9gFuvgxfmtddeExgSx44dE3geZs+ebU7NjZsBYau++dVaF6fzcTiWBB11cUpTXXUxo5xkE6BRkez286W9Nb5i7dq1vjcegxwd+4z4qoTDRX4f4LiuqqrKnL4Z99UoHaqdccgvgwwhIX9Jgo66EKSprrqYUU6yCdCoSHb7+dYeayNMnDjRXLsCa1j4TXGKr/D7AMd12C5+wIABvg0sv/x0X+eXgW49cslLgo659PdyLk119cKFeYuXAI2K4m3bvDXDio2jRo2ShoYGGTt2bN782TLEJb6CD3Dvy3pna9Mwj6epndJU1zDvGcpODgEu052cttKuKRbC2rJli2A5b3gc/KaKigpzGuW0adMEQyJMJEACJEAC6SRAT0U62z2j1nPmzDG/B42v0LEORoZiHr/wrZCeCo+3TOjZeU+GjpgFxIwAPRUxa5BCqLNy5UpzpkNdXZ3v4q+++mpZunSpKQcrdzKlmwBidjDLaMyYMTJp0iTBdyYSIIHiJ0BPRfG3sasa6oqv0LUOhiulbZn4VhgPT4UKAj506FBXC1njdtLUTmmqa1dj80OqCdBTkerm7668iq8YN25coPgKBHyuW7dO5s6dy7fTbryp+rR+/XqxGhSo/M0335wqBqwsCaSVAI2KtLa8Q72xNTrWa8AU0yABl7NmzTIXi6qpqXEohYeKncB//ud/ZlQRXop+/fplHOMXEiCB4iRAo6I429V3rZYtWyYtLS2yZs0a3zIYX+EbXVFc+MADD5jGKTZWw/ofQaYrFwWQjEq0y4V9i6W0Vy/B0EjPf6UyoWajbN/XLJcyruMXEkgGAcZUJKOdItUSS1Rjt01sjIXpon5T1PEVHL+OR0xFvvslDe2k1m4BC0zbhhcwM70j+2omyl1HvylNL86UoebrXbtcat4vP6tbKbNW7ZGS6c/Ivh/dL8P68t0vkx2/xZkA79Y4t06BdMMeF/X19VJZWaktviLIOhgFwsBiScAXAQSq4rej0owZM1z+jnpL36F3ysyVL8jrdTNFnl0k//f6RnosFEj+TQQBGhWJaKbolZw8ebLW+AoMqwSJ04ieAEskAfcE4N2DdwLTaB966KEeF16+fLnHsewHrpVhD3xPnp75WdlftVp+1vxh9qw8QwIxI0CjImYNEid1dMVX6FgHI05cqEu6CcDrhqE9rMeCheMwnIPhwscee0zefvttgUFeXl7eBem2224z95XpOuDmQ+/PyfCxmDHTID9tOCXtbq5hHhKIAYFPxEAHqhBTAgi43Lp1q/nAvPXWW33HVyDyf8OGDeY+I9hrhIF7MW1wqtWDAAyIt956S9588005fvy4uZMtMsFQgOFw9913y8MPPyw33nhjxgwX7Hb74osvmvKQD78lb+lK+fygIVIiL8irTS1ySYbJtd4EMDcJFIQAjYqCYE9Oodb4CkTy47ufpNbBwD4j27dvl/79+/sRw2tIIDQC+QyI22+/XY4cOdLDgHBSCEYEPBZMJJA2AjQq0tbiPuqLhyOmB2LDsAMHDvh46+ooFBHwL730kmBYJcg+Iz6qwEtIIIMAgikxVHHy5El55ZVXZP/+/V0LdmGtluHDh5u79w4cOLBABvDH8rtTb0irlEhFWan0zdCeX0ggvgRoVMS3bWKlGTwMBw8eNPf3WLVqlW/dEF8xceJEwT4jWGSLiQTCJuDGgMBwReEMCAcC7b+X4y+/LlIyWR6svEkY/ObAiIdiSYBGRSybJX5KwZ2LyPYBAwYI3MB+XbuMr4hf2xaTRphhhGE6Jw/E7Nmz5Y477pDYGRA9GuCCnHjmb2Xe5nelvHa6VNxwZY8cPEACcSVAoyKuLRNDvRAHgQWxMAef8RUxbKCUqQQD4vTp02YA5YkTJ0xP2s6dO00KMCBGjBghTzzxhAwaNMh3LFC0SK2LX70q5Yu2yPPfGcOhj2gbgaUFJMAVNQMCTOPlK1askB07dgSKrwC36upqwfz+bdu2+Y7TsPJPw0qN1vo6fU4CAz86ujEgEEQcpQGBwE7vAcdYpvsxGXbXD6TVqQFluEyvXSSTJ0yQe0aXcNjDkREPxpkAjYo4t05MdcMDfurUqebbX5D4CsgZP368TJo0SRYvXhy4tn46q8CFxkxAEhi40RHG5qlTp6SxsTHDA4GhizFjxgimOEdpQDg1M4YDsVYFApCxuy9mODGRQNoJ0KhI+x3gs/54S0N8hfO+Bu6F6tpnBCW66azca5bMnElgYNdRGRD4e+zYMdm0aZMJXxkQw4YNM2dj4H7zvt5DeO1o3d8DpWDtChoY4fGm5GQQoFGRjHaKpZa6NgzDuhVTpkwxx8e9u5O70dg7q+4z6fkUdwbKiFy3bl2iDAinO0jVxekcDQwnKjyWBgI0KtLQyiHWUbmAd+3albGioNcidcRXxL1D9crET/44MbAuJoX1SZQHQq1GiVlEN910k7lia5w8EF64g3e+hPoG/X3kK4PnSSAuBGhUxKUlEqoH4iIWLFhgar9x40bftdARXxGnDtU3iIAXFoqB1YBwWs5aGRD25awDVrfgl3/1q1+VF154IaceDQ0NXJo+JyGeLCYCNCqKqTULVBd0KFi3AotZYUzZb1LuZExbraio8CymUB2qZ0VDvCAKBmk1IKz1tnpesjUnPBRckj4bHR4vVgI0Koq1ZSOul+74Cj/rYETRoUaM1XNxuhm4WY1y8ODB8VqN0jO1nhdYDYhcnhdsNPbXf/3XPQTQoOiBhAdSQoBGRUoaOopq6oqv8LsOhu4ONQpmussIwoAGhPNOpLmGbpR3zdqOWHiLe9tYifBzmgjQqEhTa4dcV53xFX7WwQjSoYaMJjLxbhmgrfItZ12MHgi74VRbW9vVNmojMdT75ptvdh14DOYq0aBQJPg3rQRoVKS15UOqt4qvQGxFkA3DIAfrEtTX17veZ8RthxpS1WMh1okBDIh8y1lHvRplFLDsBoTTTqQ6DKc5c+aYM1swTTbIPR8FE5ZBAmEToFERNuEUyj969KiMGjXK3Dp67NixvgmoxYXcxlc4dai+C0/ohWAAXogDyLYfBg2I/lpbF6tqIgUJUtaqEIWRQAEJ0KgoIPxiLhoPWsRYBI1+9xJfkUajAmP6cV/OWvd9HjfPC/RJ6jobutuG8kiARgXvgdAIwC2MFCRoDQ9st/EVxW5UKAMCf5O0nHWQGyxuBkSQuvBaEkgDARoVaWjlAtURY9oTJ0403cJBxppVfEW+fUaKyahIowGB2xT1dhq6wT4gX/rSl8xN7Aq9kViBfk4slgQSQYBGRSKaKblK6oqvcLMORlKNCuuaCNZFlazLWQ8fPtwMXC0mN3taDafk/pqpOQnkJ0CjIj8j5ghIQFd8Rb51MJJgVFgNiFyLKhXbctY0IAL+iHg5CSSEAI2KhDRU0tXUFV+Ra5+RuBkVaTUgVL2PHDmSEftR7J6XpP9GqT8J6CBAo0IHRcrIS0DFV0yaNEkWL16cN3+2DOiwsu0zUkijwu2aCF4WVcrGIE7HlQGB5arT5HmJUxtQFxKIEwEaFXFqjSLXBS7wsrIy8bthmMKTLb4iKqPCrQExcOBA6d9f75oIikEh/tKAKAR1lkkCySJAoyJZ7ZV4bbFuxZQpU8wVHoN0uE7xFWEYFZjSmG05a+uyzsVmQNgNJx3LWSf+5mUFSIAE8hKgUZEXETPoJlBdXW1OHdy2bZvvRYPQ2dvjK4IaFWldE8FuQIS1nLXu+4jySIAE4keARkX82qToNULnPX78eNEVX6H2GfFiVNCAOCmvvPKK0IAo+p8bK0gCkRKgUREpbhamCOiKr1DrYPzkJz+Rv/mbv5F3333XcXdJNaWxsbFRDh48KDt37jRVKeZFldJqOKl7jH9JgASiJ0CjInrmLLGTgK74irlz58rGjRtNqZi2uHr1avnwww/NIRYuZy2C7bhHjBjB1Sj5yyMBEgidAI2K0BGzgFwEcsVXqNkG+XY6xbCHPcEDMWbMGBk2bJgU62qUXM7a3ur8TgIkUGgCNCoK3QIpLx8ueqcNw9S25/X19ea6FLkwwXg4dOhQVxYEgH7961/v+p70D2roBn8L63lplwv7HpNhd/1AWhXUijppenGmDO2tDvAvCZBAmgl8Is2VZ90LTwB7WWB66IABA+T222+Xu+++W9asWSNLliwxlTtx4kReJZF/3LhxZj64+uGlSGrKZ0CAD6ayglfk+4C0n5Zf/cMvug0KKZGKr/2FDKFBkdTbjXqTgHYCNCq0I6VArwSwXgUWxKqsrJS77rpL9u7d2yXi/fff7/qc7QOGRy5fvmyufTF06NBs2WJ3XA3vZFvOuqAGRA9a7f9/e+cTEkUUx/GvG0SILCFeNjyI1a4XoVqPQrKVIWlC5CUCRaGDfyhBKigpw8A2CFMoApVc6mIUgoEmZYEGYlmXKPMkGAoFkbInwzV+s+067s6uQ27r7L7vgDjz3sy89/u8Yec7773f78H/8Rke5NzF0poH9qh8JpAACZAAQFHBp8BSBPSCQiomLo9mNvlqt7KgCAmIWOGsRUA0NDTAuguJ/cTUwGOMekdw0/ULx4uPwuOktDDzbPIcElCJAOdUqNTaFrRV5lTohzuMqri2tmaUvKU0KVeCZ3V1dSV8GGEzASHDPPn5+RYWENFoA7N9KHPVYTScVYqLT++i9VQBssJp3CEBElCdAEWF6k/ANtovL9+2tjb09PTErcX8/HxwDY3ADPrKPKgbDU8TNLjOjYuvRnDLk2OQF0zSlyshuLfSwxEZjTLdw1kHFqcxNDyAzjov3uAEbr9/hBb37pismUECJKAWAQ5/qNXelrJ2bGxsU0EhFZb5EtpmK0DtiwXUaF/N93AgSjwsY6avDb44VoqgkFVOQ94i4pZpVlRECgijaJQTExNIt3VA9DhtDjcqa92oKDuKq2eqcWfgA865OcdCz4j7JKAyAYoKlVt/m22X8Nrl5eXavImOjo7wiz6yWnNzcyZf/HYUnK5C0YfIOwSPZXXT5ubmDeXE8i4xIyDEyySdBYQxxWCqzXEEl1tr8PDsS7y/UgKPnS4g8XgxjwRUIUBRoUpLW9TO7OxsredAeg/kpS/hs/VDCFJtv99vqvaB2RcYwmGcKtkVdX5oufTIDAnZbSacdXt7O/Ly8kyKm8hS0vHYhqzcfSgsBHKzKCjSsYVpEwn8CwH+GvwLNV7zXwiIa6jX69VcQ7u7u8NlxOpNCJ+g7axg8dNnGDmg+ny+cByLjddAEzGZmZlwuVwYHh6G3W5HfX29tty5TBCV8N+NjY0oLS2loNgALwD/t+9wXzrJwFcbuPCABNQmwImaare/pa2XHoTx8XFtDQ95sYe2aE+EUE4Ver/6UOtc76mQwFpNTU2hEwz/Dw4OpnTALEOjEpq4gsXpl5jCQVS4HbBhBYtTfeh8vhcXrh+Dg58mCaXNm5FAKhPgz0Eqt16a111iT0gPgV5QrJssXh4/IL0Jwb8lfOk9hB3rJ0B6KDYTFHL66uqq7iruGhJYeofOoj3YkZGBPdVdeOv3oPUGBYUhKyaSgMIEKCoUbvz0Mt0OZ/FB6J0bZSKouKP29/fH7YmYnJxMLxQJt2YnHJ5reP1XwC30t+C0x8n4FAnnzBuSQOoToKhI/TakBX8J2JzHUakb+pBkCQEu4kKGOGIJDLNROwmaBEiABEggPgGKivh8mJtyBGSNinFMLweiah5LYEjMCnEh5UYCJEACJLA1AhQVW+PHqy1FQCYQ3sf5J7+xf5O4CZECw1JmsDIkQAIkkKIE6P2Rog2nZLUTFKZbSXY0mgRIgASSQICiIgmQWQQJkAAJkAAJqECAwx8qtDJtJAESIAESIIEkEKCoSAJkFkECJEACJEACKhCgqFChlWkjCZAACZAACSSBAEVFEiCzCBIgARIgARJQgcAfN3/zFqCqzEgAAAAASUVORK5CYII="></p>
<p>Each panel is 1.6 m long and 0.95 m wide. All the panels must be arranged in uniform rows, with <strong>the shorter edge</strong> of each panel parallel to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}}">
<mrow>
<mtext>AB</mtext>
</mrow>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AC}}">
<mrow>
<mtext>AC</mtext>
</mrow>
</math></span>. Each panel must be at least 0.3 m from the edge of the roof and the top of the roof, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AF}}">
<mrow>
<mtext>AF</mtext>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Olivia estimates that the solar panels will cover an area of 29 m<sup>2</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}}">
<mrow>
<mtext>AB</mtext>
</mrow>
</math></span>, giving your answer to <strong>four significant figures</strong>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total area of the two rectangles that make up the roof.</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 maximum number of complete panels that can be fitted to the whole roof.</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 percentage error in her estimate.</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>Olivia investigates arranging the panels, such that <strong>the longer edge</strong> of each panel is parallel to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}}">
<mrow>
<mtext>AB</mtext>
</mrow>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AC}}">
<mrow>
<mtext>AC</mtext>
</mrow>
</math></span>.<br><br>State whether this new arrangement will allow Olivia to fit more solar panels to the roof. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A company is designing a new logo. The logo is created by removing two equal segments from a rectangle, as shown in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The rectangle measures <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mtext>cm</mtext></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mtext>cm</mtext></math>. The points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> lie on a circle, with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mtext>cm</mtext></math>, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext><mo>=</mo><mi>θ</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>θ</mi><mo><</mo><mi>π</mi></math>. This information is shown in the following diagram.</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 area of one of the shaded segments in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>.</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>Given that the area of the logo is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>4</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Using geometry software, Pedro draws a quadrilateral <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCD</mtext></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>8</mn><mo> </mo><mtext>cm</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CD</mtext><mo>=</mo><mn>9</mn><mo> </mo><mtext>cm</mtext></math>. Angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BAD</mtext><mo>=</mo><mn>51</mn><mo>.</mo><mn>5</mn><mo>°</mo></math> and angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ADB</mtext><mo>=</mo><mn>52</mn><mo>.</mo><mn>5</mn><mo>°</mo></math>. This information is shown in the diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CE</mtext><mo>=</mo><mn>7</mn><mo> </mo><mtext>cm</mtext></math>, where point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math> is the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext></math>.</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>Show that angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>EDC</mtext><mo>=</mo><mn>48</mn><mo>.</mo><mn>0</mn><mo>°</mo></math>, correct to three significant figures.</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>Calculate the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BDC</mtext></math>.</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>Pedro draws a circle, with centre at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math>, passing through point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. Part of the circle is shown in the diagram.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Show that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> lies outside this circle. Justify your reasoning.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>A Ferris wheel with diameter <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>110</mn></math> metres rotates at a constant speed. The lowest point on the wheel is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> metres above the ground, as shown on the following diagram. <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> is a point on the wheel. The wheel starts moving with <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> at the lowest point and completes one revolution in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> minutes.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" 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"></p>
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> metres, of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> above the ground after <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> minutes is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mi>cos</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>c</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>c</mi><mo> </mo><mo>∈</mo><mo> </mo><mi mathvariant="normal">ℝ</mi></math>.</p>
<p>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a water wheel with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> metres. Water flows into buckets, turning the wheel clockwise at a constant speed.</p>
<p><br>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> metres, of the top of a bucket above the ground <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds after it passes through point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>13</mn><mo>+</mo><mn>8</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mi>t</mi></mrow></mfenced><mo>-</mo><mn>6</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mi>t</mi></mrow></mfenced></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="specification">
<p>A bucket moves around to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> which is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>06</mn></math> metres above the ground. It takes <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> seconds for the top of this bucket to go from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
</div>
<div class="specification">
<p>The chord <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mtext>AB</mtext><mo>]</mo></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>0</mn></math> metres, correct to three significant figures.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> above the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of seconds it takes for the water wheel to complete one rotation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the number of rotations the water wheel makes in one hour.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></math>.</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>Determine the rate of change of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> when the top of the bucket is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Two points P and Q have coordinates (3, 2, 5) and (7, 4, 9) respectively.</p>
</div>
<div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\mathop {{\text{PR}}}\limits^ \to }">
<mrow>
<mover>
<mrow>
<mrow>
<mtext>PR</mtext>
</mrow>
</mrow>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</math></span> = 6<em><strong>i</strong></em> − <em><strong>j</strong></em> + 3<em><strong>k</strong></em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{PQ}}}\limits^ \to "> <mover> <mrow> <mrow> <mtext>PQ</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\mathop {{\text{PQ}}}\limits^ \to } \right|"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>PQ</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle between PQ and PR.</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>Find the area of triangle PQR.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise find the shortest distance from R to the line through P and Q.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The Tower of Pisa is well known worldwide for how it leans.</p>
<p>Giovanni visits the Tower and wants to investigate how much it is leaning. He draws a diagram showing a non-right triangle, ABC.</p>
<p>On Giovanni’s diagram the length of AB is 56 m, the length of BC is 37 m, and angle ACB is 60°. AX is the perpendicular height from A to BC.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Giovanni’s tourist guidebook says that the actual horizontal displacement of the Tower, BX, is 3.9 metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative to the<br>horizontal, is 85° to the nearest degree.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni's diagram to calculate the length of AX.</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>Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error on Giovanni’s diagram.</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>Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is formed.</p>
<p><img 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"></p>
<p>Find the angle of elevation of A from D.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the points A(−3, 4, 2) and B(8, −1, 5).</p>
</div>
<div class="specification">
<p>A line <em>L</em> has vector equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \left( {\begin{array}{*{20}{c}} 2 \\ 0 \\ { - 5} \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 1 \\ { - 2} \\ 2 \end{array}} \right)">
<mi>r</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>5</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. The point C (5, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>, 1) lies on line <em>L</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AB}}} "> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\overrightarrow {{\text{AB}}} } \right|"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> </mrow> <mo>|</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AC}}} = \left( {\begin{array}{*{20}{c}} 8 \\ { - 10} \\ { - 1} \end{array}} \right)"> <mover> <mrow> <mtext>AC</mtext> </mrow> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>10</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AB}}} "> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AC}}} "> <mover> <mrow> <mtext>AC</mtext> </mrow> <mo>→</mo> </mover> </math></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>Find the area of triangle ABC.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> with respective equations</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}\,{\text{:}}\,y = - \frac{2}{3}x + 9">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>:</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mn>9</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}{\text{:}}\,y = \frac{2}{5}x - \frac{{19}}{5}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mtext>:</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mfrac>
<mrow>
<mn>19</mn>
</mrow>
<mn>5</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="specification">
<p>A third line, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_3}">
<mrow>
<msub>
<mi>L</mi>
<mn>3</mn>
</msub>
</mrow>
</math></span>, has gradient <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{3}{4}">
<mo>−<!-- − --></mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the point of intersection of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></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>Write down a direction vector for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_3}"> <mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> </mrow> </math></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 class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_3}"> <mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> </mrow> </math></span> passes through the intersection of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span>.</p>
<p>Write down a vector equation for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_3}"> <mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A pan, in which to cook a pizza, is in the shape of a cylinder. The pan has a diameter of 35 cm and a height of 0.5 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.14.51.png" alt="M17/5/MATSD/SP2/ENG/TZ1/04"></p>
</div>
<div class="specification">
<p>A chef had enough pizza dough to exactly fill the pan. The dough was in the shape of a sphere.</p>
</div>
<div class="specification">
<p>The pizza was cooked in a hot oven. Once taken out of the oven, the pizza was placed in a dining room.</p>
<p>The temperature, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span>, of the pizza, in degrees Celsius, °C, can be modelled by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="P(t) = a{(2.06)^{ - t}} + 19,{\text{ }}t \geqslant 0">
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mo>−<!-- − --></mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>t</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span></p>
<p>where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> is a constant and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the time, in minutes, since the pizza was taken out of the oven.</p>
<p>When the pizza was taken out of the oven its temperature was 230 °C.</p>
</div>
<div class="specification">
<p>The pizza can be eaten once its temperature drops to 45 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of this pan.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius of the sphere in cm, correct to one decimal place.</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></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>Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.</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>Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can be eaten.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of this model, state what the value of 19 represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The depth of water in a port is modelled by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d(t) = p\cos qt + 7.5">
<mi>d</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>p</mi>
<mi>cos</mi>
<mo><!-- --></mo>
<mi>q</mi>
<mi>t</mi>
<mo>+</mo>
<mn>7.5</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 12">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>12</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the number of hours after high tide.</p>
<p>At high tide, the depth is 9.7 metres.</p>
<p>At low tide, which is 7 hours later, the depth is 5.3 metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></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>Use the model to find the depth of the water 10 hours after high tide.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows a circle, centre O, with radius 4 cm. Points A and B lie on the circumference of the circle and AÔB = <em>θ</em> , where 0 ≤ <em>θ</em> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π<!-- π --></mi>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the shaded region, in terms of <em>θ</em>.</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>The area of the shaded region is 12 cm<sup>2</sup>. Find the value of<em> θ</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A restaurant serves desserts in glasses in the shape of a cone and in the shape of a hemisphere. The diameter of a cone shaped glass is 7.2 cm and the height of the cone is 11.8 cm as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.40.46.png" alt="N17/5/MATSD/SP2/ENG/TZ0/06"></p>
</div>
<div class="specification">
<p>The volume of a hemisphere shaped glass is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="225{\text{ c}}{{\text{m}}^3}">
<mn>225</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The restaurant offers two types of dessert.</p>
<p>The <strong>regular dessert </strong>is a hemisphere shaped glass completely filled with chocolate mousse. The cost, to the restaurant, of the chocolate mousse for one regular dessert is $1.89.</p>
</div>
<div class="specification">
<p>The <strong>special dessert </strong>is a cone shaped glass filled with two ingredients. It is first filled with orange paste to half of its height and then with chocolate mousse for the remaining volume.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.44.32.png" alt="N17/5/MATSD/SP2/ENG/TZ0/06.d.e.f"></p>
</div>
<div class="specification">
<p>The cost, to the restaurant, of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100{\text{ c}}{{\text{m}}^3}">
<mn>100</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span> of orange paste is $7.42.</p>
</div>
<div class="specification">
<p>A chef at the restaurant prepares 50 desserts; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> regular desserts and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> special desserts. The cost of the ingredients for the 50 desserts is $111.44.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume of a cone shaped glass is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="160{\text{ c}}{{\text{m}}^3}">
<mn>160</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>, correct to 3 significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, of a hemisphere shaped glass.</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 cost of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100{\text{ c}}{{\text{m}}^3}">
<mn>100</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span> of chocolate mousse.</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>Show that there is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20{\text{ c}}{{\text{m}}^3}">
<mn>20</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span> of orange paste in each special dessert.</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>Find the total cost of the ingredients of one special dessert.</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Abdallah owns a plot of land, near the river Nile, in the form of a quadrilateral ABCD.</p>
<p>The lengths of the sides are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = {\text{40 m, BC}} = {\text{115 m, CD}} = {\text{60 m, AD}} = {\text{84 m}}">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>40 m, BC</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>115 m, CD</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>60 m, AD</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>84 m</mtext>
</mrow>
</math></span> and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat AD}} = 90^\circ ">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">A</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">D</mi>
</mrow>
</mrow>
<mo>=</mo>
<msup>
<mn>90</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span>.</p>
<p>This information is shown on the diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.24.18.png" alt="N17/5/MATSD/SP2/ENG/TZ0/03"></p>
</div>
<div class="specification">
<p>The formula that the ancient Egyptians used to estimate the area of a quadrilateral ABCD is</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{area}} = \frac{{({\text{AB}} + {\text{CD}})({\text{AD}} + {\text{BC}})}}{4}">
<mrow>
<mtext>area</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>+</mo>
<mrow>
<mtext>CD</mtext>
</mrow>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mrow>
<mtext>AD</mtext>
</mrow>
<mo>+</mo>
<mrow>
<mtext>BC</mtext>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mn>4</mn>
</mfrac>
</math></span>.</p>
<p>Abdallah uses this formula to estimate the area of his plot of land.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BD}} = 93{\text{ m}}">
<mrow>
<mtext>BD</mtext>
</mrow>
<mo>=</mo>
<mn>93</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span> correct to the nearest metre.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat CD}}">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">C</mi>
<mo stretchy="false">^</mo>
</mover>
</mrow>
<mi mathvariant="normal">D</mi>
</mrow>
</mrow>
</math></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>Find the area of ABCD.</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>Calculate Abdallah’s estimate for the area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error in Abdallah’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two straight fences meet at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and a field lies between them.</p>
<p>A horse is tied to a post, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>, by a rope of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> metres. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> is on one fence and point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math> is on the other, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PD</mtext><mo>=</mo><mtext>PE</mtext><mo>=</mo><mtext>PA</mtext><mo>=</mo><mi>r</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext><mover><mtext>P</mtext><mo>^</mo></mover><mtext>E</mtext><mo>=</mo><mi>θ</mi></math> radians. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATgAAAFSCAYAAABmEMNWAAAgAElEQVR4Ae2d3+9mRX3H/T9aqYQuKNlbu+KSRluEsmkEqySsvZMLNkq6eMNe2GpsZW8KeAU1BS8EFgR0N5ZdMdnQpKwiGDVhQyLRXrg14UqSNdxovDjN+8HPd8/37DznOXPOnPn5muTJ85zznHNm5vWZ5/3MzGd+vK8jQAACEKiUwPsqzRfZggAEINAhcBQCCECgWgIIXLWmJWMQgAACRxmAAASqJYDAVWtaMgYBCCBwlAEIQKBaAghctaYlYxCAAAJHGYAABLIm8Nhjj3YHD944K40I3Cxs3AQBCMQicPjwTd373/9n3alTT3tHicB5I+MGCEAgFoGzZ1/sjhy5vZPIHTt2r3e0CJw3Mm6AAARiEZCoqeZ24sQDm2bq5cuXvaJG4LxwcTEEIDCXwO9+97vu1Vdf7X7zm/+b9AiJmWpuChcuvLJppqo/zicgcD60uBYCEJhF4Ctf+fJGoNSXptddd326k+CNBYnZyZMP7l0isVNz1ScgcD60uBYCEPAm8Pzzz+0TNxO5L37x/tFnSdAuXnxj7xoJnu69dOnS3rldHxC4XYT4HgIQWERAtTUTteH7tgfLuTC81o59mqkI3DbCnIcABIIQmCNw5lwYJuDo0bv3+uWG37mOETgXFc5BAALBCNx33xectbHbbvuEMw55TbcN7NV3qsn1++acD/nTSQRujA7fQQACiwjIkXDLLX/TfeAD1+wTuRtv/GD35ptvXvVs62ez5mh/WMiw2TrF4YDAXYWYExCAQAgCEjfV0iRmr7/+WnfzzR/tPv7xj3WPPPLw5KEiS9OBwC0lyP0QgMBVBPriZjU1CZ08qjEDAheTNnFBoAECErSPfOTQpvZmY900uFfNThO7WBgQuFikiQcCDRCQgKmmpqapiZuy/YMfvLQRuNgIELjYxIkPApUS2CZuyq5mMmi4SOyAwMUmTnwQqJCAids993xuX83Nsipxk8jFDghcbOLEB4HKCNhUrLGpV+p/i+1gEGYErrLCRnYgEJPAFHFT7U4CN3UVkZDpR+BC0uRZEGiIwBRxEw5dJ8dDioDApaBOnBAonIAG66pW9sQTj+/MSSoHgxKGwO00DxdAAAJ9Aupr8+lT05ARCWKKgMCloE6cECiUgK+4KZsSQ42DSxEQuBTUiRMCBRKYI25aojyVg0GIEbgCCxpJhkBMApqRoHFschTII+oT1EenaVupAgKXijzxQqAAAq5J8z7JVq1Pg39TBQQuFXnihUDmBJaKm7Kn2lsqB4PiR+AyL2QkDwIpCGhQrryfevk2Sy29Ekj1v6kfLlVA4FKRJ14IZErA5pUOVwTxTa45GCR0qQICl4o88UIgQwKhxE1ZU9NUIpkyIHAp6RM3BDIiEFLclC05F+RkSBkQuJT0iRsCmRDQQFwNA5EghWpSysEwZSrXmggQuDXp8mwIFEBg6qR5n6zYEuUpHQxKLwLnYzWuhUBlBNYQNyFKtUT50DwI3JAIxxBohMBa4iZ8OTgYlA4ErpHCTDYh0CegJYx8VgTp3zvlc6olyodpQ+CGRDiGQOUE5kya90Uih4VqiKkDApfaAsQPgYgEYoibORjmzoAIiQOBC0mTZ0EgUwIa+iFxU81q7bXZrG8vBxQIXA5WIA0QWJGAxE0zCuYsdzQnWSmXKB+mF4EbEuEYAhURiC1uQpeLg0FpQeAqKsxkBQJ9AinETfGnXKK8n399RuCGRDiGQAUE1MGvZqleMfcjVbwplygfmg6BGxLhGAKFEwg9ad4HhxwM6uvLJSBwuViCdEAgAIGU4qbky1OrPrhcAgKXiyVIBwQWEjBxk8Co/y1FUJM45RLlwzwjcEMiHEOgQAI29kw1qJQhJweDOCBwKUsDcUMgAIFcxC2HJcqHOBG4IRGOIVAQgVzETchS74HqMhsC56LCOQgUQECCoiZhLn1eah6n3APVZTIEzkWFcxDInIDEROKmGlwuIfUeqC4OCJyLCucgkDGBHMVNXlsJbuolyodmQ+CGRDiGQMYEchQ34crRwaB0IXAZF2aSBgEjoBqS+rc0SyC3WpLSmMsS5cbL3hE4I8E7BDIlkGrSvA+OHPZAdaUXgXNR4RwEMiFQgrgJVQ57oLpMhsC5qHAOAhkQMHGTeGgaVq7BlijPsemMwOVaakhX0wRsXqnmdkrocg657IHqYoTAuahwDgIJCZQkbsKUq4NBaUPgEhZkoobAkEBp4qb057RE+ZAnAjckwjEEEhFQH5aGgcgjmXuztI9Iac5pRkU/bQhcnwafIZCIQE6T5n0QmIMhVycIAudjTa6FwAoEporbY489upkOpSlRly5d6uz47NkXV0jVtEda2qddHf8qBC4+c2KEwB4BEwhNwZoSJGZHjty+ETcTOIldqpDTHqguBgiciwrnIBCBgLyPviuCHDt270bgUtba+mhydjAonQhc31p8hkAkAnMnzR88eGN34sQDkVK5OxoJtMbB5RoQuFwtQ7qqJTBX3FRrs/63HODIsaD0xNx31TffCJwvMa6HwAICEre5wypOnnywUxM1l6D+Q+Ul54DA5Wwd0lYNAZtXKkGYO6Ti8OGbulOnns6GicQ6pz1QXWAQOBcVzkEgIIEQ4hYwOcEeldseqK6MIXAuKpyDQCACtYqb8OTuYFAaEbhABZnH5E1A/Vf6QQ5fR4/evRk0u0bq1fmuWo5ec5ula6QrxDNzXaJ8mDcEbkiE42oJXLjwykbgLl58Y5NHeSXVr6XX5cuXg+Zbgqb+thKWO5qT8Rz3QHXlA4FzUeFclQQkbKrBmcApkzYbQO+hQu3iJk5aEECv3AMCl7uFSF8wAi6Bs3NqwoYILYibOOW4B6rLfgiciwrnqiRgYtavwWnYhWp1IWpwNi5MwydqDnKciFmOS5QPuSNwQyIcV0vABM7ETMfqf9P0p6V9cL6T5kuGbA6GEvKAwJVgJdIYhIAJXN+TKi9qv0Y3J6KWxE18cl6ifGg/BG5IhONqCZjALRW0PiATNy0b1ErIdQ9UF38EzkWFc1USCC1wcyfNlw5Xw180TKSEgMCVYCXSGISArcah8XBLQ6viZkuUl+BgkI0RuKUlnfuLIDCcybBkWEir4iZD57wHqqsgInAuKpyDgIOAhkdI3NREK6UG48jGolNyMOS+gkg/gwhcnwafIbCFQM2T5rdk2Xk69yXKh4lG4IZEOIbAgADidgWIaq/yHJcSELhSLEU6kxBA3K5g1zQ0jSHUeykBgSvFUqQzOgH9kDXnstYVQXyB2pg/3/tSXo/ApaRP3NkQkNNAHega36WhEK1MmvcxQO57oLrygsC5qHCuKQI27MOmcH3wg9d311//l9TcBqVADgb9CZQUELiSrEVagxOwZpeJm71fe+1fdOp/I1whIDY574F6JaVXPiFwV1jwqUECqpGYqA3fWx3r5ioG5mDIeQ9UV7oROBcVzjVDAIGbZmr1TWqISGkBgSvNYqQ3KAHV0oY1Nx3Le0q4QkD9lCXNYLCUI3BGgvcmCTz88ENXCdwNNxwoaqxXDMNpqExpDgZxQeBilA7iyJLA/fcf34jb17/+SHfu7NnuyW99a/N6/fXXuz/+8Y9ZpjlVolSrLbFPEoFLVWKINymBvrjphzt8/e+vfpU0fTlFbs34Er3KCFxOJYm0RCFg495UcxsKmx0/+eS3urfffjtKenKPpJQ9UF0cETgXFc5VSUA1kM985h823sAXnn9+q7hJ5P7re9/rXnrp+1Vy8M1UKXuguvKFwLmocK46Av1J87vETQL3wwsXujOnT1fHYU6GStkD1ZU3BM5FhXNVEfAVN2um6v33v/99VSx8MyN2pToYlFcEztfiXF8UAf1Ab731E92hQx/uptTc+uKmz7/4xS+6P/zhD0XlOWRixUACV2pA4Eq1HOneScBWBLnllr/t/vvll0f73IbCZscvvPB899Zbb+2Mq9YLNPZNY+BKDQhcqZYj3aMEQoibRO4HL73UPfPMqdG4av6ypD1QXXZA4FxUOFc0AYmbZiMcOHBd9/1z52bV3KwGp3fV4lptppa0B6qr0CJwLiqcK5aAlvPRj1Jj3T7/+c93ap5qlkJfsOZ8Vl9ea6G0PVBd9kHgXFQ4VyQBW9tN4mbhy1/+l43gfeMb/7FI5FQrbK0WV9oeqGbz/jsC16fB52IJuMTNMmO1ujvvuGN2be673/lO96Mf/dAe2cS7HAwlriDSNw4C16fB5yIJjImbZUhNTK0c8qEP3dD942c/2/nU6NTE/devfnWzX0NLtbjS9kA1W/ffEbg+DT4XR0AboWiclkRuSpDQPf74f3a33nrL5r4777yju//48e6fv/SljehpRZGTDz64OZYQHjr0V5sm7vHj/9SdPv3d7p13fjslmiquKW0PVBd0BM5FhXNFELBJ81PFbZgpiZ2ar6rZPfTQv2+aY6q1HD9+fHOsSebqe2sxKN/64yg9/whci6W3gjwvFbclCN59990ltxdxrzX7i0jsSCIRuBE4fJUnAYmbmk+qfcUOqtGcP38+drTR4ytxD1QXJATORYVzWRJQk1LThiRuqZpOcjI89dSTXe21ODXVS1yifFhwEbghEY6zJJCDuBmYV175n+6Xv/ylHVb5rv63FDXk0DARuNBEeV5wAjmJW/DMZfhAczCUtgeqCyUC56LCuWwI6MemZqleIX9wly9f7o4du3fjKVRt5dSpp7PJc+qElLoHqosbAueiwrksCEjc1N8mcVMtLlSQuB05cnt34sQDm0eePfviRuh0fmrQfg3PPfftqZcXdZ2cOKXPYDDgCJyR4D0rAmuJmzIpYTt69O59+Z1Ti5PA/frXv973nBoO9IdSg4NBtkDgaiiRleVhTXG7dOnSpramWls/HDx4o3czVel87bUf9x9TxWeJvVZcqSEgcDVYsaI8aICpmqVqJq0RHnvs0U5i1g9qms6pwfWfUctnCZtYhOwSSMkGgUtJn7j3EbDR82uJmyJT35t+wK7XxYtv7EtPiwdqmmoXrVoCAleLJQvPRwxxEyIJm2px/XDy5INX1er634991sBf9cXVsspIyXuguuyEwLmocC4qAQ1LkPCs3bFt/W/DISFqsg5FzwfAuXNnk82s8EnnlGtVe5M9agkIXC2WLDQfao5K3FSDWzu4+tokdhI4nyEiw3TKk1rD/FT1u8kWtTgYZCcEblhaOY5GIKa4WabUB2dDRC5ceGUjbnondBthk8DVFBC4mqxZUF5SiJvwyJFw+PBNm5qKxA5xu1Jo1EWgMXA1BQSuJmsWkBc1g9SRraEgNTWFhP7MmdNFrzKi2QtrerBTFE8ELgX1RuOUuKmGkHK5ozXRa5URvUoNsktNDgbZAYErtTQWlu7axU3m0Bpxpc5PtT1QNTujpoDA1WTNTPNi4qYhCLX9gDJF7p0srf1Wm4NBEBA476LADT4EJGgSttArgvikgWt3E5CDoZYVRPq5ReD6NPgclIDETf06rYlbiSv+Sty0D0NtAYGrzaKZ5KdVcRN+LWeu2Q0lhViDrWMzQeBiE28gPg3/UM1Nw0HU/9ZaKG1jGv0ZSeD0XltA4GqzaOL8xJo0nzibO6MvafK9bKY/pBoDAlejVRPlCXHzA68pY6o5aWaFgh0vmRfrl4L3rq5lD1RX3hE4FxXOeRNA3K5Gpibfz3/+s6u/6J3RUk16aQMcvZvY9S5Z/aMcDGuv5LJ6JrZEgMBtAcPp6QT041BNpLZR8NMJuK+csjGNVjLRnFgt5ZQqyHY17IHq4ofAuahwbjKBVJPmJycw8YWa2bBtk2hN/Je4DNeni5lkW6I85JaMMdO/Ky4Ebhchvt9KAHHbimbvizFnQ6om6V7ium5T667VwaB8InB9a/N5MgGJm34Y6nvbFrRKrmooeqkJZsfDHa223V/7eTVNl6wkHIKP7KjhPLUGBK5Wy66UL5tXKnGbMm5KYmY/ZBO4lP1NK2EZfaxW/B06G2z59NQsNMukVgeDjILAjRZNvuwT8BU33SvvoASu5VqbVhn55jefyHJjGtWua1uXr19mEbg+DT5vJTBH3PQweQm1k3zrQXs2TKnxxuRkDoaaZ5sgcDFLVKFxycOmpoxePj9S1dqs/63QrAdLtmpxYw6HYBF5PEhN05r2QHVlHYFzUeHcHgEJmvrb5qwIYgNY9x7Gh6wI1LYHqgsuAueiwrkNgSXipgdoVH7KMV65mVG1uJyWNK9tD1SXvRE4FxXObZqic2tu4NtO4Kmnnuzeeee32y+I9I363Wp3MAglAhepQJUUjabtSNw0RooQloCGi+RQizMHQ9jc5fc0BC4/myRNEZPm18UvR4OaqqmDHAzqV609IHC1W9gjf4ibB6zCL61xD1SXSRA4F5UGz5m41bguf47m1Li4lEFdEC2s/oLApSxlmcTNpPn4hjhz5vTWVUbWTk2te6C6uCFwLioNnUPc0hhbSyhJ5FKEWvdAdbFE4FxUGjmHuKU1dKrhInIw1LgHqsuaCJyLSuXnNAZK4qZ+mFpXcq3chIuyV+seqC4oCJyLSqRztnyQBlwOX9qAZI21wuZOmo+EpLloNCYu9rARlbWxdfxqMgICl9iati5YX8y0lLXtsKT3UAFxC0Uy3HMkcMO14sI9/eonafqdBM5n0YSrn1LOGQQusa20RZwKXF/gLElaZkjfadL60oC4LSW4zv3amEbTt2IF1dzUNdFKQOASW3pM4JQ0raem15Kgf2tNrJ6zIsiSeLl3GgGt+Bsr1LwHqoshAueiEvHcLoGzpqqarXPC0hVB5sTJPfkSqHkPVBd1BM5FJeK5XQKnJb/VTJ2z5DfiFtGQC6PSuDg1V9cOKkstec4RuLVL1I7n7xK4uTU4Ezf9Y6v/jZA3gRirjNgKIrXugeqyMALnohLx3C6BU/+bFo70CTavVGPdCGUQ0FARbUyz5pARzT1tycEgyyNwicv/mMCZF9XlYd2WbMRtG5n8z8vZsOa+DfrDq3kPVJeFETgXlYjndo2DUx/c1IC4TSXV5nXyote8B6rLqgici0qkc6qZqdPX9VLfm89+Bmp+6DmtFeBIpooWjRwNazgb1A+r8lHzHqguIyFwLiqFnWPSfGEGG0muvKnPPfftkSvmfWUOhtYcTgjcvPKSzV2IWzamCJYQCVzoWpxq9rXvgeoyAALnolLIOcStEEN5JlPOhtDeVDkXVF5aCwhcARZXs8LW8FJBPX369GY9L7n8Nd6NAIFdBFrYA9XFAIFzUcnonMRN3q+hI+K6665F3DKyU+ikqAYXao5qqw4G2QSBC10yAz/Phn4MBU7HrXUYB0ab9eO02q9WGQkxLq6lJcqHRkXghkQyO1bT1CVuOteayz8z06yenHPnzgbZmEZlqIU9UF0GQeBcVDI6NyZw9L9lZKgVkiJPaoh9GzQfuUUHg0yCwK1QMEM+8uWXX+6uuebPr6rF3X7734WMhmdVTEDOKHV1tBgQuIytbiuC3HzzR7tDhz68J3Kf/OTfd88++0zGKSdpoQioD26Js6GlPVBdzBE4F5UMzql/Tf+8alrgTMjAIImSIIFbsspIyw4GmQyBS1Rwx6I1z+mUfhNtWqIXoV4Csu9rr/14VgZbW6J8CAmBGxJJfOwjbkqq5i7qHx6RS2y4FaNfMiaupT1QXSZA4FxUEp3zFTdLpvpoNGbq/PnzQcZN2XN5L5+AhhO16mCQ9RC4TMqwmhJLCqMNDD1z5jQil4lNQydDtXWfICeVylRLS5QP+SBwQyIJjtXXtkTcLMkSOa1EoVeIEfD2XN7zIOC7yohqbq0tUT60FAI3JBL5OJS4WbIlbAwANhp1vcuumt0wNbTuYBAnBG5qaVnhOonbmoMwVaND7FYwXKJH6s/Lx5va4hLlQ9MgcEMiEY5thRCJ25oCpGebh5UmawTDZhaFuj1a2gPVhR+Bc1FZ8VwscbMsmIdVzocQ8xrtubynI6A5qrv+sGyJ8pYdDLIQAhexnMYWN8uaxlFJ4DSUxNcTZ8/gPR8C6ofbVfPXJkQtLlE+tBICNySy0rEKpPpE9Er1r6r+GzVZtYs6oVwCqpXLozoW1L/b2h6oLh4InItK4HMSN/W3SdxSzyvVj4OmamADJ3ic/qzG9m3AwfCeURC4lQtnTuI2zKqmd1GbG1Ip/1h/onIwsCAqfXCrluacxU0ZV/rUZMUBsWoxWO3hqsG5nA3mYEjdWlgt4x4PpgbnAcvnUhtFrr6QnIOaq+q0pm8uZyu506YauGuRBa0CjYPhPWYInLvsLDo7d9L8okgX3qzanLysvtOBFkbL7QsIqAbn2pim1T1QXSgROBeVBedKFDfLrn4wWpGEoSRGJP931eCGzoZW90B1WQuBc1GZec7ETU2EGoKETk4IVz9PDfmrMQ84GPZbFYHbz2P2UehJ87MTEvDGfrOVWl1AsIEfpT8gq8W1vkT5EC0CNyQy47hGcTMM+uGoGWTeVk0TIuRFQH9EtspIy3uguqyCwLmoeJyrWdz6GKx/TkJnP6b+93xOR0A1ODkbfvbTn24Gk9933xfSJSazmBG4mQZRX4e8VZqh0NKAStXgVGOwYE0jO+Y9PgHZ42Mf++vN4F4N8D1w4LqmlynvWwCB69OY+Fnipqkway93NDE5yS6TuKlGp6El9NElM8OmLErYhq+W/ni30UfgtpHZch5x2w+m30cnocPrup/P2keqvQ2FzY63efOPHbt36z26V9/XEhA4D0sibtthSeg0AVx9QcyK2M4p9DcXLryyVay2CZzSYPedPfviviRdvny5O3nywX3nSj5A4CZaT/+UGkCZw4ogE5Oc5DJ1eKu5qlVLLIgdY+mMRph39YXKu611366//oBT5DQuc1u4ePGNzT1Dgdt2fannEbgJltMPNJfljiYkN6tLNNfVanU2SwKxW2YilUcbtqM/k2effeYqgdu1FhwCt8wG1dyNuIUxpX6IEjj9MCV4qn30a3lhYqnvKfqDUL+mVnwxXvqDGHqvn3nmPZHTTlpjNTcj5BK4S5cuVdU8VV6pwZnFHe/yQqnmpn9D9b8RlhOwJqzErr9DlP5Ihj/a5bGV+QQJmdjIaWNe6l0LXErUVFanBhM4c0jYe00OBrFA4LaUCJtXmvtyR1uSX9RpCZs1Y/Wj1o9ZP/JWmrL9FZaVd2t+qubW/27MqL57oJrA9fvgVIM7ceKBsWiK+w6Bc5gMcXNAiXDKmmO2Pp390C3qGgRPeZCDQOKlfJqwm5BJ7Ofk03eJcpfAGeea3hG4gTURtwGQhIcSgv4AYhM+vaumo+90Ta5BYtVvdluT04Rb/ZDKQ/+auXlRE9NnD9QxgdMQklOnnp6blKzuQ+B65tC4IRUUud4J+RFQLUeCMKz9SDBMCCUW+t7EL4YAWpyWLjkElCa9JMYWLE1zamj2DNe7LVHus1vbtnFwEr7Dh2/q1FytISBwf7JiK5Pmayi0/TxYk89EQyLYb/qZ0Ni73Sux0XV6yeEhcbJXXxTtGnvv18KsWalnSdR0jWqWeo6eYd9bnGu9++6Bumsmw9Gjd6+V1OjPReC6rkPcope7aBGaAEpw+sKlzyZoaiqagOldgmXBrrF3eXvtWSaqdm2qd5XfXePeUqUtdbzNCxzilroIEv9SApphMzYta+nzS76/WYHTuLa77vp08yuClFx4SXu3GZ+pfmNWDnGXhiYFjknz7sLA2fIImIOBgehu2zUncIibuyBwtkwCappqDBzBTaApgZMbXYVBL3UWEyBQOgE5F9SPTHATaEbgmDTvLgCcLZsAe6CO268JgUPcxgsB35ZJQC0SHAzjtqte4BC38QLAt+USYA/U3barWuBUALSEjPoo8DLtLgxcURYBHAy77VWtwDFpfrfxuaJsAhrHqWWSCNsJVClwiNt2g/NNPQTUOlFZJ2wnUJ3Ambjxz7bd6HxTPgFzMDDcadyWVQkc80rHjc239RCwP/J6crROTqoROP2jUWVfp5Dw1PwI+C5Rnl8O4qSoCoFTzY3VFOIUGGLJgwAOhml2KFrgNPRD4qaam89yzdPQcBUE8iXgu0R5vjlZN2XFC5z+yehoXbeQ8PS8CKi8S+DULUMYJ1CkwKnmxsDdccPybb0E5GBQq4Wwm0BxAidh02ogDAPZbVyuqJOAumXUciHsJlCUwKlKbssdUT3fbVyuqJOAfgM41abZtiiBU5ZkWJqn04zLVXUSwMEw3a5FCJw6VRG16UblynoJsES5n22zFziJmzpU6XPzMyxX10nAdw/UOilMz1XWAqd+NlXH1alKgAAE3tvDlz1Qp5eErAVO2WA7tOnG5Mr6CbAHqp+NsxQ4jfNh8K6fIbm6fgLqh1aLhj/96bbOTuDUxyAj6p0AAQhcIYCD4QqLqZ+yEjj1ubEiyFTTcV1rBFii3N/iWQmcks9wEH8jckcbBNgD1d/OWQicvKTqdyNAAALbCbAH6nY2275JKnCqrelfSc1SnArbTMR5CHSblUNwMPiXhOQCx3JH/kbjjvYIsAfqPJsnETj62eYZi7vaJYCDYZ7towucxI3VEOYZi7vaJcAS5fNsH1XgbBiIBI5a3DyDcVebBBg+Nc/uUQVOSdSkecRtnrG4q00CNicbR5y//aMInAyDqPkbhzsgIALsgTq/HKwucJpeouo1K5DONxJ3tk2APVDn239VgVPNjeWO5huHOyEgAjgY5peDVQVOyWKGwnzjcCcERECVBPb9nVcWVhE4ljuaZwzugsCQgLWC5Ggg+BMILnDqL9A/DjU3f2NwBwSGBLRsmPqwCfMIBBU4+7dB3OYZg7sgMCTAHqhDIn7HQQVOUVOV9jMAV0NgjACzfsbo7P4uiMCx3NFu0FwBgTkEcDDMoXblnkUCZ/NKWe7oClA+QSAUAZYoX05ykcCpOapF+NT3RoAABMISYA/U5TxnCRzTrpaD5wkQ2EVAi8GyB+ouSuPfewucam3q+GTXq3GwfAuBpQTYA3Upwa7zEjiJm/rbWO5oOXieAIzCXqAAAAQfSURBVIExAmolycHAHqhjlHZ/5yVwgi6PKU3U3WC5AgJLCJiDYckzuHdiDU41N0SN4gKBeARYojwM6501OM1KULOUPrcwwHkKBKYQYA/UKZR2XzMqcDb1Ss1SAgQgEI8AlYowrEcFTlEwrzQMaJ4CgakE1CWEg2EqrfHrdgrc+O18CwEIhCbAHqjhiCJw4VjyJAgEISAHg1bxJSwngMAtZ8gTIBCUAEuUh8OJwIVjyZMgEISAHAz0fQdB6TeTIUyUPAUCENhGwEYusIDFNkJ+56nB+fHiagisSkA1N3lQCWEIIHBhOPIUCAQhwB6oQTDuPQSB20PBBwikJ/CpT93JJukBzYDABYTJoyCwlMDXvvZv3U9+8vrSx3D/nwggcBQFCECgWgIIXLWmJWOlEWDVnvAWQ+DCM+WJEJhFgD1QZ2EbvQmBG8XDlxCIR4A9UMOzRuDCM+WJEJhFQHswsET5LHRbb0LgtqLhCwhAoHQCCFzpFiT9EIDAVgII3FY0fAGBeAQ0g4FtAcLzRuDCM+WJEPAmwB6o3sgm3YDATcLERRBYjwB7oK7HFoFbjy1PhsAkAhI4vKeTUHlfhMB5I+MGCECgFAIIXCmWIp3VEtAmM5qmRQhPAIELz5QnQsCLAHugeuHyuhiB88LFxRAIS4A9UMPyHD4NgRsS4RgCEQlI4O6553MRY2wrKgSuLXuTWwg0RQCBa8rcZBYCbRFA4NqyN7nNjIB20JIXlbAOAQRuHa48FQI7CbAH6k5Eiy9A4BYj5AEQmEdAe6BqiAhhPQII3HpseTIEIJCYAAKX2ABEDwEIrEcAgVuPLU+GwCgBbTLDFK1RRIu/ROAWI+QBEPAnoNVD5EFF4PzZ+dyBwPnQ4loIBCKg1XtxMASCOfIYBG4EDl9BYC0CqrnJi0pYlwACty5fng4BCCQkgMAlhE/U7RJgBd84tkfg4nAmFgjsETAHg5YqJ6xLAIFbly9Ph8BVBB555OFOu2gR1ieAwK3PmBggsI+ABE77oBLWJ4DArc+YGCAAgUQEELhE4IkWAhBYnwACtz5jYoDAHgE5GG677RN7x3xYlwACty5fng6BfQTU/4bA7UOy6gECtypeHg6B/QTuuuvTnSbZE+IQQODicCYWCGwIaIoWE+zjFQYELh5rYoIABCITQOAiAye6dgloDwYm2Me1PwIXlzexNUxADgb1wRHiEUDg4rEmpsYJSNyYwRC3ECBwcXkTW8MEVINjD9S4BQCBi8ub2CAAgYgEELiIsImqXQIsjZTG9ghcGu7E2hgB9b3hYIhvdAQuPnNibJCAxE19cIS4BBC4uLyJrVEC2kELB0N84yNw8ZkTIwQgEIkAAhcJNNFAAALxCSBw8ZkTIwQgEIkAAhcJNNFAAALxCSBw8ZkTIwQgEInA/wOue1vcIpewyQAAAABJRU5ErkJggg=="></p>
<p>The length of the arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DE</mtext></math> shown in the diagram is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo> </mo><mtext>m</mtext></math>.</p>
</div>
<div class="specification">
<p>A new fence is to be constructed between points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> which will enclose the field, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is due west of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext><mo>=</mo><mn>800</mn><mo> </mo><mtext>m</mtext></math> . The bearing of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>195</mn><mo>°</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>.</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>Show that the area of the field that the horse can reach is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>392</mn><msup><mi>θ</mi><mn>2</mn></msup></mfrac><mfenced><mrow><mi>θ</mi><mo>+</mo><mi>sin</mi><mo> </mo><mi>θ</mi></mrow></mfenced></math>.</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>The area of field that the horse can reach is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>460</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math>. Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>E</mtext></math>.</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>Find the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>B</mtext><mo>^</mo></mover><mtext>C</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of new fence required.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Note: In this question, distance is in millimetres.</strong></p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = x + a\sin \left( {x - \frac{\pi }{2}} \right) + a">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>x</mi>
<mo>+</mo>
<mi>a</mi>
<mi>sin</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>a</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \geqslant 0">
<mi>x</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> passes through the origin. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mi>k</mi>
</msub>
</mrow>
</math></span> be any point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2k\pi ">
<mn>2</mn>
<mi>k</mi>
<mi>π<!-- π --></mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in \mathbb{N}">
<mi>k</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">N</mi>
</mrow>
</math></span>. A straight line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> passes through all the points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mi>k</mi>
</msub>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Diagram 1 shows a saw. The length of the toothed edge is the distance AB.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_15.10.11.png" alt="N17/5/MATME/SP2/ENG/TZ0/10.d_01"></p>
<p>The toothed edge of the saw can be modelled using the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span>. Diagram 2 represents this model.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_15.11.17.png" alt="N17/5/MATME/SP2/ENG/TZ0/10.d_02"></p>
<p>The shaded part on the graph is called a tooth. A tooth is represented by the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span>, between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mi>k</mi>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_{k + 1}}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(2\pi ) = 2\pi ">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mi>π</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
</math></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>Find the coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_0}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mn>0</mn>
</msub>
</mrow>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_1}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mn>1</mn>
</msub>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span>.</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>Show that the distance between the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mi>k</mi>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_{k + 1}}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi ">
<mn>2</mn>
<mi>π</mi>
</math></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>A saw has a toothed edge which is 300 mm long. Find the number of complete teeth on this saw.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A farmer is placing posts at points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> in the ground to mark the boundaries of a triangular piece of land on his property.</p>
<p>From point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, he walks due west <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>230</mn></math> metres to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.<br>From point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, he walks <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>175</mn></math> metres on a bearing of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>063</mn><mo>°</mo></math> to reach point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<p>This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The farmer wants to divide the piece of land into two sections. He will put a post at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>, which is between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. He wants the boundary <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext></math> to divide the piece of land such that the sections have equal area. This is shown in the following diagram.</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 distance from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</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>Find the area of this piece of land.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CÂB</mtext></math>.</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 distance from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 12\,\,{\text{cos}}\,x - 5\,\,{\text{sin}}\,x,\,\, - \pi \leqslant x \leqslant 2\pi ">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>12</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>5</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>−<!-- − --></mo>
<mi>π<!-- π --></mi>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>2</mn>
<mi>π<!-- π --></mi>
</math></span>, be a periodic function with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = f\left( {x + 2\pi } \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mi>π<!-- π --></mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">There is a maximum point at A. The minimum value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> 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;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\left( t \right) = f\left( t \right) + 17,\,\,0 \leqslant t \leqslant 5.">
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>17</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>5.</mn>
</math></span></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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, 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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, 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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\,\,{\text{cos}}\,\left( {x + r} \right)">
<mi>p</mi>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mi>r</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></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>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>The six blades of a windmill rotate around a centre point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and the base of the windmill are on level ground, as shown in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>From point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> the angle of elevation of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>6</mn></math> radians.</p>
</div>
<div class="specification">
<p>An observer walks <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math> metres from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
</div>
<div class="specification">
<p>The observer keeps walking until he is standing directly under point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. The observer has a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>8</mn></math> metres, and as the blades of the windmill rotate, the end of each blade passes <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>5</mn></math> metres over his head.</p>
</div>
<div class="specification">
<p>One of the blades is painted a different colour than the others. The end of this blade is labelled point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>. The height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>, in metres, of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> above the ground can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>p</mi><mo> </mo><mi>cos</mi><mfenced><mrow><mfrac><mrow><mn>3</mn><mi mathvariant="normal">π</mi></mrow><mn>10</mn></mfrac><mi>t</mi></mrow></mfenced><mo>+</mo><mi>q</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is in seconds and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>,</mo><mo> </mo><mi>q</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>. When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>, point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> is at its maximum height.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> metres from the base of the windmill, find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> above the ground.</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 angle of elevation of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</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 the length of each blade of the windmill.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</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>If the observer stands directly under point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> for one minute, point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> will pass over his head <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> times.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows quadrilateral ABCD.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 11\,{\text{cm,}}\,\,{\text{BC}} = 6\,{\text{cm,}}\,\,{\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{D = 100}}^\circ {\text{, and C}}\mathop {\text{B}}\limits^ \wedge {\text{D = 82}}^\circ ">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>11</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cm,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>BC</mtext>
</mrow>
<mo>=</mo>
<mn>6</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cm,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<msup>
<mrow>
<mtext>D = 100</mtext>
</mrow>
<mo>∘<!-- ∘ --></mo>
</msup>
<mrow>
<mtext>, and C</mtext>
</mrow>
<mover>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<msup>
<mrow>
<mtext>D = 82</mtext>
</mrow>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find DB.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find DC.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 2\,{\text{sin}}\left( {3x} \right) + 4">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>4</mn>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 5f\left( {2x} \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>5</mn>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> can be written in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 10\,{\text{sin}}\left( {bx} \right) + c">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>b</mi>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></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>Find the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the period of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 12">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>12</mn>
</math></span> has two solutions where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{4\pi }}{3}}">
<mrow>
<mfrac>
<mrow>
<mn>4</mn>
<mi>π</mi>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</math></span>. Find both solutions.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Adam sets out for a hike from his camp at point A. He hikes at an average speed of 4.2 km/h for 45 minutes, on a bearing of 035° from the camp, until he stops for a break at point B.</p>
</div>
<div class="specification">
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Adam leaves point B on a bearing of 114° and continues to hike for a distance of 4.6 km until he reaches point C.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXAAAADyCAYAAABUFp5YAAAgAElEQVR4Ae2dC3BV5bXHV4J1xOFSi71TCNAqOgn1ooAa5lZpiWjDo9xLJik40Bq4EMeOFRwsAQUVRUEkDNwSylh5CIJQC2HAFyFVBA1a5X21lWQYqhNI6uVRiFxEa7LvrC0bT5JzTs7jO+fsvc9vz2SSsx/ft77f2vnny/dYK8OyLEs4IAABCEDAcwQyPWcxBkMAAhCAgE0AAedFgAAEIOBRAgi4Rx2H2RCAAAQQcN4BCEAAAh4lgIB71HGYDQEIQAAB5x2AAAQg4FECCLhHHYfZEIAABBBw3gEIQAACHiWAgHvUcZgNAQhAAAHnHYAABCDgUQIIuEcdh9kQgAAEEHDeAQhAAAIeJYCAe9RxmA0BCEAAAffkO3BealeOloyMm2X69hNtW9B8SFYOyZKs6dulse1VzkAAAj4hgIB72pF7Zf4Ta2Tv2WZPtwLjIQCB2Agg4LFxc8dT3W6RvC9/J1Of2SNn3WERVkAAAkkkgIAnEbb5qnJl7Pg7pKZ0tjyz97T54ikRAhBwNQEE3NXuac+4y+WaUdNlyYRPpHTqcwyltIeL6xDwGQEE3OsOzfyBFMx+XCbUlDGU4nVfYj8EoiSAgEcJzI23Z3YfIbOXFDKU4kbnYBMEEkgAAU8g3OQVfal0Lyi1h1IWLt0ux1iUkjz01ASBFBJAwFMI32jVF4ZShm2dJY9uPixNRgunMAhAwI0ELnGjUdgUG4HM7sNl+pN/kJzJT8mRq2Mrg6cgAAHvEKAH7h1fRWDpZZI9eqqU5fxNdrzTEMH93AIBCHiZAALuZe8Fs73TzfKrBaWSF+wa5yAAAV8RyLAsy/JVi2gMBCAAgTQhQA88TRxNMyEAAf8RQMD951NaBAEIpAkBBNxHjj516pSPWkNTIACB9ggg4O0R8sj1Xbt2ybx58zxiLWZCAAImCDCJaYJiisv4/PPPZcyYMbJlyxbZv3+/9OvXL8UWUT0EIJAMAvTAk0E5wXVs3brVFm+t5rHHHhMVdA4IQMD/BBBwj/tYx70Dh060F66CzgEBCPifAALucR+vW7dOdu/e3aIVKuhMaLZAwgcI+JIAAu5ht9bW1sqkSZPatEAFXYWdAwIQ8DcBgll53L8VFRUXW1BUVCSBny9e4AcIQMCXBFiF4iO3ZmRkCJERfORQmgKBdggwhNIOIC9dRry95C1shUD8BOIU8PNSu3K0ZGTcLNO3n2hrTfMhWTkkS7Kmb5fGtlc5AwEIQAACcRCIU8CdmvfK/CfWkBXdwcF3CEAAAkkgYEbAu90ieV/+jqzoSXAYVUAAAhBwCJgRcMmVsePvICu6QzVF33USkwMCEEgfAoYE/HK5ZtR0Oyt66dTnGEpJn/eHlkIAAikkYEjAReRCVvQJNWUMpaTQoVQNAQikDwFzAq4a3n2EzF5SyFBK+rw/tBQCEEghAaMCLnKpdC8otYdSFi7dLseaU9gyqoYABCDgcwKGBfyboZRhW2fJo5sPS5PPAbqpeWzkcZM3sAUCiSeQkFgomd2Hy/Qn/yA5k5+SI1cnvhHUAAEIQCAdCZjvgdsUL5Ps0VOlLOdvsuOdhnTkSpshAAEIJJxAggRcRDrdLL9aUCp5CW8CFUAAAhBITwJEI/SR34lG6CNn0hQIREAgcT3wCCrnFghAAAIQiJ2AcQEnoW7szuBJCEAAAtEQMC7gK1askE2bNkVjA/dCAAIQgEAMBIyOgR89elR69uwpubm5snPnTunYsWMMJvFIrAQYA4+VHM9BwJsEjPbAFy9ebFPQpLraE+dILgE28iSXN7VBINUEjPXADxw4IP3792/RnpqaGsnOzm5xjg8QgAAEIGCGgJEeuE5cPvbYY20sWr58eZtznIAABCAAATMEjPTAddKyqKgoqEXV1dVy6623Br3GSQhAAAIQiJ2AkVgonTp1koqKCtsKFXLn59jN4slYCDCJGQs1noGAdwkY6YEHNh8RCaSR3J9hn1ze1AaBVBMwMgYe2AhWQgTS4GcIQAACiSNgXMATZyolQwACEIBAIAEEPJAGP0MAAhDwEAHjAq7jsBwQgAAEIJB4AsYFPPEmU0MoAsw/hCLDeQj4kwAC7k+/0ioIQCANCCDgaeBkmggBCPiTAALuCr82S+P2GZKVkSE6h9D263oZt+BF2V7bGNZa5h/C4uEiBHxHAAF3hUszpfPguVJvHZc3pt0kkr9Capos0TFty/pC6vdMk66vTpHb86bIykPhRdwVzcEICEAgKQSMCzgTaab9dql0u+kueer3T0p+w0p5+Lk9goSbZkx5EPAmAeMC7k0MWA0BCEDAewSMBLPyXrO9ZXFzw/uyZsWLUtVtgqz4r5uls7fMx1oIQCBBBIwLuE6kMYwSp7eqJkpOh4mtCrlJpr3xgkzojXy3AsNHCKQtAYZQ3Oj6NpOYFVJW/IXMv/02GbfyQzkbwmb+cIYAw2kI+JQAAu56x+okZqFMfW6DrMg/Kc9PnC1/rD3veqsxEAIQSDwBBDzxjM3UkPlduapflogckZqjbfvgtbW1ol+nTp0yUx+lQAACrieAgLveRRcMbP4/OX3iCxHpJTk9Ol20+ujRo1JQUCA5OTn215VXXima4o4DAhDwPwEE3AM+bm7YK5sWPir3rTwpeQ/dLcOuvcy2WpNJFxYWypYtW1q0QtPa7dq1q8U5PkAAAv4jYHwVChNpsbwkupX+Yel9+1PSYD8eZBVK3jRZsfllGfYfN0m3C3929+3bJ7t37w5aoYo6yaSDouEkBHxDwLiA+4ZMUhvibKWfG1Wtn376acj7z59nojMkHC5AwCcEEHAPO7JXr14hrS8vL5euXbvK8OHDpV+/fiHv4wIEIOBdAsbHwImIl7yXQYW5pKQkaIWPPPKIbN68Wfr3729PclZVVYmOmXNAAAL+IWBcwP2Dxhstefrpp+WWW265aKwKek1NjcyePVt27twp1dXV9rUhQ4bI5ZdfLkuWLBFducIBAQh4n0CGZXjWka30yX0pnn/+eRk3bpwt1OEmLXWNuPbCJ02aZBuoQj9+/HgmOpPrLmqDgFEC9MCN4kxuYSrKKt5z5sxpV4izs7Plvvvuk5MnT0pFRYUcP35cBg4cKAMGDBD9I8AGoOT6jtogYIIAPXATFFNQho5njxkzRurr6+2hko4dO0Ztha4V1+WGZWVl9rOlpaUyduxYJj2jJskDEEgNAQQ8NdzjrnXu3Lkyc+ZM2b9/f9yCq73vV155xR4f13XlI0eOlOLiYhk2bJjE8och7sZRAAQgEBEB4wIeUa3cFBeBAwcO2KtLVq9ebQttXIUFPKy9et0ctGrVKlm+fLl9RZcj5ufniw7BcEAAAu4igIC7yx/tWqMiO2jQIMnKypL169cnrIccatLzxhtvTFid7TaeGyAAgRYEmMRsgcP9H2bNmmVvn58/f35ChdSZ9Dx37lyLSU/946FLEZn0dP+7goX+J2C8B84ywsS9NLoMUNdz6yoSDWKV7EOHbl577TV77F3r1klPHS8Pt3wx2TZSHwTSiQAC7hFv6+YbFe2+ffvKsmXLUmp1qEnPvLw86dKlS0pto3IIpBMBBNwj3r777rvl4MGDdqzvHj16uMZqXYrIpKdr3IEhaUYAAfeAwzVBg8b43rZtm70ixI0m638IGnvF2empQyv33nuv/PjHP07oWL0bWWATBJJFgEnMZJGOsR4VRhVvHW/W5XxuPfS/At3pqZOe+odGDx2vdyY9ib/iVs9hl5cJGO+BexmG22wP3G1ZWVnpufFlXYq4ceNGJj3d9mJhj28IIOAudqUTqMrEbstUNlMnPXfs2CHz5s2zl0Dm5ubKgw8+KEx6ptIr1O0HAgi4S72ovVdNVKyBqmbMmOFSK6M3q3X8FW0fSSei58gTEFACCLgL3wNnt6WapjG9/RiPxJn01P8ynPgrTHq68GXEJFcTMD6JSUae+P29aNEiW9TWrl3rS/FWQs6kJ0kn4n9fKCF9CRjvgbMTM76XKVGBquKzKjlPh4q/wk7P5PCnFu8RQMBd5DOd7Bs6dGjCA1W5qMlBTXEmPXV4ReOV66SnLlEcMWKE51biBG0gJyFgiAACbgikiWKmTZtmJ1eoq6uzhxhMlOn1MlpPepJ0wusexX6TBBBwkzTjKCvVgariMD0pj4aKv0LSiaTgpxKXEjAu4C5tp6vN0hUZPXv2FE00nOpAVa4GJSIknXC7h7AvmQQQ8GTSDlGXE6jKi7stQzQpKadDTXqSdCIp+KnEBQQQ8BQ7wQuBqlKMqN3qtVe+detWCZz01JyemqCZ8Lbt4uMGDxNAwFPoPGe3pU7MaYYdjvgJkHQifoaU4B0CxgWcdeCROT8wUJVfd1tGRiIxd4Wa9CT+SmJ4U2pqCCDgqeFu/7s/btw48XqgqhThi6pakk5EhYubPUQAAU+Bs5zdln4LVJUClFFV6cRfIelEVNi42cUEEPAkO8cJVJWVlSXr16/3bayTJGONqjr1wdtvvy1Lly69uNNTJz0LCgrYQBUVSW5ONQEEPMkemDt3rp3goKamRrKzs5NcO9W1JqATySSdaE2Fz14hYFzAvdLwVNjp7LZcvXq1aI+Pwz0EnPgrJJ1wj0+wpH0CCHj7jIzcoQKhgar69u3LbksjRBNXSOv4KzpX8fOf/5z/mBKHnJJjJICAxwgu2scIVBUtsdTf70x6knQi9b7AguAEjCd0CF5Nep/V3ZZlZWVSUVHBJJmHXgWSTnjIWWlqqvEeOBt5Wr5JTqAqdlu25OLVT6Hir5B0wqse9bbdCHiC/UegqgQDTlHxzqRnYPwVkk6kyBlpXC0CnkDn6y+37rbctm2b5OfnJ7Amik4lgWCTnsOHD5d+/fql0izqTgMCCHiCnOwEqmK3ZYIAu7BY7ZWvW7fODpOwe/duGTlypL1clKQTLnSWT0xCwBPgSAJVJQCqh4pU/+/bt09WrVoly5cvty0vLy+3/wtj85aHHOkBU40LuAfanHATnd2WBKpKOGrXVxBq0pOkE653nScMZBmhYTdpoKqZM2eK9rgYAzUM14PFaY9bJzfPnTtnLyM9fvy4DBw4UAYNGmQPteiwCwcEYiVADzxWckGeI1BVECicakNA/8jrWLnuDdBDl5jqeDlLEdug4kQ7BIwLeDqvA3d2WxKoqp23jss2Ae19v/LKK7JkyRIJnPQk6QQvSKQEEPBISbVznxOoSndbFhYWtnM3lyHQkgBJJ1ry4FNkBBDwyDiFvUt7UgSqCouIixEScOKvBCad0CEWJj0jBJhmtyHgBhyuuy11uVhdXR2xTgzwpAgRkk7wFkRCAAGPhFKYezRQVVFREbstwzDiUnwEdNLztddes1c3aUlMesbH009PI+BxeJNAVXHA49GoCehQ3Y4dO4SkE1Gj8+0DxgXct6RaNUz/xZ08ebIcPHhQKisrpUuXLq3u4CMEEkcgWPwVkk4kjrdbS0bAY/SME6iqurqa9bsxMuSx+Ak4k54knYifpRdLQMBj8BqBqmKAxiMJJdB60lMr093ABQUFTKwnlHxqCzcu4H7fyOPstlS37dy5Uzp27JhaD1I7BFoRCBV/hZ2erUD54COxUKJ04qJFi+xdc2vXrkW8o2TH7ckh4MRfOXnyZIv4KwMGDCD+SnJckLRa6IFHgVqXc/Xv319Wr15tx3mO4lFuhUBKCQSb9CTpREpdYqRyBDxCjM5uy6ysLFm/fj297wi5cZu7COh7TNIJd/kkHmsQ8AjpOYGq2G0ZITBuczUBncsh6YSrXRSRcQh4BJgIVBUBJG7xLIFQk57EX3G/S40LuPubHJ2Fus5Wowv27dtXli1bFt3D3A0BDxHQXvnWrVvtic4tW7ZIbm6unYxixIgRbFRzqR8R8HYco4GqdLelxjzp0aNHO3dzGQL+IEDSCW/4EQEP4ycCVYWBw6W0IKCTniSdcK+rjQu4XzbyOLstNfLb/Pnz3etBLINAkgiQdCJJoKOoBgEPAkvHAseMGSP19fXstgzCh1PpTcCJv0LSidS/B+zEDOKDDRs2iE7iPPvss6z3DsKHU+lNQOeC7rvvPjl37pwdB19pDBw4UAYNGmTn91SB50gOAXrgrTg7uy3nzJkjM2bMaHWVjxCAQDACJJ0IRiXx5xDwAMZOoCp2WwZA4UcIREGApBNRwDJwKwIeAHHu3Ll22qqamhrRgEAcEIBA7ASCxV8h6UTsPIM9aVzAg1XihXP6suk4HoGqvOAtbPQSAWfSk6QT5r2GgIuIE6hKd1suXryYiUvz7xklQkB0iPLtt9+WpUuX2osEFAlJJ+J7MRBwESFQVXwvEU9DIFoCoeKvkHQiOpLGlxHqRh4vHbrbsqyszA58z1Z5L3kOW71MgKQTZrxnvAfupZ2YOjbXs2dPKSkpIVCVmfeJUiAQM4Fgk54knQiPM60F3AlUVVlZSbS18O8JVyGQNAIknYgcddoKuM6Ijxs3zt5Jlp+fHzkx7oQABJJCQCc9SToRHnVaCrgTqIrdluFfDq5CwC0EQk16pnvSCeMC7haHh7KDQFWhyHAeAu4noL+/JJ34xk9pJ+BLliwRjaK2f/9+6dev3zck+AkCEPAUgWBJJ8aOHZtWv9dpJeBOoCrdPKDR1DggAAHvE0jnpBNpI+D6r5eGuyRQlfd/YWkBBIIRSMdJT+MC7tZ14ASqCvbKcw4C/iTgxF/xe9IJ4zsx3fg6VFVV2VEGNVAVUQbd6CFsgoBZAu0lndBhFz8cvu+BBwaqWrZsmR98RhsgAIEYCPgx6YTvBVx3Wy5fvlzq6uqEWCcxvPU8AgGfEWg96ZmbmysPPvig5OXleW5Htq8FXANVFRUVsdvSZ7+ANAcCpggEi7/ipaQTxgXcFNh4y3ECVZWWlsr8+fPjLY7nIQABHxNwJj29lnTClwKuy4kmT54sBw8eFAJV+fi3jqZBwDAB1Y7ApBM6vFJcXCwFBQWuHIL1pYA7gaqqq6uFAPGG33CKg0CaEND4Kxs3brRXsGmTNez0+PHjW2iKMzF6+vRp+f73vy+6E7RLly7JI2R55Giqr7IeysuyMvMes96o/yKk1TU1NZaIWHPmzAl5DxcgAAEIRErg5MmTVkVFhTVy5EhbW3Jzc63Vq1dbGzdutD+r3jhfeq2uri7SouO+z/g68OAZeZrlbO0mmX5bd+nQoYN06D5OFr3fIM1t/k6dl9qVo7++R++z750h2xvPyeGtr0uXBR/ImQXfkXVbjwR5Vuyce5oeTf/tmTJlSpvSOQEBCEAgWgLaoy4sLJTNmzeL/levq1U0FLVOdrY+du/eLToCkKzDuIAHM7z52Msyd5XIxJfrpOnMX2TDL/8uU390v6yqPd/y9rP/Iy+t2dXiXNdf3iE3d26Wz06daXE+2IdFixbZyVKfffZZEhMHA8Q5CEAgLgI6JKuLIt57772Q5cycOTPkNdMXkiDgJ2TH+v+VohkFkt0pU6RTbymYeKfcIftk54fHA9rzpRyrel4WXfqEfPTPJmlq+vrr2NODpbN0kv6/KJJTU6+Xb0/9h4wd1ktaG65jUQpOd1sSZTAAKz9CAALGCVxxxRUhy9QRgKQdcQ/CtCpAx4LCH03WmTcesrKyfm1VHA0Yy276yFqRn2VlZl5vFZe9YG3eU281hS/o4lUdo9KxJx2jOnfu3MXz/AABCEAgEQRUZ1RznLHvwO/l5eVtq2yqt/ZsfsEqK+5z4ZluVt60Z22d+2dNpbW55vO2z0Rwpj21jaCIlreEFXBtREWZVXzNRGvFR2cCHrwg6pmZVubFr+ut4oXVVn0EKl5aWmpDSebkQYDx/AgBCKQhgerq6jYiXlJS0qYT2VRfbS0s7mN1Ky6zKgI6pk31e6yKsmKrm4yyVrhFwEP6sb7CKm5XnJusz2retDaUFVtZ9r3XWxMrPg7bE9+2bZst3jpLzAEBCEAgmQScFSqqPyrobY6mj62KCX0syVto7fksWG/0H9aesmJr2hvH2zwayQnjPfDwlapAV1plxddbmZlZVl7Ze9ZnQR9osj77aJVVnJVpZeavsGqCtduy7OU6+m+M/tXjgAAEIOAuAl+PLHSTm8IL9Jl3rYo3YxPw1nOBCR57z5RO2UNkavl/y9Suf5e3/vSh1LddSygimdKp950y84kikdfflw8//SqoXY8//rh9ftasWUGvcxICEIBAygg018rGp1dJg/SSnB6dQpvR+d+lMO+7oa+HuXJJmGuJu9T5Bhnyy/6y4EC4Ki6TXn0HyNVXi/zgX9uaqYGqNMrgtm3bXLnFNVzLuAYBCKQBgbP1UvNBg0i3a+WqrpcmpMHGe+DBN/K0sr35hHx84LT85Kd9JCukBeflyMH9cs2MEdK/lX5r4BmNMqiBqvLz81sVzkcIQAAC6UEgpHwaa/7Z92XBbd2l+7hF8qfaRhFplEOrFsgjX94lj/yin3z9j0Wj1G7fIpu218pZu+JGqd00WybtzJffjs5useZbg81oQmInhq8xOykIAhCAgEkCnbIk5/puJktsU1biBfzy7nLjj/rI39dOlaE//I506DBKnpOx8ubLj8jgbt/8W9H88csy6ac/lG/r9vnb5kh1hyJZ9dw46a2bfwKODRs2XNxtmdSgMQE28CMEIACBdglkXiUD7xwo0lAl2/YkJoWb8WiEiUxqrNHBcnJyZM6cOTJjxox2+XEDBCAAgZQSaNwu03vfLvNzFsqel++Xm1p1SNW25ob98tZn10hedueoTfWMgOvQyaBBg+wG7ty5k1gnUbuaByAAgeQTaJazh9bIrwePl+dzpsmKRybK6MHZAUPHr0j16X4yuvC6C+eis7Dl+ER0zwa927J0X435QwNVaaSvtWvXIt7m8VIiBCCQEAK6JHqcPLd3j2y+S2TN7TnyLxkZkpGRJbdNf1E++vZtMj5G8VZzjffAE8FA89YNHDjQDlSl2TE4IAABCEDAAwKuGaSHDh0qffv2lcWLF9P75q2FAAQgcIFAqxXW8XMxPYk5b948e+hEN+507NgxfgMpAQIQgIBPCBgfAzfJpaqqSsrKyqSiooLdlibBUhYEIOALAsbHwE31wHW3Zc+ePe1EosuWLfMFbBoBAQhAwCSBhAi4Y6COW2v+uGuvvVays7Pluuuui7gnfffdd8vBgwelsrIyuVmeHeP5DgEIQMDlBBIi4E6yz7Nnz8qZM2ekrq5OtEetx89+9jMZPXq0DB48OKSY63i3xjrRQFXEOnH5G4R5EIBAyggYn8TUlvTu3btNg3QjTkNDg/2lGZ31eOCBB+See+6xe+fOA7rbkkBVDg2+QwACEAhNwHgP/NixY/LMM8+ErlFEVMw/+eQT+fOf/2z3zFXIp0yZIldeeaWMGTNG6uvrhd2WYRFyEQIQgID5jTyRCLjD/auvvpLDhw/Lxo0b7VMlJSV2jO/9+/eTWd6BxHcIQAACIQikdBnhJZdcYg+3/OY3v5EbbrjBFu/y8nLEO4SzOA0BCEAgkIBxAe/Ro0dg+RH9/K1vfUtOnDghd9xxh0ycODGiZ7gJAhCAQLoTSMgkZrRQ33vvPXvc+80332S3ZbTwuB8CEEhbAsZ74NGSPHLkiKhwr169usVqlGjL4X4IQAAC6UYgpQKuq1Heeust0WWFRBlMt1eP9kIAAvESSKmAv/POO/YywieffDLedvA8BCAAgbQjkDIBP3TokLz77rsEqkq7V44GQwACpggYF3Bny3w4AxsbG+213/fff78UFhaGu5VrEIAABCAQgoBxAQ9Rz8XTunlHx7113fejjz568Tw/QAACEIBAdASSvozwr3/9qxw4cECqq6uJMhidr7gbAhCAQAsCxnvg4TbyaHq0l156SR5//HG59dZbWxjCBwhAAAIQiI6AcQEPVb0Onbz++ut2bsvS0tJQt3EeAhCAAAQiJJC0IRTdbamhYjVQFbktI/QOt0EAAhAIQyApPfBPP/3U3m25fPlyAlWFcQaXIAABCERDIOECrkMnr776qgwZMkTGjh0bjW3cCwEIQAACYQgkfAhFEzNoggYCVYXxApcgAAEIxEDAaA9cV5noGm/9rj1vDVTl7LbUpMYcEIAABCBgjoCxlGpVVVX2MIljWteuXW0RHzp0qKxZs8Y5zXcIQAACEDBEwIiA6+qSnJycoCZ98MEH0qdPn6DXOAkBCEAAArETMDKE4uS0DGaGijsHBCAAAQiYJ2BEwE+fPm3eMkqEAAQgAIGwBIwIeLghku9973thDeAiBCAAAQjERsCIgI8aNUpyc3PbWFBSUiI33nhjm/OcgAAEIACB+AkYEXDdGl9ZWSlz5syxLVIxLy8vl8WLF7NtPn4fUQIEIACBoASMrEIJWjInIQABCEAgoQSM9MATaiGFQwACEIBAUAIIeFAsnIQABCDgfgJmBbz5E9k08WYZsvKQNLu/7VgIAQhAwNMEjAp48+E35Pcr90rVi+/IYRTc0y8GxkMAAu4nYFDAT8v+l/4it5X9WrpVVUr14fPubz0WQgACEPAwAXMC3rhP/rjj36SwpFDu6rZBHl7xjjR6GAymQwACEHA7AUMCfl5qN/5R5IH/lOwrbpAhd90kDWtelz2NjKO4/QXAPghAwLsEzAh488dSves6GT2gi4h8V/Im3iv5DVWybc8p75LBcghAAAIuJ2BAwJulccc62XRrvvTv9HVxmdfeInfm18uaF96SY3TCXf4KYB4EIOBVAgZ2Yp6Q7dOHyu3z9wZhMEpW1DwvE7IvC3KNUxCAAAQgEA+BuHvgzbUvyUKZL2csS6yAr6ajFTKhW7W8WP0xa8Lj8RDPQgACEAhBIE4B16WDNVI48Rbp3KqCzO4/kV/clcWa8FZc+AgBCEDAFIE4BPxLadj+W5m6sINc1fXSIPZ0kh45vUSqHpZ7Hv6TNDAWHoQRpyAAAQjETiDmMfDalaMlZ+KGCzW3Hus+L7UriwOui0i3h+SNQ0/K4M5x/M2IvZ08CQEIQMB3BGIWcN+RoEEQgAAEPLLl3pcAAABDSURBVEaA7rDHHIa5EIAABBwCCLhDgu8QgAAEPEYAAfeYwzAXAhCAgEMAAXdI8B0CEICAxwgg4B5zGOZCAAIQcAj8PztnRtXcJTW/AAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>Adam’s friend Jacob wants to hike directly from the camp to meet Adam at point C .</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance from point A to point B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{B}}\limits^ \wedge {\text{C}}">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>C</mtext>
</mrow>
</math></span> is 101°.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance from the camp to point C.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\mathop {\text{C}}\limits^ \wedge {\text{A}}">
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>A</mtext>
</mrow>
</math></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>Find the bearing that Jacob must take to point C.</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>Jacob hikes at an average speed of 3.9 km/h.</p>
<p>Find, to the nearest minute, the time it takes for Jacob to reach point C.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The quadrilateral ABCD represents a park, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 120{\text{ m}}">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>120</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AD}} = 95{\text{ m}}">
<mrow>
<mtext>AD</mtext>
</mrow>
<mo>=</mo>
<mn>95</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{DC}} = 100{\text{ m}}">
<mrow>
<mtext>DC</mtext>
</mrow>
<mo>=</mo>
<mn>100</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span>. Angle DAB is 70° and angle DCB is 110°. This information is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.35.40.png" alt="M17/5/MATSD/SP2/ENG/TZ2/04"></p>
<p>A straight path through the park joins the points B and D.</p>
</div>
<div class="specification">
<p>A new path, CE, is to be built such that E is the point on BD closest to C.</p>
</div>
<div class="specification">
<p>The section of the park represented by triangle DCE will be used for a charity race. A track will be marked along the sides of this section.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the path BD.</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>Show that angle DBC is 48.7°, correct to three significant figures.</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 park.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the path CE.</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>Calculate the total length of the track.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>An archaeological site is to be made accessible for viewing by the public. To do this, archaeologists built two straight paths from point A to point B and from point B to point C as shown in the following diagram. The length of path AB is 185 m, the length of path BC is 250 m, and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{B}}\limits^ \wedge {\text{C}}">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>C</mtext>
</mrow>
</math></span> is 125°.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The archaeologists plan to build two more straight paths, AD and DC. For the paths to go around the site, angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span> is to be made equal to 85° and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\mathop {\text{C}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span> is to be made equal to 70° as shown in the following diagram.</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 distance from A to C.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{C}}">
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>C</mtext>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}\mathop {\text{A}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>C</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span>.</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 size of angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></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>The length of path AD is 287 m.</p>
<p>Find the area of the region ABCD.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Farmer Brown has built a new barn, on horizontal ground, on his farm. The barn has a cuboid base and a triangular prism roof, as shown in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The cuboid has a width of 10 m, a length of 16 m and a height of 5 m.<br>The roof has two sloping faces and two vertical and identical sides, ADE and GLF.<br>The face DEFL slopes at an angle of 15° to the horizontal and ED = 7 m .</p>
</div>
<div class="specification">
<p>The roof was built using metal supports. Each support is made from <strong>five</strong> lengths of metal AE, ED, AD, EM and MN, and the design is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">ED = 7 m , AD = 10 m and angle ADE = 15° .<br>M is the midpoint of AD.<br>N is the point on ED such that MN is at right angles to ED.</p>
</div>
<div class="specification">
<p>Farmer Brown believes that N is the midpoint of ED.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of triangle EAD.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total</strong> volume of the barn.</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>Calculate the length of MN.</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>Calculate the length of AE.</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>Show that Farmer Brown is incorrect.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total</strong> length of metal required for one support.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a semicircle with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>. Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P, Q</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math> lie on the circumference of the circle, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PQ</mtext><mo>=</mo><mn>2</mn><mi>r</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>Q</mtext><mo>=</mo><mi>θ</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>θ</mi><mo><</mo><mi mathvariant="normal">π</mi></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the areas of the two shaded regions are equal, show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>2</mn><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence determine the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A farmer owns a plot of land in the shape of a quadrilateral ABCD.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 105{\text{ m, BC}} = 95{\text{ m, CD}} = 40{\text{ m, DA}} = 70{\text{ m}}">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>105</mn>
<mrow>
<mtext> m, BC</mtext>
</mrow>
<mo>=</mo>
<mn>95</mn>
<mrow>
<mtext> m, CD</mtext>
</mrow>
<mo>=</mo>
<mn>40</mn>
<mrow>
<mtext> m, DA</mtext>
</mrow>
<mo>=</mo>
<mn>70</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span> and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{DCB}} = 90^\circ ">
<mrow>
<mtext>DCB</mtext>
</mrow>
<mo>=</mo>
<msup>
<mn>90</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.23.38.png" alt="N16/5/MATSD/SP2/ENG/TZ0/05"></p>
<p>The farmer wants to divide the land into two equal areas. He builds a fence in a straight line from point B to point P on AD, so that the area of PAB is equal to the area of PBCD.</p>
<p>Calculate</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the length of BD;</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 size of angle DAB;</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the area of triangle ABD;</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the area of quadrilateral ABCD;</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>the length of AP;</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the length of the fence, BP.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The base of an electric iron can be modelled as a pentagon ABCDE, where:</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\begin{array}{*{20}{l}} {{\text{BCDE is a rectangle with sides of length }}(x + 3){\text{ cm and }}(x + 5){\text{ cm;}}} \\ {{\text{ABE is an isosceles triangle, with AB}} = {\text{AE and a height of }}x{\text{ cm;}}} \\ {{\text{the area of ABCDE is 222 c}}{{\text{m}}^{\text{2}}}{\text{.}}} \end{array}">
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>BCDE is a rectangle with sides of length </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext> cm and </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext> cm;</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>ABE is an isosceles triangle, with AB</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>AE and a height of </mtext>
</mrow>
<mi>x</mi>
<mrow>
<mtext> cm;</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>the area of ABCDE is 222 c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mrow>
<mtext>2</mtext>
</mrow>
</msup>
</mrow>
<mrow>
<mtext>.</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</math></span></p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.05.55.png" alt="M17/5/MATSD/SP2/ENG/TZ1/02"></p>
</div>
<div class="specification">
<p>Insulation tape is wrapped around the perimeter of the base of the iron, ABCDE.</p>
</div>
<div class="specification">
<p>F is the point on AB such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BF}} = {\text{8 cm}}">
<mrow>
<mtext>BF</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>8 cm</mtext>
</mrow>
</math></span>. A heating element in the iron runs in a straight line, from C to F.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an <strong>equation </strong>for the area of ABCDE using the above information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equation in part (a)(i) simplifies to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{x^2} + 19x - 414 = 0">
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
<mi>x</mi>
<mo>−</mo>
<mn>414</mn>
<mo>=</mo>
<mn>0</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of CD.</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>Show that angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat AE}} = 67.4^\circ ">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">A</mi>
<mo stretchy="false">^</mo>
</mover>
</mrow>
<mi mathvariant="normal">E</mi>
</mrow>
</mrow>
<mo>=</mo>
<msup>
<mn>67.4</mn>
<mo>∘</mo>
</msup>
</math></span>, correct to one decimal place.</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 length of the perimeter of ABCDE.</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>Calculate the length of CF.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> lie on the circumference of the circle.</p>
<p style="text-align: left;">Chord <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>AB</mtext></mfenced></math> has length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mi>θ</mi></math> radians.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>APB</mtext></math> has length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi mathvariant="normal">π</mi><mo>-</mo><mn>3</mn><mi>θ</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><msqrt><mn>18</mn><mo>-</mo><mn>18</mn><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></msqrt></math>.</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>Arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>APB</mtext></math> is twice the length of chord <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>AB</mtext></mfenced></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in centimetres.</strong></p>
<p>A solid metal ornament is in the shape of a right pyramid, with vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math> and square base <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCD</mtext></math>. The centre of the base is <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></math>. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>5</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math> and point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The volume of the pyramid is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>57</mn><mo>.</mo><mn>2</mn><mo> </mo><msup><mtext>cm</mtext><mn>3</mn></msup></math>, correct to three significant figures.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AV</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>V</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mn>40</mn><mo>°</mo></math>, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math>.</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 height of the pyramid, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>VX</mtext></math>.</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>A second ornament is in the shape of a cuboid with a rectangular base of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo> </mo><mtext>cm</mtext></math>, width <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>cm</mtext></math> and height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mtext>cm</mtext></math>. The cuboid has the same volume as the pyramid.</p>
<p>The cuboid has a minimum surface area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>. Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A scientist conducted a nine-week experiment on two plants, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>, of the same species. He wanted to determine the effect of using a new plant fertilizer. Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> was given fertilizer regularly, while Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> was not.</p>
<p>The scientist found that the height of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mo> </mo><msub><mi>h</mi><mi>A</mi></msub><mo> </mo><mtext>cm</mtext></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> weeks can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>sin</mi><mo>(</mo><mn>2</mn><mi>t</mi><mo>+</mo><mn>6</mn><mo>)</mo><mo>+</mo><mn>9</mn><mi>t</mi><mo>+</mo><mn>27</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>.</p>
<p>The scientist found that the height of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>,</mo><mo> </mo><msub><mi>h</mi><mi>B</mi></msub><mo> </mo><mtext>cm</mtext></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> weeks can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>B</mi></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>8</mn><mi>t</mi><mo>+</mo><mn>32</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>.</p>
</div>
<div class="specification">
<p>Use the scientist’s models to find the initial height of</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>.</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>Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> correct to three significant figures.</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>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mfenced><mi>t</mi></mfenced><mo>=</mo><msub><mi>h</mi><mi>B</mi></msub><mfenced><mi>t</mi></mfenced></math>.</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>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>, find the total amount of time when the rate of growth of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> was greater than the rate of growth of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>At Grande Anse Beach the height of the water in metres is modelled by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h(t) = p\cos (q \times t) + r">
<mi>h</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>p</mi>
<mi>cos</mi>
<mo><!-- --></mo>
<mo stretchy="false">(</mo>
<mi>q</mi>
<mo>×<!-- × --></mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>r</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the number of hours after 21:00 hours on 10 December 2017. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> , for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 72">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>72</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.10.26.png" alt="M17/5/MATME/SP2/ENG/TZ1/08"></p>
<p>The point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}(6.25,{\text{ }}0.6)">
<mrow>
<mtext>A</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>6.25</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.6</mn>
<mo stretchy="false">)</mo>
</math></span> represents the first low tide and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}(12.5,{\text{ }}1.5)">
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>12.5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1.5</mn>
<mo stretchy="false">)</mo>
</math></span> represents the next high tide.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>How much time is there between the first low tide and the next high tide?</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the difference in height between low tide and high tide.</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>;</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are two high tides on 12 December 2017. At what time does the second high tide occur?</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A factory packages coconut water in cone-shaped containers with a base radius of 5.2 cm and a height of 13 cm.</p>
</div>
<div class="specification">
<p>The factory designers are currently investigating whether a cone-shaped container can be replaced with a cylinder-shaped container with the same radius and the same total surface area.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of one cone-shaped container.</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 slant height of the cone-shaped container.</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>Show that the total surface area of the cone-shaped container is 314 cm<sup>2</sup>, correct to three significant figures.</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 height, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>, of this cylinder-shaped container.</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>The factory director wants to increase the volume of coconut water sold per container.</p>
<p>State whether or not they should replace the cone-shaped containers with cylinder‑shaped containers. Justify your conclusion.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A communication tower, T, produces a signal that can reach cellular phones within a radius of 32 km. A straight road passes through the area covered by the tower’s signal.</p>
<p>The following diagram shows a line representing the road and a circle representing the area covered by the tower’s signal. Point R is on the circumference of the circle and points S and R are on the road. Point S is 38 km from the tower and RŜT = 43˚.</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>Let SR = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>. Use the cosine rule to show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} - \left( {76\,{\text{cos}}\,43^\circ } \right)x + 420 = 0">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>76</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<msup>
<mn>43</mn>
<mo>∘</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mi>x</mi>
<mo>+</mo>
<mn>420</mn>
<mo>=</mo>
<mn>0</mn>
</math></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>Hence or otherwise, find the total distance along the road where the signal from the tower can reach cellular phones.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> metres.</p>
<p>Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> lie on the circle and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mn>1</mn><mo>.</mo><mn>9</mn></math> radians.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the chord <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the shaded sector.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>The diagram below shows a triangular-based pyramid with base <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ADC}}"> <mrow> <mtext>ADC</mtext> </mrow> </math></span>.<br>Edge <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BD}}"> <mrow> <mtext>BD</mtext> </mrow> </math></span> is perpendicular to the edges <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AD}}"> <mrow> <mtext>AD</mtext> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{CD}}"> <mrow> <mtext>CD</mtext> </mrow> </math></span>.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;padding-left:60px;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AC}} = 28.4\,{\text{cm}}"> <mrow> <mtext>AC</mtext> </mrow> <mo>=</mo> <mn>28.4</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cm</mtext> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = x\,{\text{cm}}"> <mrow> <mtext>AB</mtext> </mrow> <mo>=</mo> <mi>x</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cm</mtext> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BC}} = x + 2\,{\text{cm}}"> <mrow> <mtext>BC</mtext> </mrow> <mo>=</mo> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cm</mtext> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\widehat {\text{B}}{\text{C}} = 0.667"> <mrow> <mtext>A</mtext> </mrow> <mrow> <mover> <mtext>B</mtext> <mo>^</mo> </mover> </mrow> <mrow> <mtext>C</mtext> </mrow> <mo>=</mo> <mn>0.667</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\widehat {\text{A}}{\text{D}} = 0.611"> <mrow> <mtext>B</mtext> </mrow> <mrow> <mover> <mtext>A</mtext> <mo>^</mo> </mover> </mrow> <mrow> <mtext>D</mtext> </mrow> <mo>=</mo> <mn>0.611</mn> </math></span></p>
<p>Calculate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AD}}"> <mrow> <mtext>AD</mtext> </mrow> </math></span></p>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a triangle ABC.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.20.56.png" alt="N17/5/MATME/SP2/ENG/TZ0/01"></p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 5{\rm{ cm, C\hat AB}} = ">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>5</mn>
<mrow>
<mrow>
<mi mathvariant="normal">c</mi>
<mi mathvariant="normal">m</mi>
<mo>,</mo>
<mi mathvariant="normal">C</mi>
<mrow>
<mover>
<mi mathvariant="normal">A</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">B</mi>
</mrow>
</mrow>
<mo>=</mo>
</math></span> 50° and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{A\hat CB}} = ">
<mrow>
<mrow>
<mi mathvariant="normal">A</mi>
<mrow>
<mover>
<mi mathvariant="normal">C</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">B</mi>
</mrow>
</mrow>
<mo>=</mo>
</math></span> 112°</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find BC.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle ABC.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A flat horizontal area, ABC, is such that AB = 100 m , BC = 50 m and angle AĈB = 43.7° as shown in the diagram.</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>Show that the size of angle BÂC is 20.2°, correct to 3 significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of triangle ABC.</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>Find the length of AC.</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>A vertical pole, TB, is constructed at point B and has height 25 m.</p>
<p>Calculate the angle of elevation of T from, M, the midpoint of the side AC.</p>
<p> </p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle with centre O and radius 40 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_17.31.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/01"></p>
<p>The points A, B and C are on the circumference of the circle and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{A\hat OC}} = 1.9{\text{ radians}}">
<mrow>
<mrow>
<mi mathvariant="normal">A</mi>
<mrow>
<mover>
<mi mathvariant="normal">O</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">C</mi>
</mrow>
</mrow>
<mo>=</mo>
<mn>1.9</mn>
<mrow>
<mtext> radians</mtext>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of arc ABC.</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 perimeter of sector OABC.</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 the area of sector OABC.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{16}}{x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>16</mn>
</mrow>
<mi>x</mi>
</mfrac>
</math></span>. The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> is tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8">
<mi>x</mi>
<mo>=</mo>
<mn>8</mn>
</math></span>.</p>
</div>
<div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> can be expressed in the form <em><strong>r</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} 8 \\ 2 \end{array}} \right) + t">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>8</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
</math></span><em><strong>u</strong></em>.</p>
</div>
<div class="specification">
<p>The direction vector of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x">
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ 1 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em><strong>u</strong></em>.</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 the acute angle between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></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>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right)"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right)"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the obtuse angle formed by the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8"> <mi>x</mi> <mo>=</mo> <mn>8</mn> </math></span> and the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2"> <mi>x</mi> <mo>=</mo> <mn>2</mn> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="question">
<p>The following diagram shows the chord [AB] in a circle of radius 8 cm, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 12{\text{ cm}}"> <mrow> <mtext>AB</mtext> </mrow> <mo>=</mo> <mn>12</mn> <mrow> <mtext> cm</mtext> </mrow> </math></span>.</p>
<p><img src="images/Schermafbeelding_2017-08-14_om_13.20.17.png" alt="M17/5/MATME/SP2/ENG/TZ1/05"></p>
<p>Find the area of the shaded segment.</p>
</div>
<br><hr><br><div class="question">
<p>The vector equation of line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> is given by <em><strong>r</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} { - 1} \\ 3 \\ 8 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 4 \\ 5 \\ { - 1} \end{array}} \right)">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>8</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>5</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>Point P is the point on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> that is closest to the origin. Find the coordinates of P.</p>
</div>
<br><hr><br><div class="specification">
<p>A metal sphere has a radius 12.7 cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the sphere expressing your answer in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \times {10^k}">
<mi>a</mi>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mi>k</mi>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 \leqslant a < 10">
<mn>1</mn>
<mo>⩽</mo>
<mi>a</mi>
<mo><</mo>
<mn>10</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in \mathbb{Z}">
<mi>k</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></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>The sphere is to be melted down and remoulded into the shape of a cone with a height of 14.8 cm.</p>
<p>Find the radius of the base of the cone, correct to 2 significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket is travelling in a straight line, with an initial velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="140">
<mn>140</mn>
</math></span> m s<sup>−1</sup>. It accelerates to a new velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500">
<mn>500</mn>
</math></span> m s<sup>−1</sup> in two stages.</p>
<p>During the first stage its acceleration, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> m s<sup>−2</sup>, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( t \right) = 240\,{\text{sin}}\left( {2t} \right)">
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>240</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant k">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mi>k</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>The first stage continues for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> seconds until the velocity of the rocket reaches <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="375">
<mn>375</mn>
</math></span> m s<sup>−1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> m s<sup>−1</sup>, of the rocket during the first stage.</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>Find the distance that the rocket travels during the first stage.</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>During the second stage, the rocket accelerates at a constant rate. The distance which the rocket travels during the second stage is the same as the distance it travels during the first stage.</p>
<p>Find the total time taken for the two stages.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a right-angled triangle, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ABC}}">
<mrow>
<mtext>ABC</mtext>
</mrow>
</math></span>, with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AC}} = 10\,{\text{cm}}">
<mrow>
<mtext>AC</mtext>
</mrow>
<mo>=</mo>
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cm</mtext>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 6\,{\text{cm}}">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>6</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cm</mtext>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BC}} = 8\,{\text{cm}}">
<mrow>
<mtext>BC</mtext>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cm</mtext>
</mrow>
</math></span>.</p>
<p style="padding-left: 120px;">The points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{D}}">
<mrow>
<mtext>D</mtext>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{F}}">
<mrow>
<mtext>F</mtext>
</mrow>
</math></span> lie on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left[ {{\text{AC}}} \right]">
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mtext>AC</mtext>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</math></span>.<br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left[ {{\text{BD}}} \right]">
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mtext>BD</mtext>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</math></span> is perpendicular to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left[ {{\text{AC}}} \right]">
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mtext>AC</mtext>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</math></span>.<br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BEF}}">
<mrow>
<mtext>BEF</mtext>
</mrow>
</math></span> is the arc of a circle, centred at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
<mrow>
<mtext>A</mtext>
</mrow>
</math></span>.<br>The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R">
<mi>R</mi>
</math></span> is bounded by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left[ {{\text{BD}}} \right]">
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mtext>BD</mtext>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left[ {{\text{DF}}} \right]">
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mtext>DF</mtext>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</math></span> and arc <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BEF}}">
<mrow>
<mtext>BEF</mtext>
</mrow>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\widehat {\text{A}}{\text{C}}"> <mrow> <mtext>B</mtext> </mrow> <mrow> <mover> <mtext>A</mtext> <mo>^</mo> </mover> </mrow> <mrow> <mtext>C</mtext> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle, centre O and radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> mm. The circle is divided into five equal sectors.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_15.31.24.png" alt="N16/5/MATME/SP2/ENG/TZ0/03"></p>
<p>One sector is OAB, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{A\hat OB}} = \theta ">
<mrow>
<mrow>
<mi mathvariant="normal">A</mi>
<mrow>
<mover>
<mi mathvariant="normal">O</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">B</mi>
</mrow>
</mrow>
<mo>=</mo>
<mi>θ<!-- θ --></mi>
</math></span>.</p>
</div>
<div class="specification">
<p>The area of sector AOB is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20\pi {\text{ m}}{{\text{m}}^2}">
<mn>20</mn>
<mi>π<!-- π --></mi>
<mrow>
<mtext> m</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <strong>exact </strong>value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta "> <mi>θ</mi> </math></span> in radians.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></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>Find AB.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math>. Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> lie on the circumference of the circle and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mn>2</mn><mi>θ</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>θ</mi><mo><</mo><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></math>.</p>
<p>The tangents to the circle at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> intersect at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext><mo>=</mo><mi>tan</mi><mo> </mo><mi>θ</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> when the area of the shaded region is equal to the area of sector <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>OADB</mtext></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the quadrilateral ABCD.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">AB = 6.73 cm, BC = 4.83 cm, BĈD = 78.2° and CD = 3.80 cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find BD.</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>The area of triangle ABD is 18.5 cm<sup>2</sup>. Find the possible values of <em>θ</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows part of a circle with centre O and radius 4 cm.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Chord AB has a length of 5 cm and AÔB = <em>θ</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>θ</em>, giving your answer in radians.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the shaded region.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Consider a triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AC</mi><mo>=</mo><mn>12</mn><mo>,</mo><mo> </mo><mi>CB</mi><mo>=</mo><mn>7</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>C</mtext><mo>=</mo><mn>25</mn><mo>°</mo></math>.</p>
<p>Find the smallest possible perimeter of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ABC</mi></math>.</p>
</div>
<br><hr><br><div class="question">
<p>Triangle ABC has <em>a</em> = 8.1 cm, <em>b</em> = 12.3 cm and area 15 cm<sup>2</sup>. Find the largest possible perimeter of triangle ABC.</p>
</div>
<br><hr><br>