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<h2>SL Paper 2</h2><div class="specification">
<p>A wind turbine is designed so that the rotation of the blades generates electricity. The turbine is built on horizontal ground and is made up of a vertical tower and three blades.</p>
<p>The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is on the base of the tower directly below point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> at the top of the tower. The height of the tower, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math>, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo> </mo><mtext>m</mtext></math>. The blades of the turbine are centred at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and are each of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo> </mo><mtext>m</mtext></math>. This is shown in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The end of one of the blades of the turbine is represented by point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> on the diagram. Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> be the height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> above the ground, measured in metres, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> varies as the blade rotates.</p>
</div>
<div class="specification">
<p>Find the</p>
</div>
<div class="specification">
<p>The blades of the turbine complete <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> rotations per minute under normal conditions, moving at a constant rate.</p>
</div>
<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>, of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> can be modelled by the following function. Time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, is measured from the instant when the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> first passes <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math> and is measured in seconds.</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>90</mn><mo>-</mo><mn>40</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mn>72</mn><mi>t</mi><mo>°</mo></mrow></mfenced><mo>,</mo><mo> </mo><mi>t</mi><mo>≥</mo><mn>0</mn></math></p>
</div>
<div class="specification">
<p>Looking through his window, Tim has a partial view of the rotating wind turbine. The position of his window means that he cannot see any part of the wind turbine that is <strong>more than</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="bold">100</mn><mo mathvariant="bold"> </mo><mtext mathvariant="bold">m</mtext></math> above the ground. This is illustrated in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeIAAAFQCAYAAABj633dAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACa3SURBVHhe7d0JeJTV3ffxn6kFJBGRJUWIkUBSSnBh0ZQK8taVFK2NUOtSgmDBarFUqK1AlLZuAV8EilsfsRoJWuxbaB4VHpG1KH0sSMAl0TRoMBACKgQipEIxfedMzmiALDPJJPd9z3w/15WL+5wZJkDC/HLOfc7/nPQfHwEAAEfE2F8BAIADCGIAABxEEAMA4CCCGAAABzV5sdb27du1c+cO7d692/YAABB9unXrpt69k3XGGWfYntCEHMQmgFeufFV79+61PQAAoHPnzrrqqu+HHMghBfGqVav05pubbAsAABxv6NChvo+LbKtxQQcxIQwAQHDOP/8CXXbZZbbVsKAWa23atIkQBgAgSCYz3377bdtqWKNBfPDgQa1evcq2AABAMNauXaMjR47YVv0aDeI33njDXgEAgGD961//0ltvvWVb9Ws0iAsK3rVXAAAgFFu3brFX9WswiM0WJZPoAAAgdCZHG5uebjCIg5nbBgAA9Wus7kaD25fKy8v17LM5ttWwSy8Nbpk2AOc9//zz/q0V8fHxtid0hw4d0gsvLNbIkaPUsWNH2wtEj2AXMt9009gGi3yELYinTp1mrwC43fTp0zVu3DilpKTYntDNmjVLPXr00OjRo20PEF1mzsy2Vw1rLIgbXawFAMczK0GXL1+mUaNG2R4ATUUQA1GooqLCXoXOLOB84IEHlJ09U6eccortBdBUBDEQhZYte6nJ09IrVqxQcnKyLrzwQtsDoDkIYiDK7Nu3T0lJvWwrNOb3Tpp0u+68807bA6C5CGIgyrz//vsaMmSobYVm9uzZmj//UXXq1Mn2AGgughiIMmahVVpamm0F7+9//7u2bdum4cOH2x4A4UAQA1Fm7dq16tevn20FxyzQmjZtqrKysligBYQZQQxEEXOPd8+e3SEv1FqyZIlGjLhS5513nu0BEC4EMRBF8vM36/rrb7Ct4JSVlWnBgic1YcIE2wMgnAhiIIosWbI05G1H999/vyZPnsICLaCFEMRAlDDT0oWFBSFNL69atdJfsD4jI8P2AAg3gtg1jmp33u1KTByuufkHbd/xgnlOMHYob/y5Suw/R/lHbRci3vr160OaljYLtO677z5/FS0ALYcgBlzH/qCUmFDnR9/xc7R0XbFC/VHMnLgUyrR0Tk6OP7ibczAEgMYRxIDrnKmMp97W9tX3q7866Yr5/6vS0p2+j1IVrn5Gt2ix7hjzY92ZV6pq+zsaU1xc7P812Glp8/zFi/+ksWPH2h4ALYUgdp0KFayep/F97QgoPUu5+bvrf8M9WKx1OVlK/3LE1EfpWc8pf/cR+wQf33NWz/2J+tZ6fNPOw/bBGtW7Nyk36/v2Ncyoa75WF1faR+GEmFM76tjTgmMUl3K5fnHXz3wBvUvLn16jD4JM4lWrVunGG2+0rcaZ/cL33HMPe4aBVkAQu84uvfr0Tg3NK1Tp9o1amPa2sjJu0+/z99vHa6kuVd6dP9aYxado6sYPfSOmD7VxyWQlLL1LP37k7/LHqH3OuBU9lL3avOZaTf3aBuUWHvK/hN/BTfr92NF6cM+VWmJex/d5n+i+UuOuvkd5u2oFOlwh5hs9dU6sbQTBLNLKzn5Aw4YNsz0Ny8vLU+fOnXXZZZfbHgAtiSB2ne4akT1dY/p08H11uuu7v56hyamFenLJ1ppgraX6gzV6evkB9b/+Wg3r1sbX00bdBl2soSmxOrQsX9uOBp7TRplTJykjxb7mnb9U5pdv5J+r+C/zNLfwfN1111hdYF4n8Bwt0bTHbKDDHQ4WKW/Ww8o95Ps+ufkS9Q7if7BZpDVtWlZQ249MaM+dO0dTpkyxPQBaGkHsOika3C/+qy9MXJIGDOr6ZbDWFpMyVi+Wvqfnh+zRi75RTF7eYs29JVMztgZGu0f1ccGb2qr+uuBbHW2fT4feumBI4E35ExW8/o7UaZDOTWpn+3zsc+r6vGhN+/TqpO98ecsgMfVSTcrdotjMh/RQRmKj/4HNymcTrJdddpntadiCBQs0YcItLNACWhFB7Dqnq+OpJ9tro506dKlnHrJ6l9bN+IFSL71R017+UNW+5yaNfkD3XhEI2c+1q6Rmkc6xTldivzNqLqurtP/jw773+znK6GXf7P0f39GkV/fVPAcOqr1Ya6e2b3xR8ycPl3JH69vjc1V0sOGbxFu2bPGftBRMsJrDIJYvX6ZRo0bZHgCtgSB2vc9V+Wmt+7lfqlbl+j/otpw9GjH/7yp4aopGZmQoY1iiZILVr526J5k34Art/6z2sLZCpQXlNZcx7dUxvq3U/36t3l7zZn/Mx9YpGlj75wI4KqbbQGVMnqUnMnvq0Kv361d/KW5w5fS8efN03XXX2Vb9zMjZ7BfOzp7JAi2glRHErrNVm96vtTCr8l2tXLpdsVcOVPIxgVitqv37dOj4qeyD5SouDgT3yYrvd7766yMVl9XadVr5gTZtCIx2u6rf0HN8n3alNnzwue3zqS5SztV9lHh1joqD3SMDVzHHFhrBbFlasWKFkpOTQy5/CaD5CGLX2a7cmfOVZ7YOmann2Q8rV6OUPfFCdbDPqBGjuMRvKlVvavHL7/iLO/i3IPkX8vgah/ersqpaMb0v0c0jjij3truVU1TrNb8cZLdT7yuu1YjYv2nWrBxtMtueqndr06MPadbWVE3+bYZS+C5xQLUO7irVTtv6ku9rk587VzNzt0ux6br5iqR6/xOb0fAdd9xhW/UzC7QmTbpdEydOtD0AWhNvsa4zQJnDD+sPl6YqsWeaxmwcoPkv3qeM7mZVdG2+IB44Vo/Mv06ae41SExPUM+1evZ9ym+ZPHiId+kDb9/hCNSZRGbOf0zO3/FuzLjevebFmfjFEmalf3XeO6Z6hx9f+VdO/sUyj0nr5nnO+Ri3vpul5T+gXA2st8kIrMZW1+is14yEVHr9Yy/e1ychaqYTJc7Wwzu+LGoHRcDAj3NmzZ2v+/EfVo0cP2wOgNZ30Hx97fYLy8nI9+2yObTVs6tRp9gqA0370ox/5R8ONBbFZoGXuDT/77LPcGwZCNHNmtr1q2E03jdUZZ9gFsnVgRAxEmGBHw2aB1qRJP/dX0SKEAecQxC5i7tWZGr/1fZgD2oG6mFANfJ+YEe7Pf367faR+S5Ys8W9tCuVYRADhx9S0i/z5z3/W448/5hvJDLE9x9q2bZveeKNmtNOQpKRe/jfYYKSlpdmrhvXr189eNSwhIYHRVSsyo9+nnlrgPzf4iivS9cUXR3X06Bf629/WasCAgfrVr36toUNP/F4wP9TdeOMN+utf8zjwH2iicE1NE8QuYkbEt956qz+Qm8O8jjnMvTFVVVUqKSmxrfodPHhQhYWFttWwRYsW2quGDR58oX+7TGPOPPPMBr+BA+LiYnXWWT1tq37t27ePiEVJZgR8991ZKigo0KhRP/QX7Gjbtq19tIb5we2ll170/dvE6b777j/m7z19+nT/D2Ec+A80HUEcoaLlDdKMyMwPAo356KPtvh8E6ipocizzvbpjxw7bql+wswrG6NFj7FXDgp1VSEpK8v8g0JjGZhVMCE+c+DN17dpV3/veiBMC+HivvrpCr7zyP/rLX5b6w9iMnp98ckGzf+ADoh1BHKHMaPaaazL8FY4oruAcE3Y7d56wi/cEwc4qGBs3brRXDWtsVqFbt266+OJLfD+sXWN7Gvfaa+tVWPiennjiCaWnD9dTT/2RetJAMxHEESxw/84U3x89erTtBWq2G02efIdmzPhNoyPh45l7yWakfeaZibrrrrtsL4CmYvtSBDPTh2YRjbkve9ttt/lXwgLG0qVLdcMNN4YcwkZ6err+8Y9/aNKkSbYHgBsQxC5lVrI++OCDGjVqpMaP/4l/StFMWyO6PfNM3VPKn3zyiaZMmazrrrtWd9zxC3/7eAkJZ8pMgPF9BLgLQexyl112uV55ZYV/WsPcO541axYj5Chlvu5Dh15U52h4wYIntXPnDh0+/Ll27SrT1Kl1Tz2fc845QS2SA9B6CGIPMPf1zCpqE8h9+vTxV0IyJQzN6ldGN9Hl1FOPPfoj4K23turIkcP697+P+H89ePAz+8ix4uPj/VueALgHQewhgUA2205MGG/enK/+/c/130cmlKPDZ59V2qtjnXdef7Vp01Zf/3ob/69xcafaR4718ccfB12cBUDrIIg9ypQlNCtfi4qKlZmZeUwo5+XlUQ4zApl7w6+//poOHz5se75iVtibe8Bt27bzb2+aOXOWfeRYZgFgMHuZAbQeti9FELP39Z///Ke/7OHatWu1Z89ujRhxpQYNGqi+fVM55s6jaq8J+MMfntC3vtVXZ599tu0JnrmHvGjRIv33f79oewA0B/uI0SgzVZ2fv9k/Wt68ebM/mE0NalMJylR5+uY3v0ldaAcEqooFqobVrgp2fOWv4+uGm9XQJSUf6u677wl5C5MJ8R/8IEMjR460PQCagyBGyEwwv//++/rwww/9U5SmgpOp+Txo0CD/IjATzqa2M4cAhIf59zYBaypvmapagZAN1NkO1NGuXSe7c+fOjf7733bbrf7p5R/+8Frb0zhTWWvVqlUaP36Cf6EfgOYjiBEWZtrTjLJqh7Nh6iwHgsIs7gkmIKJd4Aed1157TcuXL/P31Z6B6NKlS1huD/z617/2j4p79eoVVK1pE8J//etSPfro47rmmh9o69a3+VoCYUAQo8WYQDGnN5ltLoFp0w0bXve/+V955fd1+umn+8MlMJKLlBONmsLclzf/NkuWLNWyZS9p4sSft/g9eXMwyA033KCcnGe+PH2prnvGdZ2+ZBbymdG5KRYDoHkIYrS6wEEIZgRttsEcH9KB+5mnnXaaf6rbCGyVibRzis2/xYoVKzR37hz/3/mqq67SgAEDWuXvaIJ43LhxdhX163r66T/6t69ddNEwtWnTRjExMXr33Xf9q6ePP4/Y/Llvuukm3XHHHRwqAjQTQQzXCSxCCgR17XOMA1PetRcf1T5ruPYRgW6fBg8cymH+HhMnTmz12YDExIQTppdNwObk5Oidd97W5MlTGvw3NLcjTNlUUyCGxXpA0xHE8KTAtLdR+6zhoqIiHThwwH99/Mrh2ucC1x5tB9R1zm9LTZcHQtjJYypNEJeWnnhEownjYI84NNuYzN+FU5iApiOIETWOr619fInGwBT58QJT5nUJ3OsO1fbt23XzzeP8NcCdUl8QG2aKes2atY3eA2aKGmg+ghhopuMDPhhmRfTNN99sW85oKIgNsz0pmIANTFGbIzdZRQ2EjiAGolRjQWwqq82bN89fk7wxZora3MdnFTUQunAFMbWmgQhjRsJmsZaZpm7M6NGjVVFR4d/WBMAZBDHgIWaxm1l53pgpU6bovvvu898Lbszdd9/t34bVlKl6AM1HEAMeYlacB7Z/NcSsmjbPM3udG2NWl5tV4OZ+cTDBDSC8CGIgQpk9zmaka0bRjTHT2ddff4N/JA2gdRHEQIQyI10Tri+88ILtaZg5y9p44okn/L8CaB0EMRDBrrvuOmVnPxDUqNiYM2eOFi/+U1ALvQCEB0EMRDCzP3j+/Ec1e/Zs29MwU/Ly+ef/5F/oZbZBAWh5BDEQ4YYNG6Z169YGvSo6sHhr2rSp/jKYAFoWQQx4iCnvmZqaalvBMSutzQEbzzzzjO1pnFm8ZcLY1NUmjIGWRRADHmPOFw5V797J/sM0QpluJoyB1kEQA1HC1J82pS9DQRgDLY8gBqJEKKUvawuE8Xe+820WcAEtgCAGokgopS9rM2G8evVa/wIuc1AEFbiA8CGIgSgSSunL45nfa45MNKc1mbOMGR0D4UEQAx5ijiaNi4u1raYJpfTl8cy+ZHNkYlZWlnJzc/1HMg4e/G3fSJljUIGmIogBD9mxY4fOOqunbTVNqKUv63Leeef5S2Gac5EfffQx3+h4A9PVQBMRxEAUCrX0ZUPOP/98f7Dn5OTYHgChIIiBKBRq6cvGmGA3NarZ4gSEjiAGIlxCQoIWLVpoW18ZPny4Nmx4PejSlw0xwT558hQ99thjtgdAsAhiIMKZgxzqYvpNeIZS+rIhJthN9a633nrL9gAIBkEMRLGMjIyQS1/WxwS7qd71wAMP2B4AwSCIAQ8xU8xmqjmcmlL6sj5Nrd4FRDOCGPCY+qaamyrc4dnU6l1AtCKIAYQ1PE0FrhEjrmxS9S4gGhHEAJpV+rIuEyZM0KRJt4dlnzIQ6QhiAH6B0pfhGBWb7UzTpmU1q3oXEC0IYgB+gdKX4aqQNXbsWH+Rj3DsUwYiGUEMeISZ5k1K6mVbLSOcpS/DvU8ZiFQEMeARe/fu9d/HbUmB0pcLFiywPc0TzupdQKQiiAEcw4Tn8uXLwhKeZlScnT1Tc+bMsT0AjkcQAzhGuKeUzT5lM5oPR/UuIBIRxABOECh9Ga660eGs3gVEGoIYQJ3CWTc6UL2LUTFwIoIYQJ3CHZ6mepcZFVP6EjgWQQx4REFBgVJTU22rdZjwnDZtathKXyYnJ1P6EjgOQQx4SFxcnL1qHeEufTlu3LiwVe8CIgVBDKBB4Sx9Ge5gByIBQQygQeEufcmoGDgWQQygUeEsfckxicCxCGIgCgwefKHKyspsK3ThLn1pjklkVAzUIIgBjygvL1dcXKxthcasVq6qqrKtpgln6UsT7Ga6m1ExQBADnrFjxw6ddVZP22p94S59aaa7GRUDBDGAEISz9CWjYqAGQQwgJOEsfcmoGCCIAYTIlL40wlH6klExQBADaAIzIg5X6UtGxYh2BDGAkIWzQhajYkQ7ghjwiEWLFiohIcG2nBfOCllXX301o2JELYIY8BCzhcgtzKg4XKUvTRlNalAjWhHEAJosnKUvqUGNaEUQA2gyc3/3wQdnhqX0JSczIVoRxACaZdSoUWErfWlGxc8//7xtAdGBIAbQLOEsfWlGxaYudjj2KANeQRADHmDuwSYl9bIt9zEHQoSr9OVVV12lefPm2RYQ+QhiwAP27t3rv3/qVmZUHK7Sl+Gs3AV4AUEMICzCGaAm1F9++WXbAiIbQQwgbMJV+tKE+oYNr4dlARjgdgQxgLAJ5xakcJ59DLgZQQwgrMJVmMMsADOj4nAUCwHcjCAGEFbhKn1pFoCZ13nhhRdsDxCZCGLAAwoKCpSammpbTVNVVWWvWl64Sl8GXoeyl4hkBDHgEXFxcfYqdGlpaSopKbGtlheu0pfmdSZO/DllLxHRCGIALSJcpS9Hjhzpv+cMRCqCGECLCFfpS3PPOTW1HwU+ELEIYgAtJlylLzMzM5Wbm2tbQGQhiAG0mHCVvjQFPgoLCyjwgYhEEAMeUF5erri4WNvylnCVvjTT3KtWrbItIHIQxIAH7NixQ2ed1dO2vCccpS+HDRvGViZEJIIYQIsLR+lLtjIhUhHEAFpFOEpfmq1Mzz//vG0BkYEgBtAqAqUvlyxZYntCZ17DaO4qbMBNCGIArcaUrJw+fWqzSl/ecssEvfLKK7YFeB9BDKDVBEpfNucgB3Ov+bHHHuFUJkQMghjwgEWLFiohIcG2vM2Uvly8+E9N3hNs9iZPm5al9evX2x7A2whiwCNMAEWCcJS+NHuTWbSFSEEQA2h1gdKXTR0Vn3feef5fqbSFSEAQA2h1gdKXWVlZtid0N954I5W2EBEIYgCOaG7pS1Npy9xrptIWvI4gBuAYU/py3rx5TQpTswLbHI+4ZcsW2wN4E0EMuJzZppOU1Mu2Iosp0JGcnNzkspXmeMSXX37ZtgBvIogBl9u7d69/72ykak7pywEDBvi3drGnGF5GEANwVHNKX5pFX+YgiPz8zbYH8B6CGIgC8fHxKioqsi33aU7py/T0dF+IL7UtwHsIYiAKdO3aVQcOHLAt92lO6Uuzp7iwsIDpaXgWQQzAFZpT+tJMbTM9Da8iiAG4QnNKX5o9yUxPw6sIYsDlCgoKlJqaaluRzZS+3LDh9ZBHxUxPw8sIYsAD4uLi7FVkM6Pi7OyZTSp9OWLElUxPw5MIYgCu0tTSlxdddJHWrFlrW4B3EMQAXMeMiEMtfRko7kHtaXgNQQzAdcw931BLX5pp7dGjx1B7Gp5DEANwpaaUvrzkkov11ltv2RbgDQQx4HLl5eWKi4u1rehhSl+aBVihlL7s2zdVa9dynxjeQhADLrdjxw6ddVZP24ouEyZMCKn0ZY8ePbRnz26VlZXZHsD9CGIArmVKX06blhVS6Uszin7vvULbAtyPIAbgamPHjg2p9OWgQQO1eXO+bQHuRxADcLVQS1+a+8SbN1PYA95BEANwvVBKXwbuE1PuEl5BEANwvVBLXw4ZMtS/yA3wAoIYcDlTLSohIcG2olcopS/T0tJUUlJiW4C7EcSAB5gRIYIvfZmUlKSNGzfaFuBuBDEAzwi29GWXLl20bds22wLcjSAG4CnBlL40C7beeCO005sApxDEQJSoqKiwV94WbOnLpKRerJyGJxDEQBQw4bVs2Uu25X3BlL40K6f37t1rW4B7EcSAi5mgMSM7HKsppS8BtyKIARczIzozssOJQi19CbgVQQzAk0ItfQm4FUEMwLNCKX0JuBVBDMCzQi19CbgRQQzA0+orfWkKerRv3962APciiAF4XqD0ZYBZbW5OYDKFPQC3I4gBFysoKFBqaqptoT6m9KU5GOOnP71Fv/vd7/zbmq6//gb7KOBuBDHgcnFxcfYK9THlLles+B8tX75MCxb8l7KzH+DEKngGQQzA87Zs2aLKykp9/nmVL5QPqbq6Wq+9tt4+CrgbQQzA82JjY3XSSScpJuZrvo8Y/3VsLDMJ8AaCGIDnmXvEaWnfVtu27dSuXXuddlpHjR8/3j4KuBtBDCAi5OYu0uLFf9Yjjzym9etfY8U0PIMgBlysvLxccXGxtoWGmOIeZk9xRkaG/1AIwCsIYsDFduzYobPO6mlbaL5KFa/7f5o7Pk2JiQk1H+lZyllXpF3r/q9mrPvUPg9oPQQxgOhQvUvrZvxYl45ZqE+HPqTVhaUqLd2p7Tmj1HHLQ77+XO3a/y/7ZKD1EMQAosB+5f9+osbk7NGI+Y/pvrHfVUpczdtfTLeBypj8sJ6bfI6/DbQ2ghhA5KvcqiVPbpJi03X9JQl1vPF1VP/rrlfiZ1Wqtj1AayGIAUS4alXmr9HSQ74cHnmJBnao+20vpvv3NSOzD2+KaHV8zwGIcNWq2r9PvhxW2y4dxHlMcBuCGHCxRYsWhq1m8uDBF6qsrMy2otPhTytVZa8BtyCIAZcz+2PDITk5WVVV0RhDJyu+3/nq77s69M527eEmMFyGIAYQ8WJ6X6KbR3SXtj6uh18srXNBVvXudZqfk6+Dtg20FoIYQOSLSdTVv83W2NQDWj5pou7JWa783Ufsg5UqXj1fP/vtDg3/YX9xVARaG0EMICrEdLtU9y7/m/LmX6w9s25RRlqvmspafSfr5c+G6rePZ6qP3VsMtCa+6wBEj5huGpgxRU+9t9NfVcv/8d4fNTljoLrxbgiH8K0HuNS+ffuUlNTLtgBEKoIYcKm9e/dqyJChtgUgUhHEAAA4iCAGAMBBBDEAAA4iiAEAcBBBDLhUdJajBKIPQQy4VElJiVJTU20LQKQiiAEXi4uj4CIQ6QhiAAAcRBADAOAgghgAAAcRxAAAOIggBlyqqKhI8fHxtgUgUhHEgEsdOHBAXbt2tS0AkYogBqLEaaedpk8++cS2ALgFQQxEiT59+ujjjz+2LQBuQRADAOAgghgAAAcRxIBLVVRU2CsAkYwgBlxq2bKXlJKSYlsAIhVBDACAgwhiAAAcRBADAOAgghgAAAcRxAAAOIggBlyorKxMgwdfaFsAIhlBDLhQVVWVkpOTbQtAJCOIAQBwEEEMAICDCGIAABxEEAMA4CCCGHAhs1gLQHQgiAEXKikpUVpamm0BiGQEMQAADiKIAQBwEEEMAICDCGIgSiQlJWnjxo22BcAtCGIgSrRv395eAXATghhwoaKiIsXHx9sWgEhGEAMudODAAXXt2tW2AEQyghgAAAcRxAAAOIggBgDAQQQxAAAOIogBF6qoqLBXACIdQQy40LJlLyklJcW2AEQyghgAAAcRxAAAOIggBgDAQQQxAAAOIogBAHAQQQy4TFlZmQYPvtC2AEQ6ghhwmaqqKiUnJ9sWgEhHEAMA4CCCGAAABxHEAAA4iCAGAMBBBDHgMmaxVkto3769tm3bZlsA3IIgBlympKREaWlpthU+PXr00Btv/N22ALgFQQwAgIMIYgAAHEQQAwDgIIIYAAAHEcQAADiIIAZcpqioSPHx8bYFINIRxIDLHDhwQF27drUtAJGOIAYAwEEEMQAADiKIAQBwEEEMAICDCGLAZSoqKuwVgGhAEAMus2zZS0pJSbEtAJGOIAYAwEEEMQAADiKIAQBwEEEMAICDCGIAABxEEAMuUlZWpsGDL7QtANGAIAZcpKqqSsnJybYFIBoQxEAUufLK76u4uNi2ALgBQQxEkdNPP91eAXALghgAAAcRxAAAOIggBlzELNYCEF0IYsBFSkpKlJaWZlsAogFBDACAgwhiAAAcRBAjRDuUN/5cJfafo/yjtgsA0GQEMQAADiKIAQBwEEHsqEoVr56v8X0TlJjo+0jP0tNzf6K+icM1N/+g73E7DZw+VuPT+9Q85+ocFVdX62DxOuVkfb+mz/fRd/wc5eXvVrX/deuaPj6q3Xm3+55rX3t3nsYnnquxcxcr98vX6aP0rDwVH6x5Fb+DxVrt/zMFHn9Om3Yetg8i3IqKihQfH29bAKIBQeyYI9qVd4+uHrdS38hercLSD7Vx6in689wVOmSf8aXCQun6pSrc/qZevDddSbtf1J1Xj9asPT/SysJSlW7fqCe6r9WkjNv0+/z99jcFY5/WzH1O718wu+bzL8yUcm/X1dnrfT8i+FSXKu/OH2vcih7KXl3o+zxrNfVrG5RbeMKfEGFy4MABde3a1bYARAOC2CnVJXr16VekzF/qrow+ilMbdfvurZqa2dM+obY0XeUbEcfFdFP//ifr9cdma7lGKfve69QnzvcljOmu7/56hianFmrub30j2loD2sbE1v78w67V9f1jdWhZvrb5RtLVH6zR08vbKHPqJGWkdKj5PHf+Upmx9jcDAJqNIHZI9Qf/q6Vb22rIBb3lizirkwZefolOyLlOvZTY5eSa6+q92v7OJ1LKAPXr1qamz4hL0oBBvpFU8Ycqqz213Ii2XTqovb1WTHt1jG9rG0f1ccGb2qr+uuBbHW2fT4feumBIJ9sAADQXQeyQ6s/2qdRefyVG7Tt0VCAK61R9SBWlh6T4jjr1mK9eO3Xo4ovwQ/u0vyqEIXG9PteukrqOyztdif3OsNcAgOYiiB0Sc2onJeqwPt5fZRdYGdWqqtzv621ATKxOT/QF7sf79dkxefu5Kj/1BXRsJ3VsH44vazt1T0rx/Vqh/Z/V3jBcodKCcnsNAGgugtghMb2/o5H9peLicpn10TUqtW3LOycu1qotprN6nmOmoLeoYPcR2+lzsERbNpsp617qYe4bn2C/3t+01V4H42TF9ztf/fWRisu++hOq8gNt2rDPNhBuFRUV9gpAtCCInRKTpCtuTpdyH9asvCJfGB/R7nWPavrcTfYJ9emiYRPv1Agt0bQZL6jI3A+u3qV1D92ruYWpmvzbDKXEdFW/oedI+xbr8UUFNa+96S9atHS7fY3gxPS+RDePOKLc2+5WTlFlzeeZ/bByWTTdYpYte0kpKWYmAkC0IIgd00bdM+7Ti89crj3TLlVqYi+lzfxMwzMH2MfrF9P9as1+cZHu+safdXlqohJ7pum2XRdrft4T+sVAs7CqnVLGPKwld56jDTOG+1/74v/6TBeObPy1jxGTqIzZz+mZW/6tWZen+j7PxZr5xRBlprJsGgDC5aT/+NjrE5SXl+vZZ3Nsq2FTp06zV2g6U3TjDqVNkuZvnKeMbnalNKKGKaxSWrrTthq2bt1ajRmT6b8ePjxd8+c/olNOOcXfrs/06dM1btw4Rt1AGMycmW2vGnbTTWN1xhn1L3JlROyUynXK6msqYuXWTC/LVMt6WY/8YaViR1ymtHhCGPUrKyvzh/AXXxzV4cOfa8WKVzRv3jz7aP3OPPNMffRRaLcoALQsRsSOOaLd+cv1p8cf1NxXd9m+Acq895ca+8NhSrELrswICahPVdVBVVdXq1279vra176mk046yT4CLwt2VgTOCteImCAGPGjfvn3q3/9cfwgfPfpvtWnTVllZd+unP73VPgNAS2NqGohinTp10sKFuYqP/4Y/hH/ykwkaM+Ym+ygALyGIAY/67ncvVn7+Fv805m9+85tGF2oBcCeCGAAABxHEAAA4iCAGAMBBBDEAAA4iiAEAcBBBDACAgwhiwLOqVbluhvomXqO5+fttHwCvIYgBr6reqTWLX9EhbdKTS7aq0nYD8BaCGPCo6g/W6OntqboiNVaHlq5RfqU5PASA1xDEgCd9qvU5udL1U/SbW9MVe+gVLV6zU0Qx4D0EMeBFle9q5bKzdfMV39KZl1yjkbG7tPzpNfqAJAY8hyAGPOdzFS9doKVXXqNLureROpyty0f2lLau1IYPPrfPAeAVBDHgNQff0cuLv667xg5WB39HJ50/6kdK1d80K+cNFm0BHkMQA55Srco3X9KThas049JkJSYm+D4SlZrxkAp9j7JoC/AeghjwkupiLZ2zQSMXbvUff/jVxzatvvf/+JJ4jVbm77NPBuAFBDHgGZUqWjhXs0qv1KihXWxfQDulpF+rK7RduTPnK6+YCWrAKwhiwBMOKn/utbp8xss6tG+OMnrdrrzdR+1jPrvzND7tdr1qrguf1qRLh2p83g7/QwDc7aT/+NjrE5SXl+vZZ3Nsq2FTp06zVwAARL6ZM7PtVcNuummszjjjDNs6ESNiAAAcRBADAOCgsE1NAwCAEzE1DQCAg9q0aWOv6tZgEHfu3NleAQCApmgsSxsMYpPiPXok2BYAAAjF2WefY6/q1+jUdFpamr0CAAChGDRokL2qX6NB3KdPH0bFAACEKDk5ucFFWgFBLdYaMWKETjnlFNsCAAANMZmZnv4922pYUEFsbjSPHp1JGAMA0AiTlSYz4+LibE/DGtxHfLy9e/dq+fLlKivbaXsAAECAuZV7zTXXBB3CRkhBHFBUVKSNGzcSyAAA+Jj7weecc65/XVWomhTEAUeOHPGPkgEAiFbm9m1jRTsa0qwgBgAAzRPUYi0AANAyCGIAABwj/X93S+yOY6tMHQAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</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>minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time, in seconds, it takes for the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> to make one complete rotation under these conditions.</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>Calculate the angle, in degrees, that the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> turns through in one second.</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>Write down the amplitude of the function.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the period of the function.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>5</mn></math>, clearly labelling the coordinates of the maximum and minimum points.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> above the ground when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></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 time, in seconds, that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is above a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mtext>m</mtext></math>, during each complete rotation.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At any given instant, find the probability that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is visible from Tim’s window.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.</p>
<p>At any given instant, find the probability that Tim can see point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> from his window. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>maximum <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>130</mn></math> metres <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>minimum <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>50</mn></math> metres <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>60</mn><mo>÷</mo><mn>12</mn><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>5</mn><mo> </mo><mtext>seconds</mtext></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo>÷</mo><mn>5</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn></math> divided by their time for one revolution.<br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>72</mn><mo>°</mo></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(amplitude =) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(period <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>360</mn><mn>72</mn></mfrac><mo>=</mo></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>Maximum point labelled with correct coordinates. <strong><em>A1</em></strong></p>
<p>At least one minimum point labelled. Coordinates seen for any minimum points must be correct. <strong><em>A1</em></strong></p>
<p>Correct shape with an attempt at symmetry and “concave up" evident as it approaches the minimum points. Graph must be drawn in the given domain. <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>90</mn><mo>-</mo><mn>40</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mn>144</mn><mo>°</mo></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>h</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>122</mn><mo> </mo><mtext>m</mtext><mo> </mo><mo> </mo><mfenced><mrow><mn>122</mn><mo>.</mo><mn>3606</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on graph <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>=</mo><mn>90</mn><mo>-</mo><mn>40</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mn>72</mn><mi>t</mi></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>55</mn><mo> </mo><mo>(</mo><mn>3</mn><mo>.</mo><mn>54892</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>45</mn><mo> </mo><mo>(</mo><mn>1</mn><mo>.</mo><mn>45107</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> or equivalent <strong><em>(A1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for either <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>-coordinate seen.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>.</mo><mn>10</mn></math> seconds <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>.</mo><mn>09784</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>09784</mn><mo>…</mo></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mn>2</mn><mo>.</mo><mn>902153</mn><mo>…</mo></mrow></mfenced><mn>5</mn></mfrac></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>580</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>580430</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>changing the frequency/dilation of the graph will not change the proportion of time that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is visible. <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>580</mn><mo> </mo><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>580430</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>correct calculation of relevant found values</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>2</mn><mo>.</mo><mn>902153</mn><mo>…</mo></mrow></mfenced><mo>/</mo><mn>2</mn></mrow><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow></mfrac></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>580</mn><mo> </mo><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>580430</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> <strong><em>A1</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>A0A1</strong> </em>for an unsupported correct probability.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows values of ln <em>x</em> and ln <em>y</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between ln <em>x</em> and ln <em>y</em> can be modelled by the regression equation ln <em>y</em> = <em>a</em> ln <em>x</em> + <em>b</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em> and of <em>b</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>Use the regression equation to estimate the value of <em>y</em> when<em> x</em> = 3.57.</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 relationship between <em>x</em> and <em>y</em> can be modelled using the formula <em>y</em> = <em>kx<sup>n</sup></em>, where <em>k</em> ≠ 0 , <em>n</em> ≠ 0 , <em>n</em> ≠ 1.</p>
<p>By expressing ln <em>y</em> in terms of ln <em>x</em>, find the value of <em>n</em> and of <em>k</em>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> one correct value</p>
<p>−0.453620, 6.14210</p>
<p><em>a</em> = −0.454, <em>b</em> = 6.14 <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution <em><strong> (A1)</strong></em></p>
<p><em>eg </em>−0.454 ln 3.57 + 6.14</p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg </em> ln <em>y</em> = 5.56484</p>
<p>261.083 (260.409 from 3 sf)</p>
<p><em>y</em> = 261, (<em>y</em> = 260 from 3sf) <em><strong>A1 N3</strong></em></p>
<p><strong>Note:</strong> If no working shown, award <em><strong>N1</strong></em> for 5.56484.<br>If no working shown, award <em><strong>N2</strong> </em>for ln <em>y</em> = 5.56484.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>valid approach for expressing ln <em>y</em> in terms of ln <em>x</em> <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,y = {\text{ln}}\,\left( {k{x^n}} \right),\,\,{\text{ln}}\,\left( {k{x^n}} \right) = a\,{\text{ln}}\,x + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span></p>
<p>correct application of addition rule for logs <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,k + {\text{ln}}\,\left( {{x^n}} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>+</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct application of exponent rule for logs <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,k + n\,{\text{ln}}\,x">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>+</mo>
<mi>n</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</math></span></p>
<p>comparing one term with regression equation (check <em><strong>FT</strong></em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = a,\,\,b = {\text{ln}}\,k">
<mi>n</mi>
<mo>=</mo>
<mi>a</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
</math></span></p>
<p>correct working for <em>k</em> <strong>(A1)</strong></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,k = 6.14210,\,\,\,k = {e^{6.14210}}">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>6.14210</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mn>6.14210</mn>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>465.030</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = - 0.454,\,\,k = 465">
<mi>n</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.454</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>465</mn>
</math></span> (464 from 3sf) <em><strong>A1A1 N2N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{{\text{ln}}\,y}} = {e^{a\,{\text{ln}}\,x + b}}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>correct use of exponent laws for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{a\,{\text{ln}}\,x + b}}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{a\,{\text{ln}}\,x}} \times {e^b}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
</math></span></p>
<p>correct application of exponent rule for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\,{\text{ln}}\,x">
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,{x^a}">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
</math></span></p>
<p>correct equation in<em> y</em> <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = {x^a} \times {e^b}">
<mi>y</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
</math></span></p>
<p>comparing one term with equation of model (check <em><strong>FT</strong></em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = {e^b},\,\,n = a">
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>n</mi>
<mo>=</mo>
<mi>a</mi>
</math></span></p>
<p>465.030</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = - 0.454,\,\,k = 465">
<mi>n</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.454</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>465</mn>
</math></span> (464 from 3sf) <em><strong>A1A1 N2N2</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>valid approach for expressing ln <em>y</em> in terms of ln <em>x</em> (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,y = {\text{ln}}\,\left( {k{x^n}} \right),\,\,{\text{ln}}\,\left( {k{x^n}} \right) = a\,{\text{ln}}\,x + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span></p>
<p>correct application of exponent rule for logs (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,\left( {{x^a}} \right) + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>b</mi>
</math></span></p>
<p>correct working for <em>b</em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = {\text{ln}}\,\left( {{e^b}} \right)">
<mi>b</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct application of addition rule for logs <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,\left( {{e^b}{x^a}} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>comparing one term with equation of model (check <em><strong>FT</strong></em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = {e^b},\,\,n = a">
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>n</mi>
<mo>=</mo>
<mi>a</mi>
</math></span></p>
<p>465.030</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = - 0.454,\,\,k = 465">
<mi>n</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.454</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>465</mn>
</math></span> (464 from 3sf) <em><strong>A1A1 N2N2</strong></em></p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media.</p>
<p>For each student, the number of hours spent on social media (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>) and the number of IB Diploma points obtained (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>) are shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_07.43.52.png" alt="N16/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>
<div class="specification">
<p>Use your graphic display calculator to find</p>
</div>
<div class="specification">
<p>Ten female students also recorded the number of hours they spent on social media in the month before their IB Diploma examinations. Each of these female students spent between 3 and 30 hours on social media.</p>
<p>The equation of the regression line <em>y </em>on <em>x </em>for these ten female students is</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="y = - \frac{2}{3}x + \frac{{125}}{3}.">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mn>125</mn>
</mrow>
<mn>3</mn>
</mfrac>
<mo>.</mo>
</math></span></p>
<p>An eleventh girl spent 34 hours on social media in the month before her IB Diploma examinations.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and 2 cm to represent 10 points on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis.</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>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
<mrow>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean number of hours spent on social media;</p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean number of IB Diploma points.</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>Plot the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x,{\text{ }}\bar y)">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> on your scatter diagram and label this point M.</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>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for these eight male students.</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>Draw the regression line, from part (e), on your scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.</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>Write down a reason why this estimate is not reliable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="images/Schermafbeelding_2017-03-07_om_08.41.53.png" alt="N16/5/MATSD/SP2/ENG/TZ0/01.a/M"> <strong><em>(A4)</em></strong></p>
<p> </p>
<p><strong>Notes</strong>: Award <strong><em>(A1) </em></strong>for correct scale and labelled axes.</p>
<p>Award <strong><em>(A3) </em></strong>for 7 or 8 points correctly plotted,</p>
<p><strong><em>(A2) </em></strong>for 5 or 6 points correctly plotted,</p>
<p><strong><em>(A1) </em></strong>for 3 or 4 points correctly plotted.</p>
<p>Award at most <strong><em>(A0)(A3) </em></strong>if axes reversed.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> sufficient for labelling.</p>
<p>If graph paper is not used, award <strong><em>(A0)</em></strong>.</p>
<p>If an inconsistent scale is used, award <strong><em>(A0)</em></strong><em>. </em>Candidates’ points should be read from this scale <strong>where possible </strong>and awarded accordingly.</p>
<p>A scale which is too small to be meaningful (ie mm instead of cm) earns <strong><em>(A0) </em></strong>for plotted points.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x = 21">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mn>21</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y = 31">
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mn>31</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x,{\text{ }}\bar y)">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> correctly plotted on graph <strong><em>(A1)</em>(ft)</strong></p>
<p>this point labelled M <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (b)(i) and (b)(ii).</p>
<p>Only accept M for labelling.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 0.761x + 47.0{\text{ }}(y = - 0.760638 \ldots x + 46.9734 \ldots )">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.761</mn>
<mi>x</mi>
<mo>+</mo>
<mn>47.0</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.760638</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>46.9734</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.761x">
<mo>−</mo>
<mn>0.761</mn>
<mi>x</mi>
</math></span> and <strong><em>(A1)</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + 47.0">
<mo>+</mo>
<mn>47.0</mn>
</math></span>. Award a maximum of <strong><em>(A1)(A0) </em></strong>if answer is not an equation.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>line on graph <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for <strong>straight line </strong>that passes through their M, <strong><em>(A1)</em>(ft) </strong>for line (extrapolated if necessary) that passes through <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}47.0)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>47.0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p>If M is not plotted or labelled, follow through from part (e).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - \frac{2}{3}(34) + \frac{{125}}{3}">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>34</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mfrac>
<mrow>
<mn>125</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution.</p>
<p> </p>
<p>19 (points) <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>extrapolation <strong><em>(R1)</em></strong></p>
<p><strong>OR</strong></p>
<p>34 hours is outside the given range of data <strong><em>(R1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Do not accept ‘outlier’.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A medical centre is testing patients for a certain disease. This disease occurs in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> of the population.</p>
<p>They test every patient who comes to the centre on a particular day.</p>
</div>
<div class="specification">
<p>It is intended that if a patient has the disease, they test “positive”, and if a patient does not have the disease, they test “negative”.</p>
<p>However, the tests are not perfect, and only <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>99</mn><mo>%</mo></math> of people who have the disease test positive. Also, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> of people who <strong>do not</strong> have the disease test positive.</p>
<p>The tree diagram shows some of this information.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Write down the value of</p>
</div>
<div class="specification">
<p>Use the tree diagram to find the probability that a patient selected at random</p>
</div>
<div class="specification">
<p>The staff at the medical centre looked at the care received by all visiting patients on a randomly chosen day. All the patients received at least one of these services: they had medical tests (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>), were seen by a nurse (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>), or were seen by a doctor (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math>). It was found that:</p>
<ul>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>78</mn></math> had medical tests,</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> were seen by a nurse;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> were seen by a doctor;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> had medical tests and were seen by a doctor and a nurse;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> had medical tests and were seen by a doctor but were not seen by a nurse;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math> patients were seen by a nurse and had medical tests but were not seen by a doctor;</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> patients were seen by a doctor without being seen by nurse and without having medical tests.</li>
</ul>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the sampling method being used.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>will not have the disease and will test positive.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>will test negative.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>has the disease given that they tested negative.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The medical centre finds the actual number of positive results in their sample is different than predicted by the tree diagram. Explain why this might be the case.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a Venn diagram to illustrate this information, placing all relevant information on the diagram.</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>Find the total number of patients who visited the centre during this day.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>convenience sampling <strong>(</strong><em><strong>A1)</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>95</mn><mo>%</mo></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>%</mo></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>98</mn><mo>%</mo></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>95</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>02</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>019</mn></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>05</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>95</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>98</mn></math> <em><strong>(M1)(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for summing two products and <em><strong>M1</strong></em> for correct products seen.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>932</mn><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>9315</mn><mo>)</mo></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition of conditional probability <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>05</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>01</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>05</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>95</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>98</mn></mrow></mfrac></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>000537</mn><mo> </mo><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>000536768</mn><mo>…</mo><mo>)</mo></math> <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>000536</mn></math> if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>932</mn></math> used.</p>
<p><em><strong><br>[3 marks]</strong></em><br><br></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong><br>sample may not be representative of population <em><strong>A1</strong></em></p>
<p><strong>OR</strong><br>sample is not randomly selected <em><strong>A1</strong></em></p>
<p><strong>OR</strong><br>unrealistic to think expected and observed values will be exactly equal <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"> <em><strong>A1</strong></em><em><strong>A1</strong></em><em><strong>A1</strong></em> </p>
<p><strong><br>Note:</strong> Award <em><strong>A1</strong></em> for rectangle and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> labelled circles and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> in centre region; <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo> </mo><mn>40</mn><mo>,</mo><mo> </mo><mn>24</mn></math>; <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>,</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math>.</p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>11</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>40</mn><mo>+</mo><mn>24</mn></math> <em><strong>(M1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>105</mn></math> <strong><em>A1</em><br><br>Note:</strong> Follow through from the entries on their Venn diagram in part (e). Working required for <em><strong>FT</strong>.</em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 800 students answered 40 questions on a category of their choice out of History, Science and Literature.</p>
<p>For each student the category and the number of correct answers, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, was recorded. The results obtained are represented in the following table.</p>
<p><img src="images/Schermafbeelding_2018-02-13_om_14.11.54.png" alt="N17/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>
<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test at the 5% significance level is carried out on the results. The critical value for this test is 12.592.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span> is a discrete or a continuous variable.</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>Write down, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, the modal class;</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>Write down, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, the mid-interval value of the modal class.</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>Use your graphic display calculator to estimate the mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>;</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to estimate the standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct answers.</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>Write down the null hypothesis for this test;</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value for the test;</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the result of the test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>discrete <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="11 \leqslant N \leqslant 20">
<mn>11</mn>
<mo>⩽</mo>
<mi>N</mi>
<mo>⩽</mo>
<mn>20</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>15.5 <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (b)(i).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="21.2{\text{ }}(21.2125)">
<mn>21.2</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>21.2125</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="9.60{\text{ }}(9.60428 \ldots )">
<mn>9.60</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>9.60428</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G1)</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{260}}{{800}} \times \frac{{157}}{{800}} \times 800">
<mfrac>
<mrow>
<mn>260</mn>
</mrow>
<mrow>
<mn>800</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>157</mn>
</mrow>
<mrow>
<mn>800</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>800</mn>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{260 \times 157}}{{800}}">
<mfrac>
<mrow>
<mn>260</mn>
<mo>×</mo>
<mn>157</mn>
</mrow>
<mrow>
<mn>800</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into expected frequency formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 51.0{\text{ }}(51.025)">
<mo>=</mo>
<mn>51.0</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>51.025</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>choice of category and number of correct answers are independent <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Accept “no association” between (choice of) category and number of correct answers. Do not accept “not related” or “not correlated” or “influenced”.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<p> </p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.0644{\text{ }}(0.0644123 \ldots )">
<mn>0.0644</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.0644123</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="11.9{\text{ }}(11.8924 \ldots )">
<mn>11.9</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>11.8924</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the null hypothesis is not rejected (the null hypothesis is accepted) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong><em>OR</em></strong></p>
<p>(choice of) category and number of correct answers are independent <strong><em>(A1)</em>(ft)</strong></p>
<p>as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="11.9 < 12.592">
<mn>11.9</mn>
<mo><</mo>
<mn>12.592</mn>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.0644 > 0.05">
<mn>0.0644</mn>
<mo>></mo>
<mn>0.05</mn>
</math></span> <strong><em>(R1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(R1) </em></strong>for a correct comparison of either their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic to the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> critical value or their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value to the significance level. Award <strong><em>(A1)</em>(ft) </strong>from that comparison.</p>
<p>Follow through from part (f). Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Fiona walks from her house to a bus stop where she gets a bus to school. Her time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> minutes, to walk to the bus stop is normally distributed with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>12</mn><mo>,</mo><mo> </mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfenced></math>.</p>
<p>Fiona always leaves her house at 07:15. The first bus that she can get departs at 07:30.</p>
</div>
<div class="specification">
<p>The length of time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> minutes, of the bus journey to Fiona’s school is normally distributed with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>50</mn><mo>,</mo><mo> </mo><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfenced></math>. The probability that the bus journey takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> minutes is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>941</mn></math>.</p>
</div>
<div class="specification">
<p>If Fiona misses the first bus, there is a second bus which departs at 07:45. She must arrive at school by 08:30 to be on time. Fiona will not arrive on time if she misses both buses. The variables <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> are independent.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that it will take Fiona between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> minutes and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to walk to the bus stop.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</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 the probability that the bus journey takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> minutes.</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 probability that Fiona will arrive on time.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>This year, Fiona will go to school on <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>183</mn></math> days.</p>
<p>Calculate the number of days Fiona is expected to arrive on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>158655</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mn>15</mn><mo><</mo><mi>W</mi><mo><</mo><mn>30</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>159</mn></math> <em><strong>A2 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding standardized value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>56322</mn></math></p>
<p>correct substitution using <strong>their</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>-value <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>60</mn><mo>-</mo><mn>50</mn></mrow><mi>σ</mi></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>56322</mn><mo>,</mo><mo> </mo><mfrac><mrow><mn>60</mn><mo>-</mo><mn>50</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>56322</mn></mrow></mfrac><mo>=</mo><mi>σ</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>39703</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>40</mn></math> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>217221</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>B</mi><mo><</mo><mn>45</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.217</mo></math> <em><strong>A2 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid attempt to find one possible way of being on time (do not penalize incorrect use of strict inequality signs) <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>≤</mo><mn>15</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo><</mo><mn>60</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo><</mo><mi>W</mi><mo>≤</mo><mn>30</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo><</mo><mn>45</mn></math></p>
<p>correct calculation for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>W</mi><mo>≤</mo><mn>15</mn><mo> </mo><mtext>and</mtext><mo> </mo><mi>B</mi><mo><</mo><mn>60</mn></mrow></mfenced></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>841</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>941</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>7917</mn></math></p>
<p>correct calculation for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mn>15</mn><mo><</mo><mi>W</mi><mo>≤</mo><mn>30</mn><mo> </mo><mtext>and</mtext><mo> </mo><mi>B</mi><mo><</mo><mn>45</mn></mrow></mfenced></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>159</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>217</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>03446</mn></math></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>841</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>941</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>159</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>217</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>7917</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>03446</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>826168</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P </mtext></math>(on time) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>826</mn></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing binomial with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>183</mn><mo>,</mo><mo> </mo><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>826168</mn></math> <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>183</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>826</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>151</mn><mo>.</mo><mn>188</mn></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>151</mn><mo>.</mo><mn>158</mn></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>sf </mtext></math>)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>151</mn></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy.</p>
<p>A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.</p>
</div>
<div class="specification">
<p>A second person is chosen from the group.</p>
</div>
<div class="specification">
<p>When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts.</p>
<p>The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts.</p>
<p>It is known that 6 in every 1000 adults are allergic to nuts.</p>
<p>This information can be represented in a tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.31.34.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c.d.e.f.g"></p>
</div>
<div class="specification">
<p>An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.</p>
</div>
<div class="specification">
<p>The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for <strong>38 </strong><strong>employees</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person is <strong>not </strong>allergic to nuts.</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 probability that both people chosen are <strong>not </strong>allergic to nuts.</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><strong>Copy </strong>and complete the tree diagram.</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 probability that this adult is allergic to nuts and the liquid turns blue.</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 probability that the liquid turns blue.</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>Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.</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>Estimate the number of employees, from this 38, who are allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{34}}{{60}}{\text{ }}\left( {\frac{{17}}{{30}},{\text{ }}0.567,{\text{ }}0.566666 \ldots ,{\text{ }}56.7\% } \right)">
<mfrac>
<mrow>
<mn>34</mn>
</mrow>
<mrow>
<mn>60</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>17</mn>
</mrow>
<mrow>
<mn>30</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.567</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.566666</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>56.7</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for correct numerator, <strong><em>(A1) </em></strong>for correct denominator.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{34}}{{60}} \times \frac{{33}}{{59}}">
<mfrac>
<mrow>
<mn>34</mn>
</mrow>
<mrow>
<mn>60</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>33</mn>
</mrow>
<mrow>
<mn>59</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct product.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.317{\text{ }}\left( {\frac{{187}}{{590}},{\text{ }}0.316949 \ldots ,{\text{ }}31.7\% } \right)">
<mo>=</mo>
<mn>0.317</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>187</mn>
</mrow>
<mrow>
<mn>590</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.316949</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>31.7</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-14_om_05.54.09.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c/M"> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each correct pair of branches.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.006 \times 0.98">
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 0.006 by 0.98.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.00588{\text{ }}\left( {\frac{{147}}{{25000}},{\text{ }}0.588\% } \right)">
<mo>=</mo>
<mn>0.00588</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>147</mn>
</mrow>
<mrow>
<mn>25000</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.588</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.006 \times 0.98 + 0.994 \times 0.05{\text{ }}(0.00588 + 0.994 \times 0.05)">
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
<mo>+</mo>
<mn>0.994</mn>
<mo>×</mo>
<mn>0.05</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.00588</mn>
<mo>+</mo>
<mn>0.994</mn>
<mo>×</mo>
<mn>0.05</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their two correct products, <strong><em>(M1) </em></strong>for adding two products.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.0556{\text{ }}\left( {0.05558,{\text{ }}5.56\% ,{\text{ }}\frac{{2779}}{{50000}}} \right)">
<mo>=</mo>
<mn>0.0556</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.05558</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5.56</mn>
<mi mathvariant="normal">%</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>2779</mn>
</mrow>
<mrow>
<mn>50000</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (c) and (d).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.006 \times 0.98}}{{0.05558}}">
<mfrac>
<mrow>
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
</mrow>
<mrow>
<mn>0.05558</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct numerator, <strong><em>(M1) </em></strong>for their correct denominator.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.106{\text{ }}\left( {0.105793 \ldots ,{\text{ }}10.6\% ,{\text{ }}\frac{{42}}{{397}}} \right)">
<mo>=</mo>
<mn>0.106</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.105793</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>10.6</mn>
<mi mathvariant="normal">%</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>397</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (d) and (e).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.105793 \ldots \times 38">
<mn>0.105793</mn>
<mo>…</mo>
<mo>×</mo>
<mn>38</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 38 by their answer to part (f).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.02{\text{ }}(4.02015 \ldots )">
<mo>=</mo>
<mn>4.02</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>4.02015</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (f). Use of 3 sf result from part (f) results in an answer of 4.03 (4.028).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A survey was conducted on a group of people. The first question asked how many pets they each own. The results are summarized in the following table.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The second question asked each member of the group to state their age and preferred pet. The data obtained is organized in the following table.</p>
<p style="text-align: center;"><img 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mrgHlCjRELhiymbUFXcoRW5RbegRA5AR3fgJzsPh1evhvx7o6tdi1DlPg1Y5+LmdTfLSwbR2vwa2sMfD7gAf8dr2NHcGVfjsAetr6Hxje5oGx+iccdb4acFac0N+JuZ16O4JHJhN/zEhW55xWroBNzRFa62KjeUtaPDtsGTCQRStHHuePIPIdDXiy5ZEulvcGPxStxW+F/xH7/9Dd6OPTIO7Vfu7XiiVutXE+X/Cagy6nAW7PfXoDzceUwQXHu9PlyHpvC9Bgj52/DsE03wQ4L9nr9H/iji4CWFD6JX7ZTKHeWhOqb0twRrXPyhdhBVb+xUe35i95U5isQ5Mr1WlfH8+HmacE51EUriPIx2wniI+ZaUyg7VdqzO5Hm12IKU2JxLRL7Yoh7tQodE2SPHyfUqbGJtJ9YfPlZXEGoWDiXOLWgm/IXQLAQI59PhrDQ9wdv0+qSOcuq8SyKTVGycIn91Tulu4fIpSxTl6cnovFB0jjC2MEbrL4XCbpdXVCtzekP4ld6q0Yvyfx1Wk5x0cb6iXNeJc/EJqzM183RCnUfU8o/u664aHd6eQ+EK9jQKh+Z6jdwH6G9D8RopXc9PsuyJEEDOQpRvd6GtsRJ2pZ8glaKu1YXt5QuRo6TpbS+mrF59alouFpRvRXtbIyrtSvdyIUrr3kX79hIsyImYwTpnFba1v4u60oWRkmG5PWirUzVRaxxyp/QVeDw71Xak0ga0tj+N1XOmArAiZ0EJtre3obHSoVYRybMV5QuUycFpyFu+CQ2KHLgcmLyPu6lyZdZOKjZOlX9qmlvn/COefCtma9gr0eT533j5vlsAdKJ5z8fhJ/xEv4rY+znc/81Z8Q1NmP/HN5NZR1MxZ1UFniuPXpNa4XMW48G32tG2uy7ywY/wOXmYug09b21CYfS61hYZy741bzmeaCiNTK9AwjUI4hzob2NhOWQZbfTUi5Ta89w3KgHNE2HiikKjipyiXPTJFEENmU0ZaZFf34m9Wxh7mkllBGbIyg11gr5iBHMY39/0/GQUI9hDxlKeIAESMCyB6chfshJ2tKPdvx1rrt4eL6m0Ebfd+NX4NB6RwJgJZKa/Zd/Q6JgNyIIkkI0E5NWPG/GqxxUbcg+rKcFe2Yg2ddg8G3WnTpNPIDP9zSI/TCuw5H8zozlUkrklgbQRoE+mDX3GNUxfyTiTpUVgPT/hE2FaTMFGSYAESIAEjEKAgdAolqAcJEACJEACaSHAQJgW7GyUBEiABEjAKAQYCI1iCcpBAiRAAiSQFgIMhGnBzkZJgARIgASMQoCB0CiWoBwkQAIkQAJpIcBAmBbsbJQESIAESMAoBJK+LCO/Y8EfCRiJAH3SSNYwtiz0FWPbx6jSJQVCvlBvVFOZUy69l1/NSYJaj0SAvjISIZ6XCeh1ljg0St8gARIgARIwNQEGQlObn8qTAAmQAAkwENIHSIAESIAETE2AgdDU5qfyJEACJEACDIT0ARIgARIgAVMTYCA0tfmpPAmQAAmQAAMhfYAESIAESMDUBBgITW1+Kk8CJEACJMBASB8gARIgARIwNQEGwrSYfwDevT9BzY5uhNLSPhslARIgARJQCDAQKiQmczvgQWPZs+gMTmajbCtjCAS82FtfBpvFAovFhiVVzej0X0gSP+Tfj61lBeFPRlmW1KDFO5CUhwlZTiDkR8dWxVeKUdXSjUCiyin6U2IxMx0zEJrJ2tTV+ARCx/Hmi25g5U/hEwJB326sPFmLovXb0RnQjB8EPsIbrVNwx0tdEEEfDqw8gXvtz8I9oMljfG0p4UUROIs/vLEfuONF+MR5+A6sxMl778QT7tOxWlP1p1gJc+4JzQ+A5oi7+gTOC59np6i0S0LmBalU1LX2iEE1s3zeJepKF0bOy3nslaKxLZqnv01USoidk6pFW39QLc2deAJm88lg7z7xft/5OAjBnkbhQKGobDsVTf9c9L7/oejTuk3Yr7R54qowxQF95ZRoqywUUmWb6I9aPDV/MoV7qErq+QmfCEfV/7mAEy2bUVj0MnCfG4MiiEH3UnSVrcGmluMIIYRA53asX/EmpmxsRVAICLmn9sh0NC/bjOc7zwK5S7Gluw2VkgRH4xEEfU9jaS7NMCozZHFm67ybYJ8zNU5D6+y5WCRpk6Zhnv1bmKNxm9DJYziU/32sXTxTm5H7WUwgyVdCp3Hs0DXYvPYG5Eb1TsoDINmfshhSiqppLqUUS5g5W+gT7HmhBaiswkOrFyAHVuQsuBVlJZfC+UIbekNn0LHrFfSUlGHDYgkRuFMh2dehxNGNvR+d5OIYM/vPxeg+/Vu4MV+5vWkrGoDX7UT1U35UvboRhTm8pLV0zLEfQsDrhrP6X9Bb9Rw2F145stpD+tPIRbMxR9L/I8xGJcdLp1Dv7/BaK1CwzoYctdJZWLrFEx7rlJPmb/HAB/nm9CbeOyuvhvlPHPjpo6htBxzr1ELcIYEUCYQw4GnHoXtK8UjCkyIG3KhasAy1frkqB3DbGiwOd9BSrJrZsoDAabirvotltZ0AJNjhQO/iVZg/ZIdoGH/KAhpjVYHdx7GS0y0XQqB7B8psM5C/7Gc4cFZeuPBXKP55CxodQFePL3lFl249TCSBKIGAB7/YMQtP31Ok6XxFz8nD7D55Qc0BNFUCtWtujw7Rk555CEQ74kEfPE0lshPAvukNnBhqzdRw/mQeaEma8okwCclFJIS82LWpGnuXu9D34urYHI7cc+/yA4suom4WNSGBs+h88R3MrH5g2CFPq7QYZc9sQ/DQUjx84CgCq7+mzhGZEJo5VbZKKCx7HC8E/4j8hz3oCazCnKS1B6n5kxkB8olwFFa35n0b65Ke7M7B61wLi2UtnJ5e9HQBBTd9HZKGbGjwLDQLmkfRIrOal8AFnHjzVzi8/AGUL9CbG0wgY52Lm9fdnJDIQ3MRmIa8m78rD5Lr/EbpTzo1ZHOS5nadzWqOk27Wa7G86m7k127Bs+4T4YUvIf//QVPzQdjrHsTaxd9CcYkNrc2voT36ArT80vO2mkfhDM/jROXIsSG/YHrk4LMAtK+HjZOkrCajCVyA3+3EritWoEQNggPo3tGM9iHfEwygr6cfy2+clzyEmtEsKHzqBEII9PXi6PIi5MfNEY7Fn1JvNStyqi9XCBF+t017zH09AgnvEcIhKpsOCF/0na6g74BoqnSo7wlKpXVid9tvhSvu/Z7zwtf2mLDL7xjidtHY87leQ0wzpU/2ix5XddQ3NO+byr7iaBQ9sp8FjwlXeaGwV+4UHp/8zmHEnxylTeLIoPblQnO5kN77YdlL4Lzoc20Ukr1SNHl8IuwWvlZR7bhbNB5R3iKUtU/Bn7IXkq5men4S9wa9XgbdmphIApNEwFw+Gb25hTtICUEQknA0Hgnf8OSb25HGciEp+eSPOrg8amdskkxjuGbM5StBMXikSZSqH+dYKErrXNGOkWKaVP1JyW+OrZ6fWGTVlUdbi8UiB0blkFsSSDsB+mTaTZAxAtBXMsZUaRVUz084R5hWk7BxEiABEiCBdBNgIEy3Bdg+CZAACZBAWgkwEKYVPxsnARIgARJINwEGwnRbgO2TAAmQAAmklQADYVrxs3ESIAESIIF0E2AgTLcF2D4JkAAJkEBaCTAQphU/GycBEiABEkg3AQbCdFuA7ZMACZAACaSVAANhWvGzcRIgARIggXQTSPo3TPJb9/yRgJEI0CeNZA1jy0JfMbZ9jCpdUiDkJ9aMaipzyqX3OSRzkqDWIxGgr4xEiOdlAnqdJQ6N0jdIgARIgARMTYCB0NTmp/IkQAIkQAIMhPQBEiABEiABUxNgIDS1+ak8CZAACZAAAyF9gARIgARIwNQEGAhNbX4qTwIkQAIkwEBIHyABEiABEjA1AQZCU5ufypMACZAACTAQ0gdIgARIgARMTYCB0NTmp/IkQAIkQAIMhGPygRAG3DWwWdbC6T03phpYiASGJnAB/o7tKLNZYLHYsKSqBd5ASCe74odyvuhfsRNevaw6pZmU6QRCCHj3oL6sIGr/YlTt6IA/yf6p+lOm8xi7/AyEY2fHkiQwAQRCCPzhHbRiNV7yCQR9u7Hy5KOwP9GOgcTWQn/Ge6+8Bb+aLsGx7tvI41WtEsnmndCJd/Hi28DK7R9BiPPwHViJk9WrsL6hAwFV8VH4k1rGfDu8ZMxnc2psZAKh4/D034CSxRLki9Mq/R02lK0Amt+DZ0Db1ZdvcC14YdY29AsB+WP5Qviwp3xBuJyRVaRs40HgHP747zOxdlMx5ufInjIV0uINeOjJm9He8AY6FF9J2Z/GQ6bMrYOBMBXbhfzobKmPDlVZYCtrwDsHTySUlIcp3HBWFUeHKeQhLSfc3oR+fMCLvfVlsIWHsgpQVt8cKWOrgVtx3oSaeWgiAta/ht1+jSaYXcDJY8eRv3kVFudqL9cz6Nj1Clprt+ApZ0uyn5kImTlVnYZ59m9hjtYlMBWz5+ZB0gJJ2Z+0hcy3H4fRfOqnovFZdDb8EEU/PYPb2vshRBDeh67Fwbf3aoakQgh0N2OjfRM+mP0j+IICItiJLbM/wJ3561HfeTbSUOg4WjatQVnXUrgHgxBiP6pntuPh2tZUBGEesxEIeOF2/hhP9d6FVzcvRo5G/5D319hS2wmgFbUb1mBZ/u2oaunWDIlpMnPXVASmLy9CfvgpMUHtYfwpIaf5DoXmB8gjLPzFEehvE5VSoahsO6VJDor+tmoh4XbR2PO5EOKUaKssFFK5S/QFNdmi6XA0ip5gtIy0Ubj6zmsyRcpCqhZt/XGFNXnMu2tOn1T8C0LWH/Zq4erp13WCoM8j3misFHY5H24VdZ6/6OYzQ6I5fUVrWfleUqrjA6n7k7a2bN3X8xM+EQ7b9wlhwPMemv3XIv9qbX/cipyr81CglB34GHuafSi46euQ4ojm4Or8a4GuXvQFTsOzpxX+ghuwUJqqlAQQzaNJ4a7ZCViRu/Rp+OQFEJ6dqEQT1thr0HLiQhIYq1SI28q3oM3Ximr7QTTsOpi8qCapFBOyj0AIgc5XseOqjbin8MoE9VL3p4SCpjmMu22bRuuUFZXnZ3o1Q6D6BUMnj+FQbOleciZ/L46dPJ+czhQSGJbAVEiFJXjmhSfh8P8eB3oS5ps1Za3SMvyvR+7SWVSjycTd7CUQ8ODFXf8F1fcUxQ2hxyucuj/Fl8v+IwbCYW2sM/msk986ey4Wxc1QJ2SS8jB39qUJiTwkgdQIWPO+jXWOkfwnOkpRkIer9eaHUmuKuTKRQOg43nzxj1j+yPexIAXbp+ZPmQhi7DIzEA7LzorcoltQIn2Cnr7YmzlACIG+XnQpZXOvR3GJDV37/y3hZdYA+no+AcI3p1koKnZACg+TapfBR/ModXFLAokEAj70HP0mbszPTTyjOZZ98v+hsGol5vOq1nDJ8t3QCbi3vYMr7vheLAgGDmOHc//QQ+Qp+VOWc0tUTzshqjeJqD1vzv3zos+1UUhSuWg8Ii9YCIrBHpeotEsC6mKZoBg80iRKpYWitGGf8IXXvPSLI43lQtIuYAgeE67yQmGvdImeQTlTv+hxVUcWOnCxjK57mc0ng30uUS45RGXTgYgfBftEW/XtorSxSwyqhM4Ln+dt8YbHJyLLq84L34Gfi8pHWqO+p2Y01Y7ZfEUMHhGuSkdkQVV4sVR0cRUk4Wg8EvaN1PzJVG4S5pWocdwyUdM5UiKNIY/7RU9rgyiVYqv4drueEQ41EMoF5QDZJhpVx5SEvbJRtCWu9hvsEa11pUIKO+5CUVrnEq66VYKrRvXhm84nB7tEY+lC9eYmldYJlxrwFEbnha/tsehKUQg5z+62Hk2gVPKZa2sqXwl3qmN+Iuse+1NWswshUvIn+olFRqA8JcrfK9QcKsncTiiBc/A6S2HvuQfdW5ZiuMGvCRXDoJXTJw1qGAOKRV8xoFEMKJKen3A2YdIMFf1Asm0DnN3K6j/5Y7iNeOrhz7B57Q0MgpNmCzZEAiRAAjECDIQxFhO8Z0Wu/T689e6i8CsAAA0tSURBVNx1+GDpjOhn2C5F4fbPcdtbL2Jz0rs/EywOqycBEiABEggT4NAoHcHQBPSGMQwtMIVLGwH6StrQZ1TDen7CJ8KMMiGFJQESIAESGG8CDITjTZT1kQAJkAAJZBQBBsKMMheFJQESIAESGG8CDITjTZT1kQAJkAAJZBQBBsKMMheFJQESIAESGG8CDITjTZT1kQAJkAAJZBSBSxKllZeW8kcCRiJAnzSSNYwtC33F2PYxqnRJgZCfWDOqqcwpl947P+YkQa1HIkBfGYkQz8sE9DpLHBqlb5AACZAACZiaAAOhqc1P5UmABEiABBgI6QMkQAIkQAKmJsBAaGrzU3kSIAESIAEGQvoACZAACZCAqQkwEJra/FSeBEiABEiAgZA+QAIkQAIkYGoCDISmNj+VJwESIAESYCCkD5AACZAACZiaAAOhqc1P5UmABEiABBgIR/KBUDecxXkodnYjNGTec/A618Jiq4F7YOhc+sVPw11VBEuxE97RFtWvkKnZQCDghbvlVdSXFaPKfXp4jUJ+dL4p5y2AxVI0cv7ha+PZjCIQQsDbjpbX61GWN9T95wL8HdtRZrPAYrFhSVULvAHebLRmZiDU0hjz/jTML98F4XsaS3OJdMwYWTBCQO583fEwdrieQcXO/xyWSsi/H1t/4MCKFh/mlrkwKDzYsnTWsGV4MnsIhLxNuOPxl+C6vwI7P9PTK4TAH95BK1bjJZ9A0LcbK08+CvsT7RjQy27SNN61TWp4qm1gAtYFKP/NLrz06ANwDCdmoAMN6zfh0KLn0fnSg/inpfORM1x+nss6Atb55fjNKy/g0Sdv19ctdBye/htQsliCfLO3Sn+HDWUrgOb34Bn16JV+E9mQykCYqhXPHMbe+jLYLPLwQgHK6vdohhcSh0ajw51LqvCiUiY6bBryd6JFSQvX82scPHk+VSmYjwSiBM6i8/kfo+HaGjy96SZIvJLpGXoErH8Nu/2acBCMnL6Ak8eOI3/zKizm6JVKjJePimK4nc/QWvE4Xp3yz+gMCojB3bjtVAPyV2xD53Bj7e3/in0zK+AV5+FrvxuLrR40rF+Hn566De2DQQixHw9d24u3dx4ernGeI4EkAiFvC2oqvkDJTZ/ilz+Q5wYtsJVtxV4vB7ySYDEhQkCed3b+GE/13oVXNy/m6IHGLxgINTCG25XKH4/1vHMWYPVDVajseQW7Os4MXUxagbJ/+jpyMBXS/GsQ6ngDDT1r8chDqzA/R0afi/mrN+ORysKh6+AZEkgicA69+95Fq30Rvv6NW7B5RxfEYBeehBOOuxuH75wl1cWE7CcQwoC7BrYr8rFswzPY+eH7+LCXHSat3RkItTSG3J+Ogpu+Hj/8lGNDfoEPzXs+TnHS+Qw8e1rhL8jD1eEgqDSWg6vzr1UOuCWBFAgE0NfzCaTFxfheYWTuBzkLcddDD8DRXoeaXd5hVjinUD2zZBkBK3KXPg2fPDLl2YlKNGGNvQYtJy5kmZ5jV4eBcOzsRlcydBrHDvlGV4a5SUCPwBC+ZM37NtY5gK4eHwJ65ZhmcgJTIRWW4JkXnoTD/3sc6OFToeIQDIQKiYneWmdh7iLbRLfC+s1AIOpL/kPHcDLpdbDpKMi3cf7HDH4wRh0jHaZLx1g6O4sxEKZk18+Se9kBH3q6bCgpvh65KdUxE0XFDkhdveiLW2ATGeZKqQpmIoEwAcWXDuKwXzO8FfbJG7Du5rmaVYJERgIJBGQ/OfpN3Jif2p0roXRWHjIQpmhWf+0WPNXSHRlyChyG875NaF5eg/vtqb68bEWu/W48t/wt3HlfM7rDwXAA3pYGPFHbmaIUzEYCMgHFlz7AvTW/jPhSyI+OxldwaPODWDt/GjGRQJhA6EQLNtiKUbWjA3559CB0Au5nn8fJmnvgmDOVlKIEGAhTcoXpcNT9EEs/eQbz5fcIr/gf+KCgHu3bVmHOaAhav4bV21zYUeDG0iumwGJZgLsPXIf76lalJAUzmYVA5D3UKfkb0IpO1C67KvkTfIm+NOUuuGbejSYuizeLk0T0HHCjynYZ8jfsBvzPYNmMq+M+B2mdMR83fceH2rtuhG2KBbYf/BJn12zDS+ULOXyu8RSLEEIox/K7SJpDJZlbEkgbAfpk2tBnXMP0lYwzWVoE1vOT0TzPpEVoNkoCJEACJEACE0mAgXAi6bJuEiABEiABwxNgIDS8iSggCZAACZDARBJgIJxIuqybBEiABEjA8AQYCA1vIgpIAiRAAiQwkQQYCCeSLusmARIgARIwPAEGQsObiAKSAAmQAAlMJAEGwomky7pJgARIgAQMT4CB0PAmooAkQAIkQAITSYCBcCLpsm4SIAESIAHDE7gkUUL58zP8kYCRCNAnjWQNY8tCXzG2fYwqXVIg5LdGjWoqc8ql911Ac5Kg1iMRoK+MRIjnZQJ6nSUOjdI3SIAESIAETE2AgdDU5qfyJEACJEACDIT0ARIgARIgAVMTYCA0tfmpPAmQAAmQAAMhfYAESIAESMDUBBgITW1+Kk8CJEACJMBASB8gARIgARIwNQEGQlObn8qTAAmQAAkwENIHSIAESIAETE2AgXAs5g94sbf+KezwnouUDnXDWWyDrcqNgbHUxzIkQAIkQAJpI8BAOGr0IQx0NKGs4iMER12WBUggVQIhBLztaHm9HmV5NXAPhHQKDsDrfhOv15chj50wHT5MAkIYcNfAZrGEPy0mf14s9rcWTqUzb3JUDIQmdwCqb0wCIW8T7nj8Jbjur8DOz/RkPAev8wE8vqMJ91fshG4WvWJMMxmBM/DsaYVfT2vHd3Fz3jS9M6ZLYyBMMrncy3aiaokt2nMqRpXTDW9A7pHLvauHsWDZM/BjNzbkXxY/HHryIN6pL1N7X7ayrdjrjR8sDfk7sKOqOFq3DUuqnHCreZTeWzGqXnwWZTa591aEKvfpJCmZkN0ErPPL8ZtXXsCjT94+hKLTML+8Ea+89AyedEhD5GGy6QkMHMbBS5+BLygg/0OFyF8Q/W2P4NZ130YeI0DYRYgh7koZQLfzAdjv/ACzt3QiKASCvh9h9gebkL9iGzoDQO7SJ9HdVg0Jt6Ox53P4tixFbrQO/869OHhtNbyywwX78PKcd+G4uxGd4SAKhE604IeFG+Ce/aOoY3bj5/n7cae9Bi0nLmgkaUXzPgnV3iCCvtfwz4tnas5xlwRIgARSIxD69Bp8r3IZJO2dPuTF61uOYvXNc6FNTq3G7MxFDlq7Dnjw0sMdWP7cj7FpsRR2Eqt0Ex746TZU9tShZpcXejM1ShVSZRUeWr0AOXKCdQ7sd62Do/1DfOSTg9xptP/kaTgLHsBDm26KOmYuFpRvwcslv8e9P9mnWWhTiJKyW7EgxwqrNA/zcmgmhTG3JEACqRPQu3+Een+HlqvXoJjDoipI3mFVFCEMeN5Ds/863LTwq/E9pRwb8guArh4fAmr+VHc+QU9fABj4GHuaOyEtmovZcdRzcHX+tfA3vweP7oKIVNthPhIgARIYicA59O7rwN9+/+8xJ+4+NFK57D5PFKp9L+DksV79SeVoHv+hYzg53COhWtfQO/7aZZgRt3LrMuRv2D10AZ4hARIggfEiEDqGfS1/heIiTrdokTIQqjSmYvbcPAy37CD5aU4tnOKOBEfjkfDcY2ziOjqB7XsaS3NpjhRBMhsJkMAYCISHRf/WjiLea+Lo8c6r4rAit+gWlEhHsP/wf8TPBQZ86OkCCvJtkfk/tcwodnKvR3GJDV37/w3+uKfKs+is/0dYip3wxqWPom5mJQESIIERCUSHRYuvVxf4jVjEJBkYCLWGzi3CD55cjHfu/RG2dfgjwTBwGM77NqE2vwJPr50PK6zIuToPBeFyIXwW+Cw+aGrri9ufBfv9NVj+zqOo2bY/GgwH4G2pxYMVQN3TqzGf1ogjxgMSIIFxJMBh0SFh8tYbh0ZexbkV7S//A05WFWKKPJd3xf9Ezz9sQ89bm1AYXb1pzStGVXU/NuRfjsvX/Aq9KT7JWeeswrb2bfiHkz+GbYr8juAM2N+cifs8L2Jz4ZVxkvCABEiABMaTAIdFh6ZpEfJkVfQnf3pHc6gkc0sCaSNgWp8ccKNqwTLUqp8EkeeX3XinfEF0RbP24w6KeeR3W3eifL45vxZiWl9RzD/sVv4S0aP49Teq8aDJO916fsJAOKzz8GS6Ceg5bbplYvvGJEBfMaZdjCaVnp9waNRoVqI8JEACJEACk0qAgXBScbMxEiABEiABoxFgIDSaRSgPCZAACZDApBJgIJxU3GyMBEiABEjAaAQYCI1mEcpDAiRAAiQwqQQYCCcVNxsjARIgARIwGgEGQqNZhPKQAAmQAAlMKgEGwknFzcZIgARIgASMRoCB0GgWoTwkQAIkQAKTSuCSxNbkt+75IwEjEaBPGskaxpaFvmJs+xhVurhAyO+MGtVMlIsESIAESGCiCHBodKLIsl4SIAESIIGMIMBAmBFmopAkQAIkQAITReD/A0kwBL6ZIvzXAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test is carried out at the 10 % significance level.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the total number of people, from this group, who are <strong>pet owners</strong>.</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>Write down the modal number of pets.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the median number of pets.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the lower quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the ratio of teenagers to non-teenagers in its simplest form.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected number of teenagers that prefer cats.</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>State the conclusion for this test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>140 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>17:15 <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{17}}{{15}}">
<mfrac>
<mrow>
<mn>17</mn>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
</mfrac>
</math></span> <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> for 85:75 or 1.13:1.</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>preferred pet is independent of “whether or not the respondent was a teenager" or "age category” <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept there is no association between pet and age. Do not accept “not related” or “not correlated” or “influenced”.</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>preferred pet is not independent of age <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (e)(i) <em>i.e.</em> award <em><strong>(A1)</strong></em><strong>(ft)</strong> if their alternative hypothesis is the negation of their null hypothesis. Accept “associated” or “dependent”.</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3 <em><strong>(A1)</strong></em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{85 \times 55}}{{160}}">
<mfrac>
<mrow>
<mn>85</mn>
<mo>×</mo>
<mn>55</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{85}}{{160}} \times \frac{{55}}{{160}} \times 160">
<mfrac>
<mrow>
<mn>85</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>55</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>160</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p>29.2 (29.2187…) <em><strong>(A1)(G2)</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.208 > 0.1 <em><strong>(R1)</strong></em></p>
<p>accept null hypothesis <strong>OR</strong> fail to reject null hypothesis <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(R1)</strong></em> for a correct comparison of their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value to the significance level, award <strong><em>(A1)</em>(ft)</strong> for the correct result from that comparison. Accept “<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value > 0.1” as part of the comparison but only if their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value is explicitly seen in part (h). Follow through from their answer to part (h). Do not award <strong><em>(R0)(A1)</em></strong>.</p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">i.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p>Sila High School has 110 students. They each take exactly one language class from a choice of English, Spanish or Chinese. The following table shows the number of female and male students in the three different language classes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test was carried out at the 5 % significance level to analyse the relationship between gender and student choice of language class.</p>
</div>
<div class="specification">
<p>Use your graphic display calculator to write down</p>
</div>
<div class="specification">
<p>The critical value at the 5 % significance level for this test is 5.99.</p>
</div>
<div class="specification">
<p>One student is chosen at random from this school.</p>
</div>
<div class="specification">
<p>Another student is chosen at random from this school.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis, H<sub>0 </sub>, for this test.</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>State the number of degrees of freedom.</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>the expected frequency of female students who chose to take the Chinese class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether or not H<sub>0</sub> should be rejected. Justify your statement.</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 probability that the student does not take the Spanish class.</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 probability that neither of the two students take the Spanish class.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of the two students is female.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(H<sub>0</sub>:) (choice of) language is independent of gender <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “there is no association between language (choice) and gender”. Accept “language (choice) is not dependent on gender”. Do not accept “not related” or “not correlated” or “not influenced”.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 <em><strong>(AG)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>16.4 (16.4181…) <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(we) reject the null hypothesis <strong><em>(A1)</em>(ft)</strong></p>
<p>8.68507… > 5.99 <strong><em>(R1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (c)(ii). Accept “do not accept” in place of “reject.” Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p><strong>OR</strong></p>
<p>(we) reject the null hypothesis <em><strong>(A1)</strong></em></p>
<p>0.0130034 < 0.05 <em><strong>(R1)</strong></em></p>
<p><strong>Note:</strong> Accept “do not accept” in place of “reject.” Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{88}}{{110}}\,\,\,\left( {\frac{4}{5}{\text{,}}\,\,0.8{\text{,}}\,\,80{\text{% }}} \right)">
<mfrac>
<mrow>
<mn>88</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>4</mn>
<mn>5</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.8</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>80</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em></strong><strong><em>(A1)</em></strong><strong><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for correct numerator, <strong><em>(A1)</em></strong> for correct denominator.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{88}}{{110}} \times \frac{{87}}{{109}}">
<mfrac>
<mrow>
<mn>88</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>87</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying two fractions. Award <strong><em>(M1)</em></strong> for multiplying their correct fractions.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{46}}{{110}}} \right)\left( {\frac{{45}}{{109}}} \right) + 2\left( {\frac{{46}}{{110}}} \right)\left( {\frac{{42}}{{109}}} \right) + \left( {\frac{{42}}{{110}}} \right)\left( {\frac{{41}}{{109}}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>46</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>45</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>46</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>41</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct products; <strong><em>(M1)</em></strong> for adding 4 products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.639\,\,\,\left( {0.638532 \ldots {\text{,}}\,\,\frac{{348}}{{545}}{\text{,}}\,\,63.9{\text{% }}} \right)">
<mn>0.639</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.638532</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>348</mn>
</mrow>
<mrow>
<mn>545</mn>
</mrow>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>63.9</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their answer to part (e)(i).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{{67}}{{110}} \times \frac{{66}}{{109}}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>66</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying two correct fractions. Award <strong><em>(M1)</em></strong> for subtracting their product of two fractions from 1.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{43}}{{110}} \times \frac{{42}}{{109}} + \frac{{43}}{{110}} \times \frac{{67}}{{109}} + \frac{{67}}{{110}} \times \frac{{43}}{{109}}">
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct products; <strong><em>(M1)</em></strong> for adding three products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.631\,\,\,\left( {0.631192 \ldots {\text{,}}\,\,63.1{\text{% ,}}\,\,\frac{{344}}{{545}}} \right)">
<mn>0.631</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.631192</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>63.1</mn>
<mrow>
<mtext>% ,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>344</mn>
</mrow>
<mrow>
<mn>545</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><em><strong>(G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>There are three fair six-sided dice. Each die has two green faces, two yellow faces and two red faces.</p>
<p>All three dice are rolled.</p>
</div>
<div class="specification">
<p>Ted plays a game using these dice. The rules are:</p>
<ul>
<li>Having a turn means to roll all three dice.</li>
<li>He wins $10 for each green face rolled and adds this to his winnings.</li>
<li>After a turn Ted can either:<br>
<ul>
<li>end the game (and keep his winnings), or</li>
<li>have another turn (and try to increase his winnings).</li>
</ul>
</li>
<li>If two or more red faces are rolled in a turn, all winnings are lost and the game ends.</li>
</ul>
</div>
<div class="specification">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
<mi>D</mi>
</math></span> ($) represents how much is added to his winnings after a turn.</p>
<p>The following table shows the distribution for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
<mi>D</mi>
</math></span>, where $<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> represents his winnings in the game so far.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAaoAAABuCAYAAAB2gVfgAAAbqElEQVR4Ae2dD1BU173Hv6w8a60opdp6V61UCGgriRGedowvWSQucWxSK1XzTAWDzWijSSY8hAfRTlKMSYTBmMY01dkNSGKrEZ6aZ1QMSPswqcyusdEGl64JJrCXjg7hz8Younve3GWX3b27wILs3ru7P2aYvffcc8/5nc/vd+7v3vM3gjHGQH9EgAgQASJABGRKQCFTuUgsIkAEiAARIAI2AuSoyBCIABEgAkRA1gQiHdJFREQ4DumXCBABIkAEiIDkBBw9U32OSpDIESi5dGEmgPCSEO7siQFADIiB8OgjO/BkQE1/YeYUqbhEgAgQgWAjQI4q2DRG8hIBIkAEwowAOaowUzgVlwgQASIQbATIUQWbxkheIkAEiECYESBHFWYKp+ISASJABIKNADmqYNMYyUsEiAARCDMC5KjCTOFUXCJABIhAsBEgRxVsGiN5iQARIAJhRoAcVZgpnIpLBIgAEQg2AqHnqKw89OUvoqT2mosurOiq/S1+pr0Eq0souupQUliFJrNbqGsMOiYCRIAIEAGJCUjvqG7rURIfYVs2RFg6xO1fmYWSQ+9Dz/f4hsnaitotL+BgVAY2LJoIwApzUy20+UswIa0Ix9bNwtSsnTjV1NWb3vgFeGwZjxczilDrax6+SUKxgoZAD3h9BfJTlYiISELWzjPgQ/69pQtNtUdwqCQL8fm1sNcGd43ZXvjykSrUSWUWdjbw7i957rGD68zchFMlWVDanjdKpOZXeH/GhDID9IBv2I0spfDMFRj088IuFwbCflTCX+9Sf/aTQP9YGplGzTFgPas03erN3WJiusN7WJ6KY+CymaaxcxCpvmK64tUsu7KZWRwxO2tYHqdmBTVfsK9qtrKlmkZ2y1TPSjOzmcbwjT2WhXU3lrHs7DLW2N13pyOFgPxKyj4gJRw8E2kYWFi3rpSpVM+zGtNNxiwtrKZgKVMVn2Xdg4s84jECw+AbZtBks9WZyxgHMC6vhnnWLKEuLWOqgmpmsjBmMVWzAtUyVqz7asTLLE7Q7wwszexw6R9YtaG31Bbb82A2g6qU6dzqfwgzYBbWfe4wKztrsj0rHQw8bUE+DITFUG1/fjcQR0befh2OSq1hBpGvsLRUsmwOXgzJPSGLQcPUbvdbWGdNAeO4AlbTeYt12h2VkLzFcIId7nNUQjpC5V3N1JpGp5NzT96vZ5Ky92vJfE9cEgY2u1vA8mquOgW1vdyscHmRcV7y91FAGdjrnOfDSagfGqa21RtHZbTXJbf65R8a/mZgMdaz0y033YS3lRfJbnYQygyY5TN2+vQXLs8612elQ+fysgPpm/6ERoN/fYq/VPOIW3wPZogkUky5H4+tSQbq3sHBhvZ+mhiuoU6jAVYtQLzofvDvofzQP9DtcqciIR0/TxjjEjIG8QvTgC37UNcV8u0+LuUO70Or8UMcqJ6CxKnjnCDG3430Na04UN8cOk1dztL5cHQDxvoTqE6Kx9RxjsqkwPiUB7HmwgnUG2/4kIZ8oyji7oNqymg3ARWTYzGHcw0KbQZQ/Agq1TQ4tAv0oK35ChJzlmHeeEeovBg4pHLVUoCPrehq1OEUkpExdzrc9h2xSTIGEyZFAehAW8c33mXr+gQnK6Zg1cJYF/gKjFdtxNsFSuxbtwQri/7P+732UEX8AqxK+gtO6vpzhgPeHsQXzdCXpNr7BpVIdx1wYr2CqnW/QIneDOAGmrQrERGxEtqm4H5Y9SrLXhG5eMROdn9wATdRfeBDGMPxncXajPoD9eDmxGKyx9OhPnQd+NifYn7i+F7TCCcG5ibUan+HF41rsT9nHvpe2WTGwMMUA//EbYfuZDV4pGD+rOhhZG9Fl+4DVMDLA0cxBYu2leFs6WJ8XleHY+ueQUHVJQiPXe9//8L55mth9iY9Dsm5p8E6a5DH8bhgMNn59KD1cDE2ab/E1U7BMY1BwsrfQpN5C+3dt73jC6pQM1oMnwFuXw5BVQD/CGs2wXABSEpUOh9a/slJJqkKz486nN+QCbXjSyssGAgjoQuhjEpE2rqXsO+j0/jI6DKsRmYMpHdU1mtoPm8C1PMw+wee31PCm3znVaHhLhqTo7/txbiFz1YjeC9XbEEKDvOefQuXagrAoRo7MlZgo/aip7NSTETsnGiXB3V/CYZo+Pi7MH9xHPjzzWgTviTMF/D+kX+4f8mOjQQiU5GaODZEIVCxwo6AWYc95ROxfUNKmDhmh4YVGL9oO0zsJky6fchDGTJUhahq9XGEtSOZAP1K7qh6+wkAtbf+JQGCrVlPD3BqpKfE3AGWSMzdU42PSufi1Lq1KHKbZ+VMtu9B7QwK0qPb4Ks2uA/3Fw//F87jS6C3fSB9F9OTpgGX29Ft7YD+oAFzn9uIxbiOto6vYYXwhXUYnU9mIrmv7yJI0djEHoepiTOAC0a00Dw6pyLHKZGYhDB5YeuAfu9xxBSsdbfpsGIwGlzyGrz0x21Q83/DWYP9q0pmDCR2VFaYW4y4ACXmxE506V9y1JsO6PeUYgc/G9mvr4eqr6PPcX2Iv6OmYd4zBdimNqHi5Cde5494b5sfYj6yiB4Jbvmbti3uhdkH/f4bc5Fs+5CNRFTMJOCyEZ//9QiORN+He6ME8+Bxuf1r3G49jt1XFuGJ5OE0z8oCiEgIYQDNQ1CLQmH7wu/o/8VJHD/UzhWxWLhqoUeprG3NOM8vFPUDe0QLooAetB75My4ueRbZM+19Uw7pw4aBo8CArY9e/S2XAHnZgcSOyt4/5fVrqQd87S7kbj4HVUEpti2b7sWRCVxHY3JsPNwG7dhw30BT+V7Ueh3FN7afNvhv9RPu1F/oHkUiKlr4YtVh7wffw3qB96TpSIoDrvN/Q/luHhlPhFbziNcBNLa2+bkh9EAeqsX2OvCkig+g66s79hdK9UNYGO86WnaoacslvvBs0eJg1MNY0+ekunCpvMI+6jccGIh0Idj95XudA0ogLwYSOiorzJeOobxCDyxOwSzH15IwE/rIIWjzH4Yy7RB+WPou9m9bDK5fSe1DZ2FEc5uofdVSh6IX33GZdd6BpsP7UHHhIaxPn+Hu+Gxv0ujny06k1FA+5X6K9RvVmOLCm//TOYzKXO3ePBIKDBQJWLn9l2go2t27MomwssnLpWjIycVKt+kLoVBY38ugSFiO7TmNKHq5xrZKh5WvwctFjcjZvhwJLnbhe4pyitmFpqrnsTrtN8hJm4pRfc3hEzBr/y0o7c3aoczA2lqFdcp05Jc39K7CYrP7N9FWuME5oASArBg4Zr75e6KdI5/e3y9YZWacbTUMIV+Pfy6TFb97jOmE1QJ8+rvKavIWeJmw28kMNX9mxZmz+/LgMkv7ZqW7Ju05wc/1qn+PA8u+v7LcYqbKjSKGgp6WsYKaFpfJgf3df2fh0jG4yUxnX2eZwqRyqFle2Vnbagx3Vprh3R0YBvbJnW71zssEZ4uJnS3NtK1eAVUeK9P1rmIwvJL5fpd/GdxkLZUbe8vkVn5B95zI9oWVAUKRAWOs+wLTuD0Ti1llf/qVCYMIwYSE9x1hjT37oZxef3yWxdqkxZKngN8fz/by1icMxXweq5tX42j2TPcvKVsOwhyhdXgKW3Hc63WfxRhWxGBnP6xCi24iBsFfB0UqHdYp2QHZgWA4YjsIGUclTAjWl2zEazEF2J09e0hDTYVP4Seyr+DJymckad4SK2VYNTzIbyIGnpUzyFU6LPHJDsgOBMMR20HQtzg7a0M0knN2IMv4O+/zpJwRXY6E1dWrUFDYiMfKNkripFyEoUMiQASIABHwQiCEvqgcpRM6S9/A0ehfI9e21Ycj3MuvsB/Vy18i9alVSObEy+h4ie+nIPHbg5+ykXWyxMDzLVLWCvOTcGQHZAeCaYntIAQdlZ9qkB+TFSvFj1nJNmli4Fk5ZassPwpGdkB2IJiX2A5CqOnPj7WHkiYCRIAIEAHJCJCjkgw9ZUwEiAARIAK+ECBH5QslikMEiAARIAKSESBHJRl6ypgIEAEiQAR8IUCOyhdKFIcIEAEiQAQkI0COSjL0lDERIAJEgAj4QsBteLovN1AcIkAEiAARIAKBIOBY1s9tS11HYCAEoDycBMRzBpxXwueIGHjOHQkf7TtLSnZAdiBYg9gOqOnPWUfoiAgQASJABGRIgByVDJVCIhEBIkAEiICTADkqJws6IgJEgAgQARkSIEclQ6WQSESACBABIuAkQI7KyYKOiAARIAJEQIYEyFHJUCkkEhEgAkSACDgJkKNysqAjIkAEiAARkCEBclQyVAqJRASIABEgAk4C5KicLOiICBABIkAEZEiAHJUMlUIiEQEiQASIgJMAOSonCzoiAkSACBABGRIgRyVDpZBIRIAIEAEi4CRAjsrJgo6IABEgAkRAhgTIUclQKSQSESACRIAIOAmQo3KyoCMiEKYEutBUewSHSrIQn1+LrrCj0IWmUzuRpYywbS8RkZqPcj0PazhykKkdkKMKO2OkAhMBVwI30KR9Fi+Ul+Hpzftw3fVSWBz3oPVIBY5hKXabGJjFhLOPtKEg5QmU6jvCgkBvIeVtB247/NLGidLYpXiTMGmkkDZXYuC5WVxANWK9BO2SRdgy521cemURxgc0c2dmAbcD6+eo+2sk7ldNQ99bu8QsAs7AiR+QuOwOUcQM3Hb4dUSiXyJABIhAWBBQ/AgqlaikiomInaMUBdKplAT6XiKkFILyJgJEgAjIi8D3sGR+HMbJS6iwlYYcVdiqngpOBIiAVwJdn+Dk+YfwpNqlOdBrRAoMFAFyVIEiTfkQASIQBAQ6oN9zFJO2P47kcfR4lIvCSBNy0QTJQQSIgMQErDDr/4yDMb/GhuRoiWWh7F0JkKNypUHHRIAIhC0Ba+sJ7L24EFuzZ1PflMysgByVzBRC4hABIhB4Ala+FrsOjsGjaxxOygrzpUPQ1l0LvDCUowcBclQeSCiACBCB8CFghbmpCgWrf4WcnDQoR9lXp4gYhahZBwEljfuTgy2Qo5KDFkgGIiAZASu6aguhHDUL66p58DvSMCFiJbRNNySTKJAZW1sP4xlVBnbU8Z7Zqh/CwvgxnuEhGSJvO6CVKXw0utv6EsxM2YzL4KDW1OJ49kznTHYf0+gvmngWdn/xQjmcGEi8MoVMjIvsgOxAMEWxHYzIF5W1SYv0CMcns+tvErJKDqC2yZdlLrvQVPUaSqouwWyrNGboS1J7F4n0SFtIdz+OBHDhyMjkXDQZNFDjB/ih4RB2nWqyyymTGk5iEAEiQARClMCIOCpFQjZOsm9g0KwA1BoYLAyMWdBteAGTjz2LNNWz0F4awFlZW1FbWIij0zORu3ymfcTNOCTnHu9NE3HIrPwCwlqEjN2ESfcSHrhajmUpajyuvRggh3EDxvoTqOaW4D+fy8Wjo97FxsJT4MNvieUQrQpULCJABORKYEQclffCKTAuYTle+uM2qHkttryl62f7gA7oSzehKCZzgLkLc/HA7En2bEaDS/4Zsl/ag8psYN+6/8abAVnl2IwWw2dAUjymjhsDbtFGPB3zBlaXNgTIUXqnTKFEgAgQgVAn4EdH1YtOMTkWcziAP9+MNo+vD2GC3VvI3fxvWPPI3V7mLlzFxb+cA+Lm4Z4Zok5NxTQ8+NjD4HAMpQfP9eMER1B9t6/gXKUJ6lULEG+jFo17H3kYozeX4GCYdDyPIE1KiggQASLgMwG/OyprWzPO8wA3JxaTPXJrR8PBd1DX3+iarn/i7KnL4DLm4i6Pdd4VGDshBmMB8G0d+NrnIvsa0XUztXTkv7ofxy4rMSd2Yt8gCsWMe7A47l1s0Xzof0fpq9i+xuOrkOXo+0vdCb3ZCit/BjuzkhARkYoSfW9Poa/JBV+82+CrNtj7QJVILXF8GdtHPyk3oaq1J/iKRRITgRAk4OE67riMF86g3j54Qnjw7XpxJ6qxFDkr53rucSMs/lih78eJWdGl+wAVfBwWz7/L894BBf0SVVnx/QzEcA72iC/R47a3dGx9ZiuQuP0qfl7XCUvLelwrLUUdp0Z6SozzjsjvY8Z9ceArPoCuy+Nz0RlPjkfccpSzm2ip3Aiu7h0crH4Pu179DEt2/x2MnUZucqjPH4kEt/xNMEsjNGqg7tRFmGwqVGDcrFSsTfwKHV8HmU7laGckExEYAQIj76h4LdbNmmBzEqOUC1GMLFTq9iLHy9pZt/95DpU8MHbSBNuXkXt5etDWbAQP1/4p1xhWXO9st+1Iyk2OxndcL2Ealpcb7YMvhAEY3v+Nucnw+FCD0Ge2Hmlld6Hy7eexPGE8FNyPcV8SZ++fckX2XUxPmgbwRjS3BePb92hMeXA51nB67Nh0CtOfXoWZ4bYQp2Iq7lmcCFxuR7fdLyl+MA3xM+bjHuVoN6sKtRNhCLAv/6FWbkd5fCm7axzHfcH661qWkToOFAvXp+7I5Nk36q/XOZjKc7E8metrLvM5E2sz6g/UA/01C6IdupPV4JGMNel3D/GLq38prE1VKNx8Duptm7BsSu+Dysp/ijMX4NI/Jb7/Ktq7vX6biSPK73z83UhfkwwkzcVsLrQfzN7hRyIqZhJw2YgrVwUd9qD18FtoWPpz3BviTru/FzhxuHduwR8qLudg58Fe4sHKN5zrgWIy8o5qpCQ3m2C4wPfbLGjWV6Bohx5cdiGeVk0U5Trcpj/HEPS1yP9lgt25duDjP2mh5d37p0QZBu+p9Wt0XLsJVJ9AvTE8ViNwV1YkoqJdmnPN53FQtwBbl00f+suVe8J0RgSIwAgRkKmjcvRPef9asvI12J5bjDrV83h7288wxaMUw236s48yHBuDCWOFRB2jEo8B4v4pNwVMQkyUZyOiWxRZnghfD2/g2MQHoMJnMLSE+gAKb0pQ4DvRMeBgwGdfGlG74xSmb1zixaa83UthRIAIBIKAxyN++JneQHf7daCnE93XfeuEjrxrLjI44PrVTltfU1/e5k9xqPw98EjB/FmOfWF6wOvfR5U2H2lKNcp++BzO7i/AohFtrvo2oidHA9ebceVfZvANe1B0JAZrcoSmse+g+dD7aHIr2g10Xu0GuHjETg6+ZjNr6/+iqHo+fvfiJqxRm1Bx8mO06t9EYdUVuBWzTzGheOAYPXoNH+9+E3WqtX1NvqFYWioTEQhKAsz+BwhjDob3ZzFomBpgQhq9/xxTaxqZZdDkrrKavGQGtYYZbJFvMVPlepd0HOk5fmezzOJ32GGdyYe0B83cSwQL624sY5mckJ+a5ZWdZSbLF6wyM46By2aaxk73eyyNTKPmGJdXw0RX3OMNcnYn7AdJ2uvlW7piFgeOqfIqmaFbAP8V0xUv7S1zZSPr9nqXfwMDzcC1NL32O5tlai5IUnaHLFIycMgg9S8xYLbnn9R6kDp/sR1IviitsE7gksQTWGXYh+wE0aRembv+kZJdGIEjdGSG85+UDKxN5XiiTIlt2xaDG8E2hqHqU0oGQ5XVX/GJgeeCrP5iLed0xXYgYbXsxaRIWI7txbdQcfSTIFuKqAMfH30PPcW5WBlkDlbOBhpw2cwN2KVRYHNhmqROKuDlds3QyqNhZxaUtuHq6cjvWxjaNVIoHwvdChXIT1Xahusrs3bilE8LaQcrE2EPrpMosU3uF6YopCO/vEG0bql94rvXKQyB3wZGckcFRCM553Vsbddie21rkPSN9ICv3Y3X2p/E/px5XpZ+ClYDDhO5zQ0oSb0P/6U9hJ1F53D/1sfCb/5Yn6o78PHhM8Cje2ESFnw++wjaNv0KRbXhsrOtMGBqN9a+1oWM/c1grBO1D1xElqowZFcmsbaewN5jwCO2yf12nRcsE61b6pj+02cozoN+pww5o4z4kaMtUtwm6AgP3G8nM1TuYsUS9ZH4Xs6Rl1N69r6X3l8xA8qgs4blcUIf3T6mM930V5GGnG5AGdilsxjr2ekWVwa9/cZ32u865MLbbwg4A1s/8wKWV3PVKbKlmVVmz77jvmdngkM78i+Db5jx9EesxW0AwTfMoFnBwBWwmk77hc7TrHhrNTO5xbOwzpqtbKlP4w+GVmZxbDEDyfuoRtzzBmGC4vbYICzCHYtMDGTSN2G9BO2SArRvfwu5XlaTuWNFD5JAoO3Aez/zDTRpM5G4JR41l7Zh0fjANjwFmoEwDaerdgtm/gp4215eK38Zn0f9CHGuk95ttlEE/F7j9/EEYgaB1cAgRkqXiQARkIqA0G9RC23BqzDmv+51yTOpJPNfvlaYW4y44JHBaEyOjQcXtEujeRTIp4CxS1KQaHdMCi7O3UkJs0qNH6JqagbS4wM/6I0clU8qpEhEIJQJXENt/jxEJaZh3Y6j+OjkWRjN4TCTToFxU+ORhHocqG/27B8P0vmRQ7dUoT+qFRueXDTARHdh1Z4G/OSx+weIM/Scfb2DHJWvpCgeEQhZAhOx6BUdmMUEXdkaYEcGVM8cRmsY+CpFwiPIz1Oieksxyuy7kFt5Hf7npB68bZPUUH9ECoNJ9qN80sYBNq4VPqeaUV/1fffdIwJYH0JdCwFESVkRgSAnoOCQnPUC/qhZAf64Doaw+KqaiEVb96M65za2CLs+KLNQeubv+LTh8gCLUAe5nl3FN+uw9+B3UbAhZcDRy7Zmv5+okBLg/jqHqOSoHCTolwgQAQBjEL/wIajDicW4BCzOLYdJ2A7IVI6cu0fhvGGly8LUIQrDegVH9n6OJYNOz7A3+43gLhVDJUqOaqjEKD4RCGkCvQMMLrt0rId0cUWFs/KnsGX9e1j8Xl7AR/uJRPHvqbA57K7jiHr0F845hOaLKNee8dytXOJmPwEEOSr/mgOlTgRkTKAHrVWboEzNR7metw0mEHYmePmVdhRuflCSTnPJYJmbUHuoBI//x9uY9MoboT3q0XwJVQXZSMv5DdKU33Junhmlxn58z6MJUOpmP8EmyFFJVjMoYyIgNYFITPjxv2OxYQfWpigxKiIJj7/TjYyy15A9c7zUwgUm/65a5CsjEBH1FE52zcVz59/Cs/OGsdFrYKS981ysV1D1zApk7Kj2ktZCrFoYK3IKQrOfAaqVc0dsc1ovGQ8aRBN+B0Xk/wjiyW3+z1F+ORADmUz4ldg0yA7IDgQTFNsBfVFJXDEpeyJABIgAERiYADmqgfnQVSJABIgAEZCYADkqiRVA2RMBIkAEiMDABMhRDcyHrhIBIkAEiIDEBMhRSawAyp4IEAEiQAQGJkCOamA+dJUIEAEiQAQkJkCOSmIFUPZEgAgQASIwMAFyVAPzoatEgAgQASIgMQFyVBIrgLInAkSACBCBgQmQoxqYD10lAkSACBABiQmQo5JYAZQ9ESACRIAIDEyAHNXAfOgqESACRIAISEyAHJXECqDsiQARIAJEYGAC5KgG5kNXiQARIAJEQGICbtt8SCwLZU8EiAARIAJEoI8AY8x2HOkIcQQ4zumXCBABIkAEiIAcCFDTnxy0QDIQASJABIhAvwT+H3GUUSGr0zT3AAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of rolling exactly one red face.</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 probability of rolling two or more red faces.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{3}}">
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down 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">[1]</div>
<div class="question_part_label">c.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="y">
<mi>y</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>Ted will always have another turn if he expects an increase to his winnings.</p>
<p>Find the least value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> for which Ted should end the game instead of having another turn.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">valid approach to find P(one red) (M1)<br></span></p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_n{C_a} \times {p^a} \times {q^{n - a}}">
<msub>
<mrow>
</mrow>
<mi>n</mi>
</msub>
<mrow>
<msub>
<mi>C</mi>
<mi>a</mi>
</msub>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>p</mi>
<mi>a</mi>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>q</mi>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mi>a</mi>
</mrow>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\left( {n{\text{, }}p} \right)">
<mrow>
<mtext>B</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>n</mi>
<mrow>
<mtext>, </mtext>
</mrow>
<mi>p</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3\left( {\frac{1}{3}} \right){\left( {\frac{2}{3}} \right)^2}">
<mn>3</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 3 \\ 1 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span></span></p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">listing all possible cases for exactly one red (may be indicated on tree diagram)</span></p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">P(1 red) = 0.444 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \frac{4}{9}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>9</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> [0.444, 0.445] </span><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"> </span><em style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><strong>A1 N2</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"> [3 marks] [5 maximum for parts (a.i) and (a.ii)]</span></em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">valid approach <em><strong>(M1)</strong></em><br></span></p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><em>eg</em> P(<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(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X = 3">
<mi>X</mi>
<mo>=</mo>
<mn>3</mn>
</math></span>), 1 − P(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> ≤ 1), binomcdf<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {3{\text{,}}\,\,\frac{1}{3}{\text{,}}\,\,2{\text{,}}\,\,3} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></span></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{9} + \frac{1}{{27}}">
<mfrac>
<mn>2</mn>
<mn>9</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span>, 0.222 + 0.037 , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - {\left( {\frac{2}{3}} \right)^3} - \frac{4}{9}">
<mn>1</mn>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mfrac>
<mn>4</mn>
<mn>9</mn>
</mfrac>
</math></span></p>
<p>0.259259</p>
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">P(at least two red) = 0.259 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \frac{7}{27}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mn>27</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> </span><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"> </span><em style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><strong>A1 N3</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks] [5 maximum for parts (a.i) and (a.ii)]</span></em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that winning $10 means rolling exactly one green <em><strong>(M1)</strong></em></p>
<p>recognition that winning $10 also means rolling at most 1 red <em><strong>(M1)</strong></em></p>
<p><em>eg</em> “cannot have 2 or more reds”</p>
<p>correct approach <strong><em>A1</em></strong></p>
<p><em>eg</em> P(1G ∩ 0R) + P(1G ∩ 1R), P(1G) − P(1G ∩ 2R),</p>
<p> “one green and two yellows or one of each colour”</p>
<p><strong>Note:</strong> Because this is a “show that” question, do not award this <strong><em>A1</em></strong> for purely numerical expressions.</p>
<p>one correct probability for their approach <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3\left( {\frac{1}{3}} \right){\left( {\frac{1}{3}} \right)^2}">
<mn>3</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{6}{27}}">
<mrow>
<mfrac>
<mn>6</mn>
<mn>27</mn>
</mfrac>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3\left( {\frac{1}{3}} \right){\left( {\frac{2}{3}} \right)^2}">
<mn>3</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{9}}">
<mrow>
<mfrac>
<mn>1</mn>
<mn>9</mn>
</mfrac>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{2}{9}}">
<mrow>
<mfrac>
<mn>2</mn>
<mn>9</mn>
</mfrac>
</mrow>
</math></span></p>
<p>correct working leading to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{3}}">
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{{27}} + \frac{6}{{27}}">
<mfrac>
<mn>3</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>6</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{12}{{27}} - \frac{3}{{27}}">
<mfrac>
<mn>12</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>3</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{9}} + \frac{2}{{9}}">
<mfrac>
<mn>1</mn>
<mrow>
<mn>9</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>2</mn>
<mrow>
<mn>9</mn>
</mrow>
</mfrac>
</math></span></p>
<p>probability = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{3}}">
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</math></span> <em><strong>AG N0</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[5 marks]</span></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{7}{{27}}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span>, 0.259 (check <em><strong>FT</strong></em> from (a)(ii)) <em><strong>A1 N1</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[1 mark]</span></em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of summing probabilities to 1 <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum { = 1} ">
<mo>∑</mo>
<mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x + y + \frac{1}{3} + \frac{2}{9} + \frac{1}{{27}} = 1">
<mi>x</mi>
<mo>+</mo>
<mi>y</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>2</mn>
<mn>9</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>1</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{7}{{27}} - \frac{9}{{27}} - \frac{6}{{27}} - \frac{1}{{27}}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mn>7</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>6</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.148147 (0.148407 if working with <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> value to 3 sf)</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{4}{{27}}">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span> (exact), 0.148 <em><strong>A1 N2</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[2 marks]</span></em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into the formula for expected value <em><strong>(A1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - w \cdot \frac{7}{{27}} + 10 \cdot \frac{9}{{27}} + 20 \cdot \frac{6}{{27}} + 30 \cdot \frac{1}{{27}}">
<mo>−</mo>
<mi>w</mi>
<mo>⋅</mo>
<mfrac>
<mn>7</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>10</mn>
<mo>⋅</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>20</mn>
<mo>⋅</mo>
<mfrac>
<mn>6</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>30</mn>
<mo>⋅</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>27</mn>
</mrow>
</mfrac>
</math></span></p>
<p>correct critical value (accept inequality) <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> = 34.2857 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \frac{{240}}{7}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>240</mn>
</mrow>
<mn>7</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> > 34.2857</p>
<p>$40 <em><strong>A1 N2</strong></em></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Don took part in a project investigating wind speed, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, and the time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> minutes, to fully charge a solar powered robot.</p>
<p>The investigation was carried out six times. The results are recorded in the table.</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>M</mtext></math> is the point with coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><menclose notation="top"><mi>x</mi></menclose><mo>,</mo><mo> </mo><menclose notation="top"><mi>y</mi></menclose><mo>)</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>On graph paper</strong>, draw a scatter diagram to show the results of Don’s investigation. Use a scale of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math> to represent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> units on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math> to represent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> units on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate <math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>x</mi></menclose></math>, the mean wind speed.</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>Calculate <math xmlns="http://www.w3.org/1998/Math/MathML"><menclose notation="top"><mi>y</mi></menclose></math>, the mean time to fully charge the robot.</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>Plot and label the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> on your scatter diagram.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, Pearson’s product–moment correlation coefficient.</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>Describe the correlation between the wind speed and the time to fully charge the robot.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>, in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>c</mi></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>Draw this regression line on your scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise estimate the charging time when the wind speed is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Don concluded from his investigation: “There is no causation between wind speed and the time to fully charge the robot”.</p>
<p>In the context of the question, briefly explain the meaning of “no causation”.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img 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"> <em><strong>(A4)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(A1)</strong></em> for correct scales and labels.<br>Award <em><strong>(A3)</strong></em> for all six points correctly plotted.<br>Award <em><strong>(A2)</strong></em> for four or five points correctly plotted.<br>Award <em><strong>(A1)</strong></em> for two or three points correctly plotted.<br>Award at most <em><strong>(A0)</strong></em><em><strong>(A3)</strong></em> if axes reversed.<br>If graph paper is not used, award at most <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em><em><strong>(A0)</strong></em><em><strong>(A0)</strong></em>.</p>
<p><em><strong><br>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo> </mo><mfenced><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math> (minutes) <em><strong>(A1)</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>point in correct position, labelled <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)<br><br></strong></em><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for point plotted in correct position, <em><strong>(A1)</strong></em> for point labelled <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> Follow through from their part (b).</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>r</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mo> </mo><mn>0</mn><mo>.</mo><mn>944</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>943733</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(G2</strong></em><em><strong>)<br><br></strong></em><strong>Note:</strong> Award <em><strong>(G1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>943</mn></math> (incorrect rounding).<br><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(very) strong positive correlation <em><strong>(A1</strong></em><em><strong>)</strong></em><strong>(ft)<em>(A1</em><em>)</em>(ft)</strong><em><strong><br><br></strong></em><strong>Note:</strong> Award <strong><em>(A1</em><em>)</em>(ft)</strong> for (very) <em>strong</em>. Award <strong><em>(A1</em><em>)</em>(ft)</strong> for <em>positive</em>. Follow though from their part (d)(i). If there is no answer to part (d)(i), award at most <em><strong>(A0</strong></em><em><strong>)</strong></em><em><strong>(A1</strong></em><em><strong>)</strong></em> for a correct direction.<br><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>465</mn><mi>x</mi><mo>+</mo><mn>23</mn><mo>.</mo><mn>2</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>465020</mn><mo>…</mo><mo> </mo><mi>x</mi><mo>+</mo><mn>23</mn><mo>.</mo><mn>1646</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1</strong></em><em><strong>)</strong></em><strong><em>(A1</em><em>)(G2)</em></strong><em><strong><br><br></strong></em><strong>Note:</strong> Award <strong><em>(A1</em><em>)</em></strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>465</mn><mi>x</mi></math>. Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn><mo>.</mo><mn>2</mn></math>. If the answer is not an equation, award at most <em><strong>(A1)(A0)</strong></em>.<br><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>regression line through their <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> <em><strong>(A1</strong></em><em><strong>)</strong></em><strong>(ft)<br></strong></p>
<p>regression line through their <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>23</mn><mo>.</mo><mn>2</mn><mo>)</mo></math> <em><strong>(A1</strong></em><em><strong>)</strong></em><strong>(ft)</strong><em><strong><br><br></strong></em></p>
<p><strong>Note:</strong> Award a maximum of <em><strong>(A1)(A0)</strong></em> if the line is not straight/ruler not used. Award <em><strong>(A0)(A0)</strong></em> if the points are connected.<br>Follow through from their point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> in part (b) and their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-intercept in part (e)(i).<br>If <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> is not plotted or labelled, then follow through from part (b).<br><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>y</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>465020</mn><mo>…</mo><mfenced><mn>27</mn></mfenced><mo>+</mo><mn>23</mn><mo>.</mo><mn>1646</mn><mo>…</mo></math> <em><strong>(M1</strong></em><em><strong>)<br></strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into their regression equation.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo>.</mo><mn>7</mn></math> (minutes) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>35</mn><mo>.</mo><mn>7201</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1</strong></em><em><strong>)</strong></em><strong>(ft)<em>(G2</em><em>)</em></strong></p>
<p><strong><br>Note:</strong> Follow through from their equation in part (e)(i).</p>
<p><strong><br>OR</strong></p>
<p>an attempt to use their regression line to find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> value at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>27</mn></math></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for an indication of using their regression line. This must be illustrated by vertical <strong>and</strong> horizontal lines or marks at the correct place(s) on their scatter diagram.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo>.</mo><mn>7</mn></math> (minutes) <em><strong>(A1</strong></em><em><strong>)</strong></em><strong>(ft)</strong></p>
<p><strong><br></strong><strong>Note:</strong> Follow through from part (e)(ii).</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wind speed <strong>does not cause a change</strong> in the time to charge (the robot) <em><strong>(A1</strong></em><em><strong>)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(A1)</strong></em> for a statement that communicates the meaning of a non-causal relationship between the two variables.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>It is known that the weights of male Persian cats are normally distributed with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>1</mn><mo> </mo><mtext>kg</mtext></math> and variance <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo> </mo><msup><mtext>kg</mtext><mn>2</mn></msup></math>.</p>
</div>
<div class="specification">
<p>A group of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> male Persian cats are drawn from this population.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a diagram showing the above information.</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 proportion of male Persian cats weighing between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>kg</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>kg</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>Determine the expected number of cats in this group that have a weight of less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>3</mn><mo> </mo><mtext>kg</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>It is found that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> of the cats weigh more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>kg</mtext></math>. Estimate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</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>Ten of the cats are chosen at random. Find the probability that exactly one of them weighs over <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>25</mn><mo> </mo><mtext>kg</mtext></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <strong><em>A1A1</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for a normal curve with mean labelled <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>1</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math>, <em><strong>A1</strong></em> for indication of SD <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>)</mo><mo>:</mo></math> marks on horizontal axis at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>6</mn></math> and/or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>6</mn></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> and/or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> on the correct side and approximately correct position.<br><br></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>6</mn><mo>.</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mn>5</mn><mo>.</mo><mn>5</mn><mo><</mo><mi>X</mi><mo><</mo><mn>6</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> <strong>OR </strong>labelled sketch of region <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>673</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>673074</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo><</mo><mn>5</mn><mo>.</mo><mn>3</mn></mrow></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>0547992</mn><mo>…</mo></math> <strong><em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0547992</mn><mo>…</mo><mo>×</mo><mn>80</mn></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>.</mo><mn>38</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><mo>.</mo><mn>38393</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>15</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>85</mn></math> <strong><em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mi>x</mi></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>15</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo><</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>85</mn></math> <strong>OR </strong>labelled sketch of region <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>62</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>6</mn><mo>.</mo><mn>61821</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mn>6</mn><mo>.</mo><mn>25</mn></mrow></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>382088</mn><mo>…</mo></math> <strong><em>(A1)</em></strong></p>
<p>recognition of binomial <strong><em>(M1)</em></strong></p>
<p>e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mo>(</mo><mn>10</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>382088</mn><mo>…</mo><mo>)</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0502</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0501768</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A2</em></strong></p>
<p><br><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.</p>
<p>From those who did not encounter traffic, the probability of being late for work is 15 %.</p>
<p>The tree diagram illustrates the information.</p>
<p style="text-align: center;"><img 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wicaB8OieULH8LkqpiATIB1Y5kEv3pKgI2yp8S4PBMYgwDrxmPA4UNuEWD5wi1MXIgJjE1AqRsvWLAArBuPzYuPuibAV8qu2fARJuAWAUrF9MorryAjI0PSjadOnerWeVyICTgjwEbZGRXexwTcIEC6cXl5Oa5fv87+xm7w4iLuEWCj7B4nLsUEhgiQbvzmm2/i1KlT2L17NzQazdAxfsMEJkqANeWJEuTzo4YA6cYUUpP8jSlbNOnGbJCjZvoDNlC+Ug4Yam4onAmwbhzOsxdefWejHF7zxb0NMAHWjQMMnJsDG2X+EjABJwRYN3YChXcFhABrygHBzI2ECwFZN16xYgUSEhJYNw6XiYugfvKVcgRNJg9lYgRINyYXt7lz50oP9OhhHm9MINAE2CgHmji3F3IESDd+++23Qa+7du3CwoULQ66P3KHoIcDyRfTMNY/UgQDpxlVVVVi/fr0UUpP8jtkgO0DijwEnwEY54Mi5wWATUOrG1BfyN6ZUTLwxgVAgwPJFKMwC9yFgBFg3DhhqbshLAmyUvQTHp4UXAdaNw2u+orm3LF9E8+xHwdhJqlDqxseOHWPdOArmPZyHyEY5nGeP+z4mAYpTkZ6eLpU5e/Ysp2IakxYfDBUCLF+EykxwP3xGoLu7W3JtI3/jo0ePSn7HPqucK2ICfibARtnPgLn6wBHgVEyBY80t+Y8Ayxf+Y8s1B5gAZfz4zne+I7VKbm5kpHljAuFGgI1yuM2YR/01Qf/efhQfuQKrR+e5KmyCvrEYS2NiEBOjRmbNH2DSN0K7VI0Y2pe5H41vrUWMuhitJt+06KonrvaTvzEZZFoiTXGPSVemh328MYFwIcBGOVxmypt+mjpRnbsXXRZvTh59jlX/Dl5afRpzGvpgEQY0bYjFOy9tRt2cKvRbBETTy1j1gxMQhhIsSwjeV+uBBx5ATk6OlC/vww8/lB72kX8yb0wgHAgE7z8nHOhwH50QuA/TpzyIEV+c6VMwecQOJ6cFYRfJGWVlZdLDPgo0tHHjRim+RRC6wk0yAfcJCN4ik8BAiyhUQQD2P1WRaBn4VLQUpghkFIq3ynOEio5J+y1CWAyis6Fc5AydoxIZhdWiRTcghLgtdNVrhuuS6xzxmiIKW/5sKyfXKZG9KwydtaIwQ2U7X5Ujypt1YjAI1JuamsSiRYvE66+/Lm7cuBGEHnCTTGB8AiF4feP+DwqXHINAwjKUXmlBoUoFTfVlWJSSQtsv0D61AHpxF4a255CWYEJX5UY88e4D2NR1F0IICMtvsTPuOJY/V40u8yTMzTsBi64aGqSgsOW6vcxlVGtUUBW2YEB0onTZDIcO3cPVxq1IST0KvNSKQWHBYOsy9OSuxpbGP/lI53ZocoyPlE+P9eYxAPGhkCDARjkkpiHAnVA9gdynv4F4TIJq7sOIN13EicpryM7NQppqkq0zsTORsSELmrYP8JHhnncdtH6Mpp81AoVa/GjVPMQjFvHzHkdu9n2o+VkLeoPwLJD1Zu+mks8KHAH2Uw4c69Btia6qDZ2AWY/Wxl/hFvX01gUcyC9DG9Ygy8ueW3t/g+PNQHKWGvFDdUzHstJOSVMZ2hWEN7LeTDExCgsLcfjwYRQUFPBCkyDMBTc5kgBfKY/kEaWfTLhSkw/15CQsP3DBZpSnrMRPO9+CBh9D12+OWC606o/iKK9Zs0aKq1xSUsL+zRE72+ExMDbK4TFPfu0lubptye/ASnJ1+2Up8latwqpV/wD1wH+gx68th07lrDeHzlxEe0/YKEf7NwBWmPt70YP5WLzgywpXty8weMs0ITqxiY8iSwP06AwYvta+A33NWsTErEWN/s6E6vf1yc705ubmZl83w/UxgTEJsFEeE0+YH4xXIyn5r2yD+NwMs9MHa7FISH0M2ap21B3+NYxSmXswdhxC8eaDME4EQewcrNQ+h6SyUuxtvSp5W1iNv8bhuovIKN+GtXPvn0jtfjtX1pspmNFPfvITPPXUU+zf7DfaXLEjATbKjkQi6bNkFLNxL38+4h7Mw4leF8uNE5bgh6dLkfZBLtRxtIQ6Bdt/NR25p06iUDURIJOgWlaE+s71sLy2CHExMYhTV8CyoR71W9MUD/8m0ob/zpX15hdffFHSm+mBIMfT8B9vrtlGIIZcmRkGE2ACYxOg+BlnzpzB6tWrceTIEenBIMkdvDEBXxPgK2VfE+X6IpIAGWAKdnTjxg309/dL8TRYb47IqQ76oPhKOehTwB0IRwLk30zxNK5fvy7F1yCpgzcm4AsCbJR9QZHriFoCFH3ulVdeQUZGBrZv3w56SMgbE5gIAZYvJkKPz416AosXL5biaVBwfYrfXFtby/Gbo/5bMTEAbJQnxo/PZgJgvZm/BL4kwPKFL2lyXUwAkHyaWW/mr4K3BNgoe0uOz2MC4xBgvXkcQHzYKQGWL5xi4Z1MYOIEWG+eOMNorIGNcjTOOo85YASc6c2UzJU3JuCKAMsXrsjwfibgBwJK/+Zdu3Zh4cKFfmiFqwxnAmyUw3n2uO9hS0CpN7/88suYNWtW2I6FO+5bAixf+JYn18YE3CKg1Jtp+XZVVRX7N7tFLvILsVEOgzmmqyoKiMNbZBGQ9eazZ89KA0tPTwfrzZE1x96MhuULb6gF6Byl/lhWVsb54wLEPVjN0Hy//fbbkp8z683BmoXgt8tGOfhzMKoHFLO3vr5eWrJL8RTo9pa36CFAd0a0+ISCHLHeHD3zLo+U5QuZRAi8kkRBt68rVqyQenPu3Dk2yCEwL4HuAunNx44dA8XTYL050PSD3x4b5eDPgdQDujp65pln8OGHH0qGefPmzVJMhRDpHncjwARYbw4w8BBqjuWLIE8G64hBnoAwaZ6/J2EyUT7oZgheKd+DsasO2qVqxMQkI3ffeXsyz7FGa4VZ34SK3GTExFCOuUxoj3Q4P8/UCq2aysh/wcmqTLoxuUGtX79euk09deoULyQYa4qj/Bjpy/Swt6CgAPQQkPIFUgYU3iKPQIgZZSvMXQexbtvHyKzvg7CcRe71PVhX2aFIUT96EqxXz+LQvwH/dPAjCHEXhgv/hGtFTzk57x6uvt+IOmWKZs0KLEkMXFZl1o1Hzx/vcZ8A683uswrbkpQ4NWQ2y2VRrXlUFLZcH+7SQIsoVK0R1brbw/tGvLsten/5gei3KHfeFrrqNQKqItEyoDgweEGUa3aO3Kc8zc/v29vbxZNPPikKCgrEJ5984ufWuPpIJ3Djxg1x4MABsWjRItHQ0BDpw/VgfBYxqDsryot+LnSKf/+RFdhthKZ6jDIjz5A+DepEc/lucdilPXJyjoe7QupK2dr7GxxvnomkWfHDP3IJ30Rm9lUcb++DdXiv4t39+FrGdzBzxEgm4aHZiVApSgFWmDpOobL5bbz2ejUaW/VjXn2POHWCH+g2k243yc2Jbj/pNpSX1U4QKp8upZ6iB8JHjx6VHhA/9dRToAfGvN1ER/WPUNB1x8coyIYcRm7BR7D4uGZldSNMmfJA4N/fQW/7WTSrEjH7oUkOzd9F8/HfoNe5VXYoO/zxr1amIinePkSrHu+UHoYRRrSV/QCrl2fgCW0j9GYPKx2uftx3JFWQbkxuTeTeRG5OdPvJGxPwJQGl3kw//HQBQA8GeQtPAiFklM3o130MJCdilmxIvWZ6E51NV/H8i8uGr6Bj5yGvyQBhMaDz1FsozADayjbjuTc7/XLFTP7GtGyWNlpGS4aZ3Jx4YwL+IqDUm+kBMl0Q0APl8Ng+Q6s2FTGZB9HaIT/oj0GMOhcV7znc1Zr1aK3RYqn8sH6pFjVDd75UzwosL+sCmvORFJcKbetn7iGwGtHVWIHcIUcANZZqa9CqN0G6027dgXnL98CIk8hPegBqbSvoCKB0TrA7GtS0en3BF0JG2T1u45eih4X1ODJjE55PmTK6eKwKKU9uRGnLb9FSlIy2ylPoMPnuarm7uxt0G0n+xnRbSbeXnOF49DTwHv8QcPRvpoVIdIEQNrFTml/Haw0PIv90v+2h/dE5+DfNVrzZdcsGzHwJNZtWY/25r6LUcNdWpvSrOLc+A09UkEPAdCwrPYuWwhRAUw2dpROly6a7AfsWuio34ol3H8CmLqpXQFh+i51xx7H8uWp0mYGEZbtxpaUIKqxBte42DKXLkIB7uNq4FSlPvI+HSrtgofMG/wVJ57YgY8spXPXCtISQUY7HrKQ5QE8v+iciKZg7cejE36Do+VQolOnRkxI7E8u2a1GIZjR1TvxqQtaNyV1J1o3ptpI3JhAMAnQhQBcEZJDpAoEWJoWF3qzagJ0/egpzpbvlSVCl/j3SVBfx3kfXYJWeC9Vjx3vpqCrZiDQVyZyToEp7AQeOboCuoAIn9F7qyKaLOFF5Ddm5WfZ6AcTORMaGLGjaPsBHhnvOp9HUjv2bG5G8uwhb0lSQDGr8AuQdeAPZZ0qwv83Nq3RF7SFklO9H4pIV0Cg6J721foa+7lvQZD2KxPF6a/0T3j30H1i583uY544EEq9GUnLSyAeLju2P85l143EA8eGgEqAHyvRgmS4WwlJvlv5HgR6dAWaQLNkMY/IjWCAZZBltLOJnJSIZH0PXb5Z3evaasAylhk6Upt1Ea2Oj9GPWWKPF8qR8NLusyQpT5/uoM6qxcPZ0m0GWy0r9NqCu6fd2iUM+MP7reGZu/Bp8WCI28VFkJZ8beeVqNkDX8wiylsweOWjHdq1X0frGGUz+H/992CCbL+FIzXnXUMwG9Kbk4+m53vkps27sOAn8OVQJUIYTWqBED5zDT2+2U5Uu0AxjIDagu+8zF15aY5wmHTLhSk0+1JOTsPzABUhiyZSV+GnnW9CMa+y7ULZ8hmJBWgxi4uYjv1m5IGK89oePh5RRRuxcrC15Gh2vHUSr8R5AhnZvJTq2bsPaIcNJGs5mqJfuQ5csc5ivoLEoD8u3voDl6vuG4UzWoB7TJBnDauzCu+92Da3ysxrPY9/rF/HYS0uQMMzDrXeybnzmzBnWjd0ixoVChQA9cKZAV7SFnd4cOx2zF6rHQOnkinWM0spDVv072JLfgZUNfbD8shR5q1Zh1ap/gHrgP9CjLOj0vU1jlnRo0pQVfzbd2elJLneGllFGLOJTNqG+dDqOpNyHmLg8NCW9ivqtaa71Yeuf0LhlDVaXObvJWKK4wr6JC//zCajjbE90K8//Fx7fuRXLRtwGueQkHaAn2eRu9IMf/EDSjQ8dOsQxjsdGxke9JWDW472KXKjJw2DpZmgphEBiBbq+8LbC4fPoYWBY6s2YitRMDVQ9F3GJLtqGNivM/b3owRwvpUj5/PlYvODLijvyLzB4y+ZfMdTUiDexSEh9DNmqyzh/6dORV+jmDlQsTURmzZWR+0ec7+KDh4tNorL4559/Lo4cOSIASCun6DNvTMBfBCyGZlGU8TWRUdggdIP/JQZaioQKEKrCFjHgh0Z/97vfDa001el0fmjBnSqvi5bClNGrcKVVvqrhsQ/2iOqcBUKVUyUuGO4KISxi8PJhkaNSiYzyC2JQakq5Wu+2GBz8LycdUJYRQkgrh1Uio6hZGKRVgHeF4UKVyFFBAClDq4wtumqhAa0w/k/xn4P/KSziruhv2CRUqhxRecEgpFMHL4uGQo1ARqXoHHS5pNBJn2y7QuxK2cUvRxB3Nzc3S/7G5F1x48YN9jcO4lxERdPWP+HUjq04PKcMR/eswtz4LyFhfiq+CxWSk9Su7xgnACes9GbybDjYgKPpf4ZWkirjMPmFPyD9aBtOb5PvqO9H4sqNKLq3A0lxc7D6RO/4V6sJS/DD06VI+yDXdjcdk4Ltv5qO3FMnUahYGhybmAlt0QDykx7Eg6v/Fb3WSZi5qgRtR9NxTZuCOLqzmbwG7854Dp31m5DijsOBw9xx6E4HIPJHWhFFUsWMGTMkqYLd22Qy/Oo/Ajaf10Wr/z/s1tUiz/4c5YuuCsxL7UCxYp+/+kDeRNXV1UNZb1auXMmLnvwF20W9fKXsAEbWjekJNfkbs27sAACen3QAACAASURBVIg/+o+A9WM0/awRKHxe4RF0Cx/9sg1/dBp+wPddCV+92fcsglUjG2U7ebpCqK2txbRp0yS3IXpCzXEqgvW1jNJ2JfdPKGQKWp36v7Ct4N+A76ZifkLg/l0d/Zs3btzI8TQC9LUM3CwHaEDeNMO6sTfU+Bz/EDCi5/wfYLTeg7HjMN5s+CMAFTRLJsPwO+P42qiPOyXrzSRj0N1jSUlJGMXT8DGMAFUX1UaZdGO6AvjJT34i+RsXFxdznIoAffG4GScEElLx/d15QM1qzJq1ET8fWILnX1qGr8KI5vrfYOChaQp3LSfn+3GX7N+ckJAg3U2GVTwNP3LxR9VR+aCPdOM333xTWuG0e/duaDSjFnf7gzXXyQQiggD9/+zduxdtbW3Yt28fy3w+ntWoMsqkG9MqvNWrV+PIkSNYs2YNP1n28ReKq4seAuyh5J+5jhr5giJkUXxjiphF/sY5OTlskP3zneJao4QAuYlSPA26uGG92XeTHvFGWdaNKUIWxTemiFkc39h3XyCuiQmQ/EfeSuSxQd5L3uvNJugbi+3B69XeLVEOkemw6muQGeNBgH1FvyPWKJPuRU+K6RecfsnpF50XgChmnt8yAR8SIP9muvuku1C6G6W7Uk/jN1NQoJdWn8YcCgokDGjKmxe0B5s+RONxVRFnlEk3pl9q+sWmX276BecHeR5/L/gEJuAVAboLpbtRuiulu1PP/Zvvw/QpD0alMZaBR5RRVurGn3zyCevG8izzKxMIMAHP9OY70NesRZwUUN4em1hdjFYpTZsJ+tYaaJeq7SF5M6Edkf/OnttvqRaH5Kh6Q+cOD9qpnGBqhVYdo8i1R+Vt9Q3l3xszHyAAqQ7K5bcfFRTJL8ZW38Bw0/Z39njN6lzs6xjH39xlqKIwOkCRrQoKCqRIVxTxijcmwARCh4AyyuJY/5+2CGzDEdmEGBCXq/NGRGCzGNpFZc4CRQQ2e3Q5LBA51T1iUNwVBl2fPVqcgoFjtDlhGYq+B0210MnB3KRocfY+jIpIJ0eOU0Skk8pDQJUnqi8PCGH5VOh6B8TIscjjsJdRdMvZWwrIHLbbjRs3xIEDB8SiRYukkJphOxDuOBOIAgL0/zpW2NuRhkwOp7lA5DX02UJiyozsYTY11ZeFRbgI+SmXHXp1CNUpbJ9V63LEOhWF4rwthQGVwqSqikTLgD1kqmqTaOinEKHyJhtz+zl2o+wYVnV4LL32Hxb3DDK1EpbyhawbU+YE2kg3phVHvDEBJhC6BEhvpgeC7m1y/jvHwPMARuTtc682wJ4DtPks2nvvANY+tB+/iuwN38fy5Kv23H62HIDIfgypCbd8kA/wLq417cML+WeQvLsAG+a5l+Mo7Iwy6caUmZee8NIDPcqg4P5EuzuBXI4JMIHgEriHa329GCvLnbG7D9es7vdSygGquYjj7X2wUvCnP6Yj89tpWJI105bgVMoBeB+yM7+JBJ/kA7yE2rJ/xyOFS9Gzowqnriqzpbju95dcHwqtI+Rv/Pbbb0uRqigzLwVK4Y0JMIFIJTAJD81OhAq9LgeoWjgbD8UC/S5LOByInY0lWY9gh+4TXO38Jeq+loj8+PuldnC8DwZ9H473pEObOhXk/iHlA+x2qGPoo5wPcKxErikobPk5SjM+w991L8PmV5fh24dWYeY4l8LjHB7qQdDekL9xVVWV5G9MmXjJ35gNctCmgxtmAgEiMFb+O8pwrwxx6m6XbIYedT/BjupmJGc9isRYezs9ddizpw49knRBZtGH+QClhNAFSKopwf62z8btbMgaZdaNx507LsAEIpuAFDUvDWc2v4o3ZDcy8yXUvLQFZUkFKFk710N/ZrsBxinU1gMLZ0+3nS9p1DrU1g7apAuJaiwS0tZh93fPYXPxIXRIiVqtMF+pw0vrDyOpfBvW2jPDjD8JlBD6+6gofwhlr9Whyzy25hKSRrm7u3tINyYndNaNx592LsEEIo9AAubl7XPIf/fP0KW/Ad3pLV7lv0PCN5GZnQKoNMgkmYI2SdZYAjhmw3YrH6C71KfgW8/kIU9Xjm1vdsI8xmkhFSWOkpPu379f0o0pFRNn/hhj5vgQE2ACEUkgJK6USaog3Zjc2kg3PnbsGBvkiPy68aCYABMYj0DQjTK5tVHwEtrOnj0rGWZ2cRtv2vg4E2ACkUogaC5xpBuTaxutkSfdmCO4RepXjMfFBJiAJwQCbpRZN/ZkergsE2AC0UYgYPIF68bR9tXi8TIBJuANgYAYZVk3NplMrBt7M0t8DhNgAlFDwK/yhTKxIuvGUfOd4oEyASYwAQJ+McqcgnwCM8KnMgEmENUEfCpfkG5cW1srpWIif2MKqckLQKL6+8WDZwJMwEMCPjPKzc3Nkr8xeVdQ8kRaCML+xh7OBhdnAkwg6glMWL5g3Tjqv0MMgAkwAR8S8Noos27sw1ngqpgAE2ACdgIeyxesG/N3hwkwASbgPwIeGWVZN7506RLrxv6bE66ZCTCBKCbglnxBunF5eTmuX7/OcSqi+MvCQ2cCTMD/BMY0yqQbv/nmm1IKpt27d0Oj0fi/R9wCE2ACTCCKCTiVL0g3pqXR06ZNw6xZsyR/YzbIUfwt4aEzASYQMAKjrpTPnz+PV155BRkZGZJuPHWqPWVKwLrEDTEBJsAEopfAkFFm3Th6vwQ8cibABEKHgCRfUMD5pKQkqVeUiokDzofOBHFPmAATiC4CklFeuHChJFX8zd/8jbRUmlzfeGMCTIAJMIHAExiVzVpeNk1dKSsr46vmwM8Jt8gEmEAUExhllGUWygd+27dvBz/wk8nwKxNgAkzAfwScusRRcxRyk0JvUghOco2jkJzkKscbE2ACTIAJ+I+AS6NMTVLoTQrBSaE4KSRneno6WG/232RwzUyACTABl/KFMzRKtznWm50R4n1MgAkwgYkRGPNK2bFqcpU7dOgQCgoKsH79ehQWFoKWYvPGBJgAE5gYgTvQ16xFTGYN9FYPajLr8V7F6ziiv+PBSS6Kmq+gUZuJmJgYxMSsRY0v6nTR1Fi7PTLKckWsN8sk+JUJMIHgEbDC1HEYuQUfwTLhTtyB/sSrWF33dTT034UQJ5A39/4J1+pNBV4ZZWqI9WZvcPM5TIAJhDaBBEyZPLTQOShd9dooy70lV7ni4mIppOfJkyfx1FNPgbRn3pgAE2ACEyJgNaKrsQK5apIT6E+NpdoatOpNAKwwte7AvOV7YMRJ5Cc9ALW2FXQEuAdjVx20S9X28zKhrWmF3uxCF7FeQU3mHCTlnwSMe7D8r+OG6zLr0VqjxVKp/RjELNWiplUPszwwUyu0aurXflTkJkvtDfdDLuThq/Dx1t7eLhYtWiQKCgrEjRs3fFw7V8cEmEBkErgtdNVrBDTVQmehEf5FdJY/LlQ5VeKC4a5tyJZ+0VKkEcioFJ2DVMgiBlqKhAprRLXuth3LXdHfsEmoVDmi8oJBSFUN9ojqnAVCldcg+qUdzgja21cViZYBeyH5vKE+3BWGC1UiR6USGeUXxCBVM9AiClUQUOWJ6ssDQlg+FbreAWcNuL1vwlfKjr8BjnpzVVUV+zc7QuLPTIAJjE3AdBEnKq8hOzcLaapJtrKxM5GxIQuatg/wkeGe8/NN7di/uRHJu4uwJU0FycDFL0DegTeQfaYE+9s+c37eqL2kV9djx3vpqCrZaO/DJKjSXsCBoxugK6jACcWDQFX29/D0vAQg9m8x92sJo2rzZIfPjTI1rtSbTSaT5N9M8Zl5YwJMgAm4RSBhGUoNnShNu4nWxkYpvntjjRbLk/LhOjKPFabO91FnVGPh7Ok2gyw3Fq9GUrIBdU2/t0sc8gFXrzfR2dQMY/IjWCD/KEhFYxE/KxHJ+Bi6/iERw1UlXu33i1GWe6LUm8+cOSPpzRSRjjcmwASYwNgETLhSkw/15CQsP3ABt6jwlJX4aedb0IxrELtQtnyGXU+269Fx85HfbBy7SeVR62fo6zYo9zi8N6C77zO4UKkdynr2MSCPGWX/ZoqnsWvXLinI0csvvyxlNfGsu1yaCTCBaCBg1b+DLfkdWNnQh0OrHrZf9dLDvWb0AFg4JoQ1qNbVTsylLXY6Zi9UAy6vIeWr8bEM95iddHnQr1fKjq2S3kzxmimeBi3fZr3ZkRB/ZgJMgDwrzP296MF8LF7wZYUM8QUGb9n8K5xTikVC6mPIVl3G+UufjryKNXegYmkiMmuujNzvvCIAU5GaqYGq5yIuGZX6tdy3OUiaFe/y7IkcCKhRpo7KevPZs2elflM8DdabJzKFfC4TCA8CFD/HvRXAsnFtR93hX8MoaQT3YOw4hOLNBzEsQsj6Lo3fis/Nn8OasAQvV6XjzOZX8UaH0WaAaaXeaztRgE0oWTtXYeTH4haLhLR12P3dc9hcfAgdkmG2wnylDi+tP4yk8m1Y66fFJQE3yjIG0ps3b94s+Td/+OGHrDfLYPiVCUQYAYouSXfFdHf85z//2b3RJSzBD0+XIu2DXKjjSBdOwfZfTUfuqZMoVA1XEZuYCW3RAPKTHsSDq/8VvdZJmLmqBG1H03FNm4I48i+evAbvzngOnfWbkBLvgckjr42DDTia/mdo1fchJiYOk1/4A9KPtuH0tjT45zoZ8Cgg0TAK378jvbm8vJz1Zt+j5RqZQNAI0F3w3r17kZOTg3Xr1nFcdjdmImSMMvWVflHJS0OexPz8fEnucGMcXIQJMIEQIkBeVvJD/WeffZYzGHkwNyFllOV+k+5UX18vBdanrCd028MbE2ACoU+AdOP9+/dLoRYomiQ93OfNMwIhaZTlIVAMjbfffluaYPrVpQSvvDEBJhB6BOgut7q6euhCauXKlXyX6+U0eaB6e9nCBE4j/2YKpk+/uGSUKX4z/RLzxgTCjgAF1zliD2yjzsU+2TNgvIFQQJzGelTkZkLb6mqJ8Gdo1aYqFkuoPXD9Gq8D4x8n3Zi8qGgjryq6syUvK968IxDSRlkeEvs3yyT4NTwJ3EJX5YvYpnsM9RYBS9d6XNe+iMouaZ2a6yFR9LL/sQNHGvagoPaGy3LWq7/Cz+u6FMeXIGvJbDddvxSnefiWdGOKCkneU0ePHpW8qTjBsocQnRV3O3RRiBSkyHMHDhyQItE1NDSIzz//PER6xt1gAs4JWHTVQqOMPiZHNxuKiOb8PHmvdD5SRGHLdXmX4pWiqeW4OKYo5sO3n3zyiRQF8sknnxQUFZI33xIIiytl5Y+Jo3/zM888A3Kn440JhCaBO+htP4vm5ETMGvKRtS+O6DmL9t4JpjGSoqnVouy1ctQ0trmOGewDOEp/Y1qVS6tz+UGeD8A6VBF2Rlnuv1JvJv9m0ps5uL5Mh19DhoC1D+3H26FaOBsPjfpva8fx9j43l/06G9Ed6N95E2W0xK2tDPmrlyLpiR1olILAOyvv3T4yxpGlG9vzAaqL0WryR0gh7zjLZ436msgHwuVVqTdTMldaOeTeUs5wGSH3M6wJmA3Q9QDJSWo/rAC7H3PzTkCIuzB0nkZ1oQZo24PVz1Wjy1WWDQ9h0l0o3Y2ybuwhuAkUD3ujTGOX42mcO3dOQrFixQrpl51+4XljApFPYBJUKf+IvNLTMLTsQkbbz3GiY2JZ5umuk+4+6S6UvJ/IC4ruTnnzP4GIMMoyJjLOFE+DbrXol531ZpkMvwaNgBRcHejRGYbzuvmtM5OgWrYJOwvhQTD3kZ2hu0y626S7zsDpxs7kBArTWQx1TOpIV0ApJ55in1c59N63xWdWDt18CTW5yVDnHrQHH1IeDOz7iDLKMrpZs2ZJv+zk28x6s0yFX4NCIHY2lmQtGdW09Vofuo3+cF2Lx6ykJI/lElk3prtM2uiuM3D+xvcjcckKaIzNaOqUr/DtmT+gDCZvzywCDTJTpwJkSDetxvpzX0Wp4a5Nxin9Ks6tz8ATFR2KH0Ej2uo+wtSi8xCWT9H2gzRMUc6IVM8z2IFtaD34wnD6KWWZAL6PSKMs86MVgKdOnZJ+8Vlvlqnwa2AJ2AxOct376Bx6qGSPyatZgSWJ9/u4O2b09yZD+7S7ISoheS/JujHdZdLdZqAXf8QmPoosza3hbB5S5g9gXc630XP8N+iVnsfZDDWyH0NqAnyTQ2+wBzWbZIOcjXlDHjI+nhYPqotooyxzoF981ptlGvwaaAKxc1ehZOtlvLa3RYoNbDW2YO9rl7G1ZBXm2v8DrVcbka/+R1SMt6BE2XlaJfjuL9AlB2G3GtGxrxJtj2UjI2H8f22lbkx3laQb011mUDbpjuIRNNsNsLX3Nzjeo8GGTf8NyT296KcHl6bfo6kOyM78JhLgixx6f0JTZSHya+dj94+yQsIgE/vxZy4oM+T7Rllv9j1TrtFdAlOQsvUnKJ1xFClxMYhb9z6SKn6CrSkjbqKdVGZbPh0nJQu1553LrIF+yIvLioELbyBVivWbjNzKX8H8+Hb8eNnMMf+xHXVjupsMflwZu4TRTL7bn0uZR/6Y/Ri+nfr3yEo+J8kakuQjSxe+yKFnrEfZxa+jMOcydpT+AleHuDqZikDu8u1alPCp7Xe/+52gFUkFBQVCp9OFT8e5p0zASwK0+pVWwS5atEhaFRtyq2Etl0W15lFR2PL/ipbCR4Wm+rKwiOv29xfF5eo1QlXYIgak8dP+FAEnqyJHrIAcaBGFKijOo5NvC131GgH7Kktb+QUir6FPWLxk68vTouZK2fGHjvVmRyL8OZIJKP2Ng6Ubj8tXSlZ6F3XVpaium2mP30G58tLRU1eBPXVX7dIF1eS7HHqSvFT+MGo2/wxtQ7r/uL31W4GoNcoyUdabZRL8GokEQko3HhewzdCivhb1SMTshyZJCmv8rEQkt9WjVpdu87qQ6vFlDr0pSHn+VZQnncBrb3UqvDbG7bBfCkS9USaqjnozhSHkeBp++b5xpQEiEJq68XiDlxOmAirJw8JmnmyeGSpgRPwQAL7MoRe/EM+8tAK6gh/jTU8eto43JC+Oh3SQey/G45NT5FQ2M2bMkFYz8Uomn2DlSgJAgPyNOaVaAED7sQk2ymPAJe2N8gVSzNjnn3+ekz6OwYoPBZ8A3d1x8uHgz8NEe8BGeRyCdOVx8uRJ5ObmoqGhAZzmZhxgfDjgBEg3JmN8/fp1KUNP8N3bAo4gohpkTXmc6SS9mdKj37hxQ4qnwXrzOMD4cMAIkG5cUlIixamgi4XQ8DcO2PAjtiG+UvZwauWn2aw3ewiOi/uMgKwbr169GgcOHEB+fn7Al0X7bDBc0SgCIXilfA/Grjpol6oRE5OM3H3npaWpo3o+Yodj4siY4SSSI1ZAAZCiTCmOx6xFjd797A/00I+uSNasWSNdodCVCl2x8MYEAkGAdGO6W6MoiHT3Fow4FYEYZzS3EWJG2Qpz10Gs2/YxMuv7ICxnkXt9D9ZVKiM+OZkuaU28MnGkXEYFTdajSBwa5T1cfb8RdZSpQd68DAqj0WikeBoUK2DatGkcv1nmya9+IUB3aBs3bpS0Y0pSSnEqOEmpX1AHvdIhcxX0nlAHrHqcKH4HaTs3YZlqEhA7E8u2b0VaZQVOuLyapXB+l3Df0X5YhIAY+ruOlsJ/GpnV19yNYz+biqMDluFyTXlDQWE8ZcB6s6fEuLynBJS6Md2d0V0au2h6SjG8yoeUUZYiQzXPRNKs+GGKCd9EZvbVMXKZfYH/nPUkCh2CsFj1/zdKu9MUoRGtMHWcQmXz23jt9Wo0tup9tnKHrljoyoWuYOgpOF3R0JUNb0zAWwJyfGO6C6O7MYpySHdnvEU+gRAyyvasvyp5eaUS/t2hkH7Kvbb3k6Ca+7BD/jOq6zxmPbd8WLqw6vFO6WEYYURb2Q+wenkGntA2+jT7L+vNo2eH93hOwFE3Ju8fuivjLToIhJBRNqNf9/HopZTezANlEG6cie899pXhEIax85DXZICwGNB56i0UZlAC4M147k3fr3VnvdmbSeNzWDfm7wARCCGj7LsJIRmk8e8ykOos0HesCilPbkRpy2/RUpSMtspT6PBDZCjWm303n5FeE+vGkT7Dno0vhIwy5RabA8hZBjwbh6I0SRcd+DspO4Fit+Nb6SGiFoVQ5gVzLDTxz456My3ZZr154lwjoQbWjSNhFn0/hhAyyvbMA45jlDIM3HJwbXMspPgsSRd/qwjxpzjm+FbKNJw08sGiYxkffZb15hdffFHyb6b07ezf7CO4YVgN68ZhOGkB6nIIGWVACtFnT/0yNH6zAbqeR0a6tg0dHP1mTOnCsbjZgN6UfDw919fJKx0bGv4s680LFiyQ/Jtra2tBV0y8RQcBukuiuyXy0mF/4+iYc09HGVJGGbFzsbbkaXS8dhCtlAzSehWteyvRsXUb1g4Zznu42rgZ6qX70EXJFEdsrqULq7EL777bNbQ60Go8j32vX8RjLy1Bwog6/P9BqTf39/dLK7Sam5v93zC3EDQCdFdEd0eUVZ3ultjfOGhTEfINh5ZRRiziUzahvnQ6jqTch5i4PDQlvYr6rWkOLm8uuJJ0cf4bWJs21UmBm7jwP5+AOi4GMepcVJ7/Lzy+c6ttkYqT0oHYRXpzcXGxdMVEkeh8qzdbYWothjpmLQ61tuGINtO+9DwZuRVNDq6AJuhba+xL22kJeia0Na0OZQJBJPLaoLsguhsif2O6O2J/48ibY5+PyJcJ/7iuiRFob2+XklpSMtcbN25MrDJhEQMtRUIFCGQUiQadLd2kxdAsijK+JjLKL4hBqYUBcbk6T6hUOaLygkFKHGkxtIvKnAUCGZWiczAUUklOEEWQTm9qapLm8/XXX/fBfAZpENxswAnQcmPeQoiAnHEYgDhy5IjwPuOwbJRTRGHLdcUIHbIAS9l+nWTylfar7BmFFafz23EJUHZ0ypT+7LPPcqb0cWlxAUcCISZf+PxGIOwqJL2ZkrlSBDD/6M1K18MvYOp8H3XG+Vi84MsjndYlzxSgR2fw2XL0sJsMDzus1I0LCgpw6NAhjlPhIUMuHqGLRyJhYh31Zv/4Nt/Dtb5eKIPmObIzdvfhmuPzVMdCUf5ZqRt/5zvfkXTjxYsXRzkVHr63BPhK2VtyATqP/Jv9d8U1CQ/NToRqjLGoFs7GQ/wtcUmIvGYovjHd1dDdDd3lcJwKl7j4gBsEvuRGGS4SsQTklO6ncf7Sp9gw9+FhCUPyDweSs9Tueb5ELCPnA6M7F3Jxoww05G/M4TSdc+K9nhNgo+w5s8g6IyEV39+dhmWbX8Ubs/ZiS5oKseZLqHlpC8qSCtC5du6woY6skXs1GtKNKcN5W1sb9u3bB5YpvMLIJ41BgG9Mx4ATHYcSMC9vH9qOpuOaNgVxMTGImfzP0KW/Ad3pLUiJ568IfQ9YN46O/4ZQGCUnTg2FWeA+hDQB0o137NghLe55/vnnOQ1TSM9W+HeO5Yvwn0MegZ8IdHd3Y9euXawb+4kvV+ucABtl51x4bxQTIE+K/fv3s24cxd+BYA6dBcNg0ue2Q4oA6cZVVVX4yle+AvY3DqmpiarOsFGOqunmwboi0NjYKPkb03H2N3ZFifcHggDLF4GgzG2ELAFZNyY/Y/Y3DtlpiqqOsVGOqunmwcoEZN2YFoFQnAr2N5bJ8GuwCbB8EewZ4PYDSkDWjWk5NOnGx44dY4Mc0BngxsYjwEZ5PEJhfdwE/Xv7UXzkCnwTU8gEfWMxltICkxg1Mmv+AJO+cTg4fuZ+NL61FjHqYrT6IUP4RKdCqRufPXuW41RMFCif7xcCLF/4BWuIVGrqRHXuXnTv1vikQ1b9O3hp9WnMaehDy6qHEWu9gpqVm1E3pwr9LaswU/qJfxniBz5pzmeVsG7sM5RcUQAIsFEOAOTIauI+TJ/y4Mh4GNOnYHII3nOxbhxZ37yoGY1j1Hv+HCEEpMwhEJTBRPpTFYmWgU9FS2GKQEaheKs8x5YqStpvEcJiEJ0N5SJHJZ+jEhmF1aJFSiN1W+iq1wzXJdc54pUynPzZVk6uU0J5Vxg6a0VhhsrejxxR3qyzp6LyD2vK1nLgwAEpFVNDQ8MEsrf4p39cKxMYi0AIXt9Eze+hfweasAylV1pQqFJBU30ZFkMJliXYp7vtF2ifWgC9uAtD23NISzChq3Ijnnj3AWzqukspwiAsv8XOuONY/lw1usyTMDfvBCy6amiQgsKW6/Yyl1GtUUFV2IIB0YnSZTMcxkSZx7ciJfUo8FIrBoUFg63L0JO7Glsa/+QjnXtkk6wbj+TBn8KPABvl8JuzifdY9QRyn/4G4jEJqrkPI950EScqryE7Nwtpqkm2+mNnImNDFjRtH+Ajwz3v2rR+jKafNQKFWvxo1TzEU7byeY8jN/s+1PysBb2+efo41DfyrPjwww+lz9/61rc4cNAQGX4TTgRYUw6n2fJXX+mq2tAJmPVobfwVblE7ty7gQH4Z2rAGWV62a+39DY43OwbKn45lpZ2SRuJltS5Po4wfZWVlkAPQHz58WPJB5gD0LpHxgRAkwFfKITgpge+SCVdq8qGenITlBy7YjPKUlfhp51vQ4GPo+s2B79IEWiQjfOrUKaxZswbr169HSUkJKDg9b0wgHAiwUQ6HWfJzH8nVbUt+B1Y29MHyy1LkrVqFVav+AeqB/0CPn9v2Z/UajUZKYjpr1ixMmzYNpDeTxMEbEwhlAmyUQ3l2AtI3K8z9vejBfCxe8GWFq9sXGLxlmlAPYhMfRZYG6NEZMHytfQf6mrWIiVmLGv2dCdXvzskkaeTk5EhBhkhvpiSn58+fd+dULsMEgkKAjXJQsAeo0Xg1kpL/ytbY52aYnT5Yk5OntqPu8K9hlMrcg7HjEIo3H4RxIl2NnYOV2ueQVFaKva1XJW8Lq/HXOFx3ERnl27B27v0Tqd2jc6dOnSrpzRR0qLy8HBs3bpS0Z48q4cJMIAAE2CgHAHLQmpCMYjbu5c9H3IN5ONHr4tY9YQl+eLoUaR/kQh1HtvhjOAAADoFJREFUS6hTsP1X05F76iQKVRPp/SSolhWhvnM9LK8tkvL/xakrYNlQj/qtaUHJks1680Tmk88NBAHO0RcIytxGSBIgffnkyZPIzc3FkSNHpAeDJHfwxgSCSYCvlINJn9sOKgGl3nzp0iVJb6YkqbwxgWAS4CvlYNLntkOKgOzfTJ0if2f2bw6p6YmazrBRjpqp5oG6S4C8M1555RVkZGRg+/btvDLQXXBczicEWL7wCUauJJIIUBaSc+fOSUHwyb+5traW/ZsjaYJDfCxslEN8grh7wSFAejNlJ6EkqhQClPybWW8OzlxEW6ssX0TbjPN4vSJAejP5N1+/fp31Zq8I8knuEmCj7C4pLscEAGk1IOvN/FXwJwGWL/xJl+uOOAKsN0fclIbcgNgoh9yUcIdCnQDrzaE+Q+HdP5Yvwnv+uPchQID15hCYhAjqAhvlCJpMHkpwCbB/c3D5R0rrLF9EykzyOIJOwFFvrqqqYv/moM9K+HWAjXL4zRn3OIQJKPVmk8kk+TdTcH3emIC7BFi+cJcUl2MCXhBQ6s27du3CwoULvaiFT4kmAmyUo2m2eaxBI0B6My0+oSBHL7/8MihFFW9MwBkBli+cUeF9TMDHBEhvPnbsmBRPg5Zvs97sY8ARVB0b5QiaTB5KaBOQ9eazZ89KHaV4Gqw3h/acBaN3LF8Egzq3yQQAKUfg22+/Lb2y3sxfCZkAG2WZBL8ygSARYL05SOBDtFmWL0J0Yrhb0UOA9ebomWt3RspG2R1KXIYJ+JkA681+BhxG1bN8EUaTxV2NHgLk38x6c/TMt3KkbJSVNPg9EwgxAqw3h9iEBKA7LF8EADI3wQS8JcB6s7fkwvc8NsrhO3fc8ygh4Epvvn37dpQQiK5hsnwRXfPNo40AAkq9uaCgAHQ1zVvkEGCjHDlzySOJMgJKvfnZZ5+V4mpEGYKIHC4b5YicVh5UtBAgCePMmTPYu3cvcnJysG7dOkydOjVahh+R42RNOSKnlQcVLQRkvfncuXPSkFesWCHF02C9OXy/AWyUw3fuuOcRSeALGBufR0xMjO0vtxFGN8ZJxnnz5s2SQf7www/xzDPPgOQN3sKPAMsX4Tdn3ONoIGBqhXbeenTvbsWZvHnw9Oqpu7sbFOSI4jez3hxeXxhP5zq8Rse9ZQJhScAKU+f7qDMuQdaS2R4bZBoyZTg5deqUFL95/fr1UvzmmzdvhiWNaOs0G+Vom3EebxgQuInOpmYYv5aG/2PO/RPqLwXUZ715QggDfjIb5YAj5waZwDgEvvgTLjZ0QbX6EXz9S+OUdeMw681uQAqhImyUQ2gyuCtMgAhYP/4I7/0xBc8kDeJ/azPtD/0yoW28AvMEEFFewLKyMklrpnyBhYWFUoD9CVQZoqdaYdY3oaK4Hnqrqy7egb5mLWIya8Yo4+Rcsx7vVbyOI/o7Tg76ZhcbZd9w5FqYgI8IfIFPL3WgGV04dq4f8394GmKwB9U5BpStfhUnfGAMIl9vvomO6h+hoMvXhtMKU8dh5BZ8BIuPZttZNWyUnVHhfUwgaARu4fKFTiCjEqcPvoA01SQgfh5WPklLqa/j5uAXPusZ680+Q+nTitgo+xQnV8YEJkjA9Hs01RmgyV6Jb8XL/55fYPAWeU4kYY56Yg/+HHvnqDdTMtfg+Dd/hlZtKmIyD6K1ow7apWqbbKPORcV7+pGyjVmP1hotlsq+3Eu1qGmVy1A9K7C8rAtozkdSXCq0rZ85Dtv5Z6sRXY0VyFXbfcRj1FiqrUGr3kSiEkytOzBv+R4YcRL5SQ9ArW0FHQHuwdil6HNMJrQ1rdCbXWonztuX9wremAATCBkCFl210CBFFLZcH+6T5bKo1qiEKq9B9FuGd/vj3e9+9zvx5JNPimeffVbodDp/NOGizuuipTBFACqRUdggdIM00LvC0LJLZOBxUd75F9t5gz2iOmeBUOVUiQuGu7YyF6pEjkolMsoviEGplL0uTbXQueR1W+iq1wgMlfmL6Cx/XFGvEMLSL1qKNAIZlaJT6o9FDLQUCRXWiGrdbfs47or+hk1CpcoRlRcMQmpO7qOX8yX/FMs2ml+ZABMIGoE76G0/i2aVBpmpcvyKe7h6qgo7elZid8FjmOnn/1hZb165ciXIv7mkpAQB9W9WbcDOHz2FudJdwiSoUv8eaaqLeO+ja7DS1WpHPXa8l46qko02aQeToEp7AQeOboCuoMJ7zd10EScqryE7N8teL4DYmcjYkAVN2wf4yHDP+bfC1I79mxuRvLsIW9JUNp/y+AXIO/AGss+UYH+bm1fpitr9PMWKlvgtE2AC4xC4jkvnLkKV/RhSE2IBup0+shPrV/87Nhz9MTbMSxjnfN8dlvVm8tiYNm1a8OJpxKuRlAz06Awww+6/nfwIFpDWPrTFIn5WIpLxMXT9XvqnJCxDqaETpWk30drYKI23sUaL5Un5aB5qx/GNvMhHjYWzp49c5CP124C6pt/bJQ7Hc11/ZqPsmg0fYQIBJvBl/J8vl2HrtS34a9JL41Kw7Q9J2Kk7iZJlM0f+0wegZ6Q3U+S5GzdugOJpBE9vtg/W+hn6ug1jjNyA7r7P4J2Sa8KVmnyoJydh+YELuEWtTFmJn3a+Bc24xr4LZctnDMcrkeZuPvKb3YlaMno4PnBNH10p72ECTMAbApOgSlmFbUfoz5vz/XMOhQIl/2YKrk++zYcPHwYF16e4GgHdYqdj9kI10O2qVSdXrK6KOuy36t/BlvwOrGzow6FVD9t/AOnhXjN6aNm6Q/mRH9egWleLvLm+eQjLV8oj6fInJsAEXBAgI0zxNNasWRMcvRlTkZqpgarnIi4ZlRqvFeb+XvRgDpJmxbvo/Vi75fPnY/GCLyvuSMjrxeZf4fzsWCSkPoZs1WWcv/TpyCt0cwcqliYis+bKyP3OKxqxl43yCBz8gQkwgfEIaDQaKZ5G4PXmWCSkrcPu757D5uJD6JAMsxXmK3V4af1hJJVvw1rpajUes5Lm2IdxB2bzeL7dsnFtR93hX8Mo6R/3YOw4hOLNBxWhU2Xtmqq24nPz57AmLMHLVek4s/lVvNFhtBlg8xU0vrYTBdiEkrVzFUZ+PLK242yU3ePEpZgAE1AQCJreTJ4NBxtwNP3P0KrvQ0xMHCa/8AekH23D6W1psF0n34/ElRtRdG8HkuLmYPWJ3vGvVhOW4IenS5H2QS7UceSnnILtv5qO3FMnUagaHnhsYia0RQPIT3oQD67+V/RaJ2HmqhK0HU3HNW0K4khPnrwG7854Dp31m5Ay5Gs+XMd47zie8niE+DgTYALjEpD15hkzZgRHbx63h+FTgI1y+MwV95QJhDyB5uZm7NixA0899RSef/55zhfoxYyxfOEFND6FCTAB5wSCpzc770847mWjHI6zxn1mAiFMwJneTFfQvLlHgOUL9zhxKSbABLwkIOvNdHpVVRXIa4M31wTYKLtmw0eYABPwIQG6Wp49e3bgF534cAyBqIqNciAocxtMgAkwATcJsKbsJiguxgSYABMIBAE2yoGgzG0wASbgBgET9I3F9uD1aq+WKLvRSECKWPU1yIzxIMC+olcckEgBg98yASYQPAIUFOil1acxp6EPLUNBgYLXn2C1zFfKwSLP7TIBJuCEwH2YPuVBj+NFOKkobHexUQ7bqeOOM4FIIXAH+pq1iJMCyttjE6uL0WqiyEAm6FtrhnP2jcp/Z8/tt1SLQxW5UFPsiaFzh/k4lRNMrdCqYxS59qi8rb6h/Htj5gOk7lEdlMtvPypyk6WYynTuwHDT9nf2eM3qXOyTAxeNKmPbwUbZBRjezQSYQKAI3I+5eSdg0VVDgxQUtlyHMJRgWYIZV2peQcb6c3iotAsWIWAxvIqHzm1B0hNvoEuZmLTtF2ifWgC9uAtD23NIo8wtii028VFkaZSZQOSsIYCxuw/X5Mj4UuJaIDvzm0gwX0LNptVYf+6rKDXchaC6S7+Kc+sz8ERFhyKZqxFtdR9hatF5CMunaPtBKv5a0Tb9sNA4lu0AdrcewCty2qgRZYY/jOz58H5+xwSYABMILgFTJ/7Xjg6srPrxUP67WNVivHLgDRTqylF8Qj8c/U31BHKf/gbiKWff3Ift0eIU3Y+djSVZSxQG+B6u9fUC63Kwrucs2nvv2DJWd76POlCOxCke5QNUZX8PT1O6rti/xdyvKdN2DSgM8j7kuZHSi42yYt74LRNgAqFCQL6SdQw8D2BE3j53+3s/EpesgKbZboCtfWg/fhXZG76P5clX7bn9bDkAIeVIvIXOpmYYJ5QP8C6uNe3DC/lnkLy7wO0ci2yU3Z1TLscEmEAACdiuZMfKcjdCdnCjZzYJ4yKOt/fBajZA98d0ZH47DUuyZtoSnEo5AO+zSRc+yQd4CbVl/45HCpeiZ0cVTl1VZktx3WE2yq7Z8BEmwASCRmASHpqdCEV8+VE9US2cjYc8sWCShPEIenSf4CrJFF9LxKz4+6V20N0Hg/43ON6TjszUqYCcD3BUq/IOd/IBkj7+c/zLnp3YndyIza/+P7gqa9dyNU5ePRmSk9N5FxNgAkzAHwTkFE3O8t8ZoOsBkpPUo7XjMbtiM/So+wl2VDcjOetRJMba2+mpw549deiRpAsyiz7MBxg7F2tLCpBUU4L9bZ+N2UM6yEZ5XERcgAkwgaAQSEjF93enOeS/u4Sal7agLKnAi/x3dgOMU6itBxbOnm4zgJJGrUNt7aBNupAG624+QHfIxCI+5fuoKH8IZa/VjfQacXI6G2UnUHgXE2ACoUAgAfPy9jnkv/tn6NLfgO70Fq/y3yHhm8jMTgFU5GEx1TZIu2cGHLNhu5UP0F1OU/CtZ/KQpyvHtjc7Fe50o8/nKHGjmfAeJsAEmEDQCPCVctDQc8NMgAkwgdEE2CiPZsJ7mAATYAJBI8BGOWjouWEmwASYwGgCbJRHM+E9TIAJMIGgEfj/AaCFLkGKIoPAAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (<em>P </em>), car (<em>C </em>) and bicycle (<em>B </em>).</p>
<p>The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.</p>
<p>Some of the information is shown in the Venn diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>There are 54 employees in the company.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>a</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic and was late for work.</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>Use the tree diagram to find the probability that an employee was late for work.</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>Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>y</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.</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="n\left( {\left( {C \cup B} \right) \cap P'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>∩</mo> <msup> <mi>P</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>a</em> = 0.2 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>b</em> = 0.85 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award <em><strong>(M1)</strong></em> for a correct product.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.2\,\,\,\left( {\,\frac{1}{5},\,\,\,20\% } \right)">
<mo>=</mo>
<mn>0.2</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>1</mn>
<mn>5</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>20</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 + 0.75 × 0.15 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their (0.25 × 0.8) and (0.75 × 0.15), <em><strong>(M1)</strong></em> for adding two products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.313\,\,\,\left( {0.3125,\,\,\,\frac{5}{{16}},\,\,\,31.3\% } \right)"> <mo>=</mo> <mn>0.313</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.3125</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mn>5</mn> <mrow> <mn>16</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>31.3</mn> <mi mathvariant="normal">%</mi> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em><strong>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award the final <em><strong>(A1)</strong></em><strong>(ft)</strong> only if answer does not exceed 1. Follow through from part (b)(i).</p>
<p><strong><em>[3 marks]</em></strong></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.25 \times 0.8}}{{0.25 \times 0.8 + 0.75 \times 0.15}}"> <mfrac> <mrow> <mn>0.25</mn> <mo>×</mo> <mn>0.8</mn> </mrow> <mrow> <mn>0.25</mn> <mo>×</mo> <mn>0.8</mn> <mo>+</mo> <mn>0.75</mn> <mo>×</mo> <mn>0.15</mn> </mrow> </mfrac> </math></span> <strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for a correct numerator (their part (b)(i)), <strong><em>(A1)</em>(ft)</strong> for a correct denominator (their part (b)(ii)). Follow through from parts (b)(i) and (b)(ii).</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.64\,\,\,\left( {\frac{{16}}{{25}},\,\,64{\text{% }}} \right)"> <mo>=</mo> <mn>0.64</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mn>25</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>64</mn> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award final <strong><em>(A1)</em>(ft)</strong> only if answer does not exceed 1.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>x</em> =) 3 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>y</em> =) 10 <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Following through from part (c)(i) but only if their <em>x</em> is less than or equal to 13.</p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>54 − (10 + 3 + 4 + 2 + 6 + 8 + 13) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting their correct sum from 54. Follow through from their part (c).</p>
<p>= 8 <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> only if their sum does not exceed 54. Follow through from their part (c).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6 + 8 + 13 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award (M1) for summing 6, 8 and 13.</p>
<p>27 <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>In a school, all Mathematical Studies SL students were given a test. The test contained four questions, each one on a different topic from the syllabus. The quality of each response was classified as satisfactory or not satisfactory. Each student answered only three of the four questions, each on a separate answer sheet.</p>
<p>The table below shows the number of satisfactory and not satisfactory responses for each question.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.16.22.png" alt="M17/5/MATSD/SP2/ENG/TZ2/01"></p>
</div>
<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test is carried out at the 5% significance level for the data in the table.</p>
</div>
<div class="specification">
<p>The critical value for this test is 7.815.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>If the teacher chooses a response at random, find the probability that it is a response to the Calculus question;</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>If the teacher chooses a response at random, find the probability that it is a satisfactory response to the Calculus question;</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>If the teacher chooses a response at random, find the probability that it is a satisfactory response, given that it is a response to the Calculus question.</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>The teacher groups the responses by topic, and chooses two responses to the Logic question. Find the probability that both are not satisfactory.</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>State the null hypothesis for this test.</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 the expected frequency of satisfactory Calculus responses is 12.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic for this data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion of this <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{5}{\text{ }}\left( {\frac{{18}}{{90}};{\text{ }}0.2;{\text{ }}20\% } \right)">
<mfrac>
<mn>1</mn>
<mn>5</mn>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>18</mn>
</mrow>
<mrow>
<mn>90</mn>
</mrow>
</mfrac>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.2</mn>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>20</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for correct numerator, <strong><em>(A1) </em></strong>for correct denominator.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{9}{\text{ }}\left( {\frac{{10}}{{90}};{\text{ }}0{\text{.}}\bar 1;{\text{ }}0.111111 \ldots ;{\text{ }}11.1\% } \right)">
<mfrac>
<mn>1</mn>
<mn>9</mn>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>90</mn>
</mrow>
</mfrac>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mrow>
<mtext>.</mtext>
</mrow>
<mrow>
<mover>
<mn>1</mn>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.111111</mn>
<mo>…</mo>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>11.1</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for correct numerator, <strong><em>(A1) </em></strong>for correct denominator.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{9}{\text{ }}\left( {\frac{{10}}{{18}};{\text{ }}0.\bar 5;{\text{ }}0.555556 \ldots ;{\text{ }}55.6\% } \right)">
<mfrac>
<mn>5</mn>
<mn>9</mn>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>18</mn>
</mrow>
</mfrac>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.</mn>
<mrow>
<mover>
<mn>5</mn>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.555556</mn>
<mo>…</mo>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55.6</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for correct numerator, <strong><em>(A1) </em></strong>for correct denominator.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{6}{{20}} \times \frac{5}{{19}}">
<mfrac>
<mn>6</mn>
<mrow>
<mn>20</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>5</mn>
<mrow>
<mn>19</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for two correct fractions seen, <strong><em>(M1) </em></strong>for multiplying their two fractions.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{{38}}{\text{ }}\left( {\frac{{30}}{{380}};{\text{ }}0.0789473 \ldots ;{\text{ }}7.89\% } \right)">
<mfrac>
<mn>3</mn>
<mrow>
<mn>38</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>30</mn>
</mrow>
<mrow>
<mn>380</mn>
</mrow>
</mfrac>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.0789473</mn>
<mo>…</mo>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>7.89</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{H}}_0}">
<mrow>
<msub>
<mrow>
<mtext>H</mtext>
</mrow>
<mn>0</mn>
</msub>
</mrow>
</math></span>: quality (of response) and topic (from the syllabus) are independent <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept there is no association between quality (of response) and topic (from the syllabus). Do not accept “not related” or “not correlated” or “influenced”.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{18}}{{90}} \times \frac{{60}}{{90}} \times 90">
<mfrac>
<mrow>
<mn>18</mn>
</mrow>
<mrow>
<mn>90</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>60</mn>
</mrow>
<mrow>
<mn>90</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>90</mn>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{18 \times 60}}{{90}}">
<mfrac>
<mrow>
<mn>18</mn>
<mo>×</mo>
<mn>60</mn>
</mrow>
<mrow>
<mn>90</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution in expected value formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( = ){\text{ }}12">
<mo stretchy="false">(</mo>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>12</mn>
</math></span> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The conclusion, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( = ){\text{ }}12">
<mo stretchy="false">(</mo>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>12</mn>
</math></span>, must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3 <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\chi _{calc}^2 = ){\text{ }}1.46{\text{ }}(1.46\overline {36} ;{\text{ }}1.46363 \ldots )">
<mo stretchy="false">(</mo>
<msubsup>
<mi>χ</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
<mi>l</mi>
<mi>c</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1.46</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>1.46</mn>
<mover>
<mn>36</mn>
<mo accent="false">¯</mo>
</mover>
<mo>;</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1.46363</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.46 < 7.815">
<mn>1.46</mn>
<mo><</mo>
<mn>7.815</mn>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.690688 \ldots > 0.05">
<mn>0.690688</mn>
<mo>…</mo>
<mo>></mo>
<mn>0.05</mn>
</math></span> <strong><em>(R1)</em></strong></p>
<p>the null hypothesis is not rejected <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>OR</strong></p>
<p>the quality of the response and the topic are independent <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(R1) </em></strong>for a correct comparison of either their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic to the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> critical value or the correct <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>-value 0.690688… to the test level, award <strong><em>(A1)</em>(ft) </strong>for the correct result from that comparison. Accept “<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\chi _{{\text{calc}}}^2 < \chi _{{\text{crit}}}^2">
<msubsup>
<mi>χ</mi>
<mrow>
<mrow>
<mtext>calc</mtext>
</mrow>
</mrow>
<mn>2</mn>
</msubsup>
<mo><</mo>
<msubsup>
<mi>χ</mi>
<mrow>
<mrow>
<mtext>crit</mtext>
</mrow>
</mrow>
<mn>2</mn>
</msubsup>
</math></span>” for the comparison, but only if their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\chi _{{\text{calc}}}^2">
<msubsup>
<mi>χ</mi>
<mrow>
<mrow>
<mtext>calc</mtext>
</mrow>
</mrow>
<mn>2</mn>
</msubsup>
</math></span> value is explicitly seen in part (f). Follow through from their answers to part (f) and part (c). Do not award <strong><em>(R0)(A1)</em></strong>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Mackenzie conducted an experiment on the reaction times of teenagers. The results of the experiment are displayed in the following cumulative frequency graph.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Use the graph to estimate the</p>
</div>
<div class="specification">
<p>Mackenzie created the cumulative frequency graph using the following grouped frequency table.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Upon completion of the experiment, Mackenzie realized that some values were grouped incorrectly in the frequency table. Some reaction times recorded in the interval <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>t</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>2</mn></math> should have been recorded in the interval <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn><mo><</mo><mi>t</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>4</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>median reaction time.</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>interquartile range of the reaction times.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the estimated number of teenagers who have a reaction time greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>4</mn></math> seconds.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mtext>th</mtext></math> percentile of the reaction times from the cumulative frequency graph.</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>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</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>Write down the modal class from the table.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find an estimate of the mean reaction time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest how, if at all, the estimated mean and estimated median reaction times will change if the errors are corrected. Justify your response.</p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>58</mn><mo> </mo><mfenced><mtext>s</mtext></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>7</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>42</mn></math> <em><strong>(A1)(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for correct quartiles seen, <em><strong>M1</strong> </em>for subtraction of their quartiles.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>28</mn><mo> </mo><mfenced><mtext>s</mtext></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> (people have reaction time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≤</mo><mn>0</mn><mo>.</mo><mn>4</mn></math>) <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>31</mn></math> (people have reaction time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>></mo><mn>0</mn><mo>.</mo><mn>4</mn></math>) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>90</mn><mo>%</mo><mo>×</mo><mn>40</mn><mo>=</mo></mrow></mfenced><mo> </mo><mn>36</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>8</mn><mo> </mo><mi>s</mi></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>a</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>6</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>b</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>4</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>6</mn><mo><</mo><mi>t</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>8</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>55</mn><mo> </mo><mtext>s</mtext></math> <em><strong>A2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the mean will increase <em><strong>A1</strong></em></p>
<p>because the incorrect reaction times are moving from a lower interval to a higher interval which will increase the numerator of the mean calculation <em><strong>R1</strong></em></p>
<p> </p>
<p>the median will stay the same <em><strong>A1</strong></em></p>
<p>because the median or middle of the data is greater than both intervals being changed <em><strong>R1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Do not award<em><strong> A1R0</strong></em>.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were able to determine the median and interquartile range from the given graph. Some lost marks due to use of one significant figure values or because of incorrectly reading the quartiles as 0.75 and 0.25. Candidates were also able to find the estimated number of teenagers with reaction time greater than 0.4s in part (b), but determining the 90th percentile in part (c) proved to be more challenging. Most made a good attempt at completing the frequency table in part (d), but some used cumulative values from the graph incorrectly. Candidates who lost marks in part (d), were able to get “follow through” marks in parts (e) and (f). In part (e), most candidates were able to determine the modal class correctly. Not all candidates used the correct formula to find an estimate for the mean. Candidates who used their calculators usually obtained the correct answer. In part (g), few candidates were able to produce correct statements related to the changes of the mean and the median, and even fewer were able to support these statements with well-articulated reasons.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A pharmaceutical company has developed a new drug to decrease cholesterol. The final stage of testing the new drug is to compare it to their current drug. They have 150 volunteers, all recently diagnosed with high cholesterol, from which they want to select a sample of size 18. They require as close as possible 20% of the sample to be below the age of 30, 30% to be between the ages of 30 and 50 and 50% to be over the age of 50.</p>
</div>
<div class="specification">
<p>Half of the 18 volunteers are given the current drug and half are given the new drug. After six months each volunteer has their cholesterol level measured and the decrease during the six months is shown in the table.</p>
<p><img 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"></p>
</div>
<div class="specification">
<p>Calculate the mean decrease in cholesterol for</p>
</div>
<div class="specification">
<p>The company uses a t-test, at the 1% significance level, to determine if the new drug is more effective at decreasing cholesterol.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the name for this type of sampling technique.</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>Calculate the number of volunteers in the sample under the age of 30.</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 new drug.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The current drug.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State an assumption that the company is making, in order to use a t-test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the hypotheses for this t-test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the p-value for this t-test.</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>State the conclusion of this test, in context, giving a reason.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>stratified sampling <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 \times 18 = 3.6">
<mn>0.2</mn>
<mo>×</mo>
<mn>18</mn>
<mo>=</mo>
<mn>3.6</mn>
</math></span> <em><strong>M1A1</strong></em></p>
<p>so 4 volunteers need to be chosen <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>34.8 mg/dL <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>24.7 mg/dL <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER </strong></p>
<p>The decreases in cholesterol are distributed normally <em><strong>A1</strong></em></p>
<p><strong>OR </strong></p>
<p>The variance of the two groups of volunteers is equal. <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_0}\,{\text{:}}\,\bar N = \bar C">
<mrow>
<msub>
<mi>H</mi>
<mn>0</mn>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>:</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mover>
<mi>N</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{H_1}\,{\text{:}}\,\bar N > \bar C">
<mrow>
<msub>
<mi>H</mi>
<mn>1</mn>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>:</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mover>
<mi>N</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>></mo>
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p>where N and C represent the decreases of the new and current drug</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>df = 16, t = 2.77 <em><strong> (M1) </strong></em></p>
<p>p-value = 0.00683 <em><strong>A2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Since 0.00683 < 0.01 <em><strong>R1 </strong></em></p>
<p>Reject H<sub>0</sub>. There is evidence, at the 1% level, that the new drug is more effective. <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows a probability distribution for the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X) = 1.2">
<mrow>
<mtext>E</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1.2</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.18.09.png" alt="M17/5/MATME/SP2/ENG/TZ2/10"></p>
</div>
<div class="specification">
<p>A bag contains white and blue marbles, with at least three of each colour. Three marbles are drawn from the bag, without replacement. The number of blue marbles drawn is given by the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>A game is played in which three marbles are drawn from the bag of ten marbles, without replacement. A player wins a prize if three white marbles are drawn.</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="q">
<mi>q</mi>
</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="p">
<mi>p</mi>
</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>Write down the probability of drawing three blue marbles.</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>Explain why the probability of drawing three white marbles is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{6}">
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
</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>The bag contains a total of ten marbles of which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> are white. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Grant plays the game until he wins two prizes. Find the probability that he wins his second prize on his eighth attempt.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X)">
<mrow>
<mtext>E</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
</math></span> formula <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0(p) + 1(0.5) + 2(0.3) + 3(q) = 1.2">
<mn>0</mn>
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>1</mn>
<mo stretchy="false">(</mo>
<mn>0.5</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mn>0.3</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>3</mn>
<mo stretchy="false">(</mo>
<mi>q</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1.2</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = \frac{1}{{30}}">
<mi>q</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>30</mn>
</mrow>
</mfrac>
</math></span>, 0.0333 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of summing probabilities to 1 <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p + 0.5 + 0.3 + q = 1">
<mi>p</mi>
<mo>+</mo>
<mn>0.5</mn>
<mo>+</mo>
<mn>0.3</mn>
<mo>+</mo>
<mi>q</mi>
<mo>=</mo>
<mn>1</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \frac{1}{6},{\text{ }}0.167">
<mi>p</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.167</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P (3 blue)}} = \frac{1}{{30}},{\text{ }}0.0333">
<mrow>
<mtext>P (3 blue)</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>30</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.0333</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid reasoning <strong><em>R1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P (3 white)}} = {\text{P(0 blue)}}">
<mrow>
<mtext>P (3 white)</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>P(0 blue)</mtext>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P(3 white)}} = \frac{1}{6}">
<mrow>
<mtext>P(3 white)</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
</math></span> <strong><em>AG</em></strong> <strong><em>N0</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid method <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P(3 white)}} = \frac{w}{{10}} \times \frac{{w - 1}}{9} \times \frac{{w - 2}}{8},{\text{ }}\frac{{_w{C_3}}}{{_{10}{C_3}}}">
<mrow>
<mtext>P(3 white)</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mi>w</mi>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mi>w</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mn>9</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mi>w</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mn>8</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<msub>
<mi></mi>
<mi>w</mi>
</msub>
<mrow>
<msub>
<mi>C</mi>
<mn>3</mn>
</msub>
</mrow>
</mrow>
<mrow>
<msub>
<mi></mi>
<mrow>
<mn>10</mn>
</mrow>
</msub>
<mrow>
<msub>
<mi>C</mi>
<mn>3</mn>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>correct equation <strong><em>A1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{w}{{10}} \times \frac{{w - 1}}{9} \times \frac{{w - 2}}{8} = \frac{1}{6},{\text{ }}\frac{{_w{C_3}}}{{_{10}{C_3}}} = 0.167">
<mfrac>
<mi>w</mi>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mi>w</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mn>9</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mi>w</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mn>8</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<msub>
<mi></mi>
<mi>w</mi>
</msub>
<mrow>
<msub>
<mi>C</mi>
<mn>3</mn>
</msub>
</mrow>
</mrow>
<mrow>
<msub>
<mi></mi>
<mrow>
<mn>10</mn>
</mrow>
</msub>
<mrow>
<msub>
<mi>C</mi>
<mn>3</mn>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.167</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w = 6">
<mi>w</mi>
<mo>=</mo>
<mn>6</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing one prize in first seven attempts <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 1 \end{array}} \right),{\text{ }}{\left( {\frac{1}{6}} \right)^1}{\left( {\frac{5}{6}} \right)^6}">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>7</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>1</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mn>6</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 1 \end{array}} \right){\left( {\frac{1}{6}} \right)^1}{\left( {\frac{5}{6}} \right)^6},{\text{ }}0.390714">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>7</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>1</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mn>6</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>6</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.390714</mn>
</math></span></p>
<p>correct approach <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 1 \end{array}} \right){\left( {\frac{1}{6}} \right)^1}{\left( {\frac{5}{6}} \right)^6} \times \frac{1}{6}">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>7</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>1</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mn>6</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>6</mn>
</msup>
</mrow>
<mo>×</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
</math></span></p>
<p>0.065119</p>
<p>0.0651 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Two events <em>A</em> and <em>B</em> are such that P(<em>A</em>) = 0.62 and P<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {A \cap B} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩<!-- ∩ --></mo>
<mi>B</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> = 0.18.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find P(<em>A</em> ∩ <em>B′ </em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that P((<em>A</em> ∪ <em>B</em>)′<em> </em>) = 0.19, find P(<em>A </em>|<em> </em><em>B</em>′<em> </em>).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach</p>
<p><em>eg</em> Venn diagram, P(<em>A</em>) − P (<em>A</em> ∩ <em>B</em>), 0.62 − 0.18 <em><strong>(M1) </strong></em></p>
<p>P(<em>A</em> ∩ <em>B' </em>) = 0.44 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find either P(<em>B</em>′ ) or P(<em>B</em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHsAAABeCAYAAAADpmv6AAATgElEQVR4Ae2dC9BV0xfAd6SZKKHxiEmR9MKE5JFHXo1RmSKPpEyKPKKMZhivphnGqxkZzUijTIjiU5S+mchEUaKUkomIKBFRSqbE+c9v/a1r3/c55+597r3jrpnvO+fss89ee6+119prr732vg2CIAhMDbIosHv3brNixQrzySefyLtTTjnFdO7cOStfNSU0rKbKJlXXNWvWmPPOO89s2rQpDWVdXZ257LLL0tKq6aFBTbKz2TVw4EDzwgsvmD59+piLLrrI7Nixw4waNco0b97cfPfdd6Zx48bZH1VDCsyuQToFWrZsGdTX16clDho0iOEumD9/flp6NT3sVQ0dMsk6bty40fz++++mR48eaWi7d+8uz59//nlaejU9VOSY/ccff5hXXnnFcL300kvNwQcfnBhNV69ebY499liz9957p+E87LDD5JnOUK1Qkcy+//77zdixY4WmkydPNosWLcoivi+Cw8wDDjggq/g9e/ZIWsOGFUmyrPrmSqg4Nc50B0b37NnTDB8+3Hz44Yfm7bffzlV3L2lI8M6dO7PK/v777yWtZcuWWe+qJaHimD1lyhSh3QMPPGBuuukmuX/55ZcTo2eLFi3MF198kYWP6Rhw1FFHZb2rmoRKsyabN28edO7cWaq1Z8+eoG3btkHTpk2DnTt3JlLVLVu2iNW9cuXKNHzUA2t8/fr1aenV9FBRkr1s2TKzZcsW07dvXxEWjKShQ4ea7du3y7idhAQddNBBhj9burdt22bWrl1rkPojjzwyiWp4wVFRzF66dKk08txzz001VqdAr732WirN902rVq0MVrnC8uXL5fakk04yTL1wslQjVBSzv/nmG6Hh0UcfnaLl8ccfb9q2bWsmTpxofvjhh1S6zxs8ZV999VUKxYIFC+R+zpw5pn379qZp06bm9ttvNz/99FMqTzXcVBSz169fLzRr1qxZinao8nvvvdewMPH666+n0n3ewOyVK1emUFx44YWmW7du4mhB0/B+3LhxBg1UVU6WSjIwMMxatWqVVSWMJoy0Fi1aBBhtvmHEiBFijOXDtX379mDkyJGSp2fPnr6r46z8ipFsxkHm2BdccEFKovQGg2nkyJGyClVfX6/J3q6tW7eWsvN5y5o0aWKuueYayfPxxx97q4frgiuK2TTu8MMPT7UR1c04TSfo1KmTpD/99NOp975u1HGybt26nCgYq6+99lp59/jjj+fMU5GJznREiQWtXbtW1OJDDz0ULFq0SNQkapu5rf517NhR7tetW1citsKfL168WPCAHzW9dOlS+QD1PXfuXPEDUCdWwvKp+sIYyvPWlAdtNtbly5cLgdu1a5dibrdu3YJhw4YFY8eODaZNmxY888wz8m7KlCnZBThMWbFiheDp1KlTqi44e7TTce3fv39ijh5XTasYZk+aNEmI2bp162Dy5Mk5PVV4r5TQrgiQq5wNGzYInq5du8r6dffu3eUZ5iPN8+bNy/VZxadVDLPHjx8vBF2yZElBoiHtMBwL3Regmh955BFR2YojKXet4vNxrQhm79ixI2jTpk3QpUuXYPfu3QXbOX36dGE20l+DaBQo++LsX3/9ZW6++WbxWDGt2meffQoasmeffba8f+utt8zgwYML5o37cv78+YY/fPI//vijOeKIIyQA8YwzzpAicet+++23ssZOYMUhhxxijjnmGGM7g+Li9vpdtL7hNveuXbsCVcuMhWEAi7hRo0YB46lLwB4YN26crLIxTLDKRd0wxHgO84cR16NHj2DMmDEyBFSa6k80uhQpZmWLWGyuv/32m1m1apVp0KCBIaITH7g6NOwejsRoRCcOltGjR5uHH37YbN26NbY0sZJFBAz4CY548803BeWQIUPMLbfcYk488US7Cln31Jm8+AVw8+I3Z8XOBnzoRKWSD+1QdnApHcXKuu+++0JJSBgpIg/z4AEDBgSUO3HiRLGcCxluWNlM4YYMGSLagTKQxj59+gRM5zZv3ixN2LRpU7GmyNyb8mxAU7EODg40FRoIHFyZPvK+nJCoZLMWTNw1UGwjytVXX50lCGiCTz/9VCQp66WVQCRor169DFfG0nnz5plnn31WpI9spGtMOO8zgwtZfculYSwUoW7xtD333HNmzJgxMv5fd911ZtKkSaG+9ZIpiZ5Gj9apFXz+P69Lx0y5y5YtkxhvrPPhw4eLtCsOrg0bNhR8WPoTJkwIMqWx9FoULwGc1I36IPGFtE/x0uLn8D71Wr16dcq9ePHFFwe4On26GCl71apVYijZTOcedYrKhum4Z5OG0aNHC8NZ2StHp/PKbPzI6mbE0i02h3ZFfNUi6omrq6sTtyvLpHYHwO+NHz4poCPeddddUod+/fp57fS52uSF2ahXph8QFmYn6V5k0QK84M8E6oUPns6gAYTkhQE+tY1dD+rA9Ay8M2fOtF95v3fObCxZ9SVzTTIac+vWrQH+a/BC1EIAc2fNmiXBEhAeiz4pYGgDJx0Ov0FS4JTZjMcqMUhWMYK7biRTKjRJlCVQOqMupU6dOtV1lfKWp9NQ7IekwBmzmV/qmJgk0ZRQqESkBTshKqDaMd74S0oTYZHTycCZlLHmhNkwGomi4nGIHZU5mflR3xCO6U1cwICks+AeTQowHMGJRkoCSmY2UqGMLtfeZYYM6hDG85WPqPixCXiE+GvWrMmXzWk6wxw+fnAmMRUsidmMjeVmNOoQjeJi6NBomVyWvFMuW4UtWLBAmE1Ejm+IzWysSO2V5VDdSpgZM2aIRLoyBpmGYc0nCToVi2JYxqlfbGZjRaJ+HnzwwTh4nX1D/LbLzoamaNy4cSSLvtTGqHHJ/N8nxGI2FiuWN3Na12u2OGCiWMQDBw507hDp3bu3OFp8Et4uGy3JcAg9fTp3YjEbZz5S7VKiaDxLjIy/YS1iOhpLnK6B+DPaF6XTlVoHdaNq2HKp5eX6PvImARb7Wbbr169f1iEzcZblCGhgk9zChQtlqZGNAS+99JLs7SpW3ty5c71soeUMNGDmzJnFquDsvW5Tfuedd5yVmVVQrh5QKI05Ib0+c7N6oW/sd6gse4mP6RLlsRoFqGMGy7gYsJDhWruAc9u2bVIn16FPhdqDgUnbMdZ8QSQ1nsmYOJVitYdG2VEhMJsxC9CYL5wchQAVy3elzK0Lla/+fd8Wsl0HOi/DmKuZhV0296HV+N9//21uu+02iQXjvBMF4rhIZ1srR0qxn3rEiBFylpjmufvuu831119vKAMVSdTmnXfeqa/lSvwWR2FprBlbYgtten/iiSfkVAY9siqtMAcPGrnK8JIUcGgQw5geSuAcbyb38z2jtpEkDAkFXTcmnT+sSb23pxHqmUIKN27cmMqDdOoKEN+pNDVo0EDy4E7MBQwF5Pfp6dJ6JeHs0Daytk67fG1vCi3ZevqAHoHx6quvytFV2vs4r4z4MD0W46mnntJXplGjRnJPTBa9V+G9995Li8hU46R3796SBRy5gJ7PURjt2rXL9dpJmp6dQpuSAtVqu3bt8oIyNLNnzZolFTjrrLNE1QwbNixVIQ6Wufzyy+X5qquukitnkuixGKgmAKub7bfK/MWLF4vqlpf//Js2bZqoZx6xygn5zQROO+jfv39mstNn9mADHG2ZNDDc+YBQzGYsJa6aqEx63y+//JImkVdeeaVR4tjx1noIjZ4YSHw2HYNjMwAk+9RTT5VpHBLPQTWUpbs+yINNkAmkdenSJTO56p/12M58hwCU2sBQzFbkerg6RpEeN0kFTjvttFQ9bINJJXq//faT98cdd5z56KOPpNOQgJTTeTin9I033kgd3s6mAObxwPPPPy9X+9+7775rOnToYCc5v2d7D+AipDhs5dQgVcEJ+13YfKGYvWHDBimPk4IUOJ9Modipf1jWEyZMMOzPYmcEOyUU8p04NGDAAMnCuI0mUYAg7MCwO5W+c3nVUxdsTeWy/FxloUGBAw88MNfrktNCMVsrsdde/2bXNGpg90TtnaSrwUEgPmO8Mkiv5MnHbLQAgHawTy6C8QwFbAPyCWxPAvR4D5+4tOxcR4PpOxfXf7lXoDSIC9iMwc2pYN/r8Vaa/8UXX8xyfTI2aZn5jpZCW2AjYMxpXsqE2Yceeqii9nLFQOLsFnDb9oMXZFahDE8Ae958QChmqxTZv5lhS/PmzZtTdVuyZIncw6Dp06cb1DHOFnsaxXabG2+8UYiZbwggD9t2KNvnFCtVcevms88+k+Mr2WyoRpP12sstGhH7hA6u0z7niHRCX+yKO5PIURs0eIFNawrqQCEeDEeMRpsSI5YJOEeiAu5LnDc+gfbg3Ijr/49TNzYmgjOfIylOmZnfhPaNq8/ajoTUcFgYij8XRlBh/ojJBvCB863dITIrEeWZ4ELK9wksRowaNconirSy8Szqerbr+AAbUWiqEeMFkdmOqsD5J8pcGKqb10jThQ7N6/LKQoqvBRBcsM2aNUssvBfmsgACzXzvnAnNbJVaAhdsQAKU4XrV5Uo7n8t7JI9APdfAsMIwdMUVV7guOm95qh2TCO8KzWxqC5FZgkOV2oDUQySNMvEd4QFhiCZxCYQDsehBh50zZ47LovOWhZYEHzECYcOR0ASM6/xB5yibJSMxm9UYKudrVSYvVTJesDrEeScugfBh2kan9bWerPWFsXRY8NGOTOHRfJlXhkY1ePkW4WIICAuRmA0yECQZwZGrIahbxm1XS5wqYeyb9q2V6Ehq28AoO2onV1vtNFX5GHM6E8K+CAuRmE2hqup8BsaFqTwNt9fWw3yTmQcJ020/ENB3mwh3UmOMEOgoljedhDoi0Woks/+cZ9bew0BkZusCO+FF5QQaiHRzYF4cQCtgSEIsiOh7To0E9+rVSzQjgR1hx2htG/WlrvypNtAZUthOH5nZIFci6VxaK5T0FS0ze/bsSGgZilQdQjja4lN1wxgcJjiVOMUxbKeiM2MbaadgH50ymwajFdSBRXqYNsRiNtMwxm4kgvtyAYwbOnRoKPQQHccO2gDiQHx2YigxQxUSMhNlMiQwLVV8jLFffvllyBKClAGne9goT5mNSleDEj6QHmZ/WixmU2NVIViTqlZCt8RhxsGDBxd0RmQyGeIwbQtrAUepKlJLh8LQU8Yw3MUJd1ZJRnoBnEhapo7dPD/66KOSTqei8xeC2MymUFWHMNx2oxZC6PodBIaBGDy2Vw3pYi6KBEMUiAEjihEkav1Qt+x7U+sYXAwNGE+l4EJ6VSvoIT9Kb2U60zd1H5OmWiBfG0o69I6lQHZljB8/3rz//vtykBy/invOOefEPmYyzkoPsW7EyBE6RczavvvuK8dlErh35plnyvGU/HqPrq9HwfHnn3/KyhvROizHEoDIvf42J78ExCoVIdSswbdp08ZZ8AE/b0UcwMknnyxtY/UR3D///LPhpy10NZLgTg775ZnA0Lxr8Pl6QdR0dnAg4SpFcSzOqDg1P/NuplA6fnXo0EHGS5U2JATfPXlQj8WMGQ7SQ2pQwSpFXPEgoh2QtCjTJq1n1CvaSduAtigEOqVjRRCtkAtKUuOZBYIE9aVjim9LF/wLFy5MjZEwlU5mNxYDEqsWl6SqRe2QjIfUkY4AY+24dzoOcewwFz98nOXYTPrEeWZxRDtcobFfN/WTN98yaUlqPJ86JKLlhhtuMPykIvFmnCJMEIMdjpTv2zDpRMYQYTpjxgzz5JNPyobAe+65R+LYVbXlK+frr782xNRxRf0TNKDniuuZ4aeffrrRs8XzlRM3ncAIAi0ZaoiCKVZf8BCmXVdXJxEsnOicbzhicyA0J3BEh5m0esbpbWG+QQXh6bGliekBBg3vogKGCCoYI8W2dvv27Vs24zBqG2zpQwLRgPX19UWLgWYq3YXWJTiXpdBavBfJtnsTMWME+z/22GOp04QxajA6CFcikpKYMt04wC/PqwZAAn/99de088ApG23B72qxc4QdKsV+fcCuTznv+eG3qVOnplWBdqOloEchuPXWW8UQxvgiHDufdBcqw+mYXaiLIs2MOYydOqZrbw1zZbUHJwWSUK7xs1D7ir1jvs/xHdgFTMlwkigdMGyLaTs93AdaxT0G07tk5+pphAczXiL17N7UzQTkZbqkUaz777+/TGs6duyY6FQuV51LTeMAA7QR25vY9QLMnj3bXHLJJXJPoGbXrl3lnjDtXJLLGexspvjggw8MNIkMxXpk7b0bCugUivFXgVmDSjdWP8C0EJsk3+JGKVO+xNS4NvC/eFVXZ/v27dOmhdBC5/JM/wD99V4MW9dLrqHixiOri9oHaRTQfWMYlGqIagY1LrkynOnPSjAd1C3MmrfUa43ZpVIwxPf6q0CZ4zDM1V8dOuGEE6Qj4JOgQwwaNMj575aV/UfcQtCq6rMw1QQy95rjKNGOcP7550ueO+64Q/zcmR3DBRFqku2CikXKYJEEsPfBodo5iwZgb7puh+bZB6MF0X/RYCpHmzHAmjRpIjtl7PUDfPC2he6zbmWZZ0sv+4/947BA9nrbO14Zm5l/67zbN0lqatw3hf8pH1Wu59DAZE6W4CCgpBhNNWqSnRCzQYNU4x20f1s0QfQ1ZidJ7HLjqqnxcnMgQfw1ZidI7HKjqjG73BxIEH+N2QkSu9yoaswuNwcSxF9jdoLELjeqGrPLzYEE8deYnSCxy43qf+VQOZfJ5YwzAAAAAElFTkSuQmCC"> (seen anywhere), 1 − P(<em>A</em> ∩ <em>B</em>′<em> </em>) − P((<em>A</em> ∪ <em>B</em>)′<em> </em>)</p>
<p>correct calculation for P(<em>B</em>′ ) or P(<em>B</em>) <em><strong>(A1)</strong></em></p>
<p><em>eg </em> 0.44 + 0.19, 0.81 − 0.62 + 0.18</p>
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{P}}\left( {A \cap B'} \right)}}{{{\text{P}}\left( {B'} \right)}}">
<mfrac>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<msup>
<mi>B</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>B</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span> <em><strong> (A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.44}}{{0.19 + 0.44}},\,\,\frac{{0.44}}{{1 - 0.37}}">
<mfrac>
<mrow>
<mn>0.44</mn>
</mrow>
<mrow>
<mn>0.19</mn>
<mo>+</mo>
<mn>0.44</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>0.44</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>0.37</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.698412</p>
<p>P(<em>A </em>|<em> </em><em>B</em>′<em> </em>) = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{44}}{{63}}">
<mfrac>
<mrow>
<mn>44</mn>
</mrow>
<mrow>
<mn>63</mn>
</mrow>
</mfrac>
</math></span> (exact), 0.698 <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The weight, <em>W</em>, of basketball players in a tournament is found to be normally distributed with a mean of 65 kg and a standard deviation of 5 kg.</p>
</div>
<div class="specification">
<p>The probability that a basketball player has a weight that is within 1.5 standard deviations of the mean is <em>q</em>.</p>
</div>
<div class="specification">
<p>A basketball coach observed 60 of her players to determine whether their performance and their weight were independent of each other. Her observations were recorded as shown in the table.</p>
<p style="text-align: center;"><img 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"></p>
<p>She decided to conduct a <em>χ </em><sup>2</sup> test for independence at the 5% significance level.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a basketball player has a weight that is less than 61 kg.</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>In a training session there are 40 basketball players.</p>
<p>Find the expected number of players with a weight less than 61 kg in this training session.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a normal curve to represent this probability.</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 <em>q</em>.</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>Given that P(<em>W</em> > <em>k</em>) = 0.225 , find the value of <em>k</em>.</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>For this test state the null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For this test find the<em> p</em>-value.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a conclusion for this test. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>P(<em>W</em> < 61) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability statement.</p>
<p><strong>OR</strong></p>
<p><img src="data:image/png;base64,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"> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct region labelled and shaded on diagram.</p>
<p>= 0.212 (0.21185…, 21.2%) <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>40 × 0.21185… <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for product of 40 and their 0.212.</p>
<p>= 8.47 (8.47421...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their part (a)(i) provided their answer to part (a)(i) is less than 1.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> </p>
<p><em><strong><img 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"> (A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for two correctly labelled vertical lines in approximately correct positions. The values 57.5 and 72.5, or <em>μ </em>− 1.5<em>σ</em> and <em>μ </em>+ 1.5<em>σ</em> are acceptable labels. Award <em><strong>(M1)</strong></em> for correctly shaded region marked by their two vertical lines.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.866 (0.86638…, 86.6%) <strong><em> (A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their part (b)(i) shaded region if their values are clear.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>P(<em>W</em> < <em>k</em>) = 0.775 <strong><em> (M1)</em></strong></p>
<p><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> <em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct region labelled and shaded on diagram.</p>
<p>(<em>k</em> =) 68.8 (68.7770…) <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(H<sub>0</sub>:) performance (of players) and (their) weight are independent. <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “there is no association between performance (of players) and (their) weight”. Do not accept "not related" or "not correlated" or "not influenced".</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.287 (0.287436…) <em><strong>(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>accept/ do not reject null hypothesis/H<sub>0</sub> <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>OR</strong></p>
<p>performance (of players) and (their) weight are independent. <strong><em>(A1)</em>(ft)</strong></p>
<p>0.287 > 0.05 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Accept <em>p</em>-value>significance level provided their <em>p</em>-value is seen in b(ii). Accept 28.7% > 5%. Do not award <em><strong>(A1)(R0)</strong></em>. Follow through from part (d).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>On one day 180 flights arrived at a particular airport. The distance travelled and the arrival status for each incoming flight was recorded. The flight was then classified as on time, slightly delayed, or heavily delayed.</p>
<p>The results are shown in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<p>A <em>χ</em><sup>2</sup> test is carried out at the 10 % significance level to determine whether the arrival status of incoming flights is independent of the distance travelled.</p>
</div>
<div class="specification">
<p>The critical value for this test is 7.779.</p>
</div>
<div class="specification">
<p>A flight is chosen at random from the 180 recorded flights.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</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>Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.</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>Write down the number of degrees of freedom.</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>Write down the <em>χ</em><sup>2</sup> statistic.</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>Write down the associated <em>p</em>-value.</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>State, with a reason, whether you would reject the null hypothesis.</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>Write down the probability that this flight arrived on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.</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>Two flights are chosen at random from those which were slightly delayed.</p>
<p>Find the probability that each of these flights travelled at least 5000 km.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>The arrival status is dependent on the distance travelled by the incoming flight <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “associated” or “not independent”.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{60 \times 45}}{{180}}"> <mfrac> <mrow> <mn>60</mn> <mo>×</mo> <mn>45</mn> </mrow> <mrow> <mn>180</mn> </mrow> </mfrac> </math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{60}}{{180}} \times \frac{{45}}{{180}} \times 180"> <mfrac> <mrow> <mn>60</mn> </mrow> <mrow> <mn>180</mn> </mrow> </mfrac> <mo>×</mo> <mfrac> <mrow> <mn>45</mn> </mrow> <mrow> <mn>180</mn> </mrow> </mfrac> <mo>×</mo> <mn>180</mn> </math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into expected value formula.</p>
<p>= 15 <em><strong> (A1) (G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4 <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if “2 + 2 = 4” is seen.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>9.55 (9.54671…) <em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(G1)</strong></em> for an answer of 9.54.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.0488 (0.0487961…) <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Reject the Null Hypothesis <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their hypothesis in part (a).</p>
<p>9.55 (9.54671…) > 7.779 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>OR </strong></p>
<p>0.0488 (0.0487961…) < 0.1 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Do not award <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(R0)</strong></em><strong>(ft)</strong>. Follow through from part (d). Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for a correct comparison, <em><strong>(A1)</strong></em><strong>(ft)</strong> for a consistent conclusion with the answers to parts (a) and (d). Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for <em>χ</em><sup>2</sup><em><sub>calc</sub></em> > <em>χ</em><sup>2</sup><em><sub>crit </sub></em>, provided the calculated value is explicitly seen in part (d)(i).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{52}}{{180}}\,\,\left( {0.289,\,\,\frac{{13}}{{45}},\,\,28.9\,{\text{% }}} \right)"> <mfrac> <mrow> <mn>52</mn> </mrow> <mrow> <mn>180</mn> </mrow> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.289</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mn>13</mn> </mrow> <mrow> <mn>45</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>28.9</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{35}}{{97}}\,\,\left( {0.361,\,\,36.1\,{\text{% }}} \right)"> <mfrac> <mrow> <mn>35</mn> </mrow> <mrow> <mn>97</mn> </mrow> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.361</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>36.1</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{14}}{{45}} \times \frac{{13}}{{44}}"> <mfrac> <mrow> <mn>14</mn> </mrow> <mrow> <mn>45</mn> </mrow> </mfrac> <mo>×</mo> <mfrac> <mrow> <mn>13</mn> </mrow> <mrow> <mn>44</mn> </mrow> </mfrac> </math></span> <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for two correct fractions and <em><strong>(M1)</strong></em> for multiplying their two fractions.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{182}}{{1980}}\,\,\left( {0.0919,\,\,\frac{{91}}{{990}},\,0.091919 \ldots ,\,9.19\,{\text{% }}} \right)"> <mo>=</mo> <mfrac> <mrow> <mn>182</mn> </mrow> <mrow> <mn>1980</mn> </mrow> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.0919</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mn>91</mn> </mrow> <mrow> <mn>990</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mn>0.091919</mn> <mo>…</mo> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mn>9.19</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1) (G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A transportation company owns 30 buses. The distance that each bus has travelled since being purchased by the company is recorded. The cumulative frequency curve for these data is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>It is known that 8 buses travelled more than <em>m</em> kilometres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of buses that travelled a distance between 15000 and 20000 kilometres.</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>Use the cumulative frequency curve to find the median distance.</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>Use the cumulative frequency curve to find the lower quartile.</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>Use the cumulative frequency curve to find the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence write down the interquartile range.</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>Write down the percentage of buses that travelled a distance greater than the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of buses that travelled a distance less than or equal to 12 000 km.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>m</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The smallest distance travelled by one of the buses was 2500 km.<br>The longest distance travelled by one of the buses was 23 000 km.</p>
<p><strong>On graph paper</strong>, draw a box-and-whisker diagram for these data. Use a scale of 2 cm to represent 5000 km.</p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>28 − 20 <em><strong>(A1)</strong></em></p>
<p><em><strong>Note:</strong></em> Award <em><strong>(A1)</strong></em> for 28 and 20 seen.</p>
<p>8 <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>13500 <em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Accept an answer in the range 13500 to 13750.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>10000 <em><strong>(G1)</strong></em></p>
<p><strong>Note:</strong> Accept an answer in the range 10000 to 10250.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>16000 <em><strong>(G1)</strong></em></p>
<p><strong>Note:</strong> Accept an answer in the range 16000 to 16250.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6000 <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their part (b)(ii) and (iii).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>25% <strong><em> (A1)</em></strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>11 <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>30 − 8 <strong>OR</strong> 22 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting 30 − 8 or 22 seen.</p>
<p>15750 <em><strong> (A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Accept 15750 ± 250.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct label and scale; accept “distance” or “km” for label.</p>
<p><strong><em>(A1)</em>(ft)</strong> for correct median,<br><strong><em>(A1)</em>(ft)</strong> for correct quartiles and box,<br><em><strong>(A1)</strong></em> for endpoints at 2500 and 23 000 joined to box by straight lines.<br>Accept ±250 for the median, quartiles and endpoints.<br>Follow through from their part (b).<br>The final <em><strong>(A1)</strong></em> is not awarded if the line goes through the box.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> has the following probability distribution.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.34.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/04"></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="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</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>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2|X > 0)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mrow>
<mo stretchy="false">|</mo>
</mrow>
<mi>X</mi>
<mo>></mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>total probability = 1</p>
<p>correct equation <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.475 + 2{k^2} + \frac{k}{{10}} + 6{k^2} = 1,{\text{ }}8{k^2} + 0.1k - 0.525 = 0">
<mn>0.475</mn>
<mo>+</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mi>k</mi>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>8</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>0.1</mn>
<mi>k</mi>
<mo>−</mo>
<mn>0.525</mn>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 0.25">
<mi>k</mi>
<mo>=</mo>
<mn>0.25</mn>
</math></span> <strong><em>A2 N3</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2) = 0.025">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.025</mn>
</math></span> <strong><em>A1 N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach for finding <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X > 0)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - 0.475,{\text{ }}2({0.25^2}) + 0.025 + 6({0.25^2}),{\text{ }}1 - {\text{P}}(X = 0),{\text{ }}2{k^2} + \frac{k}{{10}} + 6{k^2}">
<mn>1</mn>
<mo>−</mo>
<mn>0.475</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mn>0.25</mn>
<mn>2</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>0.025</mn>
<mo>+</mo>
<mn>6</mn>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mn>0.25</mn>
<mn>2</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1</mn>
<mo>−</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mi>k</mi>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p>correct substitution into formula for conditional probability <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.025}}{{1 - 0.475}},{\text{ }}\frac{{0.025}}{{0.525}}">
<mfrac>
<mrow>
<mn>0.025</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>0.475</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>0.025</mn>
</mrow>
<mrow>
<mn>0.525</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.0476190</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2|X > 0) = \frac{1}{{21}}">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
<mrow>
<mo stretchy="false">|</mo>
</mrow>
<mi>X</mi>
<mo>></mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>21</mn>
</mrow>
</mfrac>
</math></span> (exact), 0.0476 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The scores of the eight highest scoring countries in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2019</mn></math> Eurovision song contest are shown in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>For this data, find</p>
</div>
<div class="specification">
<p>Chester is investigating the relationship between the highest-scoring countries’ Eurovision score and their population size to determine whether population size can reasonably be used to predict a country’s score.</p>
<p>The populations of the countries, to the nearest million, are shown in the table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>Chester finds that, for this data, the Pearson’s product moment correlation coefficient is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>249</mn></math>.</p>
</div>
<div class="specification">
<p>Chester then decides to find the Spearman’s rank correlation coefficient for this data, and creates a table of ranks.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Write down the value of:</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the upper quartile.</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>the interquartile range.</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>Determine if the Netherlands’ score is an outlier for this data. Justify your answer.</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>State whether it would be appropriate for Chester to use the equation of a regression line for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> to predict a country’s Eurovision score. Justify your answer.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of the Spearman’s rank correlation coefficient <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></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>Interpret the value obtained for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When calculating the ranks, Chester incorrectly read the Netherlands’ score as <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>478</mn></math>. Explain why the value of the Spearman’s rank correlation <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math> does not change despite this error.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>370</mn><mo>+</mo><mn>472</mn></mrow><mn>2</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> This <em><strong>(M1)</strong></em> can also be awarded for either a correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>Q</mtext><mn>3</mn></msub></math> or a correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>Q</mtext><mn>1</mn></msub></math> in part (a)(ii).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>Q</mtext><mn>3</mn></msub><mo>=</mo><mn>421</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>their part (a)(i) – their <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>Q</mtext><mn>1</mn></msub></math> (clearly stated) <em><strong>(M1)</strong></em></p>
<p>IQR <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced><mrow><mn>421</mn><mo>-</mo><mn>318</mn><mo>=</mo></mrow></mfenced><mo> </mo><mn>103</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>Q</mtext><mn>3</mn></msub><mo>+</mo><mn>1</mn><mo>.</mo><mn>5</mn></math>(IQR) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>421</mn><mo>+</mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>103</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>575</mn><mo>.</mo><mn>5</mn></math></p>
<p>since <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>498</mn><mo><</mo><mn>575</mn><mo>.</mo><mn>5</mn></math> <em><strong>R1</strong></em></p>
<p>Netherlands is not an outlier <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> The <em><strong>R1</strong> </em>is dependent on the <em><strong>(M1)</strong></em>. Do not award <em><strong>R0A1</strong></em>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>not appropriate (“no” is sufficient) <em><strong>A1</strong></em></p>
<p>as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> is too close to zero / too weak a correlation <em><strong>R1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>683</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>682646</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>there is a (positive) association between the population size and the score <em><strong>A1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>there is a (positive) linear correlation between the ranks of the population size and the ranks of the scores (when compared with the PMCC of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>249</mn></math>). <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>lowering the top score by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> does not change its rank so <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math> is unchanged <em><strong>R1</strong></em></p>
<p><br><strong>Note:</strong> Accept “this would not alter the rank” or “Netherlands still top rank” or similar. Condone any statement that clearly implies the ranks have not changed, for example: “The Netherlands still has the highest score.”</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a), many candidates could use their GDC to find the upper quartile, but many forgot how to find the inter-quartile range.</p>
<p>In part (b), very few candidates knew how to show if a score is an outlier. Many candidates did not know that there is a mathematical definition to “outlier” and simply wrote sentences explaining why or why not a value was an outlier.</p>
<p>In part (c), candidates were able to assess the validity of a regression line. The justifications for their conclusion revealed a partial or imprecise understanding of the topic. Examples of this include “no correlation”, “weak value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>”, “low relationship”, “not close to 1”.</p>
<p>In part (d), about half of the candidates managed to find the correct values missing from the table.</p>
<p>In part (e), many candidates knew how to use their GDC to find Spearman’s rank correlation coefficient. Some mistakenly wrote down the value for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>r</mi><mn>2</mn></msup></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>. Very few candidates could correctly interpret the value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> as they became confused by the fact that linear correlation must go with the rank, otherwise it is about association. They could either have said “there is an <strong>association</strong> between population size and score” or “there is a <strong>linear correlation</strong> between the rank order of the population size and the ranks of the scores”.</p>
<p>In part (f), most candidates were able to work out that, even if the score changed, the rank remained the same.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in metres.</strong></p>
<p> </p>
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \sqrt {\frac{{4 - {x^2}}}{8}} ">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>8</mn>
</mfrac>
</msqrt>
</math></span>, for −2 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 2. In the following diagram, the shaded region is 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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">A container can be modelled by rotating this region by 360˚ about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis.</p>
</div>
<div class="specification">
<p>Water can flow in and out of the container.</p>
<p>The volume of water in the container is given by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 4 , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is measured in hours and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span> is measured in m<sup>3</sup>. The rate of change of the volume of water in the container is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'\left( t \right) = 0.9 - 2.5\,{\text{cos}}\left( {0.4{t^2}} \right)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.9</mn>
<mo>−<!-- − --></mo>
<mn>2.5</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.4</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The volume of water in the container is increasing only when <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="t">
<mi>t</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the container.</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 value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and 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.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During the interval <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="t">
<mi>t</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>, he volume of water in the container increases by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> m<sup>3</sup>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</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>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> = 0, the volume of water in the container is 2.3 m<sup>3</sup>. It is known that the container is never completely full of water during the 4 hour period.</p>
<p> </p>
<p>Find the minimum volume of empty space in the container during the 4 hour period.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>attempt to substitute correct limits or the function into formula involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}">
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi \int_{ - 2}^2 {{y^2}\,{\text{d}}y} ">
<mi>π</mi>
<msubsup>
<mo>∫</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mrow>
<mrow>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>y</mi>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {\int {\left( {\sqrt {\frac{{4 - {x^2}}}{8}} } \right)} ^2}{\text{d}}x">
<mi>π</mi>
<mrow>
<mo>∫</mo>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mo>−</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>8</mn>
</mfrac>
</msqrt>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</math></span></p>
<p>4.18879</p>
<p>volume = 4.19, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3}\pi ">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
</math></span> (exact) (m<sup>3</sup>) <em><strong>A2 N3</strong></em></p>
<p><strong>Note:</strong> If candidates have their GDC incorrectly set in degrees, award <strong><em>M</em></strong> marks where appropriate, but no <em><strong>A</strong></em> marks may be awarded. Answers from degrees are <em>p</em> = 13.1243 and <em>q</em> = 26.9768 in (b)(i) and 12.3130 or 28.3505 in (b)(ii).</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing the volume increases when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g'}">
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> is positive <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'\left( t \right)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span> > 0, sketch of graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g'}">
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> indicating correct interval</p>
<p>1.73387, 3.56393</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> = 1.73, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> = 3.56 <em><strong>A1A1 N3</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<p> </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find change in volume <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( q \right) - g\left( p \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>q</mi>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_p^q {g'\left( t \right){\text{d}}t} ">
<msubsup>
<mo>∫</mo>
<mi>p</mi>
<mi>q</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span></p>
<p>3.74541</p>
<p>total amount = 3.75 (m<sup>3</sup>) <em><strong>A2 N3</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Note:</strong> There may be slight differences in the final answer, depending on which values candidates carry through from previous parts. Accept answers that are consistent with correct working.</p>
<p> </p>
<p>recognizing when the volume of water is a maximum <em><strong>(M1)</strong></em></p>
<p><em>eg</em> maximum when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q">
<mi>t</mi>
<mo>=</mo>
<mi>q</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^q {g'\left( t \right){\text{d}}t} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>q</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span></p>
<p>valid approach to find maximum volume of water <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.3 + \int_0^q {g'\left( t \right){\text{d}}t} ">
<mn>2.3</mn>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>q</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.3 + \int_0^p {g'\left( t \right){\text{d}}t} + 3.74541">
<mn>2.3</mn>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>p</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>3.74541</mn>
</math></span>, 3.85745</p>
<p>correct expression for the difference between volume of container and maximum value <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4.18879 - \left( {2.3 + \int_0^q {g'\left( t \right){\text{d}}t} } \right)">
<mn>4.18879</mn>
<mo>−</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>2.3</mn>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>q</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, 4.19 − 3.85745</p>
<p>0.331334</p>
<p>0.331 (m<sup>3</sup>) <em><strong>A2 N3</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - 0.5{x^4} + 3{x^2} + 2x">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>0.5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
</math></span>. The following diagram shows part of 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 src="images/Schermafbeelding_2017-08-15_om_06.09.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/08"></p>
<p> </p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>. There is a maximum at A where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
</math></span>, and a point of inflexion at B where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
</math></span>.</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>Write down the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R">
<mi>R</mi>
</math></span> be 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> , the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
</math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R">
<mi>R</mi>
</math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 0,{\text{ }}y = 0">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p>2.73205</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 2.73">
<mi>p</mi>
<mo>=</mo>
<mn>2.73</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.87938, 8.11721</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1.88,{\text{ }}8.12)">
<mo stretchy="false">(</mo>
<mn>1.88</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>8.12</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A2</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>rate of change is 0 (do not accept decimals) <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 (using GDC)</strong></p>
<p>valid approach <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = 0">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</math></span>, max/min on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’,{\text{ }}x = - 1">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
</math></span></p>
<p>sketch of either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
</math></span>, with max/min or root (respectively) <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p>Substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(1)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4.5">
<mi>y</mi>
<mo>=</mo>
<mn>4.5</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong>METHOD 2 (analytical)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = - 6{x^2} + 6">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
</math></span> <strong><em>A1</em></strong></p>
<p>setting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = 0">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p>substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(1)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4.5">
<mi>y</mi>
<mo>=</mo>
<mn>4.5</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing rate of change is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y’,{\text{ }}f’(1)">
<msup>
<mi>y</mi>
<mo>′</mo>
</msup>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p>rate of change is 6 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute either limits or the function into formula <strong><em>(M1)</em></strong></p>
<p>involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}">
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> (accept absence of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> and/or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{d}}x">
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</math></span>)</p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi \int {{{( - 0.5{x^4} + 3{x^2} + 2x)}^2}{\text{d}}x,{\text{ }}\int_1^{1.88} {{f^2}} } ">
<mi>π</mi>
<mo>∫</mo>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>0.5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>1</mn>
<mrow>
<mn>1.88</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mrow>
</math></span></p>
<p>128.890</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{volume}} = 129">
<mrow>
<mtext>volume</mtext>
</mrow>
<mo>=</mo>
<mn>129</mn>
</math></span> <strong><em>A2</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The marks obtained by nine Mathematical Studies SL students in their projects (<em>x</em>) and their final IB examination scores (<em>y</em>) were recorded. These data were used to determine whether the project mark is a good predictor of the examination score. The results are shown in the table.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The equation of the regression line <em>y</em> on <em>x</em> is <em>y</em> = <em>mx</em> + <em>c</em>.</p>
</div>
<div class="specification">
<p>A tenth student, Jerome, obtained a project mark of 17.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean examination score.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <em>r </em>, Pearson’s product–moment correlation coefficient.</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 exact value of <em>m</em> and of <em>c</em> for these data.</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>Use the regression line <em>y</em> on <em>x</em> to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>54 <em><strong>(G1)</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.5 <em><strong>(G2)</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>m</em> = 0.875, <em>c</em> = 41.75 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {m = \frac{7}{8}{\text{,}}\,\,c = \frac{{167}}{4}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mn>8</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>167</mn>
</mrow>
<mn>4</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 0.875 seen. Award <em><strong>(A1)</strong></em> for 41.75 seen. If 41.75 is rounded to 41.8 do not award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>y</em> = 0.875(17) + 41.75 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for correct substitution into their regression line.</p>
<p> </p>
<p>= 56.6 (56.625) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (b)(i).</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the estimate is valid <em><strong>(A1)</strong></em></p>
<p>since this is interpolation <strong>and</strong> the correlation coefficient is large enough <em><strong>(R1)</strong></em></p>
<p><strong>OR</strong></p>
<p>the estimate is not valid <em><strong>(A1)</strong></em></p>
<p>since the correlation coefficient is not large enough <em><strong>(R1)</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>(A1)(R0)</strong></em>. The <em><strong>(R1)</strong></em> may be awarded for reasoning based on strength of correlation, but do not accept “correlation coefficient is not strong enough” or “correlation is not large enough”.</p>
<p>Award <em><strong>(A0)</strong></em><em><strong>(R0)</strong></em> for this method if no numerical answer to part (a)(iii) is seen.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1280</mn></math> students were asked which electronic device they preferred. The results per age group are given in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A student from the group is chosen at random. Calculate the probability that the student</p>
</div>
<div class="specification">
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> test for independence was performed on the collected data at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>%</mo></math> significance level. The critical value for the test is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>277</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>prefers a tablet.</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>is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mtext>–</mtext><mn>13</mn></math> years old and prefers a mobile phone.</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>prefers a laptop <strong>given that</strong> they are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mtext>–</mtext><mn>18</mn></math> years old.</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>prefers a tablet or is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mtext>–</mtext><mn>16</mn></math> years old.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the null and alternative hypotheses.</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 the number of degrees of freedom.</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>Write down the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> test statistic.</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>Write down the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value.</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>State the conclusion for the test in context. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>560</mn><mn>1280</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>7</mn><mn>16</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>4375</mn></mrow></mfenced></math> <em><strong>A1</strong></em><em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct numerator, <em><strong>A1</strong></em> for correct denominator.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>72</mn><mn>1280</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>9</mn><mn>160</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>05625</mn></mrow></mfenced></math> <em><strong>A1</strong></em><em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct numerator, <em><strong>A1</strong></em> for correct denominator.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>153</mn><mn>348</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>51</mn><mn>116</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>439655</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em><em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct numerator, <em><strong>A1</strong></em> for correct denominator.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>160</mn><mo>+</mo><mn>224</mn><mo>+</mo><mn>128</mn><mo>+</mo><mn>205</mn><mo>+</mo><mn>131</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>560</mn><mo>+</mo><mn>512</mn><mo>-</mo><mn>224</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>848</mn><mn>1280</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>53</mn><mn>80</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>6625</mn></mrow></mfenced></math> <em><strong>A1</strong></em><em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct denominator <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1280</mn><mo>)</mo></math> seen, <em><strong>(M1)</strong></em> for correct calculation of the numerator, <em><strong>A1</strong></em> for the correct answer.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub><mo> </mo><mo>:</mo></math> the variables are independent</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>1</mn></msub><mo> </mo><mo>:</mo></math> the variables are dependent <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for for both hypotheses correct. Do not accept “not correlated” or “not related” in place of “independent”.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>χ</mi><mn>2</mn></msup><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>23</mn><mo>.</mo><mn>3</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>23</mn><mo>.</mo><mn>3258</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>000109</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>000108991</mn><mo>…</mo></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>09</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn><mo>.</mo><mn>3</mn><mo>></mo><mn>13</mn><mo>.</mo><mn>277</mn></math> <em><strong>R1</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>000109</mn><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn></math> <em><strong>R1</strong></em></p>
<p><strong><br>THEN</strong></p>
<p>(there is sufficient evidence to accept <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>1</mn></msub></math> that) preferred device and age group are not independent <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> For the final <em><strong>A1</strong></em> the answer must be in context. Do not award <em><strong>A1R0</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>A common error was to treat these as compound probability events. Candidates who attempted to use the conditional probability formula in part (a)(iii) often accrued at least one mark for a correct method. Some lost one mark for not reducing the total sample space. In part (a)(iv) many found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>P</mi><mfenced><mi>B</mi></mfenced></math>, failing to subtract the intersection of the two events. When stating test hypotheses, terminology such as "related", "correlated", "data is independent" are not acceptable. Few candidates attempted to frame this as a Goodness of Fit test. Candidates correctly wrote down the degrees of freedom. It was pleasing to see most found the correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic and associated p-value. Relative to past examination sessions, fewer candidates appeared to compare the critical value with the p-value or the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic with the level of significance. A conclusion consistent with their hypotheses was usually seen, though this was not always expressed in context.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A common error was to treat these as compound probability events. Candidates who attempted to use the conditional probability formula in part (a)(iii) often accrued at least one mark for a correct method. Some lost one mark for not reducing the total sample space. In part (a)(iv) many found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>P</mi><mfenced><mi>B</mi></mfenced></math>, failing to subtract the intersection of the two events. When stating test hypotheses, terminology such as "related", "correlated", "data is independent" are not acceptable. Few candidates attempted to frame this as a Goodness of Fit test. Candidates correctly wrote down the degrees of freedom. It was pleasing to see most found the correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic and associated p-value. Relative to past examination sessions, fewer candidates appeared to compare the critical value with the p-value or the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic with the level of significance. A conclusion consistent with their hypotheses was usually seen, though this was not always expressed in context.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A common error was to treat these as compound probability events. Candidates who attempted to use the conditional probability formula in part (a)(iii) often accrued at least one mark for a correct method. Some lost one mark for not reducing the total sample space. In part (a)(iv) many found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>P</mi><mfenced><mi>B</mi></mfenced></math>, failing to subtract the intersection of the two events. When stating test hypotheses, terminology such as "related", "correlated", "data is independent" are not acceptable. Few candidates attempted to frame this as a Goodness of Fit test. Candidates correctly wrote down the degrees of freedom. It was pleasing to see most found the correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic and associated p-value. Relative to past examination sessions, fewer candidates appeared to compare the critical value with the p-value or the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic with the level of significance. A conclusion consistent with their hypotheses was usually seen, though this was not always expressed in context.</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A common error was to treat these as compound probability events. Candidates who attempted to use the conditional probability formula in part (a)(iii) often accrued at least one mark for a correct method. Some lost one mark for not reducing the total sample space. In part (a)(iv) many found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>P</mi><mfenced><mi>B</mi></mfenced></math>, failing to subtract the intersection of the two events. When stating test hypotheses, terminology such as "related", "correlated", "data is independent" are not acceptable. Few candidates attempted to frame this as a Goodness of Fit test. Candidates correctly wrote down the degrees of freedom. It was pleasing to see most found the correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic and associated p-value. Relative to past examination sessions, fewer candidates appeared to compare the critical value with the p-value or the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic with the level of significance. A conclusion consistent with their hypotheses was usually seen, though this was not always expressed in context.</p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A common error was to treat these as compound probability events. Candidates who attempted to use the conditional probability formula in part (a)(iii) often accrued at least one mark for a correct method. Some lost one mark for not reducing the total sample space. In part (a)(iv) many found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>P</mi><mfenced><mi>B</mi></mfenced></math>, failing to subtract the intersection of the two events. When stating test hypotheses, terminology such as "related", "correlated", "data is independent" are not acceptable. Few candidates attempted to frame this as a Goodness of Fit test. Candidates correctly wrote down the degrees of freedom. It was pleasing to see most found the correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic and associated p-value. Relative to past examination sessions, fewer candidates appeared to compare the critical value with the p-value or the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic with the level of significance. A conclusion consistent with their hypotheses was usually seen, though this was not always expressed in context.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A common error was to treat these as compound probability events. Candidates who attempted to use the conditional probability formula in part (a)(iii) often accrued at least one mark for a correct method. Some lost one mark for not reducing the total sample space. In part (a)(iv) many found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>P</mi><mfenced><mi>B</mi></mfenced></math>, failing to subtract the intersection of the two events. When stating test hypotheses, terminology such as "related", "correlated", "data is independent" are not acceptable. Few candidates attempted to frame this as a Goodness of Fit test. Candidates correctly wrote down the degrees of freedom. It was pleasing to see most found the correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic and associated p-value. Relative to past examination sessions, fewer candidates appeared to compare the critical value with the p-value or the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic with the level of significance. A conclusion consistent with their hypotheses was usually seen, though this was not always expressed in context.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A common error was to treat these as compound probability events. Candidates who attempted to use the conditional probability formula in part (a)(iii) often accrued at least one mark for a correct method. Some lost one mark for not reducing the total sample space. In part (a)(iv) many found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>P</mi><mfenced><mi>B</mi></mfenced></math>, failing to subtract the intersection of the two events. When stating test hypotheses, terminology such as "related", "correlated", "data is independent" are not acceptable. Few candidates attempted to frame this as a Goodness of Fit test. Candidates correctly wrote down the degrees of freedom. It was pleasing to see most found the correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic and associated p-value. Relative to past examination sessions, fewer candidates appeared to compare the critical value with the p-value or the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic with the level of significance. A conclusion consistent with their hypotheses was usually seen, though this was not always expressed in context.</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A common error was to treat these as compound probability events. Candidates who attempted to use the conditional probability formula in part (a)(iii) often accrued at least one mark for a correct method. Some lost one mark for not reducing the total sample space. In part (a)(iv) many found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>P</mi><mfenced><mi>B</mi></mfenced></math>, failing to subtract the intersection of the two events. When stating test hypotheses, terminology such as "related", "correlated", "data is independent" are not acceptable. Few candidates attempted to frame this as a Goodness of Fit test. Candidates correctly wrote down the degrees of freedom. It was pleasing to see most found the correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic and associated p-value. Relative to past examination sessions, fewer candidates appeared to compare the critical value with the p-value or the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic with the level of significance. A conclusion consistent with their hypotheses was usually seen, though this was not always expressed in context.</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A common error was to treat these as compound probability events. Candidates who attempted to use the conditional probability formula in part (a)(iii) often accrued at least one mark for a correct method. Some lost one mark for not reducing the total sample space. In part (a)(iv) many found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">P</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>P</mi><mfenced><mi>B</mi></mfenced></math>, failing to subtract the intersection of the two events. When stating test hypotheses, terminology such as "related", "correlated", "data is independent" are not acceptable. Few candidates attempted to frame this as a Goodness of Fit test. Candidates correctly wrote down the degrees of freedom. It was pleasing to see most found the correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic and associated p-value. Relative to past examination sessions, fewer candidates appeared to compare the critical value with the p-value or the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>-test statistic with the level of significance. A conclusion consistent with their hypotheses was usually seen, though this was not always expressed in context.</p>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>160 students attend a dual language school in which the students are taught only in Spanish or taught only in English.</p>
<p>A survey was conducted in order to analyse the number of students studying Biology or Mathematics. The results are shown in the Venn diagram.</p>
<p> </p>
<p style="padding-left: 240px;">Set <em>S</em> represents those students who are <strong>taught</strong> in Spanish.</p>
<p style="padding-left: 240px;">Set <em>B</em> represents those students who <strong>study</strong> Biology.</p>
<p style="padding-left: 240px;">Set <em>M</em> represents those students who <strong>study</strong> Mathematics.</p>
<p style="padding-left: 210px;"> </p>
<p style="text-align: center;"><img 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VVDF/l+rzYGGFXlR2Tbsv9bxi65X3K3/g95onPDBnZ4g8IeAdd3OqAEdSTp128IW9hvb968aewkVPw3zB0weySuxtOvr6TI2whA2GKzglhy885UFVK85V/lA9hvDUnWSP62WQtJlR4ycetbMr0fdr1fS3n+e/L23nKRgR0kzUX7rcEh29JtxFFxrMwccVSTwKN/DpWsHV2T6kulB8taHir6Mlq2krpNrFixwkhhxqxRdbHhFfcQwHhE2keMz2gF1ydPnhxC5jMWIqALAhi3SHmLbGexyn8WLQ11VPM1/t5N6Xi7ZG3ohxO3hi5j+lbZp8Kfk5+Ftpb9Z6yqk74XS54FO7Xj7dOhtTmpIVE5NW+XhYrW54ayJDWU9creUFkDMldNWranLUt6CLCCICGgJi3k6Y5VuFiMhQ7vuYUAxi8Wg/UtFt2iy2y7sQRusM/DrciTmV3HyvH5ebJrYte7+vVrkjdzmDy6RCR3/25ZnN2yjq5GqepwA0Z/envWgYgXXEIANjCo5cwepwf1HcwhiMdliJBLTGOzdRBQcywcUL12xm6s4/kCbMOtkoqiffJ2eY399g7X75Vvt/qWiNyUz27WzUmrBsLDDz9MYVvnZ8ILbiIA4dmnTx/Twha0wucAwhk2NKR5ZCECOiCATQw2M/A3gB+CX/wNAixwv5bPzp+R8tT/S/r+XeOaMVZ5Sv799yVRPZSVsMWqi6nwaiDjJ/cRUDvVY8eOxe24p4Ruly5d4nBYcb/PpMDfCCih27x5c/8IXbN6aTufi6Xztqvd25e3hiamSig1d3/ozkFNfwmVFW0M5WalhkR6hMat/ST0ZVjjsNN62a4Q1hV+9BkCBQUFljjuoR78FvGXhQjohICX/GViybMA2nAr5ciyH0v6jPwoy8NUycp9Tf75iR/Jj/ulVsdMhe9sGWMbBTZecg0BtbO1ygaL+jIzM6WgoCDunbJrILDhQCCAdLlQMevuNxPLhhtAgRvf2KSwjQ8vPu0cAlYLW0W5ErpQT+OUFxYioAsCXhC6FLgJjhYK2wSB42u2I6CEIk4FssO72C5hbjswbMD3CCBpCwrS5+pYYgncADtNNcwqeMfBYE81csNY8QnnEEDOboTyQO1rh7BFT5QjFbyXzR5m7xwCbCnICECljILdrtcKBW49HFPMfO211+p5gpeJgPMIQPipNHgQinYWCl070WXdiSKgvJdhz1XzdKJ1Of0ebbhREPeCnSAK2bzkcwRu3Lghw4YNiyvO1gpIcGYpnLJwvi6TvFiBKOuwAgGY/HDKkDr4wIo6ragjlkqZAjcCYRxEMHfuXOMsW04uEeDwq2sIuO1PwEWoa6xnwzEQcFLjE4OMWrcocGvBUf8XOorUjw3vuItAbm6ucW6om/4EoKFZs2ZG0hd30WDrRKAGAQjdtm3bSklJieBge7dLLIFLG+5d7oBp6og9uxxR3B4IbN+bCGB3+cUXXxg5Zd3sAfwZPv30U4GKmYUI6IIA5ms4EI4dO1Z7Bz+qlEWMPJ2DBw+W+fPnS05Oji7jiHQQAdHNxOGWHZlDgQg0hAD8DHbt2uV6YoxYO1wKXBHjMG7kR3ZTXdfQYOL94CGAwwSwarcqi5RVCIIu5F22KwbYKjpZT/AQWLhwody8eVOWLFniWudjCdzAq5SVWzmFrWvjkw1HQQA7SQhbnOSjm4kDdrI9e/YY4Ulw5mIhArogALMgzC+6mj0CvcNVTlIHDhxguIMuvxjSYSCAbDqDBg0yQh50hQSL1YsXL7q6m9AVG9LlHgLKc3nVqlWupCblDjcK75WT1DvvvENhGwUfXnIPAbU6R3yhzgUHg2M3AZU3CxHQBQFohCBsn332WYGmSKcSyB2uimkcPny4oRbTiSGkJdgIHD9+3JgovKJ1UbsJLFx1CMkI9uhh78MRwML14MGDjudc5g43nAsisnbtWiNHMlLksRABXRDAahyrcqzOvZJ0BbsJ2Jlhb6Y9V5eRRDqAgNIQKY2RDqgEbofrtR2EDoOENDiDgBfstvUhQXtufcjwupsIqDA2JzUw3OHe5bgXdxBuDla27RwCyg6qVuXOtWxNS7DnIlwIccMsREAXBFq0aGFojHTRwARqh4vUdD169KhWNegyKEhHsBGAHRSp6bwe16rsubrFDQd7dLH3QADxuSizZ8+2HRDucEWMlTdW4KNHj7YdcDZABMwiALsnUiYirlW3eFuzfVDPgf5Zs2YZ/VHX+JcI6IAA4nO3b98uMCm6WQKR+AKqZJwAhOwjXnFGcXNQsG3nENi8ebPhwOeXlKLKEVGpyJ1Dki0RgfoRwLwPOy6cEt107guESpmq5PoHIu+4h4BSwe7evVtga/JLUSry69ev+6pffuFPkPvhhGo50CplZJOiKjnIPzF9+w5VMlSwfhK2QBuq5a1bt8qiRYv0BZ+UBRIBt1XLvlYpQ3UAgKlKDuRvS+tOK5WrUsFqTWwCxCGpDL2WEwCOr9iKAFTLiHOfN2+eK6plXwtcJLgYOXIkM+DYOoRZebwIwKcAu78ZM2bE+6pnnsfEhoUufCfctJl5BjAS6hgCvXv3NmQC/CecLr614WJ1jdgrr6TIc5rxbM89BGBHgtrVqzG38SCHvjZt2pRHX8YDGp+1HQEseu+//35bQvECacNdunSpYR+jV7LtY5cNxIEAFoIITwhKeNpzzz1nHJWGfrMQAV0QgN8E/AzeeOMNR0nypUoZjlJXr17lwQSODiU2ZgYBeMzPnz8/MOFpmNjgGLZmzRoz8PAZIuAYAsrPwMnYXN8J3HBHKcc4x4aIgAkEkPawVatW4peYWxNdNh6BYxh2uFgIsxABXRCA9hN+FHCgcqr4TuDu2rVLsrKy6Cjl1AhiO6YQwEIQDkR+dpSKBQT6DTMPCxHQCYGBAwcaskJFDdhNm68ErvL+hAqLhQjohEDQF4JOT2w68Z606I3A5MmTjagBJ7zpfSVwN23aZHh++i2RgN7DldQ1hAB+yAgDevHFFxt61Nf3nZzYfA0kO2cpAp07dza0olgU2118Exak3LyZTs7uIcP640UAZ8WiTJ06Nd5Xffc8nMYGDBhAh0bfcdbbHYL8GDZsmCVhpLHCgnwjcDmpeXvA+5V6LgRrc5bx8bXx4Dd9ELBKhvhe4HJS02fQkpLaCFj1I65dq7e/cZfrbf75lXqr5IjvBS4nNb/+BLzdL6t+wN5GoS713OXWxYRX9EAAsgSZ0ZLJAudrgctJTY+BSirqIrBx40apqKig7bYuNMJdbhRQeMl1BCBPkrXl+lrgcnfr+hglAVEQgGfy4MGDxW9n3UbpakKXuMtNCDa+5AACkClpaWkJO/bFErieDgvCpIZdxJgxYxxgA5sgAuYRQIgBTqpiiFp0zFQoxtGjR6M/wKtEwCUEkAkOYXx2xOV6WuByUnNpRLLZBhHAD/bxxx9v8LkgP4CFMrNPBXkE6Nl3OxeDnha42N1yUtNz0AaZKuQM7tWrF9OLNjAIcC4pipPJ4xsgibeJgIGAXYtBzwpcTGpIBI/VCAsR0AmB9evXy4QJE3QiSVtapkyZIsgQx0IEdELArsWgZwXujh07OKnpNEJJi4EAnIFOnDghyB3M0jACgwYNkvz8fIF3KAsR0AkBLAY/+OADS0nyZKapy5cvGx5kBw4cCMy5opZynZXZhkCyHo62EaZxxVbEPmrcPZLmUQTgNNW4cWOJN11wLC9lTwpc/kA9OoJ9TnaiP1Cfw9Jg99QCurCwsMFn+QARcBKBRBbQsQSuJ1XKcJbKzs52Ene2RQQaRODgwYOyYMEChgI1iFTtB9q0aWM4mfGA+tq48Jv7CCBECPLGquI5gas8QPEjZSECOiGwefNmI9mFTjR5hRY4mcEvg4UI6ISAcsq1ypPecwIXdlt6gOo0JEkLEIBaVAtnqcpSydu2SZaNHyoz867VZU5lqfxh2XhJS0mRlJQ0+d7Mt+VI+dd1n3P4St++fY2YXDpPOQw8m2sQAThPFRQUNPicmQc8JXDxY5wzZ47gx8lCBHRCIC8vL6mE55b0papY1v3jXNmw9VcyY+P1ulVWXZAdq/NEfrJCykIhuV22WX7y2RJJH/OWHKmsqvu8g1fuu+8+WbFihRQVFTnYKpsiAg0jkJ6eLi+88IIlmac8JXDxY4SNDD9OFiKgEwLbtm0zUjm6SlOjrjJx5/vyf16dJjlRCKn69LJ8+4mJ8v3OTY27jVIHyktzpklO/r/K+4Xuh+VkZmbKypUro1DOS0TAPQSQnnXGjBliRRpSTwlc2sjcG3RsuX4EoE5G0d2voFHHgZL14DdrdaTRA+2ld2qtS659QbKBsrIyQz3vGhFsmAhEQWDEiBECc2ayxTMCF+pkLWxkySLO932HANTJjz32mHf71XiAfKfLnV2v253AOaTAk4UI6IQAzJgwZyZ7oIFnBC7UyckcCqwT80iLvxCAOtmbYWpVUlGUL8efGyc5ETtftzgEtTLwZCECOiEAMybMmcmqlT0jcKFO7tOnj048IC1EoFr9qbs6OSqrKotk1YaWsvC5dGkS9QHnLyq1Mr2VnceeLcZGAOdbJ6tW9oTAxTZ+zZo19E6ONh5qhXmkSNr41+UPpRXRnuQ1GxDwrjr5phxZvUtavDJB+jXRaxqAJoveyjYMVlaZFALdunVLWq2s1y+tHjiwjad3chRwqi7ItpdGyfhPsiXvy9sSCv1FjoyvkIVZiySvwt0wjyjU+vISskv17NnTY337Wq7s+Dc5OXyaTOyqh+02HEColaHRYiECOiEAb+XJkydLSUlJwmR5QuBiG49YKJbaCFSd2S//su5v5OnxP5Suxi7lm5Ka9aQ8/cgB2VPkfphHbWr990058qmjvLzRw6+lPG+dvP+tH8vT1cK2Qoo3vC35mizSunTpYmi0knVQ8QY/SKWXEBg+fHhSSTA8IXC3b99OgRtlVN4J6SiTwqPnpFLdryyTkrODZWh6C3WFf21C4PTp0+7H3sbVtwop3TZPxjz632X6o23kHiPbFDJOfVu6bfpPSdNEtQwHFaviHuOChw8TgQYQyMjIkH379jXwVP23tRe4OF80LS2NCeGj8bBpX3liel/JnzFJnl93Uiqrrkjesn3ywKYXJKup9qyN1iNPXdNP83JN8mamyz1dJsleOSJLHm0lKUPXSalhXfharmybLVmjfiX5dVBOlZwnvyudNBoyQ4YMkWPHjtWhlBeIgJsIwDkymVhx7Y/nQ4gAOjh16lQ3cda37apyKfz1LBk5faOUy2hZW7JRJna+V196fUQZVru7d+/mYtAGniKZCH7z0G6xEAGdEMCRfTjUACcJRSuePp7v8OHDAicKlnoQaPS30qxdP5m+dLpkyWaZ9LPFkqdBMvp6qPXNZQgEal7sY6faSTA8KBzjCin9w+syPg1mgBRJ+d5M2XCkXOq6R34t5UfelpnfS5OUlEdk/OuHpLzuQ+EV83McCCA8NVEveo2USNF7vHTpUoETBUs0BCqkeN0vZLmMkOkv/0/ZX7ZXXpF/kUc1SEYfjVo/XTt16pRA7cliHwIjR44U2MlZgAA8y9+W38sP5a2ykIRul8mHP/lMXkl/RpYfuRkGUZVUHnlLxrx8ToZuOi+h27tl/NVfyZjlhTV+HmFP82P8CCA8KFHNi9YCF/ZbuGHzsILog6KqdIu8NKlMMnq0FjCyUer3ZeHvtstSeUtmv18aZeUbvR5ejR8BrHCZiCV+3OJ5A5EJtOPeRazqivzHt38iL32/850kJY1SJeOlV2R+zlFZ/v5RqY68ryqV92dvkYyfPy/Zqd8UafSgZM+aLhnLl8n7pV/FAz+frQcBhAdBu6VyqNfzWNTLWgvckydPSq9evaISzotVUnn5jHwSCUSTDtI3o3XkVX63GAGscLHSZbEPge7duyflEWofZS7U3Ohhycpqayysq1tv1FLa906r/ooPVWf+KO/tfVC6tAnLHda0pwx9+oq8V3Cei/BaaCX+Bf4b0HLFW7QWuMXFxdxF1MvRRtI0Y6RMzyqQuc3yJTEAACAASURBVAvek2LjPNMqqSz+vWzY2kd+NrRD7R9nvfXwRrwIqJUtVros9iEAO+6OHTuSThhvH4U61Hy/DP9Ox7upOb+SMwW7ZW9qJ2n/QO1ToUT+Invf+6OcoS3XEqZB+wINbLxFa4HLXUQD7GySIdM3bZdfPbBJun3rHklJuUc6/+qGjP1goTymSTL6BnrgydsXLlzwWPytJ2E2iEY8bjKZfbzbcxOUV3wse44Pkyk5audbKZdLzok80knaaBJTbaIXnnykffv2CWlftBW4yjuRu4jY47FRaoaMX7xHQqGQ8a9sw7TqA8Zjv8m7iSJw9uxZ6dq1a6Kv8704EOjRo4ecO3cujjeC8uhNObLqt9Jq4U+1y4UdBA4gLCgR7Yu2AvfixYuSlZUVBN6xjx5DAL4FEAQs9iOAPNUIDWQJRwCeyP8m77eYLM/1axZ2o4m06dJB5JMzctkwMYXd4kfLEYD25dKlS3HVq63Axap2wIABcXWGDxMBJxBAqFrbtm2daCrwbbRs2VLy8+vmxgoyMFVXdsvqk5ny84k9Io5VvFc6ZQ6TOukYqq7J+eM3tcsm5nUePvTQQ4LFdzxFW4GLVW3r1vS2jYeZfNZ+BOAw1b9/f4aq2Q+10QIcpz766CM6Tt3Fu6o8T379/r3yj08rYQtHyS2yLv+a8USjTt+VJyMPL0F+9U/6ypOZ7elIaeG4hVoZWRDjKdoKXHiAtWvXLp6+8FkiYDsC165do6nDdpRrN5CI6q52DX74ViWVpdvklTFjZfr0RyXtnrvZplLukW91e18k7W4YUKPO8sTCx6Xwl2/dyTiH/OqLlkvh9JflCaZ8tXQgwHHqxIkTcdWprcCFQRqrWxYioBMCNHU4zw2o7s6fP+98wxq1WHVlu7yUNUqW5JfXpSpnmGR2UvnTG0mTfs/LpsUtZUO/v5GUeybKni6/kE3TMyLUz3Wr4ZX4EIBZac2aNXG99I24nnboYZVhyqHm2AwRMI0AYsMHDx5s+nk+mDwCyOrz2WefJV+Rh2to9OBjsrYsJGtN9eGbkprxvGwoe142mHqeDyWCADIgwryEiBqz0TRa7nCvXr0qzZs3TwQDvkMEbEXg5s2b0qpVK1vbYOW1EYBHeLzOKbVr4DciYA8CiKSBmcls0VLgfv755/RQNstBPucoAvRQdhRuo7HGjRsnlNXHeUrZYtAQiHcxqKXAhedXkyZhuUCDxkX2V0sE/vznPxt08TANZ9mjUjw62ypbIwINIwA5VVlZ2fCDd5/QUuAi6QU8wFiIgE4IIMgdHrMsziMwYsSIhE5ncZ5SthgkBDp06BCXuUNLgYtAd6iRWIiATgjcunVLJ3ICRQtiHol/oFjuic7GK6e0FLgIdGdIkCfGW6CIZEiQe+xu1qxZ4EOD3EOfLdeHAEKD4NdhtmgncJWdzGwH+BwRIAL+RwCHRcRjK/M/IuyhDgjE68+hncClnUyHYUQaoiGAGFymG42GjDPXKHCdwZmtxIdAPP4F2gnc+LrKp4mAcwgwBtc5rCNbijf8IvJ9ficCdiEQj3+BdgIXSS9gr2EhAkSACBABIuAnBLQTuEh6wcO9/TTE/NMXJr3wDy/ZEyJgFQLx5PrWTuBaBQLrIQJ2IBCvk4QdNASxzni9QYOIEfvsDgLI9W3Wv4AC1x0esVUiQATiQIALnTjA4qPaIqCdwKUnqLZjhYQRASJABIhAEghoJ3DpCZoEN/mqbQhcvnzZOIrLtgZYMREgAp5FwKxKWcvzcD2LOgn3LQJIK4ijuHQrSBSD2PXwEs9Rdki+Hpm3HGEOLESACJhDACFrZg+ip8A1hymfIgKOI4CDrXHWJkLl4L2PU7RwsMcXX3xR6wceeaACJgCzp22VlpbKvn37qvtWX92qTiRrR/5YN4SySjDAtK/V7OIHjyFAgesxhpFc/yGgdqnYmSqhqvKzQpgiLh2hchByOTk5BgCrV6+2DQhVtxL4aEjtmjdt2lQt8Pv372/s+iGMH3jgAWOnbKcgRt08wMA2trNiBxCgwHUAZDZBBMIRwK4SAgwOgoWFhbJjxw7j2D8ILiVUX3vtNXHbM7dFixaCfyhKkD722GPGdwhlJZDRl6KiItm8ebOx8548ebL06tXLeKd79+48iCSc+fwcaAQocAPNfnbeCQSOHz8uH3/8sSFksXNVAmnw4MEybtw42b59uxNkWN6GEshKGKMBCGIsKM6fP28I4ZUrVxq79pEjR0p6erpQAFvOBlboIQQocD3ELJLqDQTg0Xzq1CnDNqoE7KBBg2TMmDGiw87VbhQhgNVOHW1hJ3z69Gk5duyYKAGMhUafPn2kb9++ru/k7caD9RMBhQAFrkKCf4lAEghgV3f48GHZtm2bsaODQIGTTxAEbEOwYSc8cOBA49/UqVNFLUgOHDggmZmZxo5/9OjRxg5YqbAbqpP3iYAXEaDA9SLXSLMWCEDI7t27VzZu3ChI7wb75ptvvkmbZQPcgZcx/sEBbNq0aVJSUiIFBQUyd+5cw/ZL4dsAgLztWQQocD3LOhLuBgJQj+7cudPYyaJ9CFnsahmqkhg34BjWu3dv4x92v7B3RwpfqOPxHEKWWIiAlxGgwPUy90i7IwggbOfo0aOyZ88eyc/PNxyduJO1B/pw4Xvo0CGB2nno0KGyYsUKwwNahSzZ0zprJQL2IqBdakd7u8vaiYB5BGBrhGCFN/H+/fulXbt2RhgPdmLc0ZrHMdEnYfedPXu2XL9+3VDZox54O0ONj0UQCxHQAQF45OOIPjNFS4HL4HYzrOMzdiGAnVVubq6hLm7atKns3r3bCHf53e9+Z1eTrDcGAnCkUvG/8+bNM8KNkO0KiyGo+FmIgJsIII8yfDjMFO0E7oABA+TcuXNmaOczRMBSBCBosYNCKA88jKHOhLcxPWcthTmpyqByVrteLIaGDRtmLI7gwMZCBHRHgDZc3TlE+mxFAKrJXbt2yaJFi4w0hdhBYVJn0RsBLIKwGIJHM/gHjQRif7FQgiqahQjoiIB2O1wdQSJN/kMAghbexbDPIn72nXfekSVLllDYaspq7GCRoSuywHsZ6mZk64KwhXYCWgpoK1iIgBMImD2aD7RoJ3BxygkSuLMQATsQqE/QhqcnrK9dTPhUXdaHjv3XmzdvHrMR7GwheHHgAwTvM888Q37FRIw3rUAAucSRB91M0U6ljLM5w48LM9MJPkMEzCCAXQ8mYghX7GjNCNnwehua8MOf5Wf3EFBZrZTzG/iMxVK8/HavB2zZrwhoJ3D9CjT75R4C2JVC0OJc2WRttPSgd4eP8YReKAoheJGrGTbesWPHGjZf5LOmE5xCiH+tQCCehCzaqZRbtmxpJBewAgjWEWwEEDKycOFCY7KFcw3Ujck4RNGD3r3xFE/oRTiVysYLj3MUeDXDds843nCU+DkZBNasWWNae6KdwMXq86OPPkqm/3w34AgoO+39999vJKjAZKsObg84NJ7tfrJ+HRC8SFgCYQsnuaeeespII+lZQEi4JxHQTuACxf79+zOg3ZPDyX2ioT7GZIpJ9dKlS4YaEZOtFaV169bGofFW1MU64kPg4sWLph1TYtWMDGHwRodj1bPPPmtoQJg8IxZivBcLgfq85+t7R0uBm5WVJdeuXauPZl4nAnUQwK4WmYdgq5syZYoxqVqdfrFVq1Zy8+bNOm3zgv0IxGMnM0MN7LvQfGCMQM2MdJEsRCARBOJxptRS4DZr1sxwcEmk83wneAjghBnE01ZUVBiTqF3qY/oXuDe24rGTmaUSmg8kz4DH+sqVK43kGdztmkWPzwEBhASZzaOM57UUuF27dpXPP/+cHCUCMRHArhZOUVANrlq1ykj5Z5X6OFrD9C+Ihor91+wWgggXevfddw2VNXe79vPTby2YzaOMfmspcJH8ori42G98YX8sREDZalElVIPJeB/HQxaTX8SDljXPwrwEm6udJdpul57MdiLuj7rhK9KhQwfTndFS4CL5BW1lpnkYuAc3btxo2GoxCSORvZ272khwYa9hLG4kKvZ+TyQGN1GK1G4XakKYKWCuYCEC9SGAhT9OrjJbUkKhUMjsw3Y9l5KSIuFkYGWJToRfs6tt1usdBKBanDlzpkHw4sWLXUlggLASFHVcnHfQ8y6lWGBB6+U05hC2MFcgnAi2XhYiEIlApOzC/WjX1Hta7nCxY2FokGIR/wIBTH6wrw0aNMg4m9atbEEMDXJ+PMaTq9ZK6mCmwFnIBw8eNPIy221LtpJ21mU/Atjd4sCMeIqWAhcdQGgQYu9YiAB2lcoxyu2dBkKDCgsLyRQHEcjPzxd4iLtRsLBbvXq1sdDDgo8qZje4oGebSBWbkZERF3HaClycvsCD6OPipe8ehmkB55wiFy6ErlOOUbGAhI1vx44dsR7hPQsRwK4Smefc0miormCh9/rrrxsLP2VWUPf4N5gInD17VhBRE0/RVuB27NiRnsrxcNJnz16+fFlefPFFQUz2G2+8YSQo0KWL9FR2jhNOeCib7Q2SZUDYwqaMJCv0YjaLnD+fg6kjHg9loKCtwG3Xrh1Vd/4cpw32CrYROMgMHz7ccS/kBokTkV69egk8Z1nsR8At+219PUNmKsTswtyFBSGFbn1I+f86TB3xJL0AItoKXAxsqO44oP0/cMN7iDNMkZ4R6junvVLD6Yj1GWplLApY7EcAcY7QdulU4NSJfMxYeCF0CNoYlmAhoHger6lDW4EL9iHOsqSkJFicDHBvoaqbNm2aobaD+k7Xgjjxffv26Uqer+jCLqJbt25a9gnhQvPnzzcWhlyAacki24i6cOGCjBw5Mu76tRa4OH/0448/jrtTfMF7CMAmhvAL2MisPnTAajSU4xS1L1YjW7s+FYYT7y6idi32fkPebmhjunTpItDOsAQDgWPHjsXtMAVktBa4MEjDhsPiXwQgtJAP+cSJE9o5R8VCndqXWOhYc+/06dMJ7SKsad18LdDG4ChIaGcodM3j5uUnMV8hkibeomWmKdUJTMbMOKXQ8N9f8BeOJyjwRHYyRWOyaGInXllZyQxEyQIZ431oPaBNsOv0pxhNJ3QLdj34HTAzVULweealhuSS5zJNKeQxATMEQ6Hhr79K2MLxBIkFvCRswQmsbqEC17lUXdkmk9KekHWlX0WQ+bWUH3lbZn4vTVJSHpHxrx+S8qqIRzT4Cjt59+7dNaDEHAkwhWAhhoUC/rH4EwH4FSV6mIbWKmWwC6n84KnI4h8EwoUtdgNeLNh54YxW9EXLUnVBtv/iVVlXHkldlVQeeUvGvHxOhm46L6Hbu2X81V/JmOWFUhn5qIvfYb8tKyvT3p4fCZESulA5UuhGouOP7/Argn9RIkV7gduzZ0/tdxKJAB/Ud/wgbBXvsMo9evSo+qrR35tyZPlSOdSyp6RGUlVVKu/P3iIZP39eslO/KdLoQcmeNV0yli+T9+vshCNfdu67V+y30RCB0IWJhEI3GjrevwYtRiL2W/Rce4EL7z+tdxLeHz+O9cBPwhagYZULb0W9CnawG+UNGSvTh7arQ1rVmT/Ke3sflC5tmtTca9pThj59Rd4rOC+6aJZxxnF6enoNjR77BBMJha7HmGaCXKV5gYYrkaK9wMXA1XcnkQjkwXzHb8IWXETicu3icSuL5DdviLz4XLp8q85Q+0rOFOyWvamdpP0D34y4+xfZ+94f5YwmEnf79u2eFrgAVwldlQoyAnB+9SACRUVFSXnOay9wwZMhQ4ZouJPw4GhxiWQlbB9++GHDg9MlMixvVsULq6wzljcQd4U35chvNom8OE76NYn2066UyyXnRB7pJG2i3o+7QVteQBKJtLQ01w8ssKJzELpQQULoMmTICkTdrQMCF9nFEi3RfpWJ1mXbe1AtYcCyeBOBtWvXGoQjTtFvBYtBPY7rgyr532Rrh2kyvV8zT8MMJ0ld03omAqxypGKcbiLo6fMONg5z5sxJKvOZJwQuMs1gxcuzKPUZfGYpgaemSmqB1b7fSmZmpnF8oOv9qiyS1VtT5fmR7WI4ZjSRNl06iHxyRi5XaqI7jgIcdoTZ2dlR7nj3EoWud3mnKEc4EMJUk8l85gmBiw5jxcs0j4r13viLiRM2Tq8ltYgHXZzRiwWFSkMYz7vWPVslFYXbZemvRkqbe1IEgfcpKffItx/9lZTLZpnU5T5JGbpOSqvulU6ZwyQnsuGqa3L++E3JefK70snlGQHqeS+GA0VCGu07hC7SQGKnq48ZIhqlvBYNgYKCAhk9enS0W6avufzzMk2nseLFBM7iDQRgr1q0aJERi+jHnW04F3A4OWw77pVG0jR7oZSFQhKq/ndb/rT/FUmV0bK25M8S2jNROjcSadTpu/LkIwdkT9GNGnIry6Tkk77yZGb7GLvjmsft/JSXl+fr7F1IA6lOwnJ3kWYnF/1ZN8yayXrOe0bgKgcVnsqh/2DG6h2q1nfeecdziQsSQRd93bx5cyKvOv9Oo87yxMLHpfCXb0le+dciVVckb9FyKZz+sjzR+V7n6YloEYtq4OnnAqGLhC8zZ87UN3GKnxmQQN9gzkRWvGTUyWjWMwIXxEKtvHfv3gTg4itOIYBVO/gE9UuisWpO0WpVO3qolc32ppE06fe8bFrcUjb0+xtJuWei7OnyC9k0PUPCInPNVmbpc0qdDDz9XqAVgdf+q6++6veu+qJ/VqiTAYTWhxdEcgo/SEzmeniFRlLH7yr8B+k4MaEEqcA5DI59GJ8siSGgIhGCMnaC/HtJbIS48xb4hEN0rl+/bmqH69nDCyLhhVoZ23p6K0cio8d3hP80b948cMIW6EMNqgSGHtzwHhVYtPjNOzkWF+DbsHjxYsPPgTG6sZBy9x7StyL5UrLqZPTCUyplEAwvsQ8++MBdDrD1OghA1Q+P5Ndee63OvSBcUGpQ+hgkxm0soqEhUL4aidXivbcwicPXgZ7L+vJux44dMmLECEsI9JRKGT2Od3tvCUqsJCYCUPW3bdvWOIQ7aBNmODDY4VZUVPgqm1Z4/+z8vHDhQsMD1Ctn31qNBZzFdu3a5esQOqsxc6I++KQMGzZMkNvbbLSFb1TKABidXrBggcthGE6w2httYAGknKSCLGzBrR/96EeGWhmYsJhHAJMaMvjA9h/Ugt8QzDEIGWLRB4GdO3caJjKzwrYhyj2nUkaHfvCDH8jKlSsb6hvvO4AAJoiRI0cKQh2CXqAezMrK0vTIPn25k5+fbyyirZrU9O1pbMpgjsGhDbTnxsbJybvwK7BS6+JJgavsZXSecnLo1W0Ldlt4jPsxR3Ld3pq7AlvP0qVLzT3MpwwEoIp//PHHA48GFhy05+ozDLDwgZOuleGNnhS4YMmUKVPoPOXi2ITddujQoYHIJBUPzGqnT+cpc6ip3ZyVk5q5lvV8CjjMmjUrsM6HOnEFzlITJkywlCTPClzYe6B+YXo0S8eD6cqg/tq6dWvgvErNAIQ40i1btph5NPDPYFJDyAVLDQIqlpupbGswcfoTNhQwdfTt29fSpj3npRzee+jXUZAmjcU5BJRH5erVq51r1EMt0ZPeHLNUIpt4PEDN1ez9p5R3LFTM3P07z89kEtnE8lL2tMBVg5I/WOcGpJokd+/ebUkguHOUO9sSF4MN453MpNZw7d5/Aj4ScA599913TYekeL/X7vcAcuX+++83nVkqkmLfClx0FPF7Xbt2ZUq9SK7b9P2ZZ54xko9Y6blnE6muVsvFYGz4k53UYtfun7u5ubnSo0ePQGZvc4uLycbTxxK4nrXhKmbAuxHHwDH2USFi319lU6KwbRhjhAjBlotkBix1Edi0aZOsWLGCWpK60NS6AgcqaAKgWWKxHwHIEeA9ZswYWxrztEpZIYJV4IABA7jLVYDY8FftSC5dukRHKZP4wlN57NixcWWpMVm1px9TY8lsMnhPd9YC4ukzYQGIJqsA1sXFxTJ79myTb9R9zNc7XHR38uTJ3OXW5bulV6BFoFdyfJDC2QWJMLjLrY0bd7e18Wjom/Ja5tGkDSGV3H3sbjHP2RkT7nmVMiDmxJbcQGvobcRKYrc2fPjwhh7l/QgEuBisDQh2ty+88IJtKrvarfnnG0Kn5s6dS9OZjSzFwhgLZDu9wn2hUgYPqL6zZyRi1Td48GBZtWqVqAxf9rTk31pp8qjhLb23a7CI9xOxixcx88+rec6KMKxYKmXfCFxAy4nN/AAz+yRsGocPH5YlS5aYfYXPRSCgQqmCHr5G223EwIjzq5VCIc6mff94sp7J4QAFRuBylxvO9uQ/c4JMHkNVA3cnYnh/Ag8mqlGjIv6/XADHj1lDb1g9zwVG4AJYTmwNDS/z9xHjjCP3EN7CkhwCVv+ok6PG+be5GLYOc5zOBZuuytttXc3BrMlqmREogRv0ic2qnwwnSKuQrKkHaiuol5MJOaipzVufaO6xjl9wYsSJVMglz5IcAnbMc7EEri+8lMMhR8IBhK/AvZslcQTWrFljnFoS9DNKE0ew7pujR482Jkn8yINUcIwm+kwvd2u4jp0tPGmhXmZJDgGn5znfCVzAjx82TnoI2sSW3NCreRu4cYKswcOqT1i8zJ8/33Dus6pO3euBo8+8efMMFSgXb9Zxi+FmyWOpwh1VnHPyNTZcgy8FLn7Yr7/+eqAmtoZZbf4JrPpgI+IEaR4zs08iLWarVq0kKEkMENuI3RjtjWZHiLnnmHvAHE71PYWF4LRp04zFYH3P2HHdlwIXQFHtkthwUbtbTpCJ4WfmLZXEAP4Gfi7o36hRo+TFF1/0czdd6xt3uYlDv3nzZiPJhdO5BXwVhxsJPxxU2rZtm/AxS5H1BeE7nFtGjBjBHYnNzIZnZEVFha8dqDCWeNKNvQOJzmjx46vi4u06YjRQTlPh8COkhQ5U4YjE/szdbWx8rLw7adIkw4EKDkV+LMo+BkcxFvsQ4C43fmxfe+01wyEUDrZOF9+qlBWQcKCCIAmKzUz1O5G/sN1OmTIlkVf5TpwIwD6OdJlwKII9yU9F2ceQnYx+APZyVtlyDx48aG9DPqldeXY76SgVDp3vBS5+8PjhI/G3321m4YyN9zMWJfDsHjRoULyv8vkEEYD9KCMjQ2BP8lOBwyKSM0AYsNiPAHa5K1eutL8hj7eA+R/hoq+++qprPfG9wAWy+OEjnRxjc+sfZ9AA4LBr7kjqx8iOO88995yRHQ0LHj8UqMiRkAEeoCzOIKAWNlDjs9SPwMyZM405DqZGt0ogBC7AhS2JquXowwwrPxyZxsQE0fGx8yrsSFAt46B6r6uWQf+zzz5r9IcLNztHTd264fm+fv36ujd4xUDAbVWyYoOvvZRVJ9VfCFxMbADfzVWOokeXv1aelKFLn7xGB/JWo3g57SM8Zh966CEeTuDS4IN5worj5Vwi37ZmVbTKpUuXHJn3A+ulHMlBqF6gNoWXGssdBLArQYgKbG4s7iEAFSxUsV5VC8IkgQUtvK9Z3EEAcxudQ2tjj/kN8/2ePXscEba1W6/7LTAqZdV15Z2GXR2LyNGjR40AcO743R0NUMFidwLBixW5lwroHTp0qLFwoyrZPc5lZWUZpiE6h9bwYO3atdK8eXNBhjcdSuAELkBfvHixMTn4NQYynoEFuw8SXbC4j0C4BsYr9lzQCYdEXXYQ7nPRPQrgD7BgwQIj2sA9KvRpGdoibKx00mgGUuAqRxU4eAR5NYidyYkTJ5hVSp85QpQGBitzLxSEAMF2qMsOwguY2UnjD37wA0PI2NmGF+rG3AZtEbRGOmldAilwMWAQA4mVOVzFg1ry8vJ84OBSJZWl+bJtyzIZ32m25FVURWVnVXmhbJg5VODQkDb+LSks/zrqczpcfOONN4xJU3d7LuyFhYWFHgkBqpDSP7wu49NSjDGQ8r2ZsuFIudQZLZWl8odl4yUt5c5zaeNflz+UVugwLEzRoHID+yXMzFSnIx5SdlvYtFXIVMQjrn0NrMAF4uPGjTOAh9NQEAv6nZ2d7emuV5Wul3987f/I1hdnyMZb9XSlslCWj/kfUjJ0ndwO/UWOjL8mM8e8JUcq60y39VTg7GUv2HO9Zbf9Wq7seFt+Lz+Ut8pCErpdJh/+5DN5Jf0ZWX7kZg1zqy7ItpdGyfhPsiXvy9sSMsZKhSzMWlTvQq7mZX0+YV4LsvOUstsqbZE+nBGRkAbFTTJu3boV6t+/f6igoEADJJwj4dixY6HJkyc716CtLf05VLJ2dEhSXwnt/9PtiJbu3EvN3R/6U/Wdq6H9ud8N5aw9HYp8uvoRDT7s2bMnNGLEiBDGqE7Fc7+Z2+dC//7vF2vz+vbp0Nqc1FD4uLhdsjaUI/1Cufuv1sBtPPfd2tdq7mr56fr168acptu4cQIsHX4zseRZoHe4WPlgN4G43MzMTCOsQavVkI3EfPDBB0YyEBub0KPqqvNS8N5ReaRLmjSppqiFpA8dLJ+890c5o+cm16AUdtEhQ4Zodbwd1HU4bg+7KM8c4djoYcnKaiu1JrtGLaV977TqEYEPjR5oL71Ty6Tw6DmpVHcqy6Tk7GAZmu58ontFQrx/4aPSq1cvIwIh3ne9/DycYJHCF5o7ney24ZjWGoPhN4L0GSExBQUFRlIMqMr8XjBpzpkzR9LT0/3eVak680d5b28z6d2+Ze0JFz3fu1sKznylNQYqrlUXs4dS18H/wfvlfhn+nY41C7GmfeWJ6X0lf8YkeX7dSamsuiJ5y/bJA5tekKym3poqkVnvwIED3meRyR5g3lZZznQOcfTWKDIJfiKPYbWOSQQu5BBIfi6IvUXCc6yE/V2qpPLyGflEOkiXNjX7Wy/1GSt15UTltl0OIRbwatcpzCJhXlZ8LHuOD5MpOeE732bSb/pq+XB5X/nDpEfkW/dMk/NjfyHTMlLrLtYSbtiZF3EICRbVfp/LgCb6iLl7/vz5hjOsMwgn1goFbhhuUJNBFQOVmZ8LVr48p9Q7HFZmD6jLKzk08AAAIABJREFU3PJcRrvYZeOkFV3VdeY5elOOrPqttFr4U+nXJGIKbPS30qxdP5m+dLpkyWaZ9LPFkqexR3t9fQaPEJOLxbWfC4Qt5muYXrwQmhYx2vzMGnN9002FZ45q809hgAZFnSzSSJq06SSPyDkpuVxtlTMPlkZPQk2GmEL4Gjht9oBtDDGN/shBXiWVR/5N3m8xWZ7r1yyCwxVSvO4XslxGyPSX/6fsL9srr8i/yKMae7RHdKDWV5iM/K5WRhw4Mkl5xcRBgVtriN5xooIKD6ozXexmESQm9bWkpCQg6uQ7MDXq9F15MudvIjD7Wj47f0bKc4ZJZqd7I+7p+xUxhfA1QLiDU0JX2cYwselsGzPLtaoru2X1yUz5+cQeNbbbuy9XlW6RlyaVSUaP1oYKuVHq92Xh77bLUnlLZr9fWjdm12yjLj0HgYvFtV8L5udPP/3UUyYOCtwoozHcbqaOdYrymCcvYcIOlDq5UXvJfPJBeXvPx1KTvqBSLpdckZwnvyudPPYLgK8BhJ8TQhfCFu2gPc94JMf4VVaV58mv379X/vFpJWyrpLJ4i6zLvyYiyt4fUUGTDtI3o3XERW98hY8GfDX8mMIWwhabImyOPGXicCI2qqE2YsUtNfSunfcvXbrkuxhdxByjX/4qseJwQ6HQlx+Glmb9MPTK/suh26G/hMr2zwtlZS0PFX2pcxRubA5t2LDB1lhLf43926EvS7aGcrNSQ5hrav8bHVpb8uc7YBvjJDWUOm596LQxNm6Hvjy9PjSu4/OhrZf/Epshmt7dunVraMWKFZpSlxhZdo/9xKiqeSuWPAt84osamKJ/8tPEg74gkYKvyp/2h3JTwyfR1KgJLW6XFYSWj+sREkkNZeVuDBWVeXMCDecdJlIkL7E6wYEa85jY/FBuX94amlhrjISNl5y1oZKwddftsg9D63NzqoVy6rjlob0lNSlTvIaH337zSFCk+6YhlsAN1AH0iSqC/KJag3q8rKzMMw4GifIrSO9ZrVpTYx0e+15xRAkSvxPpKw6X8IPDGzzlveC8xwPoExmlYe/AWQQDFsx2KywjjJyEPx4+fNjwck24Ar6oHQIQiiqULdmYSwpb7dhrCUFYPJ06dcqSutyqxCvCtiF8POYy0lB37LvvB6G7dOlS6dKli30gsWZXELBC6FLYusI6Rxrt06ePFBUVOdKWHY2ozY4fdukUuHGMkHCh63bWnzjINh7FcV3wWPSUR1+8nQzw80roDh48OO6QISVscZwZ1cj+G0TdunWT7du3e7JjMJksWrTIFypxMOAbnuSCi0QroYtwCQgxr0xQJ0+eFKR7Y/EvAhiLTZs2NUJ5zO4GlLD1S+iPf7mbeM8QHpSWlmYsxDB/eaUo/wSzY9kL/eIONwEuYdDu3r3bU8kxYL/t2bNnAr3lK15CAPY6Fafb0CHksIv5Kc7WS3xymlakPvSKHRe+CErYIs7WS4uEhvhKL+WGEIpxX+XxRGoxJHTXWV0Lz7nr168H4MCCGAwL0C0IU6SBRKKTaEkrlBMKd7bBGBQwgcGOO3v2bK07rOZUEOm5pBZ3kaWXsk1DTGWkatasmZFAO1kvUZvINFRJI0aMoLC1C2AN64WQRRpPFUYRTiJO/VHXownj8Gf52R8IdO/eXQoLC7XuDMwbOIgAXverV6/WegOTKJBUKSeK3N33IHSxasQgScRhJcnmTb0OVRJi8ViChQByL8P+BQELFZ1S1R08eNA3TijB4mjivYVadseOHdoe16d8CeBn4hW/mES4QYGbCGpR3sEgUbYzqOt0KrDlde3aVSeSSItDCGCifffdd43dDcJDzp07Z6jq/GQXcwhKzzczY8YMuXTpknb9wHzZtm1bY/6ED4KfCwWuhdyFeg5HqEFdh12FLuXixYvSo0cPXcghHQ4jgEm2uLjYcJqDTRe2fJbgIYA5ANEKOhVoXjBfYowGwbxBgWvx6IMaDx7MUNvl5uZqocJBwgusIFmChwCcZcaOHWvsHt5//32ZP3++MRZ008IEjzPO97hjx47Gwsv5luu2CPPGM888Y0R64MzeoGhcKHDrjoWkryDuDR52Dz30kOt2XdhG4DClswd10oCzgjoIYEJbuHChrFy50rDXqt1DTk6OsZvArkLZdeu8zAu+RKBVq1ZaOE7BxAV/Fz87R9U3gChw60MmyesQcMqui90lnFfcKNeuXRPsulmCgwAWWU899ZTRYdhvI3cP+I5dBUwN8ArF8yz+RwDzAByn3CyYB5XGxc/OUfVhTIFbHzIWXcfOAvaJXbt2uaJihpPMgAEDLOoNq9EdAaiQscCbMmWK4T1fn2YD15csWSLDhw83kl94LVWp7nzQlT5ouxpKiGIH7Tdu3DDmP8yDELpK42JHWzrXSYHrAHewowhXMR8/ftyBVu80AWeZ1q1bO9YeG3IHATWhQYWMBR5Ux2YKMk3B0Q/vQQWtayy5mb7wmYYRwC731q1bDT9o4ROY74YNG2Y4biK+NlLjYmFT2ldFgesQi5SKedWqVfLss886Zj+7efOmwHbD4l8Ewie0aCrkhnqOSRjvocC25uSCsCHaeN9aBKDtgtbLiaL8CDDfYVHn95AfM5hS4JpBycJnevfubdjPKioqDDub3eodeihbyDzNqlIT2rx586ontPpUyA2RjveQwEUtCLnbbQgxb95v0qSJlJWV2U48Fm1YvKHAX4B+JHcgp8C1fejVbUBNbpgo4UBg9+SW6CRcl3Je0QUB2FwxoUE9h92pVROaWhCin9zt6sJt6+ho37694SxnXY21a1KLQOxqsXjDIo7zTw1GFLg1WDj+KXJyszo2ErtnnIHL4h8Ewm21Sk1n9YSmFoSYMLEoRDw52mXxPgKNGze2zWlKLQJxRCR2tZjfWGojwNOCauPh2jcIR0xs2KkgVMMKxwLUuWbNGsMb1bWOsWFLEMDOAR6eo0aNkq1btxrexVYL2miEot3NmzcbPgc4oB5OVizeRiDWaTaJ9AzzDExXV69eNeYaq7QtidCiwzux8OUOVwcOiRiCFqpBODUgrAOpITHZJVOQxo0pHZNBUI93oflAXC3ONEZaRgg9J4Qteo924OyCUA60P3LkSDpV6TEskqIi2bkFjaMOJE+BWQzhZdu3b7fMtJFU5zR+mQJXI+ZgcsNkikkVyQhgQ0s2PhJOEizeREBpPbB7gGoXcbPIYuZGgcYF7SMBvlIzM2GGG5xIvs1kDzGAoMUCTDlFIZUtNR/m+EKBaw4nR5/CpApnA9jo9u3bZ+wqErHvwhuRAtdR1lnSGOylcKTDzgEaD+wcdLGHIWGB0sRgksUOh/ZdS9juiUrCtS2Yn5Atyq1FoCcAiyCSAjcCEJ2+whaidhXY5SDZN3Y9ZgtS98ErkcUbCEBwQYDdf//9hg0fjic67hyUJgb0oYBeCl5vjDFQ2axZMzl//nxcBEPQwpwQrm0Juq02LgDvPkyBmwhqDr+DXQV2ORMmTDAcq+BcFY/gdZhcNhcnAuGCFq/CpAC7qVN22jjJrX4c9GGHo477o+CthkbrDzgbu7Ky0hSN4YIWqmidtC2mOqDZQxS4mjEkFjlK8CIfKoQudryxVM1ffPFFrOp4z2UEoglaL6rooFKk4HV5MFncfDRBG9T8x1ZCy7AgK9F0uC78KKDiQcHqs2/fvrV2RXBPR95U3XdKDsPmenPQTmzZssXYLWAnO2bMGF/ZwbCQ2LRpk7zwwguyYsUKQxVpRZib64zzCQFweEKJNFfAGQrneCOvNgrmFApZA4q4/osVFkSBGxeUej4MwYtjt/Lz8wWxkllZWcYEHovxevbE31SBT+vXrzcO3QafEErh58UQBC/G5KJFi4wxCc0MJ3D3xzjSLmJBBP8QFPBp586dhh0ecwcWgLo46bmPVvwUxJp3KXDjx1PbN7BzQhgRdhYLFiyQOXPmSCgU0pbeIBAWLnRw4Dbs8EETOtg5HT16tFobg129WhQGYQzo1kfME0iIA8H6wQcfGPMENRHWcYkC1zosPVETJjiVlQi7Ck5wzrNNaR2g8sdkhuPy6NUphrNf+KLwBz/4AXdTDg5Ppe7/9a9/LX//939vnJs8aNAgX2taHITXaIoC12nENWkPjC8pKane9cImAwEcaevVhFzPk6E0DMgSpnazxDo6W5W9EGkjT5w4YSwKEXZCW290vJK5qjQMypyBs2nLy8sFZ9OyWI8ABa71mHqixnDGqx8dYiehaobKGZliKBCSYyWyLeXl5RmZd1ATHFF+9KMf+coJKjmEGn47GobZ2dkUvg1DV+8TsX7vly5dYo71epFL/kb4vBtZG224kYj45Dt2WwgdQtxcZIFaqaioyMhiBZUnhG96errxj1ljItGq+x1OJwUFBUa+67S0NEPIUkDUxSmRK5HCd8iQIZKZmUm1swkwo/2uoy2qlQ1XOU2ZqJqPxIEABW4cYPnlUbM/qvCVMISzEiA9e/aULl260LYjYuS1PnXqVPUCBUcewsM4IyODuzAbfzBK+CJUBU4+amHYvXt34n738ACYjD7++GNDw4JUrlDLRxOy4WwyOzeEv8PP5hGgwDWPlW+eTPRHhfdwKoya5GD3RT7fDh06BEYAY6KHgIUWQC1CsNPq06cPVfAu/UKwezt9+rQcO3bM0CyADAgXaGaCIoCxOFYCVv0+1eIPp4KZdcpLdG5wifWea5YC13MsS55gK35U4T9wHPUH9TN+4HAIwo8beZrN/siT75E9NUC4XrhwQc6ePSuqj3AsUwK2Xbt23E3ZA31StYYvigoLC4049PDF4UMPPeRpOzp+e7C1Iucxfss4xASx9uF9TFQDZcXckBTzfP4yBa7PGRyte5iQkG4vmg032vNmr+HHqiYBeJdC1QcBBcGLnXDr1q2lVatWxpm+OiV1AB7IugWhCtUbDnbAAqJ///5GTGjQdvFm+e2V57ADBk/PnTtnaGiQcOOjjz4yBBSEL0wl2AU2btxYqwWUEqw4vP3zzz83aMdvDMLVrsUtBa69o5oC1158ta09FuOtJFrtEjFhFBcXy82bN6uTHGDSaN68uTHZqaMCMfGp0rZt26TsxJg8VFGTFr5DLY6iJl61KEDbDzzwgLE7T7Zt1S7/6omAEmZYIH722WfGYksJM7XQAuVYbKGoxaLqTTLaGywArl27pqoy2sYXtdhDnnMsVlGwa8UJPjhUAKabli1b2roooMCtZostH2LNu/RStgVyPSqNxXgnKFQTHtrCzhIFp5Soz/iOXWYyRQl01KEmLXzGxIXdDCYvel4ng7A/31UCMXyRphaL6HG4QEwEgXCBjvex0ItccCYj0BOhSb1DgauQsOdvrHmXAtcezLWoNRbjtSCQRBABIuA4AhS49kIea97l8Xz2Ys/aiQARIAJEgAgYCFDgciAQASJABAKEAJwHWdxBgALXHdwdaxV2VBYiQASIgEIAntzKUUxd419nEKDAdQZnV1qB9yNi+ViIABEgAkTAfQQocN3nASkgAkSACBCBACBAgRsAJrOLRIAIEAGFAMKfVIiSusa/ziBAgesMzq60ggw74TGvrhDBRokAEdAKASSmQVpWFucRoMB1HnPHWkQ6OxYiQASIABHQAwEKXD34YBsVyOzEQgSIABFQCCC7G9KasjiPAAWu85g71iLSyVGl7BjcbIgIeAYBnQ4W8QxoFhBKgWsBiDpXgZywLESACBABIICDRnCQB4s7CFDguoO7I60iObo6kcSRBtkIESACWiOALFNuHZqgNTAOEUeB6xDQbjbDbFNuos+2iYA+COCoQkQvsLiDAAWuO7g71iqzTTkGNRsiAtojACdKRi+4xyYKXPewd6RlnBGLMz9ZiAARIAKHDx82zoomEu4gQIHrDu6Otdq1a1f5/PPPHWuPDREBIqAvAjgLt2XLlvoS6HPKKHB9zuAOHToIVrUsRIAIEIEdO3ZImzZtCIRLCFDgugS8U81iNYtVLQsRIALBRgDzwOTJk4MNgsu9p8B1mQF2N4/VLFa19FS2G2nWTwT0RgC+HA8//LDeRPqcOgpcnzMY3aOncgCYzC4SgQYQOHv2rMCng8U9BChw3cPesZZ5apBjULMhIqAtAkjzinSvLO4hQIHrHvaOtdynTx/BGZgsRIAIBBcBHlrgPu8pcN3nge0UtGvXTgoLC21vhw0QASKgJwIqhzIPLXCXPxS47uLvSOvKcerGjRuOtMdGiAAR0AuBU6dOSUZGhl5EBZAaCtyAMB2OUxcvXgxIb9lNIkAEwhFASFB6enr4JX52AQEKXBdAd6PJAQMGyMcff+xG02yTCBABlxHYt2+fdO/e3WUq2DwFbkDGALwTDx48GJDesptEgAgoBGBKKisrY4YpBYiLfylwXQTfyabV2bhMgOEk6myLCLiPwOnTp2XkyJHuE0IKhAI3QIMAdtyjR48GqMfsKhEgAgcOHKD9VpNhQIGrCSOcIAN23GPHjjnRFNsgAkRAEwS2b99O+60mvKDA1YQRTpCBsAA4T7AQASIQDAQQf4sD53lCkB78psDVgw+OUIEfHZwn8CNkIQJEwP8IIOHNkCFD/N9Rj/SQAtcjjLKKzHHjxjHrlFVgsh4ioDkCu3btkszMTM2pDA55FLjB4bXRU/z48CNkIQJEwN8IIBxozZo10rt3b3931EO9SwmFQiG36U1JSRENyHAbBsfaB97Xr1+XFi1aONYmGyICRMBZBPbu3StFRUUye/ZsZxsOeGux5Bl3uAEcHAsWLDB+iAHsOrtMBAKDwObNm2Xw4MEa9rdKKkv3yLLxjwiEU0rKUJm5oVDKq6KQWpEnM9PwjPr3hKwr/SrKg964RIHrDT5ZSiV+hPgxshABIuBPBJQ6uW/fvtp1sOrKbln9e5GfvHVCQqG/SNmHP5HPXhkpY5YXSmUtar+WK/u2ydvlYRdzhklmp3vDLnjrI1XK3uKXJdQi21Tjxo2pVrYETVZCBPRDQF918ldyNv+43PsPA+TB6u3eV1K6bpx0mdtJ9hfPl+ymd29UFsqyUTul7+Z5Ndf0g7oORVQp14Ek2BdwJuaKFSuoVg72MGDvfYyAvurke6VjVriwBRO+KQ+07ySptfhRJRWF22X53jXyywVrZVteacTut9bDnvlSvcbwDMUk1BIE4K28cuVKS+piJUSACOiDANTJJ06cEB3VybFQajw8Xbo0uSuSqkply+L1Ui7lkr/kWRn1aJb8eOY2Ka2MZuiNVate9yhw9eKHY9QgVIBJMByDmw0RAccQ2LlzpyDeHposb5QbUrTnijw3JbtGzdyoq0zcUyah22VStH2V5GaJ5C+ZKj/7TZGnd7oUuN4YkbZQOXXqVEGeVRYiQAT8g8C2bdskJyfHIx2qksojm2RDq+fluX7N6tLcKFX6jXhGFu//SPa/8ojkL98uhRXe3eVS4NZlcWCuZGdny8aNGwPTX3aUCPgdgePHjxtdxHGcniiVRbL6/ebyynPp0iQWwY0elOxZMyVX9sqeohuxntT6HgWu1uyxlzjkVu7Vq5ccOnTI3oZYOxEgAo4g8MEHH8iUKVMcaSvpRqouyI7Vn8rwn/+TdFW221iVNkmTLo90kS5tYormWDW4fo8C13UWuEvAhAkTZP369e4SwdaJABFIGgE4S82ZM0cGDRqUdF22V1B1RfJ+vUu+9Y//rUbYVp6UDesOSUV9jVeWyZl+k+Txzt6Nw6XArY+5Abk+cOBAw6ORJwj5heEVUpq3Q7YsGy+dZuZFmbyuSd7M9LDMPSqDT4qkDF0npd41j/mFgQn3Iz8/3wj3095ZqrJYtr0yUR6d/t/l0bS/qRmL38qRTXK/oVquKj8iO3Ycqc4+VVV+SF5fcFSGvJApTRNGyP0XKXDd54HrFNB5ynUWWEQAEghMk9c2rJcXZ2yUW9FqrfhY9rx9JMqdVMl58rvSiTNCFGy8cWnRokX6O0tVXZBtL42WUUv2RgE1U57MbC93huAN+fB//VjS7kmRlLTxsvzQf8oPfz5dslO/GeU971xipinv8Mo2SqGKuv/++5l5yjaEHa64qljWDc+Wub3fkeLF2WE7giqpyHtTlskomZf94N2JDbRh1ztXzk/6XzLRw+o6h1HWqjn4YcA0tHr1aq3oCiIxzDQVRK7H0WecGoTMU1BJsfgZgb/K/9dmhOTWErYiVaW/lcXHMzydo9bPXDPTt6VLlwr8MVj0RoAKJL354xh1iNuDSgp5lln8isA3JbVzu4jwi6/kTMEhafOzR6lO9ijbS0tLDcrhj8GiNwIUuHrzxzHqELeXlZUlBw8edKxNNqQBAlXnpWDbg/JPQ9qGqZg1oIskmEYAh8zPmDHD9PN80D0EKHDdw167lidPnsz8ytpxxV6Cqs78Ubb9fZakqxNa7G2OtVuMAHa3MAV5LW+yxTB4pjoKXM+wyn5CscvFPybCsB9rPVqAOrlQ/n5ozzDHKj0oIxXmEMDudtasWR7Km2yuX359igLXr5xNsF/Y5cIBgyUACBjq5P8qQ9NbBKCz/uui2t0OHz7cf53zaY8ocH3K2ES7xV1uosh57z2qk73Hs3CKubsNR8MbnylwvcEnR6nELnfatGn0WHYUdacbozrZacStbI+7WyvRdK4uClznsPZMS8pjedeuXZ6hmYQCASS2mC1p93STSXvLpXzJo/LtlCdkXelXdeGBOvlQd3kig+rkuuDofwW72/nz59N2qz+ralHITFO14OAXhQBW0GPHjpUDBw7wR61A4V8ioAECcGqEnwXPstaAGVFIYKapKKDwUmwEsMsdN26crF27NvaDvEsEiICjCEDYMu7WUcgta4w7XMug9F9FzLHsP56yR95GYNu2bXL48GFZsmSJtzviY+q5w/Uxc+3sGnIsb9261Uj5aGc7rJsIEIGGEUDaVaRfhVMjizcRoNOUN/nmGNWI8YM99/jx4461yYaIABGoiwDMOzDzwNzD4k0EqFL2Jt8cpRrCdt68efLuu+/SgcpR5NkYEbiDAJ0YvTMSqFL2Dq+0pLR3797GqpphQlqyh0QFAIHc3FyGAfmAz9zh+oCJTnRBOVBdunRJ2rRp40STbIMIEAERgaMUFrs8XN4bwyHWDpcC1xs81IJK/vC1YAOJCBACXOh6j9mxBC6dprzHT9cofuyxx4y2IXhZiAARsB8BeCUjUoBaJfuxdqIF7nCdQNlHbVy+fFnatm0rVC37iKnsipYI7N27VzZv3kxVspbcqZ+oWDtcCtz6ceOdehCgarkeYHiZCFiEABe2FgHpQjWxBC5Vyi4wxOtNUrXsdQ6Sft0ReO2116hK1p1JCdBHgZsAaHxF5NVXXzWy3iA+kIUIEAHrEFA+Empha13NrMltBKhSdpsDHm4fNqaVK1cyIYaHeUjS9UJAJbjYvXu3ILUqi/cQoErZezzzBMU5OTmSkZEhr7/+uifoJZFEQGcEkCsZR2Li90RhqzOnEqeNKuXEseObIjJt2jQpLCwU7HZZiAARSBwBmGmQK3ngwIGJV8I3tUaAKmWt2eMN4uhR6Q0+kUp9EVCe/2+88QbzlevLJlOUUaVsCiY+lCgCCMrfs2ePTJ06VaAWYyECRMA8AjgcBAkusMO97777zL/IJz2HAHe4nmOZvgS/+eabcvHiRR6OrS+LSJlmCEA7BG/kVatWCQ4JYfE+Atzhep+HnujBpEmT5IsvvhAIXhYiQARiIwBtEOJtZ82aRWEbGyrf3KXTlG9Y6X5HoA5bvHixbNy4UQ4dOuQ+QaSACGiMALyRH374YWOHqzGZJM1CBChwLQSTVYkRzgAHEHgvMykGRwQRiI4AtECffvqp8TuJ/gSv+hEBClw/ctXlPsGJCqt3xBTCRsVCBIhADQLQ/kALBG0QnaRqcAnCJwrcIHDZhT4ilnD+/PmGuoyeyy4wgE1qiQCELbQ/0AIxuYWWLLKVKHop2wovK4fq7MSJE8L4Qo6FoCOg4tWPHTtGJykfDwZ6KfuYubp3DbG5vXr1khdffJExurozi/TZhoAK/ykoKKCwtQ1l/SvmDld/HvmCwtzcXKMfS5Ys8UV/2AkiYBYBJWzh18C0jWZR8+5z3OF6l3e+oRzxhozR9Q072RGTCChhi1hbCluToPn4MTpN+Zi5OnUN3piw48Key8QYOnGGtNiFgBK2OJCAZ9vahbK36qXA9Ra/PE0tha6n2Ufi40AgXNjCj4GFCAABClyOA0cRoNB1FG425gICFLYugO6RJuk05RFG+Y1MxObCcxmp7RCXyAQAfuNwMPtDYRtMvof3OpbTFAVuOFL87CgCSuiiUcbpOgo9G7MBASVskfAlJyfHhhZYpRcQoMD1ApcCSiOE7tq1a5kcI6D890u3kTccqUwZ+uMXjibej1gClzbcxHHlmxYgAFWySo7x1FNPMfeyBZiyCmcRQLrGLl26UNg6C7snW/uGJ6km0b5DAEI3LS3NCJ9AnlkcgMBCBHRHYO/evTJ37ly5dOkSx6zuzNKAPgpcDZhAEu4ggFjF1q1bS9u2bQUp8JgogCNDZwQQT75v3z7jIAIuEHXmlD600WlKH16QkrsIKHsYdr1IGsBCBHRCgM5+OnFDP1pow9WPJ6QoBgKdO3c2dg0HDx6UhQsX8tCDGFjxlrMIwBMZvgY4kGP16tUMZ3MWfs+3Rqcpz7PQnx2Aig6hQiiI18VEx0IE3EQAzlEwe0yZMsVw9HOTFrbtTQSoUvYm3wJFNZyoFi1aRC/QQHFdr87CXrtx40Z55513BBoYFiJQHwKxVMoUuPWhxutaIRBu1x09ejRVeVpxx7/E3LhxQ2bOnGl0cPHixdKiRQv/dpY9swSBWAKXKmVLIGYldRCoKpcjG2bK91JSBAMw5XszZV1eqVSUvi2zt12q83hDF7Cr2L17t5w8eZIq5obA4n1LEDh+/LgMGzZMBg0aZNhrKWwtgTXQlVDgBpr9dnX+phxZ/oykr79HXij5k4RCIbm9aZTcs+cF+XZw+qJ/AAAG2klEQVSX30mnHq0SahgTHg6wHz58uGFLQwwkCxGwGgF4IUOF/OyzzxoqZHrKW41wcOujwA0u7+3r+V/Pyr//5vfS8Yej5CedmxrtNErNkPFzZkpujwzp1eHepNqG4wpsaStXrpTc3Fx6MSeFJl8ORwCmC3ghV1RUyIEDB2ivDQeHn5NGgAI3aQhZQX0I3Dp9QT6vCrvb+NvywH/rK39nQboVqJjfffdd6dGjhwwePFig/mMhAokigF0tnKKQDxleyLNnz6afQKJg8r16EaDTVL3Q8EbiCNyUI8vGSvqMo5KV+6b8y89HSucm9q3tIGznzZsnGRkZ8txzz9GxJXHGBfJN7GqhKcEibtasWRw/gRwF1nWaTlPWYcmaTCHQTPpNXy0fLv++lCwZJVnP/28pLP/a1JuJPNS7d29jt4vYXTi50LabCIrBe0fZatWuFv4BdIwK3jhwssf2bTuc7AXb0g+BRqmSMW2F5K2dKLJxqnxnzK8kz0ahi1OH4NyibLvPPPMMk2XoNyq0oQhJLGCKULZanl+rDWt8TQhVyr5mrw6dq5DiddMke9I6kdz9Urw4W+64UdlLm0qWASE8adIk2uPshdsztUN9vGbNGsFf7GiZxMIzrPMMoVQpe4ZVXie0SiryVsuG0q/COtJUuj7+T/J0qkj51qPyH38Nu2XjR3gyI24XOxjsZKhmthFsD1SNBBYI9YH6eMCAAbJ9+3YKWw/wzW8kUqXsN4662p8bUrRnh5y6XBmVitRR1ngoR608ykXY4+BtCjXz5s2bZeTIkQJVIktwEICdFtoO2PZRsAjDYoyFCLiBAFXKbqDu1zarimXd8GyZ9PXTsn7ZP8vT/VKlUWWxbPvlSzJqyX+RpUXvyMv9mrnWewjbpUuXGjubyZMnc4fjGiecaVgdDp+VlWVkJ+OZtc7gHvRWYqmULYiIDDq87L9CoOrMUTn/s0Pypx6fypa1E+Se9DuZoFLHLZe9JZPk+3eTYKjnnf6LA+3xDxMxVIuYiCl4neaC/e2FL6x42ID9eLMF8whwh2seKz7pIwSgaty1a5dxChEFr/cZC34ePXqUGgzvs9LzPYi1w6XA9Tx72YFkEFCCF1mGWrVqJRMmTDB2wcnUyXedQ0DxD8c3cuHkHO5sqX4EKHDrx4Z3iEA1AkoViQtI74dTYhDfy6IfAvA63rRpk5GOEc5wjz/+OG3y+rEpkBRR4AaS7ex0ogggVSQm8/z8fCOZBiZ0Otwkiqa170XyZsyYMcwOZS3ErC1JBChwkwSQrwcTAeyidu7cacRv9urVy1A39+3bl7teh4cD+IDFD9T+KNQ+OMwANhcXAhS4ccHFh4lAbQSUQ86OHTuqd72ZmZmCHM4s9iAQjjlCuVasWCFIv8jMUPbgzVqtQ4AC1zosWVPAEVC7XiRTQEEShezsbKqcLRoXUBkXFBTICy+8YIRswYmNWgWLwGU1jiBAgesIzGwkaAhcvnxZ8vLyjExG6DuEb8+ePbnzjWMgqJ0sDntHukWo7kePHi3p6em0zcaBIx/VBwEKXH14QUp8ikC48C0rKzPSSCKHc7du3Sg4IngOrE6dOiX79u0z4mZnzJghQ4YMoZCNwIlfvYkABa43+UaqPYoA1M5FRUXGvzlz5hiqUYQYYffbpUuXwDldKQELTLCLTUtLMwRsnz59qC726Bgn2fUjQIFbPza8QwRsRwBHwZ08eVIOHz5s7OhGjBhhCBw4AHXv3t1X9l+oiC9dumT0t7i42BCwABihVVAT+62/tg8eNuA5BChwPccyEuxnBCCAz58/b+yACwsLBd7PyOkM+yV2fz169JCWLVtqr4rGzvXatWty7tw5gXAN7wt29B07dqRK3c8DmX2LigAFblRYeJEI6IGA2hVCCEMYX7x40Qg/+uijjwT2TRSc4YoCYYzStm1b21XTEKi3bt0y/kGoVlZWGjtX0IhFAnbq2KWDttatW0u7du18tVs3gOZ/RCBOBChw4wSMjxMBHRBQghhCL1zggTbEpqqC3XHz5s3VV+OvEtC1LkZ8UQI0/DISTEDQoyiBis+qPiXwGQ8bjho/E4EaBChwa7DgJyLgOwSw4wwvV69elc8//zz8Ur2flQBVD3hBla1o5V8ioCMCFLg6coU0EQEiQASIgO8QiCVwtTmAHkSyEAEiQASIABHwKwJaCNxQKORXfNkvIkAEiAARIAIGAo2IAxEgAkSACBABImA/AhS49mPMFogAESACRIAICAUuBwERIAJEgAgQAQcQoMB1AGQ2QQSIABEgAkSAApdjgAgQASJABIiAAwhQ4DoAMpsgAkSACBABIkCByzFABIgAESACRMABBP5/tU6BvSHlI44AAAAASUVORK5CYII="></p>
</div>
<div class="specification">
<p>A student from the school is chosen at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that are taught in Spanish.</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 number of students in the school that study Mathematics in English.</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 number of students in the school that study both Biology and Mathematics.</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>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {S \cap \left( {M \cup B} \right)} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mi>S</mi> <mo>∩</mo> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {B \cap M \cap S'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mi>B</mi> <mo>∩</mo> <mi>M</mi> <mo>∩</mo> <msup> <mi>S</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </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 probability that this student studies Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies neither Biology nor Mathematics.</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>Find the probability that this student is taught in Spanish, given that the student studies Biology.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>10 + 40 + 28 + 17 <em><strong>(M1)</strong></em></p>
<p>= 95 <em><strong> (A1)(G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for each correct sum (for example: 10 + 40 + 28 + 17) seen.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>20 + 12 <em><strong>(M1)</strong></em></p>
<p>= 32 <em><strong> (A1)(G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for each correct sum (for example: 10 + 40 + 28 + 17) seen.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>12 + 40 <em><strong>(M1)</strong></em></p>
<p>= 52 <em><strong> (A1)(G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for each correct sum (for example: 10 + 40 + 28 + 17) seen.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>78 <em><strong>(A1)</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>12 <em><strong>(A1)</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{100}}{{160}}"> <mfrac> <mrow> <mn>100</mn> </mrow> <mrow> <mn>160</mn> </mrow> </mfrac> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{5}{8}{\text{,}}\,\,0.625{\text{,}}\,\,62.5\,{\text{% }}} \right)"> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>5</mn> <mn>8</mn> </mfrac> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>0.625</mn> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>62.5</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Throughout part (c), award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator. All answers must be probabilities to award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{42}}{{160}}"> <mfrac> <mrow> <mn>42</mn> </mrow> <mrow> <mn>160</mn> </mrow> </mfrac> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{21}}{{80}}{\text{,}}\,\,0.263\,\,\left( {0.2625} \right){\text{,}}\,\,26.3\,{\text{% }}\,\,\left( {26.25\,{\text{% }}} \right)} \right)"> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>21</mn> </mrow> <mrow> <mn>80</mn> </mrow> </mfrac> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>0.263</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.2625</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>26.3</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>% </mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>26.25</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Throughout part (c), award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator. All answers must be probabilities to award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{50}}{{70}}"> <mfrac> <mrow> <mn>50</mn> </mrow> <mrow> <mn>70</mn> </mrow> </mfrac> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{5}{7}{\text{,}}\,\,0.714\,\,\left( {0.714285 \ldots } \right){\text{,}}\,\,71.4\,{\text{% }}\,\,\left( {71.4285 \ldots \,{\text{% }}} \right)} \right)"> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>5</mn> <mn>7</mn> </mfrac> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>0.714</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.714285</mn> <mo>…</mo> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>71.4</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>% </mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>71.4285</mn> <mo>…</mo> <mspace width="thinmathspace"></mspace> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Throughout part (c), award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator. All answers must be probabilities to award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>On a school excursion, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> students visited an amusement park. The amusement park’s main attractions are rollercoasters (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">R</mtext></math>), water slides (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">W</mtext></math>), and virtual reality rides (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">V</mtext></math>).</p>
<p>The students were asked which main attractions they visited. The results are shown in the Venn diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> students visited the rollercoasters or the water slides.</p>
</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">a.i.</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>b</mi></math>.</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 number of students who visited at least two types of main attraction.</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>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo> </mo><mi>R</mi><mo>∩</mo><mi>W</mi><mo>)</mo><mo> </mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected student visited the rollercoasters.</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 probability that a randomly selected student visited the virtual reality rides.</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 determine whether the events in <strong>parts (d)(i)</strong> and <strong>(d)(ii)</strong> are independent. Justify your reasoning. </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn><mo>-</mo><mfenced><mrow><mn>32</mn><mo>+</mo><mn>12</mn><mo>+</mo><mn>10</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>5</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn><mo>-</mo><mn>68</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong><br></strong><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting up a correct expression.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>a</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>6</mn></math> <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>-</mo><mfenced><mrow><mn>74</mn><mo>+</mo><mn>18</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>-</mo><mn>92</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>-</mo><mfenced><mrow><mn>32</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>5</mn><mo>+</mo><mn>12</mn><mo>+</mo><mn>10</mn><mo>+</mo><mn>18</mn><mo>+</mo><mn>6</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for setting up a correct expression. Follow through from part (a)(i) but only for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≥</mo><mn>0</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>b</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>8</mn></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong><br>Note:</strong> Follow through from part(a)(i). The value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> must be greater or equal to zero for the <em><strong>(A1)</strong></em><strong>(ft)</strong> to be awarded.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>+</mo><mn>5</mn><mo>+</mo><mn>12</mn><mo>+</mo><mn>10</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for adding <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mo> </mo><mn>5</mn><mo>,</mo><mo> </mo><mn>12</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math> <em><strong>(A1)</strong></em><em><strong>(G2)</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>58</mn><mn>100</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>29</mn><mn>50</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>58</mn><mo>,</mo><mo> </mo><mn>58</mn><mo>%</mo></mrow></mfenced></math> <em><strong>(A1)(A1)(G2)</strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator. Award<em><strong>(A1)</strong></em> for the correct denominator. Award <em><strong>(A0)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58</mn></math> only.</p>
<p><em><strong><br></strong></em><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>45</mn><mn>100</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>9</mn><mn>20</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>,</mo><mo> </mo><mn>45</mn><mo>%</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Follow through from their denominator from part (d)(i).</p>
<p><em><strong><br></strong></em><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>they are not independent <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>58</mn><mn>100</mn></mfrac><mo>×</mo><mfrac><mn>45</mn><mn>100</mn></mfrac><mo>≠</mo><mfrac><mn>17</mn><mn>100</mn></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>261</mn><mo>≠</mo><mn>0</mn><mo>.</mo><mn>17</mn></math> <em><strong>(R1)</strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Comparison of numerical values must be seen for <em><strong>(R1)</strong></em> to be awarded.<br>Do not award <em><strong>(A1)(R0)</strong></em>. Follow through from parts (d)(i) and (d)(ii).</p>
<p><em><strong><br></strong></em><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the hand lengths and the heights of five athletes on a sports team.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The relationship between <em>x</em> and <em>y</em> can be modelled by the regression line with equation <em>y</em> = <em>ax</em> + <em>b</em>.</p>
</div>
<div class="question">
<p>Another athlete on this sports team has a hand length of 21.5 cm. Use the regression equation to estimate the height of this athlete.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>substituting <em>x</em> = 21.5 into <strong>their</strong> equation <em><strong> (M1)</strong></em></p>
<p><em>eg</em> 9.91(21.5) − 31.3</p>
<p>181.755</p>
<p>182 (cm) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The table below shows the distribution of test grades for 50 IB students at Greendale School.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.25.22.png" alt="M17/5/MATSD/SP2/ENG/TZ1/05"></p>
</div>
<div class="specification">
<p>A student is chosen at random from these 50 students.</p>
</div>
<div class="specification">
<p>A second student is chosen at random from these 50 students.</p>
</div>
<div class="specification">
<p>The number of minutes that the 50 students spent preparing for the test was normally distributed with a mean of 105 minutes and a standard deviation of 20 minutes.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the mean test grade of the students;</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 standard deviation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the median test grade of the students.</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>Find the interquartile range.</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 probability that this student scored a grade 5 or higher.</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>Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6.</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 probability that a student chosen at random spent at least 90 minutes preparing for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected number of students that spent at least 90 minutes preparing for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1(1) + 3(2) + 7(3) + 13(4) + 11(5) + 10(6) + 5(7)}}{{50}} = \frac{{230}}{{50}}">
<mfrac>
<mrow>
<mn>1</mn>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>3</mn>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>7</mn>
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>13</mn>
<mo stretchy="false">(</mo>
<mn>4</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>11</mn>
<mo stretchy="false">(</mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>10</mn>
<mo stretchy="false">(</mo>
<mn>6</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>5</mn>
<mo stretchy="false">(</mo>
<mn>7</mn>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>230</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into mean formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.6">
<mo>=</mo>
<mn>4.6</mn>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.46{\text{ }}(1.45602 \ldots )">
<mn>1.46</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>1.45602</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>5 <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6 - 4">
<mn>6</mn>
<mo>−</mo>
<mn>4</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for 6 and 4 seen.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 2">
<mo>=</mo>
<mn>2</mn>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{11 + 10 + 5}}{{50}}">
<mfrac>
<mrow>
<mn>11</mn>
<mo>+</mo>
<mn>10</mn>
<mo>+</mo>
<mn>5</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="11 + 10 + 5">
<mn>11</mn>
<mo>+</mo>
<mn>10</mn>
<mo>+</mo>
<mn>5</mn>
</math></span> seen.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{26}}{{50}}{\text{ }}\left( {\frac{{13}}{{25}},{\text{ }}0.52,{\text{ }}52\% } \right)">
<mo>=</mo>
<mfrac>
<mrow>
<mn>26</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>13</mn>
</mrow>
<mrow>
<mn>25</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.52</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>52</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{10}}{{{\text{their }}26}} \times \frac{9}{{49}}">
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mrow>
<mtext>their </mtext>
</mrow>
<mn>26</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>49</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{10}}{{{\text{their }}26}}">
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mrow>
<mtext>their </mtext>
</mrow>
<mn>26</mn>
</mrow>
</mfrac>
</math></span> seen, <strong><em>(M1) </em></strong>for multiplying their first probability by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{9}{{49}}">
<mfrac>
<mn>9</mn>
<mrow>
<mn>49</mn>
</mrow>
</mfrac>
</math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\frac{{10}}{{50}} \times \frac{9}{{49}}}}{{\frac{{26}}{{50}}}}">
<mfrac>
<mrow>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>49</mn>
</mrow>
</mfrac>
</mrow>
<mrow>
<mfrac>
<mrow>
<mn>26</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
</mrow>
</mfrac>
</math></span></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{10}}{{50}} \times \frac{9}{{49}}}">
<mrow>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>49</mn>
</mrow>
</mfrac>
</mrow>
</math></span> seen, <strong><em>(M1) </em></strong>for dividing their first probability by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{their }}26}}{{50}}">
<mfrac>
<mrow>
<mrow>
<mtext>their </mtext>
</mrow>
<mn>26</mn>
</mrow>
<mrow>
<mn>50</mn>
</mrow>
</mfrac>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{45}}{{637}}{\text{ (}}0.0706,{\text{ }}0.0706436 \ldots ,{\text{ }}7.06436 \ldots \% )">
<mo>=</mo>
<mfrac>
<mrow>
<mn>45</mn>
</mrow>
<mrow>
<mn>637</mn>
</mrow>
</mfrac>
<mrow>
<mtext> (</mtext>
</mrow>
<mn>0.0706</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.0706436</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>7.06436</mn>
<mo>…</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)</strong> <strong><em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (d).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X \geqslant 90)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>⩾</mo>
<mn>90</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p><img src="images/Schermafbeelding_2017-08-16_om_15.40.38.png" alt="M17/5/MATSD/SP2/ENG/TZ1/05.f.i/M"> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for a diagram showing the correct shaded region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( > 0.5)">
<mo stretchy="false">(</mo>
<mo>></mo>
<mn>0.5</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.773{\text{ }}(0.773372 \ldots ){\text{ }}0.773{\text{ }}(0.773372 \ldots ,{\text{ }}77.3372 \ldots \% )">
<mn>0.773</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.773372</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.773</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.773372</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>77.3372</mn>
<mo>…</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.773372 \ldots \times 50">
<mn>0.773372</mn>
<mo>…</mo>
<mo>×</mo>
<mn>50</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 38.7{\text{ }}(38.6686 \ldots )">
<mo>=</mo>
<mn>38.7</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>38.6686</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)</strong> <strong><em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (f)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A dice manufacturer claims that for a novelty die he produces the probability of scoring the numbers <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> are all equal, and the probability of a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> is two times the probability of scoring any of the other numbers.</p>
</div>
<div class="specification">
<p>To test the manufacture’s claim one of the novelty dice is rolled <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>350</mn></math> times and the numbers scored on the die are shown in the table below.</p>
<p style="padding-left: 30px;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> goodness of fit test is to be used with a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> significance level.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of scoring a six when rolling the novelty die.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of scoring more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> sixes when this die is rolled <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> times.</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 expected frequency for each of the numbers if the manufacturer’s claim is true.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null and alternative hypotheses.</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>State the degrees of freedom for the test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the conclusion of the test, clearly justifying your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p>Let the probability of scoring <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo> </mo><mo>…</mo><mo> </mo><mo>,</mo><mo> </mo><mn>5</mn></math> be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo> </mo><mo>,</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mi>p</mi><mo>+</mo><mn>2</mn><mi>p</mi><mo>=</mo><mn>1</mn><mo>⇒</mo><mi>p</mi><mo>=</mo><mfrac><mn>1</mn><mn>7</mn></mfrac></math> <strong>(M1)(A1)</strong></p>
<p>Probability of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>=</mo><mfrac><mn>2</mn><mn>7</mn></mfrac></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[3 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Let the number of sixes be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>5</mn><mo>,</mo><mo> </mo><mfrac><mn>2</mn><mn>7</mn></mfrac></mrow></mfenced></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mn>2</mn></mrow></mfenced><mo>=</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>3</mn></mrow></mfenced></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≤</mo><mn>2</mn></mrow></mfenced></math> <strong>(M1)</strong></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>145</mn><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>144701</mn><mo>…</mo></mrow></mfenced></math> <strong>(M1)A1</strong></p>
<p> </p>
<p><strong>[4 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Expected frequency is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>350</mn><mo>×</mo><mi>p</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>350</mn><mo>×</mo><mn>2</mn><mi>p</mi></math> <strong>(M1)</strong></p>
<p><img src="data:image/png;base64,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"> <strong>A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub><mo>:</mo></math> The manufacture’s claim is correct <strong>A1</strong><br><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>1</mn></msub><mo>:</mo></math> The manufacturer’s claim is not correct <strong>A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Degrees of freedom <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[1 mark]</strong></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>p-value <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>0984</mn><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0984037</mn><mo>…</mo></mrow></mfenced></math> <strong>(M1)A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0984</mn><mo>></mo><mn>0</mn><mo>.</mo><mn>05</mn></math> <strong>R1</strong></p>
<p>Hence insufficient evidence to reject the manufacture’s claim. <strong>A1</strong></p>
<p> </p>
<p><strong>[4 marks]</strong></p>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iv.</div>
</div>
<br><hr><br><div class="specification">
<p>The stopping distances for bicycles travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> are assumed to follow a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>76</mn><mo> </mo><mtext>m</mtext></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>12</mn><mo> </mo><mtext>m</mtext></math>.</p>
</div>
<div class="specification">
<p>Under this assumption, find, correct to four decimal places, the probability that a bicycle chosen at random travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> manages to stop</p>
</div>
<div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> randomly selected bicycles are tested and their stopping distances when travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> are measured.</p>
</div>
<div class="specification">
<p>Find, correct to four significant figures, the expected number of bicycles tested that stop between</p>
</div>
<div class="specification">
<p>The measured stopping distances of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> bicycles are given in the table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>It is decided to perform a <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> goodness of fit test at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> level of significance to decide whether the stopping distances of bicycles travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> can be modelled by a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>76</mn><mo> </mo><mtext>m</mtext></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>12</mn><mo> </mo><mtext>m</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>in less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>.</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>in more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo> </mo><mtext>m</mtext></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>75</mn><mo> </mo><mtext>m</mtext></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>75</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo> </mo><mtext>m</mtext></math>.</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>State the null and alternative hypotheses.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value for the test.</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>State the conclusion of the test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of correct probability<strong> </strong><em><strong>(M1)</strong></em></p>
<p>e.g sketch <strong>OR</strong> correct probability statement, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>X</mi><mo><</mo><mn>6</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0151</mn></math><em><strong> A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0228</mn></math><em><strong> A1</strong></em></p>
<p><strong><br>Note:</strong> Answers should be given to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> decimal place.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>multiplying <strong>their</strong> probability by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> <strong> </strong><em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>451</mn><mo>.</mo><mn>7</mn></math> <em><strong> A1</strong></em></p>
<p><strong><br></strong><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>510</mn><mo>.</mo><mn>5</mn></math> <em><strong> A1</strong></em></p>
<p><strong><br>Note: </strong>Answers should be given to 4 sf.</p>
<p><strong><br></strong><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub><mo>:</mo></math> stopping distances can be modelled by <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mfenced><mrow><mn>6</mn><mo>.</mo><mn>76</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><msup><mn>12</mn><mn>2</mn></msup></mrow></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>1</mn></msub><mo>:</mo></math> stopping distances cannot be modelled by <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mo>(</mo><mn>6</mn><mo>.</mo><mn>76</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>12</mn><mrow><msup><mrow></mrow><mn>2</mn></msup><mo>)</mo></mrow></math> <em><strong> A1A1</strong></em></p>
<p><strong>Note</strong>: Award <em><strong>A1</strong></em> for correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub></math>, including reference to the mean and standard deviation. Award <em><strong>A1</strong></em> for the negation of their <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub></math>.</p>
<p><strong><br></strong><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>1</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn><mo>.</mo><mn>8</mn></math> seen <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0727</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0726542</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>7</mn><mo>.</mo><mn>27</mn><mo>%</mo></mrow></mfenced></math> <em><strong>A2</strong></em></p>
<p><strong><br></strong><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>05</mn><mo><</mo><mn>0</mn><mo>.</mo><mn>0727</mn></math> <em><strong>R1</strong></em></p>
<p>there is insufficient evidence to reject <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub></math> (or “accept <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub></math>”) <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Do not award <em><strong>R0A1</strong></em>.</p>
<p><strong><br></strong><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The maximum temperature <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
<mi>T</mi>
</math></span>, in degrees Celsius, in a park on six randomly selected days is shown in the following table. The table also shows the number of visitors, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>, to the park on each of those six days.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_17.34.22.png" alt="M17/5/MATME/SP2/ENG/TZ2/02"></p>
<p>The relationship between the variables can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = aT + b">
<mi>N</mi>
<mo>=</mo>
<mi>a</mi>
<mi>T</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</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="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the number of visitors on a day when the maximum temperature is 15 °C.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of set up <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span></p>
<p>0.667315, 22.2117</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 0.667,{\text{ }}b = 22.2">
<mi>a</mi>
<mo>=</mo>
<mn>0.667</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>b</mi>
<mo>=</mo>
<mn>22.2</mn>
</math></span> <strong><em>A1A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.922958</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 0.923">
<mi>r</mi>
<mo>=</mo>
<mn>0.923</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.667(15) + 22.2,{\text{ }}N(15)">
<mn>0.667</mn>
<mo stretchy="false">(</mo>
<mn>15</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>22.2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>N</mi>
<mo stretchy="false">(</mo>
<mn>15</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p>32.2214 <strong><em>(A1)</em></strong></p>
<p>32 (visitors) (must be an integer) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(A = ){\text{ }}\pi {r^2} + 2\pi rh"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi rh"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> seen. Award <strong><em>(A1) </em></strong>for two correct terms added together.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Units <strong>not </strong>required.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000 = \pi {r^2}h"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}h"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> equating to their part (b).</p>
<p>Do not accept unless <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = \pi {r^2}h"> <mi>V</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> is explicitly defined as their part (b).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + 2\pi r\left( {\frac{{500\,000}}{{\pi {r^2}}}} \right)"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> seen.</p>
<p>Award <strong><em>(M1) </em></strong>for correctly substituting <strong>only</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> into a <strong>correct </strong>part (a).</p>
<p>Award <strong><em>(A1)</em>(ft)<em>(M1) </em></strong>for rearranging part (c) to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh = \frac{{500\,000}}{r}"> <mi>π</mi> <mi>r</mi> <mi>h</mi> <mo>=</mo> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span> and substituting for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh"> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> in expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<p> </p>
<p><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> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>The conclusion, <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>, must be consistent with their working seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{10^6}"> <mrow> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></span> as equivalent to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{1\,000\,000}"> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> </math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{{\text{1}}\,{\text{000}}\,{\text{000}}}}{{{r^2}}}"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r"> <mn>2</mn> <mi>π</mi> <mi>r</mi> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{r^2}}}"> <mfrac> <mn>1</mn> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^{ - 2}}"> <mrow> <msup> <mi>r</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - {\text{1}}\,{\text{000}}\,{\text{000}}"> <mo>−</mo> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </math></span>.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{1\,000\,000}}{{{r^2}}} = 0"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their part (e) to zero.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3} = \frac{{1\,000\,000}}{{2\pi }}"> <mrow> <msup> <mi>r</mi> <mn>3</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> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt[3]{{\frac{{1\,000\,000}}{{2\pi }}}}"> <mi>r</mi> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mn>3</mn> </mroot> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for isolating <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>sketch of derivative function <strong><em>(M1)</em></strong></p>
<p>with its zero indicated <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(r = ){\text{ }}54.2{\text{ }}({\text{cm}}){\text{ }}(54.1926 \ldots )"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mn>54.2</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>cm</mtext> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {(54.1926 \ldots )^2} + \frac{{1\,000\,000}}{{(54.1926 \ldots )}}"> <mi>π</mi> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <msup> <mo stretchy="false">)</mo> <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> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their part (f) into the given equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 27\,700{\text{ }}({\text{c}}{{\text{m}}^2}){\text{ }}(27\,679.0 \ldots )"> <mo>=</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>700</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{27\,679.0 \ldots }}{{2000}}"> <mfrac> <mrow> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> </mrow> <mrow> <mn>2000</mn> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing their part (g) by 2000.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 13.8395 \ldots "> <mo>=</mo> <mn>13.8395</mn> <mo>…</mo> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (g).</p>
<p> </p>
<p>14 (cans) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Final <strong><em>(A1) </em></strong>awarded for rounding up their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="13.8395 \ldots "> <mn>13.8395</mn> <mo>…</mo> </math></span> to the next integer.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 66 people went on holiday to Hawaii. During their stay, three trips were arranged: a boat trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
<mi>B</mi>
</math></span>), a coach trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>) and a helicopter trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span>).</p>
<p>From this group of people:</p>
<table style="width: 691.333px;">
<tbody>
<tr>
<td style="width: 182px; text-align: right;">3 </td>
<td style="width: 526.333px;">went on all three trips;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">16 </td>
<td style="width: 526.333px;">went on the coach trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">13 </td>
<td style="width: 526.333px;">went on the boat trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">5 </td>
<td style="width: 526.333px;">went on the helicopter trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;"><em>x </em></td>
<td style="width: 526.333px;">went on the coach trip and the helicopter trip <strong>but not</strong> the boat trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">2<em>x </em>
</td>
<td style="width: 526.333px;">went on the boat trip and the helicopter trip <strong>but not</strong> the coach trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">4<em>x </em>
</td>
<td style="width: 526.333px;">went on the boat trip and the coach trip <strong>but not</strong> the helicopter trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">8 </td>
<td style="width: 526.333px;">did not go on any of the trips.</td>
</tr>
</tbody>
</table>
</div>
<div class="specification">
<p>One person in the group is selected at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a Venn diagram to represent the given information, using sets labelled <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B"> <mi>B</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C"> <mi>C</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H"> <mi>H</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3"> <mi>x</mi> <mo>=</mo> <mn>3</mn> </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>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n(B \cap C)"> <mi>n</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mo>∩</mo> <mi>C</mi> <mo stretchy="false">)</mo> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person</p>
<p>(i) went on at most one trip;</p>
<p>(ii) went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><img src="images/Schermafbeelding_2017-03-07_om_10.03.03.png" alt="N16/5/MATSD/SP2/ENG/TZ0/02.a/M"> <strong><em>(A5)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for rectangle and three labelled intersecting circles (U need not be seen),</p>
<p><strong><em>(A1) </em></strong>for 3 in the correct region,</p>
<p><strong><em>(A1) </em></strong>for 8 in the correct region,</p>
<p><strong><em>(A1) </em></strong>for 5, 13 and 16 in the correct regions,</p>
<p><strong><em>(A1) </em></strong>for <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="2x"> <mn>2</mn> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4x"> <mn>4</mn> <mi>x</mi> </math></span> in the correct regions.</p>
<p> </p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="8 + 13 + 16 + 3 + 5 + x + 2x + 4x = 66"> <mn>8</mn> <mo>+</mo> <mn>13</mn> <mo>+</mo> <mn>16</mn> <mo>+</mo> <mn>3</mn> <mo>+</mo> <mn>5</mn> <mo>+</mo> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>4</mn> <mi>x</mi> <mo>=</mo> <mn>66</mn> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for <strong>either </strong>a completely correct equation <strong>or </strong>adding all the terms from <strong>their </strong>diagram in part (a) and equating to 66.</p>
<p>Award <strong><em>(M0)(A0) </em></strong>if their equation has no <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7x = 66 - 45"> <mn>7</mn> <mi>x</mi> <mo>=</mo> <mn>66</mn> <mo>−</mo> <mn>45</mn> </math></span><strong> OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7x + 45 = 66"> <mn>7</mn> <mi>x</mi> <mo>+</mo> <mn>45</mn> <mo>=</mo> <mn>66</mn> </math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for adding their like terms correctly, <strong>but only </strong>when the solution to their equation is equal to 3 and is consistent with their original equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3"> <mi>x</mi> <mo>=</mo> <mn>3</mn> </math></span> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>The conclusion <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3"> <mi>x</mi> <mo>=</mo> <mn>3</mn> </math></span> must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>15 <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a). The answer must be an integer.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{42}}{{66}}{\text{ }}\left( {\frac{7}{{11}},{\text{ }}0.636,{\text{ }}63.6\% } \right)"> <mfrac> <mrow> <mn>42</mn> </mrow> <mrow> <mn>66</mn> </mrow> </mfrac> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>7</mn> <mrow> <mn>11</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.636</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>63.6</mn> <mi mathvariant="normal">%</mi> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for numerator, <strong><em>(A1) </em></strong>for denominator. Follow through from their Venn diagram.</p>
<p> </p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{9}{\text{ }}\left( {\frac{1}{3},{\text{ }}0.333,{\text{ }}33.3\% } \right)"> <mfrac> <mn>3</mn> <mn>9</mn> </mfrac> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.333</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>33.3</mn> <mi mathvariant="normal">%</mi> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for numerator, <strong><em>(A1)</em>(ft) </strong>for denominator. Follow through from their Venn diagram.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>As part of his mathematics exploration about classic books, Jason investigated the time taken by students in his school to read the book <em>The Old Man and the Sea</em>. He collected his data by stopping and asking students in the school corridor, until he reached his target of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> students from <strong>each</strong> of the literature classes in his school.</p>
</div>
<div class="specification">
<p>Jason constructed the following box and whisker diagram to show the number of hours students in the sample took to read this book.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" width="458" height="149"></p>
<p style="text-align: center;"> </p>
</div>
<div class="specification">
<p>Mackenzie, a member of the sample, took <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math> hours to read the novel. Jason believes Mackenzie’s time is not an outlier.</p>
</div>
<div class="specification">
<p>For each student interviewed, Jason recorded the time taken to read <em>The Old Man and the Sea</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>x</mi></mfenced></math>, measured in hours, and paired this with their percentage score on the final exam <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>y</mi></mfenced></math>. These data are represented on the scatter diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Jason correctly calculates the equation of the regression line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for these students to be</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>54</mn><mi>x</mi><mo>+</mo><mn>98</mn><mo>.</mo><mn>8</mn></math>.</p>
<p style="text-align: left;">He uses the equation to estimate the percentage score on the final exam for a student who read the book in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> hours.</p>
</div>
<div class="specification">
<p>Jason found a website that rated the ‘top <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math>’ classic books. He randomly chose eight of these classic books and recorded the number of pages. For example, Book <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext></math> is rated <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>44</mn><mtext>th</mtext></math> and has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>281</mn></math> pages. These data are shown in the table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>Jason intends to analyse the data using Spearman’s rank correlation coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State which of the two sampling methods, systematic or quota, Jason has used.</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>Write down the median time to read the book.</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>Calculate the interquartile range.</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>Determine whether Jason is correct. Support your reasoning.</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>Describe the correlation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage score calculated by Jason.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether it is valid to use the regression line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for Jason’s estimate. Give a reason for your answer.</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>Copy and complete the information in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret your result.</p>
<div class="marks">[1]</div>
<div class="question_part_label">i.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Quota sampling <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> (hours) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>-</mo><mn>7</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>M1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math> seen.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>indication of a valid attempt to find the upper fence <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>8</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo><</mo><mn>27</mn></math> (accept equivalent answer in words) <em><strong>R1</strong></em></p>
<p>Jason is correct <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Do not award <em><strong>R0A1</strong></em>. Follow through <strong>within</strong> this part from <em>their</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math>, but only if their value is supported by a valid attempt <strong>or</strong> clearly and correctly explains what their value represents.</p>
<p><em><strong><br>[4 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>“negative” seen <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Strength cannot be inferred visually; ignore “strong” or “weak”.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>54</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>+</mo><mn>98</mn><mo>.</mo><mn>8</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>96</mn><mo>.</mo><mn>5</mn><mo> </mo><mfenced><mo>%</mo></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>96</mn><mo>.</mo><mn>49</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>not reliable <em><strong>A</strong><strong>1</strong></em></p>
<p>extrapolation <strong>OR</strong> outside the given range of the data <em><strong>R</strong><strong>1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Do not award <em><strong>A1R0</strong></em>. Only accept reasoning that includes reference to the range of the data. Do not accept a contextual reason such as <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> hours is too short to read the book.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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xtJP4HTZFpF86ONNhW1vaLjbAWnmktvaTkdUBCcgti+p9voO5pEN6qxvVsn05k33DirL68cOc7l48WcVhVWeY6UnJsb93nPEhYBb2iyuKUd3dN68U41uPaeEu6d18wG/3zYT+HCDZEf6ZflWrt/NsPBlop3Nrs/Kbo4p2Dwjhbre6LtbzQfnVM4XlCzzXQbnTb1bEv8BASxHefVbvUzTWafaK3VvWq69lq1oj1OzK22clWR2Cai3Q3NhyEFwUuar77Gaed6O7jloQ812dFmMVE9IeH4PV1fzZKhCkaviCn2ksKorjX/raJedOmdCun54DmFwTldRH/GlaGZPklrSm89ZeerRkjK4hm9nb+n2ehctb7C0Q90vf5K21WUTPGs8yDKevG/ofnVZXIM8/jJmJp1Q6uUFzcOxnSZVt5i3zmN/vYuZnoo+Hg62PlY643MrqUCV3q0kx6rfCNLQkzSZH9/yXopwhHNrrWbysF4SK6lH8M9ozf/fiSu9vnke0qS6W2jZa5QiuVFlraCU+S8x485JbFtepv03p+02OZy/5rGiy+m842u1xefBd3YfKTZpd75IvXBa4rWDwUvUt9h3vnQjrbLGQ34/lfZPasaXt7ZrCMaBQGdTZcUR0pSb7Sg158Je+eTZPPuNqKL4SsaDUKC2GYoO9r+8YdxT491WBsaara4qUhs23q2k0ceObEWDzWJBVsmttmw/L/Wc66L3bvPtJjw46aqKy1NLE//l/7GAS0CVU9f9djLjaSI2Db9Cih8NaJXob7d4useD723nXsQ3ySPa/XryPAXsU/bJ74kBTddbK9pyr7upRc3Nh5Wcxrm9mm2phfhH5Y00/PErsfigctP0suRnstC+TkNnmuNONsxfLw8jUgbOpr/6npaAypn++MrtoLz+FlFjjhlsc0xMcwarUVwVHBMfXllMU7qBhVfQxrP31O0WFXUAWBJz7GpUZ8dNuQ3yzApiG3FJaln29LTr+eV99hJylDGpj2CiTl558NGqHveK5ouf6VodEYQ23oEa7/Vvf+5984PtsgWN0eKbVPIyPohQZOJxLjloYnt8ILmN/zQKDsmfRFPbmjhKxq/ZaEd0mByZbRoNOBH/dTE9vx32qheiGT8eZq+DI8RYVlEbIut0rPBnISRpBlkj8wkrWCYPJIlSh/Hy1hQEZPhG4pu7+MW3s2l6sGOuYp9AUkFtttu6b97XDL+cY87X0t7VCUCXWyS9b3r8AYtzdEl3fAQnN1t0jDS/Mudm+W1tETTnnQtHuSRtDwxkWPEN6IN3cwvKBQ+hezNGfLoiq3gPHpSoQNOVGzL05KGe7UZeX155crQHW1XHymKfqapeoKlPdlznVLx9uZ9fsyBpG7zkP82y/zykXo2pMHbt+mL5lmda7O4uW1+2bCfch/ge+UHWv1+SRcXyT2kOQzOlNrB5xsaqnfhPkNsO3OKqC1DSNhEW9xUJLZd49DkRhRRpA1V2BPbaaUsFZP21QsRT2lv56GXMLXz0+OlIZAsraJRhG/Sc5v2nr6k+fU/aMw90el5IiyLiO3sGBGJ2XUyW0VsZsNIRNhztuVt2+9t1vxTNv6VvDSQpW2PT5sfrN2N4UDCP/XfdjX7tVKftfyNhcnheEh5cFI5e+5oNX+pApmD2fyPzzN70J/e42grODYK5bedoNh+WNL0LMubrFFUns4xZ9SXV49bE8d7vePvbVb49NlmT1xm/yf/orn1wGY2+uWTlPF0SF3WodF02bDR9stGLJIOE77PSieS7PO79M2Hh4+8fh3RrRqXDLHtjoZYJ+W0g/vg2vfY4uZIsS3DCbThI1pvbOyJiB4WOxEtVnfaGG1++cEiNrVtez3bQUDh6C29VUM8XAUyuyY7a/23isa8oOW4VmOkQm3YR3qeCEthwN4a21KBmAneVHim18lsTQPEKmzztnVXbB8TD8eIbc4PaeS9p7n+lvuRX8qxFZxqSusJim0FJub/Xn11YUDT5bYaXAWuUl9eFUhclfsz4+XxAuc98RCvPu/Zzj2VY7po0dhkv3ySMp4bgyz3C//DbPyyiYNnt/5Es4s3NH3/Y/yeUvpkcy+4Gt/glQ93+r0eJ0+w2XWIbWcAqLq3HUNI2EZb3DxRbPNldcEt43P1l/0SYbw3rMAiNg+JbSVSH5IXTVxDE5xZ8ciOvKCNX24VcZiI9lQkZ8fKZw6zoR7SMy69w0eKbW1Menbt5FqpIJehN6ZrUpFnaZtHxOsaf/XipjGMRMZAp+npve3mFSVNbhDJI8CMn2pMpNdxxUPyGIgbSWllm/UCxcNI/ps12NJ0TFv21/cbOvvHHNpiKziHji++71TFdkzAR09vfXlVJFc5P4c9Fts8XO57GlU+zK8Ie/cx/mNiQEFObLdnTLtfNkSkxrNrDVT5AILcf9zZ2sger3ySl0fZhv3/ZjsxbLC9sjEMUveaVKMZOz2s2thUILbZExl3pb2oJuJKD5TnAxpwb7H6rI8m9tLP/GTb9nq2BWQ6xEMT9k+GmQno3Nc2dB8kfb1BoPumflclti2FKx2KobHOpS/Da0T4Pia2paKzvSCZjRm3D20xgUuaFrvlu+U6S7E7Fw/cbrO8IDlI3sCWr9zYjlHXS+LBlk6SN9I4Mq1/bN1WcB47p9j+0xbbcew0O4a5vrwqkKOqd+VV9jWmAqdUcYhXnzUHdre/0OTbqt+n0RI48qdfPnJP08tBcr9J7ylHOlbBaX7ZED0sp3RmfPo0bqT77/VnvL755LMYPdt5HrIWl6d0hIBs9ri0xU1FYlsXSiL6+FGyfOKOezx/oOvbX+PPuKlW60PWS1lGbHNS/BkcFu3mbI9Hw3WIbb0RoVeMuzVdz2QCh3Maza5o8SOPJa5IbIff0PzD99qnEB/59F8wpPHldfLSqAjfAmKbecnLbCKAc58R1J9QFOnZfkbj6CNFMnQjd63H4iH5WOb2Jj0/FzMithObswk0zE8fcjoLbfgINwB0PuWDxFZwyl/FckY63EgfkmQ57ombarP/kF3qSdaLGl5mPpRokzfHeKhM+r1kVSdcJC8yHbax6r1e8tdwgp/AfTv+KX45Otmntk0/ev9esnc+8jWS5Glc/LTyWeNf6jGyTK16Z5N0jqQvjMq9FT3bluyC2LZASd7ras8QErbRVq5Kim2rq9jYewIlBb6DVzrcQ74sojWsshdLHSfXuNlWcJ6WnDxGNp8E1NObU739Nu8lBhKfwhFNn/Btc1sKRbY14ytbog9xiht8cw+f/WNLmvPZlgP5RjTbkv3rvbm2c5vZ5pdP7KMal5zMt6Aa/8nkT80QcKfinw3Hz4fkSz4cO/vzJritr3+Pfz66jxDbOg353bYhJGyXLW4gtiXHsHwCARFaBXvTXSk5h4hU+RTDlbh7u63guI9u356u21+GaJ98FS599Fl8L7IEHzclsHGz4T3g4+YDNuXYQGy7eWFPYQIViW3uyV4vKVJfsZAeMp5lMzJm0CxsWCUHdr1S6br9ZTKxT74Klz76LL4XWYKPmxLYuNnwHvBx8wGbcmwgtt28sAcEFIGuVypdt79MGPbJV+HSR5/F9yJL8HFTAhs3G94DPm4+YFOODcS2mxf2gIAi0PVKpev2lwnDPvkqXPros/heZAk+bkpg42bDe8DHzQdsyrGxim2GiH8wQAwgBhADiAHEAGIAMYAYQAyUiwFTilvFtnkQ1kGgzwS4kunyX9ftL8O+T74Klz76LL4XWYKPmxLYuNnwHvBx8wGbcmz2VAQAugFiTz8JdL1MdN3+MlHXJ1+FSx99Ft+LLMHHTQls3Gx4D/i4+YBNOTYQ225e2AMCikDXK5Wu218mDPvkq3Dpo8/ie5El+LgpgY2bDe8BHzcfsCnHpqTYlpkWbWNX+BNtH2i1TWYCdNtRbo9Mv63P4FjuCo8cLZ+ts/mUbEunSn/kUk/abbdDn4J0t76mS5mdkWdFPDgxQt15JdMQBxQ0wudJcJ90ctcrla7bXybz+uSrcOmjz+J7kSX4uCmBjZsN7wEfNx+wKcemQrHNwlSmancbUXpPX8S2+Gm8nJqKbeuEL+cHpvw9JLaPyat7Wi8jmk5+ppVqT0Fsl47l9ARzBskzGkWf071V/2iuUtzQ6mpGozBppA4mFK02Vbtz8HrN+cpmbGgVTWggZdaDv2xFsz4fxB/vVNOTn9ca0wWsSA9pBx+zPn7iBGCpd0/70Q42iQ+7NS2jaVJ/DGi63D7NuQrO9s7HoQt8zqgsWL2zUfNy6B2QPPtoVH2HrzhcYmljc6TYDmk4v6GsD3tH25vLuJBU3QMtwVb1da3gsgoxFbnW46rfmE5V7ugllv3hRUS3ux1tl7P4Ju84nkh8qSavJP1T78W25ayt4NiOK79tS8vpgILgFMQ2x+T3NJpc0XrHkxNd0WQQUhC+oej2vjyaI8+oL69Mg+7pNvqOJsnTpdRfZ3k0z69uvTmfC9i8u6XFZFh7TBewJD2kFXz4PvZinnRUpKZ5/9EKNko0JfXFYEzzX5aqDvEOx3tD9iutLr+j2fVa01rxfb1pfWLLC++xIx2Qg3e0WN8TbX+j+eic2sqmIrHNpeWG5sOQguAlzVdf47zZruhqbzZAGWqS9YyG4/d0nfaIGa0TU2wnQIPgnEbz36jatq8I1MCdYdsVLeZjrTdrTJdLKQyaT2/ndHUpx53TaPbpQAWSnRcMXtGIRQoPE7m8Ts4RuzThLLydjRDLOVJi5NyCeZUKbenBC7hX5i/aLCYU8jYRGGlejSm6/idNR+eq1y0we/z0uOB9N//ejx2xtQXL+iqVUxLbX2gx+7smJiSm621ImOFRX16ZKZnrydMKKQvm7hrX/flsOsUNkG9oOHpFg5obkGbKh9b98+G6+DWNF18Omelln382RKSehIQUji7ppuphqE+k6pfPhv5Y/aUJbdFZz1sRS37ZENE6olEQ0Nl0SQ8qn5M6+GxKy3jDE3P/+NNtbCoS27ae7TtaTl/EYisVafHwhbhXXG7GySNn6zH8pHZBY34szaLy7nPSa1KH0GawIlAdYjupFBhk/l+Gcxz2aTC9djQOsnTz1xVxLeO5tUePNsGciw25plxDdpbPq4fVnIY5nx8R27ljE1YiQqQ1qh8TPqfBc6OhJua2YGkrONWYdUpi20JEVYZ9EdtcRocHhnVZ+FS0qb74LGfg7jaii+GMlqv3NILYzuDJPUzVeUMaz99TtFg57gXZaU388h87iU5o+AlYUbb++eQtVR1fzg62/LF1r3lnk5Sr+Gk/extrnhPr2TbFpqyL6LRlM/d6vFE9oTEMTZiGFzS/4bGd2TH7vaWvaPyWH0+GNEgeVdtSedo2Eag2sZ3ZG45+oGt+bEH3tF68i3u5VQF4yHp7NZ/yx2SDbzJbpWEypMnilnZ71/2LFuNnFKge5aR3pLDYlrwxl2Xyiijt3RbRTBmPvbzSnjqoG7Aawxs/8UivY+Oj97RncLz/qq9SOW2xHee19qSrgZysL68OGC9Pu9KyceDYGnZ58dn0QzWiX9F0eZf0ODXbyDLN0ddbwYd2tF19pCj6OXni12y50Hnov72zkYbI4A2N5UloODKGTugWN/vbO5+cu+0Rk2yWfzaiF1kTfqDV75d0cdGOpyM2Nkf2bJvCjYd+/Ei/pMMpJEKkgoko0oZe7Int9CZ1SMBJmodewtTO13tO9d8HW4WHxLald5ndzIne/6ZiO9e6yh2TDLERRK6lVEJKgH6uUGwfk1dlxbZ2I8n5USEfF7cattsKTjXJnLLY5rL0itxPc6ohaF6lvrwyU0rWH5Y0PZO6KaCsl8VxfA2bG/d5zwe+6Y3pdfRn/MjbwxONPZO0Df75aMbwLUM9KWxHY8Q3m4fllM64cyYZZpm++9CSnm7ffHKRo3REO4aQsF3tYLOhm/lFPJy1JTHjYnOk2JahCdqQhEB6ZSU8st7a8TyixerOEKKZMM6EabZtv7c0oHD0lt4efOlKO18X2PrvNoptEeO6bTmReker+UvVq5++mGo7Rx053VsAAAT6SURBVNCrpTQcqsgruUFo47MP9Ww7/YDYzmURna7Y5icarz30Mvi5AcSdCu/V+ynNf0XBj89ZJKu8fs0vbifbILYzOLZfqu4+Mz4yYDuw/m2+YycW23qZkXs4GiNm7qtGmn5vNQ9oeN137LC7u/Unml28oen7H2mstKGMkmgYhpGcjc0TxbZyN/sSSfAifozIm0UsSmsjfUtdhmhIoZL1+Frul+4mtNg8pF/hyAS64eWTVkWg6jbJBTV7bcNIBjNabm3DSLQvh7gKigjndPiFNjxF9fpraT/payR646hMXlUltr9mw1EwjITfDDqhr5FIOUleeBp9F78hrm1u4qetkmsiXU7DV4+lT5+JzM9YZr38bFfQ0peVmooJezpc7ocQ20S0L7blxTeI7XzsxNqkHt2TT6nomt96R16s1Rqt8vEMpcWk5V/Um2qPs7GpQGyzkTJ2JqBAHBWxrfcqPx/QIBQhqwnI8YLir/Fm2/Z6tkWopi/YaWKxMk6HxLZkLr/IZ9xQ0l59zf69Yw4Pf0k/5Zc7T/MxFeR62toLk3sMxBfp2ZYDjskrrfGk7HvkBUnJK04yjYNkaEmaf5of6RdYtOEnYm4LlraCU41ZJyi2OX8nUy9Cm/OkvrwqkOMq1puPYa8+27CgZ9tGJdum6vJX2Ve7sj2N//IeO6rM5O9RcaP10L2tOUze+YirKmbaM4SEzfLNJm6o5Rtlcey8pmjt93MkNjYViW3u1vmTogv+1JuISn60GsVd+wEPAfmBrm9/jT/xZvQCZ601TazKOG4Ra5qAk5fuqh8fKQJVGgQS6dpSXoYSUTxwfPqPP2eYTnihf8ZPu1buJ08a81PKK8hdNz7wuBkk8xWZulLpvOJWojY2Sj3B+E86LMjZMOLEJP/0lx+3NxQlM2Hm4kI/JsfG74qt4FRiUdqAsuRRJQnEF6nNftNGfnr17bfJy87JTrXte1psmulpaMxXm++TFzW+vG0mmK178zkzIf8LYlvjEQ8xSt9n2q3penZBQ+eXqbRTG/jpP3bkayTJ4//kCXj19/bjYPrnE9vdtiEkbJV3Nom2SD9YocrWiELp8D0uyys5y8ampNiuxI4TvkjWWMgaECfs7hGuxS1P7tXOei6k8dSGWbFsLtkKju244ttcj97raZFXb7/FU60Bxell//U2JExLGvFVJSovTCe+hiOaRn4m42jOZ5O2Yx1iWwOjDQnkcsGTtrTks39sZCtiR0SSqjeMeTY0kj5+toJPiz5pp+eBfzbckP2QzefBHb3jn2ipvhSnW9r8bxsbiO1K8wFi+1Gcaa+6Lsji323pzTB9sBUc85g2r3fd/jJs++SrcOmjz+J7kSX4uCmBjZsN7wEfNx+wKccGYtvN64g9ENtFoO3WS4r2ZhaNWtEitdnf9Uql6/bb8sS1rU++CoM++iy+F1mCj5sS2LjZ8B7wcfMBm3JsILbdvLAHBBSBrlcqXbe/TBj2yVfh0kefxfciS/BxUwIbNxveAz5uPmBTjg3EtpsX9oCAItD1SqXr9pcJwz75Klz66LP4XmQJPm5KYONmw3vAx80HbMqxsYpthoh/MEAMIAYQA4gBxABiADGAGEAMlIsBU4rviW3zAKyDAAiAAAiAAAiAAAiAAAgcRwBi+zhuOAsEQAAEQAAEQAAEQAAEHiUAsf0oIhwAAiAAAiAAAiAAAiAAAscR+H84K1TEyb3XugAAAABJRU5ErkJggg=="> <em><strong>A1A1</strong></em></p>
<p><strong><br>Note:</strong> Do not award <em><strong>A1 </strong></em>for correct ranks for ‘number of pages’. Award <em><strong>A1</strong></em> for correct ranks for ‘top 50 rating’.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>714</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>714285</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A2</strong></em></p>
<p><strong><br>Note:</strong> <em><strong>FT</strong></em> from their table.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">i.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>there is a (strong/moderate) positive association between the number of pages and the top <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> rating. <em><strong>A1</strong></em></p>
<p><em><strong><br></strong></em><strong>OR</strong></p>
<p>there is a (strong/moderate) agreement between the rank order of number of pages and the rank order top <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> rating. <em><strong>A1</strong></em></p>
<p><em><strong><br></strong></em><strong>OR</strong></p>
<p>there is a (strong/moderate) positive (linear) correlation between the rank order of number of pages and the rank order top <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> rating. <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Follow through from their value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>s</mi></msub></math>.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">i.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">i.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">i.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Emlyn plays many games of basketball for his school team. The number of minutes he plays in each game follows a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> minutes.</p>
<p>In any game there is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mo>%</mo></math> chance he will play less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>6</mn><mo> </mo><mtext>minutes</mtext></math>.</p>
</div>
<div class="specification">
<p>In any game there is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo> </mo><mo>%</mo></math> chance he will play less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>8</mn><mo> </mo><mtext>minutes</mtext></math>.</p>
</div>
<div class="specification">
<p>The standard deviation of the number of minutes Emlyn plays in any game is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math>.</p>
</div>
<div class="specification">
<p>There is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mo>%</mo></math> chance Emlyn plays less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> minutes in a game.</p>
</div>
<div class="specification">
<p>Emlyn will play in two basketball games today.</p>
</div>
<div class="specification">
<p>Emlyn and his teammate Johan each practise shooting the basketball multiple times from a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>. A record of their performance over the weekend is shown in the table below.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>On Monday, Emlyn and Johan will practise and each will shoot <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math> times from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a diagram to represent this information.</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>m</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>7</mn></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 probability that Emlyn plays between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>minutes</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mtext>minutes</mtext></math> in a game.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Emlyn plays more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>minutes</mtext></math> in a game.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></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 probability he plays between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>minutes</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mtext>minutes</mtext></math> in one game and more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>minutes</mtext></math> in the other game.</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>Find the expected number of successful shots Emlyn will make on Monday, based on the results from Saturday and Sunday.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Emlyn claims the results from Saturday and Sunday show that his expected number of successful shots will be more than Johan’s.</p>
<p>Determine if Emlyn’s claim is correct. Justify your reasoning.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong><img 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"> </strong> <strong><em>(A1)(A1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for bell shaped curve with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> <strong>or</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>6</mn></math> indicated. Award <em><strong>(A1)</strong></em> for approximately correct shaded region.</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>17</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability equation using <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>3</mn></math> <strong>OR</strong> correctly shaded diagram indicating <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>8</mn></math>. Strict or weak inequalities are accepted in parts (b), (c) and (d).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>13</mn><mo>.</mo><mn>6</mn><mo>+</mo><mn>17</mn><mo>.</mo><mn>8</mn></mrow><mn>2</mn></mfrac></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mfrac><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>13</mn><mo>.</mo><mn>6</mn><mo>+</mo><mfrac><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M0)(M1)</strong></em> for unsupported <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>13</mn><mo>.</mo><mn>6</mn><mo>+</mo><mn>17</mn><mo>.</mo><mn>8</mn></mrow><mn>2</mn></mfrac></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mfrac><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>13</mn><mo>.</mo><mn>6</mn><mo>+</mo><mfrac><mrow><mn>17</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math> <strong>OR</strong> the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>6</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>8</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>7</mn></math>. <br>Award at most <em><strong>(M1)(M0)</strong></em> if the final answer is not seen. Award <em><strong>(M0)(M0)</strong></em> for using known values <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>7</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mn>4</mn></math> to validate <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mn>17</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>7</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>7</mn></math><strong> </strong> <strong><em>(AG)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mn>13</mn><mo>≤</mo><mi>T</mi><mo>≤</mo><mn>18</mn></mrow></mfenced></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability equation <strong>OR</strong> correctly shaded diagram indicating <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math>.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>468</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>46</mn><mo>.</mo><mn>8</mn><mo>%</mo><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>467516</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)(G2)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>≥</mo><mn>20</mn></mrow></mfenced></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability equation <strong>OR</strong> correctly shaded diagram indicating <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math>.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>141</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>14</mn><mo>.</mo><mn>1</mn><mo>%</mo><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>141187</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)(G2)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo><</mo><mi>t</mi></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><strong><img src="data:image/png;base64,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"> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability equation <strong>OR</strong> for a correctly shaded region with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> indicated to the right-hand side of the mean.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>.</mo><mn>7</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>16</mn><mo>.</mo><mn>7133</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)(G2)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>467516</mn><mo>…</mo><mo>×</mo><mn>0</mn><mo>.</mo><mn>141187</mn><mo>…</mo><mo>×</mo><mn>2</mn></math><strong> </strong> <strong><em>(M1)(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>467516</mn><mo>…</mo><mo>×</mo><mn>0</mn><mo>.</mo><mn>141187</mn><mo>…</mo></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>141187</mn><mo>…</mo><mo>×</mo><mn>0</mn><mo>.</mo><mn>467516</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(M1)(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for the multiplication of their parts (c)(i) and (c)(ii), <em><strong>(M1)</strong></em> for multiplying their product by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> or for adding their products twice. Follow through from part (c).</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>132</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>13</mn><mo>.</mo><mn>2</mn><mo>%</mo><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>132014</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(G0)</strong></em> for an unsupported final answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>066007</mn><mo>…</mo></math></p>
<p><br><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>69</mn><mn>102</mn></mfrac><mo>×</mo><mn>200</mn></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct probability multiplied by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math>.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>135</mn><mo>.</mo><mn>294</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(A1)</em><em>(G2)</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>67</mn><mn>98</mn></mfrac><mo>×</mo><mn>200</mn><mo>=</mo></mrow></mfenced><mo> </mo><mn>136</mn><mo>.</mo><mn>734</mn><mo>…</mo></math><strong> </strong> <strong><em>(A1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>137</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>136</mn><mo>.</mo><mn>734</mn><mo>…</mo></math> seen.</p>
<p><br>Emlyn is incorrect,<strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135</mn><mo><</mo><mn>137</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>135</mn><mo>.</mo><mn>294</mn><mo>…</mo><mo><</mo><mn>136</mn><mo>.</mo><mn>734</mn><mo>…</mo></mrow></mfenced></math> </strong> <strong><em>(R1)</em></strong></p>
<p><strong><br>Note:</strong> To award the final <em><strong>(R1)</strong></em>, both the conclusion and the comparison must be seen. Award at most <em><strong>(A0)(R1)</strong></em><strong>(ft)</strong> for consistent incorrect methods in parts (f) and (g).</p>
<p><br><strong>OR</strong></p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>67</mn><mn>98</mn></mfrac><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>684</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>683673</mn><mo>…</mo></mrow></mfenced><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>69</mn><mn>102</mn></mfrac><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>676</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>676470</mn><mo>…</mo></mrow></mfenced></math><strong> </strong> <strong><em>(A1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for both correct probabilities seen.</p>
<p><br>Emlyn is incorrect,<strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>676</mn><mo><</mo><mn>0</mn><mo>.</mo><mn>684</mn></math> </strong> <strong><em>(R1)</em></strong></p>
<p><strong><br>Note:</strong> To award the final <em><strong>(R1)</strong></em>, both the conclusion and the comparison must be seen. Award at most <em><strong>(A0)(R1)</strong></em><strong>(ft)</strong> for consistent incorrect methods in parts (f) and (g).</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> is normally distributed with mean, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
<mi>μ<!-- μ --></mi>
</math></span>. In the following diagram, the shaded region between 9 and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
<mi>μ<!-- μ --></mi>
</math></span> represents 30% of the distribution.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.15.49.png" alt="M17/5/MATME/SP2/ENG/TZ1/09"></p>
</div>
<div class="specification">
<p>The standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> is 2.1.</p>
</div>
<div class="specification">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y">
<mi>Y</mi>
</math></span> is normally distributed with mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ<!-- λ --></mi>
</math></span> and standard deviation 3.5. The events <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X > 9">
<mi>X</mi>
<mo>></mo>
<mn>9</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y > 9">
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
</math></span> are independent, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( {(X > 9) \cap (Y > 9)} \right) = 0.4">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>∩<!-- ∩ --></mo>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.4</mn>
</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="{\text{P}}(X < 9)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
</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="\mu ">
<mi>μ</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</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>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y > 9">
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
</math></span>, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(Y < 13)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo><</mo>
<mn>13</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < \mu ) = 0.5,{\text{ }}0.5 - 0.3">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mi>μ</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.5</mn>
<mo>−</mo>
<mn>0.3</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 9) = 0.2">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.2</mn>
</math></span> (exact) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = - 0.841621">
<mi>z</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.841621</mn>
</math></span> (may be seen in equation) <strong><em>(A1)</em></strong></p>
<p>valid attempt to set up an equation with <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z">
<mi>z</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.842 = \frac{{\mu - X}}{\sigma },{\text{ }} - 0.842 = \frac{{X - \mu }}{\sigma },{\text{ }}z = \frac{{9 - \mu }}{{2.1}}">
<mo>−</mo>
<mn>0.842</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mi>μ</mi>
<mo>−</mo>
<mi>X</mi>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>0.842</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mi>X</mi>
<mo>−</mo>
<mi>μ</mi>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>z</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>9</mn>
<mo>−</mo>
<mi>μ</mi>
</mrow>
<mrow>
<mn>2.1</mn>
</mrow>
</mfrac>
</math></span></p>
<p>10.7674</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu = 10.8">
<mi>μ</mi>
<mo>=</mo>
<mn>10.8</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X > 9) = 0.8">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.8</mn>
</math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(A) \times {\text{P}}(B)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>A</mi>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>B</mi>
<mo stretchy="false">)</mo>
</math></span></p>
<p>correct equation <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.8 \times {\text{P}}(Y > 9) = 0.4">
<mn>0.8</mn>
<mo>×</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.4</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(Y > 9) = 0.5">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.5</mn>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda = 9">
<mi>λ</mi>
<mo>=</mo>
<mn>9</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(9 < Y < 13) = 0.373450">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>9</mn>
<mo><</mo>
<mi>Y</mi>
<mo><</mo>
<mn>13</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.373450</mn>
</math></span> (seen anywhere) <strong><em>(A2)</em></strong></p>
<p>recognizing conditional probability <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(A|B),{\text{ P}}(Y < 13|Y > 9)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>A</mi>
<mrow>
<mo stretchy="false">|</mo>
</mrow>
<mi>B</mi>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>Y</mi>
<mo><</mo>
<mn>13</mn>
<mrow>
<mo stretchy="false">|</mo>
</mrow>
<mi>Y</mi>
<mo>></mo>
<mn>9</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{0.373}}}}{{0.5}}">
<mfrac>
<mrow>
<mrow>
<mtext>0.373</mtext>
</mrow>
</mrow>
<mrow>
<mn>0.5</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.746901</p>
<p>0.747 <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>The heights of adult males in a country are normally distributed with a mean of 180 cm and a standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma {\text{ cm}}">
<mi>σ</mi>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span>. 17% of these men are shorter than 168 cm. 80% of them have heights between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(192 - h){\text{ cm}}">
<mo stretchy="false">(</mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span> and 192 cm.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>finding the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z">
<mi>z</mi>
</math></span>-value for 0.17 <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = - 0.95416">
<mi>z</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.95416</mn>
</math></span></p>
<p>setting up equation to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ</mi>
</math></span><em>, <strong>(M1)</strong></em></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = \frac{{168 - 180}}{\sigma },{\text{ }} - 0.954 = \frac{{ - 12}}{\sigma }">
<mi>z</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>168</mn>
<mo>−</mo>
<mn>180</mn>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>0.954</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>12</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma = 12.5765">
<mi>σ</mi>
<mo>=</mo>
<mn>12.5765</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><strong>EITHER (Properties of the Normal curve)</strong></p>
<p>correct value (seen anywhere) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 192) = 0.83,{\text{ P}}(X > 192) = 0.17">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.83</mn>
<mo>,</mo>
<mrow>
<mtext> P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.17</mn>
</math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 192 - h) = 0.83 - 0.8,{\text{ P}}(X < 192 - h) = 1 - 0.8 - 0.17,">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.83</mn>
<mo>−</mo>
<mn>0.8</mn>
<mo>,</mo>
<mrow>
<mtext> P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo>−</mo>
<mn>0.8</mn>
<mo>−</mo>
<mn>0.17</mn>
<mo>,</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X > 192 - h) = 0.8 + 0.17">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>></mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.8</mn>
<mo>+</mo>
<mn>0.17</mn>
</math></span></p>
<p>correct equation in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{(192 - h) - 180}}{{12.576}} = - 1.88079,{\text{ }}192 - h = 156.346">
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mn>180</mn>
</mrow>
<mrow>
<mn>12.576</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mo>−</mo>
<mn>1.88079</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>192</mn>
<mo>−</mo>
<mi>h</mi>
<mo>=</mo>
<mn>156.346</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p>35.6536</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 35.7">
<mi>h</mi>
<mo>=</mo>
<mn>35.7</mn>
</math></span> <strong><em>A1 N3</em></strong></p>
<p><strong>OR (Trial and error using different values of <em>h</em>)</strong></p>
<p><strong>two</strong> correct probabilities whose 2 sf will round up <strong>and</strong> down, respectively, to 0.8 <strong><em>A2</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(192 - 35.6 < X < 192) = 0.799706,{\text{ P}}(157 < X < 192) = 0.796284,">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>192</mn>
<mo>−</mo>
<mn>35.6</mn>
<mo><</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.799706</mn>
<mo>,</mo>
<mrow>
<mtext> P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>157</mn>
<mo><</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.796284</mn>
<mo>,</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(192 - 36 < X < 192) = 0.801824">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>192</mn>
<mo>−</mo>
<mn>36</mn>
<mo><</mo>
<mi>X</mi>
<mo><</mo>
<mn>192</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.801824</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 35.7">
<mi>h</mi>
<mo>=</mo>
<mn>35.7</mn>
</math></span> <strong><em>A2</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Arianne plays a game of darts.</p>
<p style="text-align: center;"><img 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"></p>
<p>The distance that her darts land from the centre, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>, of the board can be modelled by a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>cm</mtext></math>.</p>
</div>
<div class="specification">
<p>Find the probability that</p>
</div>
<div class="specification">
<p>Each of Arianne’s throws is independent of her previous throws.</p>
</div>
<div class="specification">
<p>In a competition a player has three darts to throw on each turn. A point is scored if a player throws <strong>all</strong> three darts to land within a central area around <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>. When Arianne throws a dart the probability that it lands within this area is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>8143</mn></math>.</p>
</div>
<div class="specification">
<p>In the competition Arianne has ten turns, each with three darts.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>a dart lands less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>cm</mtext></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>.</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>a dart lands more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mtext>cm</mtext></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Arianne throws two consecutive darts that land more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mtext>cm</mtext></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</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 probability that Arianne does <strong>not</strong> score a point on a turn of three darts.</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 probability that Arianne scores at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> points in the competition.</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>Find the probability that Arianne scores at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> points and less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> points.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that Arianne scores at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> points, find the probability that Arianne scores less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> points.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> be the random variable “distance from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>”.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>10</mn><mo>,</mo><mo> </mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo><</mo><mn>13</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>841</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>841344</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mn>15</mn></mrow></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>0</mn><mo>.</mo><mn>0478</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0477903</mn></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mn>15</mn></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>></mo><mn>15</mn></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>00228</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>00228391</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>8143</mn></mrow></mfenced><mn>3</mn></msup></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>460</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>460050</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi></math> be the random variable “number of points scored”</p>
<p>evidence of use of binomial distribution <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>10</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>539949</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>P</mtext><mfenced><mrow><mi>Y</mi><mo>≥</mo><mn>5</mn></mrow></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>717</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>716650</mn><mo>…</mo></mrow></mfenced></math>. <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math> be the random variable “number of times a point is not scored”</p>
<p>evidence of use of binomial distribution <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>10</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>460050</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>P</mtext><mfenced><mrow><mi>Q</mi><mo>≤</mo><mn>5</mn></mrow></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>717</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>716650</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mn>5</mn><mo>≤</mo><mi>Y</mi><mo><</mo><mn>8</mn></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>628</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>627788</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for a correct probability statement or indication of correct lower and upper bounds, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math>.<br><br></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>P</mtext><mfenced><mrow><mn>5</mn><mo>≤</mo><mi>Y</mi><mo><</mo><mn>8</mn></mrow></mfenced></mrow><mrow><mtext>P</mtext><mfenced><mrow><mi>Y</mi><mo>≥</mo><mn>5</mn></mrow></mfenced></mrow></mfrac><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>627788</mn><mo>…</mo></mrow><mrow><mn>0</mn><mo>.</mo><mn>716650</mn><mo>…</mo></mrow></mfrac></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>876</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>876003</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Candidates appeared well prepared for straightforward questions using the normal distribution. Most were able to earn marks through recognition of the compound probability event in part (b). The wording of the information in part (c) required careful thought. This acted as a clear discriminator, causing difficulty for most candidates. One common error in this part was the calculation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>8143</mn></mrow></mfenced><mn>2</mn></msup></math>. Though at the end of the paper, it was pleasing to see many candidates identify the event in part (d) as binomial. A common error was the use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>8413</mn></math>. It is recommended that candidates write down the distribution with associated parameters and support this with a probability statement. This will allow method and follow-through marks to be awarded in subsequent parts. Weaker candidates incorrectly used <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> as the upper bound. Those who made it to the end of the paper were often rewarded for correct division of their probabilities found in parts (d)(i)&(ii).</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates appeared well prepared for straightforward questions using the normal distribution. Most were able to earn marks through recognition of the compound probability event in part (b). The wording of the information in part (c) required careful thought. This acted as a clear discriminator, causing difficulty for most candidates. One common error in this part was the calculation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>8143</mn></mrow></mfenced><mn>2</mn></msup></math>. Though at the end of the paper, it was pleasing to see many candidates identify the event in part (d) as binomial. A common error was the use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>8413</mn></math>. It is recommended that candidates write down the distribution with associated parameters and support this with a probability statement. This will allow method and follow-through marks to be awarded in subsequent parts. Weaker candidates incorrectly used <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> as the upper bound. Those who made it to the end of the paper were often rewarded for correct division of their probabilities found in parts (d)(i)&(ii).</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates appeared well prepared for straightforward questions using the normal distribution. Most were able to earn marks through recognition of the compound probability event in part (b). The wording of the information in part (c) required careful thought. This acted as a clear discriminator, causing difficulty for most candidates. One common error in this part was the calculation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>8143</mn></mrow></mfenced><mn>2</mn></msup></math>. Though at the end of the paper, it was pleasing to see many candidates identify the event in part (d) as binomial. A common error was the use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>8413</mn></math>. It is recommended that candidates write down the distribution with associated parameters and support this with a probability statement. This will allow method and follow-through marks to be awarded in subsequent parts. Weaker candidates incorrectly used <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> as the upper bound. Those who made it to the end of the paper were often rewarded for correct division of their probabilities found in parts (d)(i)&(ii).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates appeared well prepared for straightforward questions using the normal distribution. Most were able to earn marks through recognition of the compound probability event in part (b). The wording of the information in part (c) required careful thought. This acted as a clear discriminator, causing difficulty for most candidates. One common error in this part was the calculation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>8143</mn></mrow></mfenced><mn>2</mn></msup></math>. Though at the end of the paper, it was pleasing to see many candidates identify the event in part (d) as binomial. A common error was the use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>8413</mn></math>. It is recommended that candidates write down the distribution with associated parameters and support this with a probability statement. This will allow method and follow-through marks to be awarded in subsequent parts. Weaker candidates incorrectly used <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> as the upper bound. Those who made it to the end of the paper were often rewarded for correct division of their probabilities found in parts (d)(i)&(ii).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates appeared well prepared for straightforward questions using the normal distribution. Most were able to earn marks through recognition of the compound probability event in part (b). The wording of the information in part (c) required careful thought. This acted as a clear discriminator, causing difficulty for most candidates. One common error in this part was the calculation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>8143</mn></mrow></mfenced><mn>2</mn></msup></math>. Though at the end of the paper, it was pleasing to see many candidates identify the event in part (d) as binomial. A common error was the use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>8413</mn></math>. It is recommended that candidates write down the distribution with associated parameters and support this with a probability statement. This will allow method and follow-through marks to be awarded in subsequent parts. Weaker candidates incorrectly used <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> as the upper bound. Those who made it to the end of the paper were often rewarded for correct division of their probabilities found in parts (d)(i)&(ii).</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates appeared well prepared for straightforward questions using the normal distribution. Most were able to earn marks through recognition of the compound probability event in part (b). The wording of the information in part (c) required careful thought. This acted as a clear discriminator, causing difficulty for most candidates. One common error in this part was the calculation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>8143</mn></mrow></mfenced><mn>2</mn></msup></math>. Though at the end of the paper, it was pleasing to see many candidates identify the event in part (d) as binomial. A common error was the use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>8413</mn></math>. It is recommended that candidates write down the distribution with associated parameters and support this with a probability statement. This will allow method and follow-through marks to be awarded in subsequent parts. Weaker candidates incorrectly used <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> as the upper bound. Those who made it to the end of the paper were often rewarded for correct division of their probabilities found in parts (d)(i)&(ii).</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates appeared well prepared for straightforward questions using the normal distribution. Most were able to earn marks through recognition of the compound probability event in part (b). The wording of the information in part (c) required careful thought. This acted as a clear discriminator, causing difficulty for most candidates. One common error in this part was the calculation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>8143</mn></mrow></mfenced><mn>2</mn></msup></math>. Though at the end of the paper, it was pleasing to see many candidates identify the event in part (d) as binomial. A common error was the use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>8413</mn></math>. It is recommended that candidates write down the distribution with associated parameters and support this with a probability statement. This will allow method and follow-through marks to be awarded in subsequent parts. Weaker candidates incorrectly used <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> as the upper bound. Those who made it to the end of the paper were often rewarded for correct division of their probabilities found in parts (d)(i)&(ii).</p>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 7 adult men wanted to see if there was a relationship between their Body Mass Index (BMI) and their waist size. Their waist sizes, in centimetres, were recorded and their BMI calculated. The following table shows the results.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the BMI of an adult man whose waist size is 95 cm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> (or for correct <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^2}">
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> = 0.955631 seen in (ii))</p>
<p>0.141120, 11.1424</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> = 0.141, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> = 11.1 <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.977563</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> = 0.978 <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into <strong>their</strong> regression equation <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.141(95) + 11.1</p>
<p>24.5488</p>
<p>24.5 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( 8 \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{y'}"> <mrow> <msup> <mi>y</mi> <mo>′</mo> </msup> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 16{x^{ - 2}}"> <mo>−</mo> <mn>16</mn> <mrow> <msup> <mi>x</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></span></p>
<p>−0.25 (exact) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>u</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} 4 \\ { - 1} \end{array}} \right)"> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> or any scalar multiple <em><strong>A2 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct scalar product and magnitudes <em><strong>(A1)(A1)(A1)</strong></em></p>
<p>scalar product <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 1 \times 4 + 1 \times - 1\,\,\,\left( { = 3} \right)"> <mo>=</mo> <mn>1</mn> <mo>×</mo> <mn>4</mn> <mo>+</mo> <mn>1</mn> <mo>×</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>magnitudes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \sqrt {{1^2} + {1^2}} "> <mo>=</mo> <msqrt> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> </msqrt> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {{4^2} + {{\left( { - 1} \right)}^2}} "> <msqrt> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \sqrt 2 {\text{,}}\,\,\sqrt {17} } \right)"> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <msqrt> <mn>2</mn> </msqrt> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <msqrt> <mn>17</mn> </msqrt> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>substitution of their values into correct formula <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 - 1}}{{\sqrt {{1^2} + {1^2}} \sqrt {{4^2} + {{\left( { - 1} \right)}^2}} }}"> <mfrac> <mrow> <mn>4</mn> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <msqrt> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> </msqrt> <msqrt> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 3}}{{\sqrt 2 \sqrt {17} }}"> <mfrac> <mrow> <mo>−</mo> <mn>3</mn> </mrow> <mrow> <msqrt> <mn>2</mn> </msqrt> <msqrt> <mn>17</mn> </msqrt> </mrow> </mfrac> </math></span>, 2.1112, 120.96° </p>
<p>1.03037 , 59.0362°</p>
<p>angle = 1.03 , 59.0° <em><strong>A1 N4</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">attempt to form composite <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> <strong><em><span style="font-family: 'Verdana',sans-serif;">(M1)</span></em></strong></span></p>
<p><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">eg </span></em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {f\left( x \right)} \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {\frac{{16}}{x}} \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{16}}{{f\left( x \right)}}"> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">correct working <strong><em><span style="font-family: 'Verdana',sans-serif;">(A1)</span></em></strong></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{16}}{{\frac{{16}}{x}}}"> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </mrow> </mfrac> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="16 \times \frac{x}{{16}}"> <mn>16</mn> <mo>×</mo> <mfrac> <mi>x</mi> <mrow> <mn>16</mn> </mrow> </mfrac> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right) = x"> <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> <mo>=</mo> <mi>x</mi> </math></span> <strong><em><span style="font-family: 'Verdana',sans-serif;">A1 N2</span></em></strong></span></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right) = \frac{{16}}{x}"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{{16}}{x}"> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{16}}{x}"> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span>) </span><strong style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><em>A1 N1</em></strong></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>A0</strong></em> in part (ii) if part (i) is incorrect.<br>Award <em><strong>A0</strong></em> in part (ii) if the candidate has found <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right) = \frac{{16}}{x}"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span> by interchanging <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>.</p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[1 mark]</span></em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>recognition of symmetry about <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> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> (2, 8) ⇔ (8, 2) <img src="data:image/png;base64,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"></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">evidence of doubling <strong>their</strong> angle <strong><em> (M1)</em></strong><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times 1.03"> <mn>2</mn> <mo>×</mo> <mn>1.03</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times 59.0"> <mn>2</mn> <mo>×</mo> <mn>59.0</mn> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06075, 118.072°</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06 (radians) (118 degrees) <em><strong>A1 N2</strong></em></span></p>
<p> </p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><strong>METHOD 2</strong><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">finding direction vector for tangent line 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> <em><strong>(A1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 1} \\ 4 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ { - 4} \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">substitution of <strong>their</strong> values into correct formula (must be from vectors) <em><strong>(M1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 4 - 4}}{{\sqrt {{1^2} + {4^2}} \sqrt {{4^2} + {{\left( { - 1} \right)}^2}} }}"> <mfrac> <mrow> <mo>−</mo> <mn>4</mn> <mo>−</mo> <mn>4</mn> </mrow> <mrow> <msqrt> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> </msqrt> <msqrt> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{{\sqrt {17} \sqrt {17} }}"> <mfrac> <mn>8</mn> <mrow> <msqrt> <mn>17</mn> </msqrt> <msqrt> <mn>17</mn> </msqrt> </mrow> </mfrac> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06075, 118.072°</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06 (radians) (118 degrees) <em><strong>A1 N2</strong></em></span></p>
<p> </p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><strong>METHOD 3</strong><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">using trigonometry to find an angle with the horizontal <em><strong>(M1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta = - \frac{1}{4}"> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta = - 4"> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mn>4</mn> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">finding both angles of rotation <em><strong> (A1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\theta _1} = 0.244978{\text{, 14}}{\text{.0362}}^\circ "> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> </mrow> <mo>=</mo> <mn>0.244978</mn> <mrow> <mtext>, 14</mtext> </mrow> <msup> <mrow> <mtext>.0362</mtext> </mrow> <mo>∘</mo> </msup> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\theta _1} = 1.81577{\text{, 104}}{\text{.036}}^\circ "> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> </mrow> <mo>=</mo> <mn>1.81577</mn> <mrow> <mtext>, 104</mtext> </mrow> <msup> <mrow> <mtext>.036</mtext> </mrow> <mo>∘</mo> </msup> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06075, 118.072°</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06 (radians) (118 degrees) <em><strong>A1 N2</strong></em></span></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></em></strong></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights, in grams, of oranges grown in an orchard, are normally distributed with a mean of 297 g. It is known that 79 % of the oranges weigh more than 289 g and 9.5 % of the oranges weigh more than 310 g.</p>
</div>
<div class="specification">
<p>The weights of the oranges have a standard deviation of σ.</p>
</div>
<div class="specification">
<p>The grocer at a local grocery store will buy the oranges whose weights exceed the 35th percentile.</p>
</div>
<div class="specification">
<p>The orchard packs oranges in boxes of 36.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that an orange weighs between 289 g and 310 g.</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 standardized value for 289 g.</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 σ.</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>To the nearest gram, find the minimum weight of an orange that the grocer will buy.</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 probability that the grocer buys more than half the oranges in a box selected at random.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The grocer selects two boxes at random.</p>
<p>Find the probability that the grocer buys more than half the oranges in each box.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>correct approach indicating subtraction <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.79 − 0.095, appropriate shading in diagram</p>
<p>P(289 < <em>w</em> < 310) = 0.695 (exact), 69.5 % <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p>eg 1 − <em>p</em>, 21</p>
<p>−0.806421</p>
<p><em>z</em> = −0.806 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>(i) & (ii)</p>
<p>correct expression for <em>z</em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{289 - u}}{\sigma }">
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mi>u</mi>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> 1 − <em>p</em>, 21</p>
<p>−0.806421</p>
<p><em>z</em> = −0.806 (seen anywhere) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempt to standardize <em><strong>(M1)</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma = \frac{{289 - 297}}{z},\,\,\frac{{289 - 297}}{\sigma }">
<mi>σ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mi>z</mi>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span></p>
<p>correct substitution with their <em>z</em> (do not accept a probability) <em><strong>A1</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.806 = \frac{{289 - 297}}{\sigma },\,\,\frac{{289 - 297}}{{ - 0.806}}">
<mo>−</mo>
<mn>0.806</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>0.806</mn>
</mrow>
</mfrac>
</math></span></p>
<p>9.92037</p>
<p>σ = 9.92 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>(i) & (ii)</p>
<p>correct expression for <em>z</em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{289 - u}}{\sigma }">
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mi>u</mi>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> 1 − <em>p</em>, 21</p>
<p>−0.806421</p>
<p><em>z</em> = −0.806 (seen anywhere) <em><strong>A1 N2</strong></em></p>
<p>valid attempt to set up an equation with <strong>their</strong> <em>z</em> (do not accept a probability) <em><strong>(M1)</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.806 = \frac{{289 - 297}}{\sigma },\,\,\frac{{289 - 297}}{{ - 0.806}}">
<mo>−</mo>
<mn>0.806</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>289</mn>
<mo>−</mo>
<mn>297</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>0.806</mn>
</mrow>
</mfrac>
</math></span></p>
<p>9.92037</p>
<p>σ = 9.92 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> P(<em>W</em> < <em>w</em>) = 0.35, −0.338520 (accept 0.385320), diagram showing values in a standard normal distribution</p>
<p>correct score at the 35th percentile <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 293.177</p>
<p>294 (g) <em><strong>A1 N2</strong></em></p>
<p><strong>Note:</strong> If working shown, award <em><strong>(M1)(A1)A0</strong></em> for 293.<br>If no working shown, award <em><strong>N1</strong></em> for 293.177, <em><strong>N1</strong></em> for 293.</p>
<p>Exception to the <em><strong>FT</strong> </em>rule: If the score is incorrect, and working shown, award <em><strong>A1FT</strong></em> for correctly finding their minimum weight (by rounding up)</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of recognizing binomial (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \sim {\text{B}}\left( {36,\,\,p} \right),\,\,{}_n{C_a} \times {p^a} \times {q^{n - a}}">
<mi>X</mi>
<mo>∼</mo>
<mrow>
<mtext>B</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>36</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>p</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<msub>
<mrow>
</mrow>
<mi>n</mi>
</msub>
<mrow>
<msub>
<mi>C</mi>
<mi>a</mi>
</msub>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>p</mi>
<mi>a</mi>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>q</mi>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mi>a</mi>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>correct probability (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.65</p>
<p><strong>EITHER</strong></p>
<p>finding P(<em>X</em> ≤ 18) from GDC <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.045720</p>
<p>evidence of using complement <em><strong>(M1)</strong></em></p>
<p><em>eg</em> 1−P(<em>X</em> ≤ 18)</p>
<p>0.954279</p>
<p>P(<em>X</em> > 18) = 0.954 <em><strong>A1 N2</strong></em></p>
<p><strong>OR</strong></p>
<p>recognizing P(<em>X</em> > 18) = P(<em>X</em> ≥ 19) <em><strong>(M1)</strong></em></p>
<p>summing terms from 19 to 36 <em><strong>(A1)</strong></em></p>
<p><em>eg</em> P(<em>X</em> = 19) + P(<em>X</em> = 20) + … + P(<em>X</em> = 36)</p>
<p>0.954279</p>
<p>P(<em>X</em> > 18) = 0.954 <em><strong>A1 N2</strong></em></p>
<p><strong>[<em>5</em><em> marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct calculation <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{0.954^2},\,\,\left( \begin{gathered} 2 \hfill \\ 2 \hfill \\ \end{gathered} \right){0.954^2}{\left( {1 - 0.954} \right)^0}">
<mrow>
<msup>
<mn>0.954</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mn>0.954</mn>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>0.954</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>0</mn>
</msup>
</mrow>
</math></span></p>
<p>0.910650</p>
<p>0.911 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows a probability distribution for the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X) = 1.2">
<mrow>
<mtext>E</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1.2</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.18.09.png" alt="M17/5/MATME/SP2/ENG/TZ2/10"></p>
</div>
<div class="specification">
<p>A bag contains white and blue marbles, with at least three of each colour. Three marbles are drawn from the bag, without replacement. The number of blue marbles drawn is given by the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>A game is played in which three marbles are drawn from the bag of ten marbles, without replacement. A player wins a prize if three white marbles are drawn.</p>
</div>
<div class="question">
<p>Jill plays the game nine times. Find the probability that she wins exactly two prizes.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}(n,{\text{ }}p),{\text{ }}\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){p^r}{q^{n - r}},{\text{ }}{(0.167)^2}{(0.833)^7},{\text{ }}\left( {\begin{array}{*{20}{c}} 9 \\ 2 \end{array}} \right)">
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>p</mi>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>n</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mi>p</mi>
<mi>r</mi>
</msup>
</mrow>
<mrow>
<msup>
<mi>q</mi>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mi>r</mi>
</mrow>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.167</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.833</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>9</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>0.279081</p>
<p>0.279 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Ten students were surveyed about the number of hours, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, they spent browsing the Internet during week 1 of the school year. The results of the survey are given below.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\sum\limits_{i = 1}^{10} {{x_i} = 252,{\text{ }}\sigma = 5{\text{ and median}} = 27.} ">
<munderover>
<mo movablelimits="false">∑<!-- ∑ --></mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</munderover>
<mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>252</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>σ<!-- σ --></mi>
<mo>=</mo>
<mn>5</mn>
<mrow>
<mtext> and median</mtext>
</mrow>
<mo>=</mo>
<mn>27.</mn>
</mrow>
</math></span></p>
</div>
<div class="specification">
<p>During week 4, the survey was extended to all 200 students in the school. The results are shown in the cumulative frequency graph:</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.35.16.png" alt="N16/5/MATME/SP2/ENG/TZ0/08.d"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the mean number of hours spent browsing the Internet.</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>During week 2, the students worked on a major project and they each spent an additional five hours browsing the Internet. For week 2, write down</p>
<p>(i) the mean;</p>
<p>(ii) the standard deviation.</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>During week 3 each student spent 5% less time browsing the Internet than during week 1. For week 3, find</p>
<p>(i) the median;</p>
<p>(ii) the variance.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the number of students who spent between 25 and 30 hours browsing the Internet.</p>
<p>(ii) Given that 10% of the students spent more than <em>k </em>hours browsing the Internet, find the maximum value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>attempt to substitute into formula for mean <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Sigma x}}{{10}},{\text{ }}\frac{{252}}{n},{\text{ }}\frac{{252}}{{10}}"> <mfrac> <mrow> <mi mathvariant="normal">Σ</mi> <mi>x</mi> </mrow> <mrow> <mn>10</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mn>252</mn> </mrow> <mi>n</mi> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mn>252</mn> </mrow> <mrow> <mn>10</mn> </mrow> </mfrac> </math></span></p>
<p>mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 25.2{\text{ (hours)}}"> <mo>=</mo> <mn>25.2</mn> <mrow> <mtext> (hours)</mtext> </mrow> </math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 30.2{\text{ (hours)}}"> <mo>=</mo> <mn>30.2</mn> <mrow> <mtext> (hours)</mtext> </mrow> </math></span> <strong><em>A1 N1</em></strong></p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma = 5{\text{ (hours)}}"> <mi>σ</mi> <mo>=</mo> <mn>5</mn> <mrow> <mtext> (hours)</mtext> </mrow> </math></span> <strong><em>A1 N1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>95%, 5% of 27</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.95 \times 27,{\text{ }}27 - (5\% {\text{ of }}27)"> <mn>0.95</mn> <mo>×</mo> <mn>27</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>27</mn> <mo>−</mo> <mo stretchy="false">(</mo> <mn>5</mn> <mi mathvariant="normal">%</mi> <mrow> <mtext> of </mtext> </mrow> <mn>27</mn> <mo stretchy="false">)</mo> </math></span></p>
<p>median <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 25.65{\text{ (exact), }}25.7{\text{ (hours)}}"> <mo>=</mo> <mn>25.65</mn> <mrow> <mtext> (exact), </mtext> </mrow> <mn>25.7</mn> <mrow> <mtext> (hours)</mtext> </mrow> </math></span> <strong><em>A1 N2</em></strong></p>
<p>(ii) <strong>METHOD 1</strong></p>
<p>variance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = {({\text{standard deviation}})^2}"> <mo>=</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mtext>standard deviation</mtext> </mrow> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> </math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p>valid attempt to find new standard deviation <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sigma _{new}} = 0.95 \times 5,{\text{ }}4.75"> <mrow> <msub> <mi>σ</mi> <mrow> <mi>n</mi> <mi>e</mi> <mi>w</mi> </mrow> </msub> </mrow> <mo>=</mo> <mn>0.95</mn> <mo>×</mo> <mn>5</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>4.75</mn> </math></span></p>
<p>variance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 22.5625{\text{ }}({\text{exact}}),{\text{ }}22.6"> <mo>=</mo> <mn>22.5625</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>exact</mtext> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>22.6</mn> </math></span> <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>variance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = {({\text{standard deviation}})^2}"> <mo>=</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mtext>standard deviation</mtext> </mrow> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> </math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p>valid attempt to find new variance <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{0.95^2}{\text{ }},{\text{ }}0.9025 \times {\sigma ^2}"> <mrow> <msup> <mn>0.95</mn> <mn>2</mn> </msup> </mrow> <mrow> <mtext> </mtext> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.9025</mn> <mo>×</mo> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> </mrow> </math></span></p>
<p>new variance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 22.5625{\text{ }}({\text{exact}}),{\text{ }}22.6"> <mo>=</mo> <mn>22.5625</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>exact</mtext> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>22.6</mn> </math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) both correct frequencies <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>80, 150</p>
<p>subtracting <strong>their </strong>frequencies in either order <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="150 - 80,{\text{ }}80 - 150"> <mn>150</mn> <mo>−</mo> <mn>80</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>80</mn> <mo>−</mo> <mn>150</mn> </math></span></p>
<p>70 (students) <strong><em>A1 N2</em></strong></p>
<p>(ii) evidence of a valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>10% of 200, 90%</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.90 \times 200,{\text{ }}200 - 20"> <mn>0.90</mn> <mo>×</mo> <mn>200</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>200</mn> <mo>−</mo> <mn>20</mn> </math></span>, 180 students</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 35"> <mi>k</mi> <mo>=</mo> <mn>35</mn> </math></span> <strong><em>A1 N3</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the mean weight, <em>y</em> kg , of children who are <em>x</em> years old.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdMAAABRCAYAAACJ8UzKAAAgAElEQVR4Ae2dC3RUVZrv/1UwyGAAmyUjJ+DAmEiGmaS1TVa47TjXCpGKttPKBQEbhwo3uXdkDbauyzIVw5W5OtrSpLLi6EiPtlPVPFq6QSsL2+s0BCvW7YXdk6wKLcJdUOngAB2q6BtXJA+RV9W+a59XnTp1KnXqEfL6aq2sOnXOfnz7d76zv72//e0TC2OMgT5EgAgQASJABIhAxgSsGeekjESACBABIkAEiIBIgIwpKQIRIAJEgAgQgSwJkDHNEiBlJwJEgAgQASIwVUFgsViUQ/omAkSACBABIkAEUhDQhhypxpTn0V5IUQZdnmQE+GBrsusHMQCIATHgXR/pgcRAawbIzaulQcdEgAgQASJABDIgQMY0A2iUhQgQASJABIiAlgAZUy0NOiYCRIAIEAEikAEBMqYZQKMsRIAIEAEiQAS0BMiYamnQMREgAkSACBCBDAiQMc0AGmUhAkSACBABIqAlQMZUS4OOiQARIAJEgAhkQICMaQbQKAsRIAJEgAgQAS0BMqZaGnRMBIgAESACRCADAmRMM4BGWYgAESACRIAIaAlkbkyjp+CpyhdfK8VfLZVf34YBbck39DiKoc5XUWHJR5XnFKI3tO7Rqyza5UGVJR8VTR0YGj0x0qw5iqEuP1rea0J14Ra0DZi5WwPoOvwqqvMtkr5V1GNXZ9j4Pg+0oV5JZ+Hp18DTdTlNGUcyOW//ITRVl8jPThXqd3UgnBLDRGJgxPcqwh075Hucj4r6FnQNpYQiF/QF2urL1L7IMiH6gas43/IU8qs86DKLQaSRaT6je3IjzkUx0LYF+eKzKj/fKdusf4ZKUN10yEBfMik7izbzfw7OP9KreeUfJr4iQTezA2I+nhdYzdzBr03kHIEkkZPMbRcYhAbm64+MQAVjtche5nOW3hD26epHMmJcbx5e52DrBJi8X1dYz4E3WHNrkA3yQiMh1t7sYAIeZq7Al7pqrrAe7yYmaPXS7mbBHKlELhhEej5kzc0HWXCQC3WFhdrfYA5BYDZXu9Q+XYuknxOLQWITI2zw6AG2sz3EOJVI6AhrdhQzwelj/YmJE85EeryshuuTet9Hti/KhR4kNEJ3Qm1TmvqbaT5d9Sl/5oxB5Azz1hRr7p3A7O6Toh4kE0JqYzFzuI/LfUIP8zXYE/Ulg7KT1Wl0Xs+Av7xc/OgvKOeNv79mQfdqEYCw+Q32YxFGagjGZWV7NsL6fQ1iB2r24cu2xrGT/8a1PT39SEVI1h8zg5/I5+zjj8/FP1zy4Cnhfg+2M5d964gNqLJn8DXr/vg3rCfOuJtgMaEYGOhGQvtkvTajH+xLFnA5mNPXa1DwyJzKXg9SyMX12PEMczqKGdIxppnmSyGO0eXcMIiwwUAzs5scNElyGD8v4uQuTl8yKduopcnP6Rlk5uaNnsGRfUcAlGL9w6ux9onvQkAYrft+je4El4RuSi666LrQ0VQhumUKmzpxXZxZ83Rt8NRXye4a7urxoK0rlfO4D4FDrQijAMuX3olZmc7SVbd1oqtYcqdaYMlX3JImZR3qwuGmao0Lg7sjWtAZvipL+Xu0VBfCYqnAD1vew5YK7jZX6h9AV5sH9eK5mHvT09alcelaMWtJGZYDCO/5CAFTLtNMAY1SPuufwWa7HXGKar0Vi+7O1wkUxUDHATS3/ite+oEbLXGcdElH7ed0FNj+E+bHNWYa5i0qhDCcTBOKgUFDE9p3FRfOnEXR5hUonxUHKzHzwFHsb96Nxpdc8LT4DVx9iVnG9pmL6HxzL/D036Nq3k1piJppvjSqyHnSPnTsfwetjdvxA0+Lib6eCyA/L+HPcPR3im2IYqinG6fXP4AyVV8yKTvLBip2V29llfNG36qLVxkJ9PuYU3SzJLreVLeD6oLh7r0VzLFOmtoXuALsGnftJLhqZLeNUMPcJ4dx9qh1x7t2IqEAO+D9MXPan2HenitiMyKhVtZgE5KM9mKzvPjRoGYWLo+gTMma4GKIuaGEGq88OznHvI4CjYuDpyllTt8fxBGbTctMPdYxVlzcYr6RG52nox9GOhN/znh0GZ9muF/cvW1nNd4zsRmrykHhLDCb0yu7U4cry/y13DJQ6pX0rkDVCeV8qu+JxEDT1sEg87kbmKOhlYXiZvCaNOph7Nnk90b8szUwb3CY/kLNm/nByOgBl4fPpl5jDtHlLy/hmJqZZppvdBmodkS5d7Azp/fkMMsdsrx8Bs77cdk28H59q/NfWHtI6udFkgnLkCbLTgOJXg8ycPPGFDjmZlPW7qDzW8fSwvYC84mNvcJCvheYYigkY6rk1/jBWT876a5J6b5Vb4hi2DmMkJc51Bskr0cpN4CfT6agRoZZ7aQVY21OVlUuWzMLyOtj6npegYsF+AiCaYypki7yFRv8qp8FXDbJja66QLg762Gpw4iTX5FnZN3sesVJQ+cMkmZpTPl9sitcdcVHQixw4MfMyR82pFqL1OVN8TO3DJTK+P1zGKz/KteTfE8oBryNmsEsf0bTMopXWCjwAXM77bJBTaIbSVCme3pk9IAxJrppX5P7C/m5jnvWk0iaab4kxZk5nUsG4sTH7ZRtgm6ykEQYZV2dy5G0PxfX3wPsQJplJ6ky4bSeQfrGVDVKfAalzIQ0D4LWqKmGSN/RKwYATDSm1wLMVaDMKAy+tWXqmnQt4GIFHKhqoJQEGuMjrGA129xxIxclVfy3Ipcir+R3Fw2/otRpyirNkL3Mq95QbeCNYkyV+hRp4gNpBIeLvev1Mu+BgMFofVA1vMosXykll996xcmu7GyMKb+vz6Q2PhEpKCGXQWm5ZcAJamcU6RCdSAz07eaGcbc0GBI2qV4lfSrj38pAXds3GafM5mzu9YBL8yULNG/TtNesMc00XzYE0g9YNVOb4jmMTdKGyTV4knldLuYSB1ACs6XwZKRV9jDVai/p9SDFgoTehyyvS/nDADrRWDlXXt+cgtmV28DPItyKQ4E+KWP0K/Sd5mfzcfeiWzXrXtMxe+7MWOG9Z3H8dOxnwlG4Dxe/SliMBXAdvWe7YZz1FpT+3WY4+WJU+CKWLF+DcmFaQtHxJ+agfM0TsKnrv5Lf3Y9i1DxZiUJOy6ysQyfgqS7BlPwyrFi1CqtqG+FXKpsxB7NnaNHr+UzD/BX/Ex/sdMLGxd9dh9W8jBVlyJ9ShfqWU5p1U6XQyfDNt0D9HPvn/DdsLL1l+AZb52PZc/VwQqOPw+e48VeHAnh7/zfQsLEMeaZrn2AMEto9DULpemx762XYw/+O9qCyLpaQ0ODENAjLNmGrE9hz6LNR3KpnINqwp6R76l34PayYn6qP0haUaT5tGWPn2CpU4rmtG4BU8R+8b33mJ8D3nsaz2z9AyPcksK0a65qTbxE0XXYWOLQ9uolilGCf4ZJ2Ys87v8J5bvusN2NOAbdmIXx65gvNvsDL6O8djBVy8y2YJ0Zg2OAKDPLZsu7vTawUpsbSq0dTMXdhIQrU37qDWd9E1fpSAEEcPtajqV+XTv1pRd63HsJ6uwC0HsSRwL/j0J5OQPgunnhADoIxJet1dO3/R9TuPgHYnHB7P0QgdAXXAq4kss7E3NnTVSnEA6uA0urt+JhFMBj8GF6vF++6HBDQisZV/4D9Y2rvZLzoI/Urev4g3j5xH7bWFJszPnn5KCopQtEC86ZqpGRPKDd6Fu+//R94aOsT+PM884/hhGKQACV2wlp4L9ba0wnAUfLmYUFREUqK8s3piJJtVL/5oP1fsW3VIkxR91vORWVjJ9Bai6IpSlCiXshM8+nLGSu/rchbUIiSkkIsSPpMXJb61p4iFIuTIz6A2ooPAnVAXdMw/aKZsrPjYP4p5vUMfCYZF5TC6evVGbwI+n0NYlRi2PNzHOq+DFgX4b619/G5FVr37INfjGK9inDbDrzEFUX5qEbPj+bXvTjFN2tHz6NtixTZO9wLIawz50gG6lIf+i9pZ68D6GrZi6Nz79fMNJUKh/lWZT4Cd/027AkDgjZKzJSsQ+gJfi5WItyxFFUrvoPS23rxK+/hJLNonTzRs2ip5Zv681GxxYfBQhtWrlyJld97FA8lhH0qAxMBBXNu1sz+dWWO85/RcBte2z8dj69XDGkUQ6feg8f/RfKWDYXQXVqLxxbrBirJc9yYK1y3X/slZj7+X2KGdOgEdnk+GXY2NaEYpCI9FELw9LewtCjd+Pwh9HSXoP6xxePoWbgVy7YHdP1pL3zOUsDuRjASwqGaPzdoT6b5UsEfres8Kvf/obT+ESxOaplifWtMSivy7rwL5Ql9YywFYKZsbfoMjhUfsN7/q5yPfWvWRfEk84bECJrYZX6kBvDE1gANI18TonkjbPDkTuaI23gtr52mFc17IRakg2Ip2lNdt5XWUSKho+zjFNF+8TIrgUdKU83IGr/mydmKf/famC3uZQXKmqmNuQLiKwnkSjRrtUpezXcsGpgvu8kvrJgo0bxiFHSp5iUGETYY9MoBRfr19Ni9EdemNWvKYoCC0yUHvSn3Lrvv1M+IifL5Wo8SKKO5pzxYSt2sPtEZ6DBJz5udOXe2SzEB4nr36timfDm9lE4ToCIGm33IAkoUp/hCjwa21dcTi/LW1ZWLnznRg5SCGK+ZJjBIKMc4X0KyLE9kz4CvjX/IDgSkF3VILzD5F+bcqoviNnoWAs3MhsRg1VhEvMmyc8yAj4bET2o4SnDOcNFTRml4Z3iQufgGZIAJjmbWGuwxCJrh6XyxiDw1baowd6VObixPyW8E0oZBa4yfzcl2qjdPabnRt1JmsraakJU/6DuVCDW+TWM3C4S65a0wSoBEMmPKZUqsAzx03O2L3+6hDGCGCdIyamG651Lrh8kSFXlVQ6IxImKz+RtRYsY0fmCjM6ZKUJgYtSdve+LlCg7mevfjeE4mxRsuWdYMhtkuFfcGMV0HMqEYGAEePM7ccv8g9REu5jV4ThMMiRJkJupSMXO4fs58KQbKRtWney5rPTBVodwHaXScZ0tgkFCWcb6EZFmeyJ6BEiwmPdNikKVPfsuZVjbdsyBd0gSpqfdeeasYT2GybG09GRzrGaRhTDOojcUiTaGNzFMjgguYw3suk4I1eWIzZlNRYJqcSQ/Vh1vX0SfNMFoXRqDtSZqiV5wkySb0aWIwMlGc401pSA9ID7jO6vUgqWc6A4+xQZYZKKp4RIxIRXgHVi24SYr+nbkUdTwiWHgQjy69zSBfOqesmFW+ApttQvZvAQq3oJoHAMwskYKHhA1jfO1FCQhbjZdr78387U/p4Ka0RIAIEAEikEBghI2pFXmlm7A34IXLUaypXIDN6YbP/wpWphUKrilCe5hXhr/bugGCdluO9rrZ47kLUaKEBtsa4PU/h2Xq66nMFnLj0kXP/wrv7OmE4Nw49oJsbhwGqokIEAEiMOoELPJ0VZwxSjPXUZeJBBiDBPi/2Zvs+kEMQP0EiAHvnuhZSGQwwjPTMWgVSCQiQASIABEgAjkmQMY0x0CpOCJABIgAEZh8BMiYTr57Ti0mAkSACBCBHBMgY5pjoFQcESACRIAITD4CZEwn3z2nFhMBIkAEiECOCZAxzTFQKo4IEAEiQAQmH4G4rTGTr/nUYiJABIgAESACmRHQbheM+79m2guZFU25JioB2leWuK9sot7r4dpFekB6wPWD9EBioH1WyM2rpUHHRIAIEAEiQAQyIEDGNANolIUIEAEiQASIgJYAGVMtDTomAkSACBABIpABATKmGUCjLESACBABIkAEtATImGpp0DERIAJEgAgQgQwIkDHNABplIQJEgAgQASKgJUDGVEuDjokAESACRIAIZECAjGkG0CgLESACRIAIEAEtATKmWhp0TASIABEgAkQgAwJkTDOARlmIABEgAkSACGgJpGFMv0BbfZn4Gqn8+jYMqKVEMdC2BfkWi3itsKkT19Vrl9HlWSOet1R50BVVLwxz8Hu0VBfCYilEdcvvh0lndCmdvAPoatuHpo070BkT2KhQABfR2fQ3sFjWwNN1OUkas6fTkTFVmQrfv0FT58VUicfB9SiGuvxoea8J1YVb0DZgpDBXEe7cg/qKfFgsJah+9ROEjZKNg9Yai8j18n2811SNwrjnTJM6GkbHq9XyM1eF+pZTGNJcHv+HJhhoGxk9i5baMlR5TmHiqEIqBrH+mL/aL+7PdF+rhTgWj1MxABANo3NXPSpEBiWobjqErqHR0YI0jGkeFhTdIRIPf3oGF1R5r+LCmW6E5Xtx+vAxfK5eG0JP8HMAAuxr70VhGrWN9K293vljfKfycdR99HXKqqJdLdhS9yEE50Y8tnh6yvQ3LsF0LH5sI5zCh6jb0mJysHLjpEu3pmjXTjz+4k/gfboOuy8Z5Y5iqHMH1j37Oar2ngGLHER17zasa+6YIMaED47+B17ctRNP1+2GIQJcxG8PfAI8/jZC7ApC7Y/gwlN/i5favjACNg7PmWGgbdZVnD/gwlOekPbkOD82wWDgMxza02nQzrHX1xoIaeKUCQZ8ktP8LF7vewR7Iwxs8Ge4//izsD1zAOdVG2SiqhwlScO8Tccdd5WjgFfc2oETf5Cnc9EzOLLvSEwc7bXrZ3HUy294Pu5edCvMVXY7Vu7qBmPd2LXy9li5o3b0BfzuH6EVpVhf9U3MGjU5klQ865uoWl8KtP4Ibv/47lCti2vwv995C//r5dXGjY12Yf+W91C+dROWCdMA63wse24zypubsD9rj4FxlTf27HQsrnHjnZ9sw8t2wbDq6On/i/6lj6Cctx/TIJSvRfV6YM+hzzTeIsOs4+RkagaxhvDB1ZvY8slNWG6MK5Z0XB2lYhDFQOAEbvppDyKMgf+DEumvFz7nI1h73yKTfe1YhpKKASBOcpoXorr22xC4cckrxoZXXsRDv3wFr49CX2jOvsnMp955D1aJShvE5yHJ3Rnt/jX2tYYB+zNwruOmNoD2k5LLMfr5MRw+zTOXYemSW6RShrrQ5lGm5RZYKurhaevSzCySuEGHunC4SePa2tWB33c0oZBP7wubDFy1WndgPirq96AzfBXAdYRbNuKPyuogina6DmV/ZEG8e1qjZOoIUNMGzeVcHEbDh7FFcVt6TsgsuMvzEJqqSyQXTkU9dnV2oaOpQudOvwVLlpYB6JxAHaoxVUnX5qNoQV4sgTiYOI99R85MIBdfrHn6I2vBX8E2nxtS+RP9Amc+vR2b19wz9gZ6iowj9T0UwJuvA09vfhDzRqqOMVnudXy14FE4l82PM5rRrl9g+6fluK9wLHnPRgrgZXQfOYjWkkIsyIuZMavwF/irktCo9IUxKcy0edadWLqcG8wgDh/rQRRyg0Q3bjX+a+U9mk49iqGebhzn5drLUXzbVICvbTyzCpW1jfAr9fkbUVu5CptUI6Jc0HzL+ex1u2V3cisaN9TiuR2fJHGFXcK59/8B68ocaPRzB3QY/kYHyjb8NE1XKB8BfoQ9vAilDRqxAO7Tb4Gnfg1qW86KnXn0fAtq8/NR0WTO9cgN6fPrqrHND9hcbuyoKQY3FdHzB/CM7UHU7T4h1ehvxIbv1mPHb/Wzz6m4rbgcdt7KPR8hYLjOGCf0OP0h65pQiEXzNMZEbM0VtO77NbpHwbUzejD5YKsNnoZ/Qnf9G9hcKg9WR0+gG1zzRXS+uRd42oHSmVNucN2jXd00CIsXiv1ETBL+fHyCBU9WjqnltJh8uT5SlhB15VpvxaK78xG/FKlLM0I/0zOmmIvi+7nBDON4MIQhKA0qwvK77sTi+x6UOnVxTfUSfnf0N6LxK1h+F+6wRjHgfwtPeU5AcOzEycEIGItg8OROOIQT2P38XnQkMQTRbh/e8nCjYkeDT3JtRELNWHiuXV2rjecThv/cQnw/2A/G15V8L8DGE4guaEBY+SauBVySy7rAhcA1hu5nSxH3z13FAmPrwcLdizAvjhaf4TpRVLkKtY3vwvN+J/7A81hn4rYiwH/4BEKpOveLR7Hzuc2SIW3Yhb2by+UH5DK6D/0cHm7EbS/AF7oiteOnd+PcXtm4ahpsnbcId3OPQbgbZy7w2fdE/Mi6phuJTsSWpm4TDz4px8yiStQ2/gK/OdSO7lEKukgt60ik4O7d3Xgd67Bx0g0ikvDky20t8/HEA7fHzVaTpJ4Ap+UYntaDONKdGBSa2F+PfJPjzEPq6qZh3qJCiP229yh+1ycvggvfxj13zoD1jrsgTlx5A7t+h2OHgwBKseqehZiKmHEN796AJTOnwGKZgplLNmC3OHlsxaFAn4EIyuyX29K12GCTXBtWoRLPbd0gypKYSYB9vQMrFvMVzmkQyv4a5RmtqVzHYF+vWPyMubMxI66iqRBW/gj9vgZJhgsXMRgFrMJy/GNTHVakDLg6jd21K1DLZ57CSnx/0/2S35/Xoa5D83ashU1ZH1u2CVudpXFSSMLNxlxRuF70DaYMTU7MT2fGGYFbsWx7ACwSQmDneqBx1agFXYwKuKEA3vYuxCvq4HNUpBhTlfIlkJa/tKFsVppd+phqRTrCKMGX7+L5H+zDKXEwyZf2folDHRdRUpSvm7mnU3ZmadMkb8WsJWVYzus6/QkOe1pEF6iw/gHpJk5diHtW8c7+cwRPnEDwOLeSylrjlzh7fLitLhdx4aJRZG3MoMWPNqyYMXuOzsApEGZg3i03x0ZoMxRjo1w3+51KZi2PPtGY8m00x47dhufXLI7Vn6q6cAv++WefxtaNo1+h7zRnpw/cmo7Zc2emKm2CXpdHose70TOpZmHD3E6rgNLqF/GWezXCvwwgOCm4XETn221YuOkhzE+z9xqG5Di/xCccHfjLsRggOZJkZ9mw1X8Qm9EkTs7yq1/HJ8dOoMN/z6gEYaWvjrf9Be4XIw0PoKFuB8JxUa5zUFZlh4BONK52oJHbA3Wt8Y9xyzxpXafAFcA1NQJNiURLFr07FTPnzBVvSbwfPIpL/X1J1kxzdQe/gYUlJiOKL/Wh/9J1DHX+G47d9R2UahbFk0pja0agpxVOIQx/nSYi1Xoz5hTwqXQIn575QhNYcxn9vYNJi5vYF6ajUF5GiGunGIBzccxtvYqTcUR/JOEyonWOYuEDR7Hf1YBVC26K7a2cXYnGcBittUswJSd7wUexfZlULbp4/wRVZXMyyT2O81iRt7gKz+46LkYzh3Y9hW/iPxAcpS2M6RtTeYFXvQOCXXMTrchbUIgS9SIQm00qhhY43fwj7D7FX/twFeG2F6UNt/nJNulrOovWfdjpPy8F+oR9+OFLO5OsmWoEyOowZsgv9fYbG+65C1HCY7LCfbh4IYD9x4qwxtQ6TgEc338MpfPvx9NvbIKAd/H89n+T9kdZF+G+tfeJa9Ote/bBL0Yhc1Y78FKjwd6yS/3oFTclzsWcmYkrv1khGEOZrYX3Ym3J/4lfDhgKIXh8dEaiYwONFOh3+qEyFJkZwI0NoTOXYtYybA8pA3D5u98HpyDA7j6JCNuPmjG1FzzzpprNOflcvEZkeP+4HU/u+TY+2Goblcj29I0pYkZRbJIuIETs8NQ9ctq9mVbMKl+Hlx3FQNiD2iWzYbHchPzKF+BHMRwvr0N5En+/tbAST9YU8wgibKtcgCkWC6bkb8bZP12aZM3UCHb8OevMOVIA0rBbYzRrxHEvqogvS/oVxPvuIO5a8600ffXTMN/uwGabgLDHg5/9lm8rmo7CqsdRwyen/hdQmc9H4Tch/28/xZ+u4xziP9ELZ/Ap9wIYRrrGpx3Xv6yLseaVx9Dx0g608QFG9DzaftiMjs3PYs2k6ECv4nzLU8gXt0mFY4PK7X3YUvcAuT3HtXJnKvwkdfGquKS3pr3X9N/x17tuxfa9m8x5BdX8OTxg8gfgM2Vzn0jQzewAAwRmd59kkbhsgyzgsjFeHrCauYNfx11lg0HmczuZTbwOBsHBXK1BNqimOse8jgIGFDCH95x6ludrdTmYwPPJeb4MuFgB/13gYoFrPGmSvNcCzFXA5XmSeUNiQsYiIdbeLJcHgdlc7RoZYtWyfh9zCrzOBubrj2+pmEot+2HmCnypyZjs0EjGCBsMNEtM7G4WFKuJsMHgQeZyFIssBUczaw32qGwLXAEmtSTC+n0NIhfB6WP9yarN8nw6+pFxVQprRTcM9esKC7W/wRz8nsDOnDvbWcjgtmQswzAZR55B7F5Kz4/+GYqwwZM75bbza8XM4fKyQOjKMFLn9tLoMzBoj6g3Rn2RQdocnBpTDCInmbvmNRYYvEEPgcxv9BlonhWbk7l9WhuSg5tsogg9A9WC6i+YKOuGJbmmGE0UsxrvGdl4f8kCroclo+3wstCISdPLfM5SBpQyp683sRbRmA5jjBNzmDijGZAIm5i3R+4sB9uZyyboBhop5DNRm5kkY1k/zMifizTEgInPWy5YjucySA9ID7j+6vUgAzdvDqfFJouaWvSfsdHGfZ4n4Fm1SHTzWizfQFndhwCKUfNoKW4zWVb6yeagfM0TsKlvGOJ73F5FRcWr6ByKgr/lyX//G/hpTsP0Z6Co4hFpb2x4RyzYYuZS1PGXUAgP4tGlcouVNzTZ/x61tlvTbx7lIAJEgAgQgawJjAtjirxybN77AbwuR/waqc0Jt8+L11YuNL8NJW1kVuSVrhf3d0pvGBpC8ONfwO9/B/s7uvHbI9Px4msrcrxexevchL0BL1x8jVn9CLA53fD5X8FK8ZVyV3H+I749qRTO+keweHzcTbU1dEAEiAARmCgELPJ0VQwzl2auE6VpI9UOPjN9Dd8tcwHON/DW1hVYPAmiKPm/eJrs+kEMQP0EiAHvWelZSGRAxnSkbO4EK5censSHZ4LdYlPNIT0gPeCKQnqQyIAcg6a6EEpEBIgAESACRCA5ATKmydnQFSJABIgAESACpgiQMTWFiRIRASJABIgAEUhOgIxpcjZ0hQgQASJABIiAKQJkTE1hokREgAgQASJABJITIGOanA1dIQJEgGwqhMcAAACNSURBVAgQASJgikDc1hhTOSgRESACRIAIEAEiELf3Xv1/XZN9Qz7pBREgAkSACBCBTAmQmzdTcpSPCBABIkAEiIBMgIwpqQIRIAJEgAgQgSwJkDHNEiBlJwJEgAgQASJAxpR0gAgQASJABIhAlgTImGYJkLITASJABIgAESBjSjpABIgAESACRCBLAv8fMGkX3Eytx1cAAAAASUVORK5CYII="></p>
<p style="text-align: left;">The relationship between the variables is modelled by the regression line with equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of<em> a</em> and of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your equation to estimate the mean weight of a child that is 1.95 years old.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> correct value for <em>a</em> or <em>b</em> (or for <em>r</em> seen in (ii))</p>
<p><em>a</em> = 1.91966 <em>b</em> = 7.97717</p>
<p><em>a</em> = 1.92, <em>b</em> = 7.98 <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.984674</p>
<p><em>r </em>= 0.985 <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into their equation <em><strong>(A1)</strong></em><br><em>eg</em> 1.92 × 1.95 + 7.98</p>
<p>11.7205</p>
<p>11.7 (kg) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A healthy human body temperature is 37.0 °C. Eight people were medically examined and the difference in their body temperature (°C), from 37.0 °C, was recorded. Their heartbeat (beats per minute) was also recorded.</p>
<p><img 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wA6s23FLmqjqW40WZDfYNvtUKgwyL5EK3LvB9h78E781HZtuIOvjZeRcPJ6mWeUYy9jCPi82ONywAoPNpeuwdaWsxmRPOQRm/oSB3DqeCeORsnYf/IsPtVcNzQWxk7ChLGxRc0rvA6Tlbw0BgM/d+o42qIKcgZnP9VYFWGjY0H0H9mGstwrkVu8AKWl92L5ZsEkFUo0lFuRJUIgikyho4+f4HibupxpeG5ncfLsZ+GnoRphlikTcZUSQ8dGOZ9kIIoeQo7+aGwTbyMIWX3p87iu8FqN4OfhO9auOTYKJlGmUTYG50LrTeWfd8dNmK5twmMnYLJgFX+MtuOfaHIah8kTwlcCSqp9CbmOx4y55dj06h7pLUUL3K3HEf5CQhzxaAtZBUkjlmHwXzBxijwyegZn+8JzNUwWdjJW++YJJqLoJ6tFB8t/FjfccR9mWbLJUA5TKn0n+r14btvV2LCyeJBOR/pETCrn8XOxyccfhgdQ5wA2l96LVfXHE3vbklTBmUp0NeZu8oIFfPDWLeEKwrpqj7I6WaakyEg5I7WNZgQeFZI6AmfR8tyfMXnDsqx7S5msjmZLEe4p34QGH58t0SrNnEk2t/jTac2X+FPFHdOMqyZOEkb3keeE9xKf+qP727ZIvB53npEjHt33Po4p9n4Q53rOqKP9V03EFGG6ijQ9SC8H000n0TsowQ7sWlWJ7XwakuM5uPd44QuoU3IiS5XclVDjUDXKxKk/OobCVCCtwSyXORrjJonuU+h0DB0bOXqy/wfFNtVtZAxyp4uj8Th5NsKocqrLVMGF1pvKP7RtAjjXg1PCC4VrUXjd59UM0hXKKcZP1i+FBRbkTboqfIRFmH5wIoEpSFzQSSgusUn372G8c+ifSRp2eocvAoTxN6JkSRGAdux7vzvJsiLknfTpAfjrV0beZ0bei4TvZzImFwWFQFu7bxAj5mfR8vvXMalyaRY+/HIwtWA60NaJ7kGMmJsts1C28Um4bP8Prx84OghW8VaqvMdMhD1HpDrMr34PY6bmoxDH0N49iEVPzRYUlf0HnnXdC//rXrQPglV8GsarXwsGcoZjG03gHhxITRuNj3u2xDIjJxXtNqPqpKKeguhveQm7Jv1vrMya6X6p0EusCLNlHh5ZvxQImxWTnopKu7MwvvjbWMKN9KPb8NT2Q0LHH/TvQ5WwBncxKiJMiUhKXc9OuPaIa1cH/e/Cte1VcR506a348iTZ0GhCzVNuHOEddPAEGquktbJjrZksvJ7lc36+gOm32bDwniJ88Z/vwv1arFFsrols7B/Fvtf+Jo4k8bJ/8yy2x6WoapQdrfktth/hqztfhL/xP8QNt3QbaKlZjkH+7DvBZ8fDsxN1TScEA0vLRo07iJBixCXD1ozUtpHR+OLMWWE6o/8QaoWN1PjGch3IyUi71PLfgifqxPYvtLtfb8Jm3pysd2NOQdjEm0FUBl+K+Tjqlxcit2yb2M6F3OS3SbNx/+xpYc5CclOQzBhvXYGnpe92an9Tj/cMDR/eVnej0R/pzYPqVEWezteLjvoX0Tr5W7DCH2P+u8YZzpuU5j1ARsOyaGv4IIh+MIJ/u3TFNMy+f3ZY3Yr7XRjXS2jkizjxyks4NP/nKBemaoZeHfojTXvXCiN8C3MWtvtvR368TxyzMStttqkLX4tF2zpj1mHnmiJckX877rddqStamu5puxOz88PfCuoiS4cRWBlHHuTZ+PUbHYF7drfRBO7B0RG4J9NGB1krmUxuTlm7zZTUg6+n4Ik38PtDs7G+XJr+mynRo5YzeL3U7CUnMNlpn2pGcYXi7brjysww0vhiLHu8HBbNtwKjcm3Ch4kW+8NYNiuV86P5HK4bhO8RRuXOFjcTszyIp382G+MxCbOWPQy7BVDm/Y+ainkbPYClHI8vK47+UWdOHm6bL37MXFs6DaNMJozKLcPb+JIwsqoYOearMClPmIyOtcXjpB2Sx6Pgtq8L8fy1pZg6ygQTL/vtixCmkhuC0540Y/ysB/A4/2Bb+fbjSuTOexRN/MPZxx/ALGUDLW06wJw/DysEY86DjfOmSnJLbEKjDuJokGxT3EbMMxZhg/BxvKqzSf5OxroCFfOnw5ziMiPBU2XRfCsjtzssgLM6Da9Hg6dx7O1DQjuf++DvxA2jgifwF3czvuH6d9wXtuFZMlOQJI3N12HRk38UFixA02rc9eCT2KfZTCvob0F99Wqs67oes0I+BNcSi/RBsryjMx/x/QY24R6sXv1jLLFZAM9v4Wo6jaD/PTRpyhNzVb/VCZ0Wpi1zKMLig6IwZCRImk8c09DkDlctdo27C0sUR6EXR7btQFPIt1ZDoZdapmCUFL4d+g2VMNByq6GTqqbUh/jc3p4s+ShRI5tgTF+j+9aOy3oiMWeI73je3Ymj84tRkMz3HRqRUhukNpp+oyi1NRZXbilrt3GVlpJIg+lLgv5GPLlrDL6/RHYU+DTy3ajli5sM8W8weoWKzvuQ/0FRxd26b/ZCY6XsSL+wkn65JP31iMfK0o9Gm7LJyzfK+yzo17xXl07Nc3qZvEeY4cZhYeVoltQU1t/fruznYLHXKBsZiXLr9wIAC4sjL4+pLCmqahzwHWB1yh4NNuaoO8B83dK+DMpSrvKGO9LSl/Lyf3zd/zp5jwRpf4e/e6SN7MKXTtVyUCTQ77PA93iQNx9RIhkEktlnQchGt5yqcM64rsL3sEiMbfieB/o2oq1nN/Mpasry6JalNdxnwa3bmyBWu1QK0QSMmKiyGdZbovssKJsayrqBafM1vC80EjK+UZRXvQ/E/UqeY3uUvUlCIjPDdcd1UWIfcpZuzR4mvP3zOnwpviXehKUZ9RupaZaKE/aa4FIEWN/hOnEp5bB9VGQp5XTZt89CPBteicsQa5bV5e3HXanur6Jdgle/DKuMIMr/pPv4KHmql+LYcEhYzrlI3ahNPlb2DhE3OrMpS2uruccTSq9+8WzKJi3LLPf9TD5W9/0Rlv21rVCX7I5HMSlO2vWLY1O2dLbR9OuXRBvV1s9wXDqVyz8SN2WT+w5l00du47kVG5C3JfVPv1yutlITCw+ujcbR/pQ+Q954kz/TX9M8w7md+TvmWC9u7pmY9PHF1uvIX72G/PQRQi5m5YFqqMGuNSKzUlgSiggQAUMCyRv4YdkZOh5hsQxPZKT/U3YVNdo4krFQQyzyfiChO6sbqmN4Mv06agdMpEEV7fYeYQ943V4k2o0uDTWIfjL9+vGdt6VdtIUNFvUbJMrOgfyg1zi4gvHCnWj9wEV0nbRXM6Gfsos2l9fAKU9nG82IfnxARdhFmxuT8bRRXgOa/WAUIzQ5AzQzOmpbjRiO3m7D4yd7JnX6JVZPYrvUOgiacBIDK5H0H7x+MfQychb4TvFSu7PYnezleDbkjaRAHOf1Opp4Gu1rCpPJJMzd1J7L7jD/uOkh5JY+C9jd8KXwg+ns1pukIwIjiQD/GO1J3FW8Gu2OBhzZNDf6tMCIqgfR27gO18+rQ6GrEa+XXx/2fUbEpIDwobKuS4wWfVheG359fGKYSb/EeGVb7JFef5z3SNeR9Mu2uypxefR1OCKn5yWOhVIQASIwtATMyClagvWOIoM9TxKQLPgx3nzhVfgtS1GxeEZCjkICpVBUIkAEiAARIAKXDYER8GbhsqkrUpQIEIE0E9CPpqS5uCHJfqTrSPoNSbNKWaEjvf44qJGuI+mXstthyDLS1yG9WRiyqqCCiQARIAJEgAgQASJABIhAdhMgZyG764ekIwJEgAgQASJABIgAESACQ0aAnIUhQ08FEwEiQASIABEgAkSACBCB7CZAzkJ21w9JRwSIABEgAkSACBABIkAEhowAOQtDhp4KJgJEgAgQASJABIgAESAC2U2AnIXsrh+SjggQASJABIgAESACRIAIDBkBchaGDD0VTASIABEgAkSACBABIkAEsptAyD4LfF1V+hEBIkAEiAARIAJEgAgQASJw+RJgjCnKj1ZCAPgF/UYM2usUJgJEgAiMZAKXQ/830nUk/Yb3HTrS64/XzkjXkfQb3veg3Ea1WtA0JC0NChMBIkAEiAARIAJEgAgQASKgECBnQUFBASJABIgAESACRIAIEAEiQAS0BMhZ0NKgMBEgAkSACBABIkAEiAARIAIKAXIWFBQUIAJEgAgQASJABIgAESACREBLgJwFLQ0KEwEiQASIABEgAkSACBABIqAQIGdBQUEBIkAEiAARIAJEgAgQASJABLQEyFnQ0qAwESACRIAIEAEiQASIABEgAgoBchYUFBQgAkSACBABIkAEiAARIAJEQEuAnAUtDQoTASJABIgAESACRIAIEAEioBAgZ0FBQQEiQASIABEgAkSACBABIkAEtAQG6Sz0o6V6jrB1eX51Cwa0OWMA/vqVwjVTWT38IdfSfdCLjsadqF75DFpkoQZaUJ1vgsmUj7L6j9MtgJp/fwcad1dj5RY9HzWKGjqLlurvwmS6D7Ud59XTcYfOo6P2PphM30V1y9m4U1FEIkAEsoNA0N+CV3ZXoyzXBFNuFRp7g5JgF+FvfkY8b8rFnIp6dPTL17JD9ohS9Daigutj0v/loqT2CAQt4okTsYAhvhC37Bfhb9mBijm5MJkKUbblHfiHRRWeRmNFsUH9mWAqqUWHoQ4XcaL+IeRGvD7EdRal+Mj3IE8URG9jFXK1bXnIdYy3fnrRsW+L1Ifw/qUM1fs60B+FRdZdivNeC/qbsa2iRGyzw0LPIPo79qK6rFC6zwpRVr03ch8f9KPllRel+MWoaDyd9qoapLOQdvmSKmCg5Tl8Z973sfbNz5JKn7pE/WjZugLz7l2LNwOxcw121KNq7WuwOFZi8YwxsROExRiDGYtXwmF5DWur6iN04mGJ6AQRIAJDTkB0BpYVLUV917Uoa+oB823A3PG8iw6i/73X4cEiPO9jCPhext0nfwnrY03oHXK5YwkQRK/3TewwHC2ajftnT4OZG2Ax48QqZ6iuxyt7EP0tz+CBNcdQ8mIXWOANlJ3aiAdqmrPfWOv9AHt3tBgAtsB2/+3IN7Aigif+G//+0DMZHiQ0EDGhU9HuQSmj4Md484VXNXpFZpBQ0YOJHFf9cOetCtayQ/hWYw8YYwi0/AhnNizDYxkwNAejnpo2znutvxk1S5/FmdI6BFgAfY1z0VZWilX1x8WBCTXDrAkFT+zBKusatH3rj+hjTOwfztQY9vFB/zvYssyGu+p9mFbmRh/zYtPcq9Oui8FtnvYyqQBDAqfR5PotPCjCkpIbMd4wThwnx9+IkiVFgOe3cDWl39uMQyKKQgSIQFQCkiG5sBk37/Hg+TX3Y+4MTQ8QPA5vz61YMssC3mGbLf+K5WV3ATvehFd58xC1gCG8eAbe1sn4g++CYKBwI0X462mAY8GdmJ3PB0XiiTOEKkQtOk7Zgx3YVbUbs9Y/iLmWKwDzNZj7yGrMqqnGrqTeIkcVKoUXuYF2CFf+oRsBue6E/6fQ4LhbcvZ0xXFjreovuPqOmboL2XwY4x4UROdOez2evfpJ9CgsfNhbfr1wXw6NdnHWT/AY9j5bDyz5IRZfL/YtZsu/YemSa7Bj7wfDYNCB043nXjuPjl3VqLn5h1gu9Jdm5Fz/A2x4+lt4/aFn0ZSV/eV5dO59CbW4C2WLv4Icrqr5GliX3o9CfR/P760HVuHgzVvR8vwaLJ47Q4yfgcY3BM4Cf93SiFr5FZHwSr0WjR26MbL+DuyrLtO87uOvZerR4r8oYfkY9WX5MJnm4Nf1u1ElvNoVX3N/rngtjvJYR9ei+HMmhE2RCp5A8xY5b6PXPamQkct3M4rXNgnyHl1bjM+Z5qC6JcJLP2V0oBi33TBxEFU/ETfcVgygZRh1AoNQl5ISgeFOoN+LrWtewPSnf4VVkkMQopL5S7Bar9UYJBdxsus4ClYvxCzhzUNI7Ow6CAYx9XvLRQNZkew8Ona7cHCRNCodTxwlbZYF4pQ92PlX7PRcg4KpgikgKiEM7JzAzv1dWTviCVCnDSwAAA4eSURBVAzg06n3wDH3Gk37A4Idf8amg7MkZ09bJ2fRsvVF4Gc/RcmUK7UXsjsc6x4UpD+D5l0vwLN5E56orQ+3WYZEwzjrx3w1pt2cC3/z+/hQmb7Yj+72c4MbnMykzvHca8Eu7N/ZisKCXI0RfQUsM29Fod+Dvd4zmZQ4zrKuwJRp+bD4P0Drh7IdHER/dyeOLvk2ipU+nt9bv0LN9CpsWPUNWDJtvTPdD+ADP/H++pjXaWU8TZ7Tyy6FJLvEfO4VwjXY3cwnXQt0u1m5BeJ5aP5bypnrcI8YK9DF3OUzw+MAzFLuZt0BHu0j5rbn6eLkMav1a7pzkmyXvMyZpylPWzbP117HDvcJGbPUyGgkn5U5vX0hlCSFWU9DJbNwmWwu1i6KoYkXYH3tbzG3y8Fssv4yI2sN80pyywkC7S5m43lZKllDT1hmcjT6TwSIgI5AYv2fLnFSh5+xdte9DFYHc73sZHahb5zJ7M43WLvuvhay72tnDa5KZq/0MF+St3bmddSBCRxmrgWrmLv7gu6C5jCeOJro2mD26SfVcVh/fIo1OIoi9PlajULDQ64f4/qUs3J3FwttggHW532S2Z0HWB9LTjeuaeb1i+8eVJ6riu1gYw73YWb0RA+tsfCj9OpoVD+8bmqYVbF1PmO+Bidz1OxPuh8J10o9k1791HKYvp/oaWAOi4XZXIdD22ak85qsEgmmXL++A8xptTBIdnDA52HrHb9jB3xqHym2PxtzuLYzp120jy32GuZpl+zmRBSII65exzDPQB8hep6qs8DTRfxTnAWpA8FMZne1STdZDzvsKhcMZYujgXG1lZtSMYQvsG73g6IxnedkXsEr0RjjcrzAp6zv0wC75HWyPC6PEpcxpnUWrI+yBqESLjBfw6PCDQQUMUfDKcbkTi4lMqp8wp0pLVmps+I3ssRAe5X53Myu8F3B3L5LjAW6WUOljQH3Mlf7ZyHRmXBj8PowuBYak46IABHQEEis/9MkTDbIH3a2PGZ1bGdeoU8KsL7DdcxusTCrYHTJGQfUAQXeF1grmTvJh0TGdZRVkP7z/n2BUT+niRdPHE30kGD26RfJcI50PkSdsIOh1k800NaHD0Rxg8f+pDR4lZxuXNmM6xf3PShWRcDnZXtcDsluWMCc3k/C6ijWibTqKBjQBvXDLjDfgaelAQkDgzqW0AlcT6t+GjnC+gmhLi3hDrhgE8k2niaDJIPp0C/g289qJCcgfNBYdWjrvD7REeprYy4eX7Z/k9QlUjK9jpl9kTFwHK1u/qHUIWxfXohxwooCE3DD8lrhgyG/ND/LPKMce/kHOC9+E92ePaivXY8flUofS507g55z2uUXLLAtmY9bcsyAeSxyxsZSKQ/2h8ul1+JXwDL3Qax3FAnTdtytxzGQFhljvY0aQN+ZU0KksZMnYKw+umURtvE5vhZ+4QzO9g2Ic15/tQHOhfK8X02isRMwWcjkFM7wuPQjAkQgOwn0+9DeNhGzSuajiM9lB59jez9+8fhsNK3Vzmc3Y/zcDfCxC/B5t8OBOpRaq1B/Qp6WmZ3qhUt1Hp37m/HVqN9lxRMnPOfsODOcZY+PIJ9SVf9Vq2Z6BE93Fi2/b8T0DStRxJ/Fw+kX9z0oKmW2FOGe8k1o8HlQaW1Fza7WrJrzb1w/XPbRGDdxKgpXb4TDCniWr8K6xhNZPAUuViMyuNfMM7C4Yiksni14ou6QuHgAXznoT3vR7J8eOg0wVvYZvm4e9wVcV1gGp8MGeNZhxbp9mtXS+JSxY7DMKsH3isRv15AzE0t/8XPYmpyo2tWR9npM2V2d5/TikvLRD/+I7RJ87hWhuE8dR5vwMUHoaeXIfwZnPw0C/YdQW1aIUbnFWFhaitLlmyHO/AcwdhImhDgEubh52tUh8ymV/AwD16Lwus9rrozBhMnj1OO0yKhmbxz6BMfbYiznOv7LuO2OPACyAxBE//vtmLRuEWakrBaNpaOzRIAIpIdA8GQXDoatFDQG+bPvhA3H0N6t/8bpCliKlmDjs4/D5v+/ONAuz3FNj3wpz5XPKa7/XygpnhQ563jiRE49tFcMZc/B1ILpQFsnupX54kMrZvKlGxhofLWulpfgvu4HWHgNd3iH1y/xe1DUz2yZh0fWL82yhQaM6ofLG0T/kR1YVRPAD1Y/gk0Nf0NDJbBx3grUDNdl1g3vNT6o8giaPOXAOj4gXYiymjfx/j8OoslmMLCaLU2V27yrngd+8DOs2fQqfA0rgI1l6mppwdPoOugLk9acfzvutwFt7b60r6qWWTPzqomYIoyOW+H09oWujiE4GluxyDKAjl2/wvLthwCrAy73a/D6LuCS1wluKof/xmHyhESWGW3Hvve7NV7YefSc6lOzTYuMavbGoc/jusJrjS+Fne3DqZ7zQP972PV+Ae4rGszH0GGZ0wkiQAQySMA8ZRputvhwsOu0pk+SBYg8EiY+JIbRB6SSSpFHPWWdgXjiqLGzK2Qsu+z86WQVDICzEZcf1cXOjkNDA41/+Ptf2Fg6DaOU/QcmY97mFj58jYJRmv00skOLECmSvQeFt4BT81FYmI+p2fI2xbB+uK/QgV2rHkP3rK+IH8by1bg27ITXiWG7zLrxvcardjxm3PFzbPPxQes2bFv9NeBgPxwVd2fpwCpfwelXWN5dgJnC22U+42U9XvWuBeS3y/IH6ge7cFI7sUZoyWN1H3SHNO+UHWTWWZCX9UQTap5y4wgfZQmeQGOVuHlGbkUjeiG+buEaWqbfhpKF30HRF0/hL+594gpHg1bdD8+O7dgjrL50Ef7GZ/AY79RQhNJbr8PoIZFxNMZNmixodu5UD84Z6ig7FGdx8uwJtOxqx0333aL54l+T6FwPTgmZTMakcaM1FyhIBIhAVhEQ+ptctL3zD80rZ3EljLZoI2F86sTRW3BbgWaJ1axSzEiYSKOe2rjxxNHGz6ZwZNkF567w7dDVWITpL7caLz+aTWppZDE20K7G3E1e3eAfX1q1CLC50B4Y6uVFNQoYBZO9B/lofff/oCiLjFDj+gEgtDW9ZTEeX771Rgjjt0Zcsvpc5HstRGxuX65bgx13bMH6DOxFEFJ23AeqzasmMSPnyzdhllI5k1BcYoOlrRWHlBVB5XrNTB+SWWcBkzBr2cOwWwD/9qW4YdwomEZNxbyNHsBSjseXFWM8xqPgtq8LDdhfW4qpo0xinLcvwsrBhX2zoOKVQ+Zxk8S3EJGWTm3aiNKCCTCZrkTuvEeFKU6W8ir8zMo3tkiljKoTEH3pVGnpLAB+Q89R1oz/P4ePXtmJ92/6TsS5ocprVUs+pk0Zfq+FtdpSmAiMbAJXw/qzKsx//ZeokubYBv3vwrXtOFZvEKcYBk/UY3luCSq2NYsOBX8A/norTlathG04TfuINOqpreB44mjjZ1M4muzmGbhvw2I0P/YMGvnDXqjDGjSvXoP7ktqAcygUj9NAGwrRBlVm7HsQ4Ltv/x+80uKX3gDyDdyewxNNRXhYsBsGJUCKEkepn/G34r7Vt8Kzzom6I9LUxf5/YPe2dzF/xTzDjfVSJFR6sol2rwkl9qKjcSeql/0I2yZX4sXVs4wHVtMjXYK5TsKs+34Iq/Y7C/TiyO4X4J7/fZQIe9GYMd66Ak/PfxsPVf1RGmj3o9n1Ag5mqg/Rfwmt/wJafz30ONpqP8ZLpzLGlwFtYC4HX8lHXEEpbPmngI956+TVBizSSiGd0lKp8hft8mpIBsuRBnzsQI1dXD0J0qoiympIecz+8rua/I2WKUyVjIyFfOGOKCsnyCsYhS2vJxOXWetXSZGvy//VVVMMV1aSo9F/IkAEwggk1v+FJU/yBO9v3lCWw+PLqCorXvAc5VUvlP7SydzyihhJlDg0OvJV7upYecgKT+HCxxMnPFXomezVT7sajY056g4ktWzlUOknrIJULq92FMo8/GgYrYYkCB/jHuQrCSkrJ/Kl1p3s5Yb2pJZN5cWlpQ75SkDR6ifEruJLq9uZ05O8DuF1rp5Ji35q9lH6EqndcbvP4WINSa4YpynKMJh6/S4wn3c7c/DlU4V+3sgu5c+CduZxyrZt8n2IoVK6k3odTfy61g0ymUzC60TtOQpngsBpNFbciXmbAUfDGwbbd/ejpfouFL92N7yvror4VgGIlU8mdKEyiMDwJHA59H8jXUfSb3jee7LUI73+uJ4jXUfST27Nw/e/vg4zPA1p+IJLv+TSqyjtzsv9zaie8z1U89UKgt14v+kmuP/wYBRHAYC8E7Ttp1ieNa9H00+PSiACRIAIEAEiQASIABFIPQFyFlLPNMkczcgpWiLs+SDvNzHQ/hdsbdqDml1/w4n3WoH/eBSLos5RvogTb9Zjh78oi7/8TxIPJSMCRIAIEAEiQASIABHIOAGahpRx5AkUyN8s3LUQa7EU7mcfwaIZw2nlkwT0pKhEIEsI6F+9ZolYKRVjpOtI+qW0uWQ8s5FefxzoSNeR9Mv4bZPyAvV1SM5CyhFThkSACAxXAvoOcrjqEU3uka4j6Ret9rP/2kivP14DI11H0i/777NYEurrkKYhxSJG14kAESACRIAIEAEiQASIwGVKgJyFy7TiSW0iQASIABEgAkSACBABIhCLADkLsQjRdSJABIgAESACRIAIEAEicJkSIGfhMq14UpsIEAEiQASIABEgAkSACMQiQM5CLEJ0nQgQASJABIgAESACRIAIXKYEQlZD4l8/048IEAEiQASIABEgAkSACBCBy5cAY0xRfrQSAqC9oD1PYSJABIgAESACRIAIEAEiQAQuPwI0Denyq3PSmAgQASJABIgAESACRIAIxEXg/wMWB92XgIHd7AAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean temperature difference from 37 °C, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean number of heartbeats per minute, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y">
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</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>Plot and label the point M(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y">
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>) on the scatter diagram.</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>Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient, <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">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence describe the correlation between temperature difference from 37 °C and heartbeat.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>0.025 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{1}{{40}}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<mn>40</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>74 <strong><em>(A1)</em></strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the point M labelled, correctly plotted on their diagram <strong><em>(A1)(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for labelled M. Do not accept any other label. Award <strong><em>(A1)</em>(ft)</strong> for their point M correctly plotted. Follow through from part (b).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.807 (0.806797…) <strong><em>(G2)</em></strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(moderately) strong, positive <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for (moderately) strong, <em><strong>(A1)</strong></em> for positive. Follow through from part (d)(i). If there is no answer to part (d)(i), award at most <em><strong>(A0)</strong></em><em><strong>(A1)</strong></em>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>their regression line correctly drawn on scatter diagram <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for a straight line, using a ruler, intercepting their mean point, and <strong><em>(A1)</em>(ft)</strong> for intercepting the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis at their 73.5 and the gradient of the line is positive. If graph paper is not used, award at most <strong><em>(A1)</em></strong><strong><em>(A0)</em></strong>. Follow through from part (e).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A teacher is concerned about the amount of lesson time lost by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> students through arriving late at school. Over a period of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> weeks he records the total number of minutes they are late. He also asks them how far they live from school. The results are shown in the table below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question">
<p>Which of the correlation coefficients would you recommend is used to assess whether or not there is an association between total number of minutes late and distance from school? Fully justify your answer.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>Spearman’s rank correlation should be used <strong>A1</strong></p>
<p>Because the product moment correlation coefficient is distorted by an outlier. <strong> R1</strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award <strong>A1R0</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Adam is a beekeeper who collected data about monthly honey production in his bee hives. The data for six of his hives is shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.46.13.png" alt="N17/5/MATME/SP2/ENG/TZ0/08"></p>
<p>The relationship between the variables is modelled by the regression line with equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = aN + b">
<mi>P</mi>
<mo>=</mo>
<mi>a</mi>
<mi>N</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>Adam has 200 hives in total. He collects data on the monthly honey production of all the hives. This data is shown in the following cumulative frequency graph.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.49.33.png" alt="N17/5/MATME/SP2/ENG/TZ0/08.c.d.e"></p>
<p>Adam’s hives are labelled as low, regular or high production, as defined in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.51.25.png" alt="N17/5/MATME/SP2/ENG/TZ0/08.c.d.e_02"></p>
</div>
<div class="specification">
<p>Adam knows that 128 of his hives have a regular production.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</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>Use this regression line to estimate the monthly honey production from a hive that has 270 bees.</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>Write down the number of low production hives.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</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>Find the number of hives that have a high production.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Adam decides to increase the number of bees in each low production hive. Research suggests that there is a probability of 0.75 that a low production hive becomes a regular production hive. Calculate the probability that 30 low production hives become regular production hives.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of setup <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 6.96103,{\text{ }}b = - 454.805">
<mi>a</mi>
<mo>=</mo>
<mn>6.96103</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>454.805</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 6.96,{\text{ }}b = - 455{\text{ (accept }}6.96x - 455)">
<mi>a</mi>
<mo>=</mo>
<mn>6.96</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>455</mn>
<mrow>
<mtext> (accept </mtext>
</mrow>
<mn>6.96</mn>
<mi>x</mi>
<mo>−</mo>
<mn>455</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A1A1 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = 270">
<mi>N</mi>
<mo>=</mo>
<mn>270</mn>
</math></span> into <strong>their</strong> equation <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6.96(270) - 455">
<mn>6.96</mn>
<mo stretchy="false">(</mo>
<mn>270</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mn>455</mn>
</math></span></p>
<p>1424.67</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = 1420{\text{ (g)}}">
<mi>P</mi>
<mo>=</mo>
<mn>1420</mn>
<mrow>
<mtext> (g)</mtext>
</mrow>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>40 (hives) <strong><em>A1 N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="128 + 40">
<mn>128</mn>
<mo>+</mo>
<mn>40</mn>
</math></span></p>
<p>168 hives have a production less than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 1640">
<mi>k</mi>
<mo>=</mo>
<mn>1640</mn>
</math></span> <strong><em>A1 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="200 - 168">
<mn>200</mn>
<mo>−</mo>
<mn>168</mn>
</math></span></p>
<p>32 (hives) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognize binomial distribution (seen anywhere) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \sim {\text{B}}(n,{\text{ }}p),{\text{ }}\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){p^r}{(1 - p)^{n - r}}">
<mi>X</mi>
<mo>∼</mo>
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>p</mi>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>n</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mi>p</mi>
<mi>r</mi>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mi>p</mi>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mi>r</mi>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>correct values <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 40">
<mi>n</mi>
<mo>=</mo>
<mn>40</mn>
</math></span> (check <em><strong>FT</strong></em>) and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0.75">
<mi>p</mi>
<mo>=</mo>
<mn>0.75</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 30,{\text{ }}\left( {\begin{array}{*{20}{c}} {40} \\ {30} \end{array}} \right){0.75^{30}}{(1 - 0.75)^{10}}">
<mi>r</mi>
<mo>=</mo>
<mn>30</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mn>40</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>30</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mn>0.75</mn>
<mrow>
<mn>30</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mn>0.75</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mn>10</mn>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>0.144364</p>
<p>0.144 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The manager of a folder factory recorded the number of folders produced by the factory (in thousands) and the production costs (in thousand Euros), for six consecutive months.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.30.09.png" alt="M17/5/MATSD/SP2/ENG/TZ2/03"></p>
</div>
<div class="specification">
<p>Every month the factory sells all the folders produced. Each folder is sold for 2.99 Euros.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a scatter diagram for this data. Use a scale of 2 cm for 5000 folders on the horizontal axis and 2 cm for 10 000 Euros on the vertical axis.</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>Write down, for this set of data the mean number of folders produced, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</math></span>;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean production cost, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar C">
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</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>Label the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{M}}(\bar x,{\text{ }}\bar C)">
<mrow>
<mtext>M</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> on the scatter diagram.</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>State a reason why the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is appropriate to model the relationship between these variables.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> on the scatter diagram.</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>Use the equation of the regression line to estimate the least number of folders that the factory needs to sell in a month to exceed its production cost for that month.</p>
<div class="marks">[4]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="images/Schermafbeelding_2017-08-17_om_06.54.04.png" alt="M17/5/MATSD/SP2/ENG/TZ2/03.a/M"> <strong><em>(A4)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for correct scales and labels. Award <strong><em>(A0) </em></strong>if axes are reversed and follow through for their points.</p>
<p>Award <strong><em>(A3) </em></strong>for all six points correctly plotted, <strong><em>(A2) </em></strong>for four or five points correctly plotted, <strong><em>(A1) </em></strong>for two or three points correctly plotted.</p>
<p>If graph paper has not been used, award at most <strong><em>(A1)(A0)(A0)(A0)</em></strong>. If accuracy cannot be determined award <strong><em>(A0)(A0)(A0)(A0)</em></strong>.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x = ){\text{ }}21">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>21</mn>
</math></span> <strong><em>(A1)(G1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar C = ){\text{ }}55">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>C</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
</math></span> <strong><em>(A1)(G1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept (i) 21000 and (ii) 55000 seen.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>their mean point M labelled on diagram <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b).</p>
<p>Award <strong><em>(A1)</em>(ft) </strong>if their part (b) is correct and their attempt at plotting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(21,{\text{ }}55)">
<mo stretchy="false">(</mo>
<mn>21</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
<mo stretchy="false">)</mo>
</math></span> in part (a) is labelled M.</p>
<p>If graph paper not used, award <strong><em>(A1) </em></strong>if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(21,{\text{ }}55)">
<mo stretchy="false">(</mo>
<mn>21</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
<mo stretchy="false">)</mo>
</math></span> is labelled. If their answer from part (b) is incorrect and accuracy cannot be determined, award <strong><em>(A0)</em></strong>.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the correlation coefficient/<em>r </em>is (very) close to 1 <strong><em>(R1)</em>(ft)</strong></p>
<p><strong>OR</strong></p>
<p>the correlation is (very) strong <strong><em>(R1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their answer to part (d).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>the position of the data points on the scatter graphs suggests that the tendency is linear <strong><em>(R1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their scatter graph in part (a).</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C = 1.94x + 14.2{\text{ }}(C = 1.94097 \ldots x + 14.2395 \ldots )">
<mi>C</mi>
<mo>=</mo>
<mn>1.94</mn>
<mi>x</mi>
<mo>+</mo>
<mn>14.2</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>C</mi>
<mo>=</mo>
<mn>1.94097</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>14.2395</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(G1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.94x">
<mn>1.94</mn>
<mi>x</mi>
</math></span>, <strong><em>(G1) </em></strong>for 14.2.</p>
<p>Award a maximum of <strong><em>(G0)(G1) </em></strong>if the answer is not an equation.</p>
<p>Award <strong><em>(G0)(G1)</em>(ft) </strong>if gradient and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>-intercept are swapped in the equation.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>straight line through their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{M}}(21,{\text{ }}55)">
<mrow>
<mtext>M</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>21</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>-intercept of the line (or extension of line) passing through <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="14.2{\text{ }}( \pm 1)">
<mn>14.2</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>±</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes:</strong> Follow through from part (f). In the event that the regression line is not straight (ruler not used), award <strong><em>(A0)(A1)</em>(ft) </strong>if line passes through both their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(21,{\text{ }}55)">
<mo stretchy="false">(</mo>
<mn>21</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>55</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}14.2)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>14.2</mn>
<mo stretchy="false">)</mo>
</math></span>, otherwise award <strong><em>(A0)(A0)</em></strong>. The line must pass <em>through </em>the midpoint, not <em>near </em>this point. If it is not clear award <strong><em>(A0)</em></strong>.</p>
<p>If graph paper is not used, award at most (A1)(ft)(A0).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.99x = 1.94097 \ldots x + 14.2395 \ldots ">
<mn>2.99</mn>
<mi>x</mi>
<mo>=</mo>
<mn>1.94097</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>14.2395</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.99x">
<mn>2.99</mn>
<mi>x</mi>
</math></span> seen and <strong><em>(M1) </em></strong>for equating to their equation of the regression line. Accept an inequality sign.</p>
<p>Accept a correct graphical method involving their part (f) and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.99x">
<mn>2.99</mn>
<mi>x</mi>
</math></span>.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C = 2.99x">
<mi>C</mi>
<mo>=</mo>
<mn>2.99</mn>
<mi>x</mi>
</math></span> drawn on their scatter graph.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 13.5739 \ldots ">
<mi>x</mi>
<mo>=</mo>
<mn>13.5739</mn>
<mo>…</mo>
</math></span> (this step may be implied by their final answer) <strong><em>(A1)</em>(ft)(G2)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="13\,600{\text{ }}(13\,574)">
<mn>13</mn>
<mspace width="thinmathspace"></mspace>
<mn>600</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>13</mn>
<mspace width="thinmathspace"></mspace>
<mn>574</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their answer to (f). Use of 3 sf gives an answer of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="13\,524">
<mn>13</mn>
<mspace width="thinmathspace"></mspace>
<mn>524</mn>
</math></span>.</p>
<p>Award <strong><em>(G2) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{13.5739}} \ldots ">
<mrow>
<mtext>13.5739</mtext>
</mrow>
<mo>…</mo>
</math></span> or 13.524 or a value which rounds to 13500 seen without workings.</p>
<p>Award the last <strong><em>(A1)</em>(ft) </strong>for correct multiplication by 1000 <strong>and </strong>an answer satisfying revenue > <strong>their </strong>production cost.</p>
<p>Accept 13.6 thousand (folders).</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>In a large university the probability that a student is left handed is 0.08. A sample of 150 students is randomly selected from the university. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> be the expected number of left-handed students in this sample.</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="k">
<mi>k</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>Hence, find the probability that exactly <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> students are left handed;</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 probability that fewer than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> students are left handed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of binomial distribution (may be seen in part (b)) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="np,{\text{ }}150 \times 0.08">
<mi>n</mi>
<mi>p</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>150</mn>
<mo>×</mo>
<mn>0.08</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 12">
<mi>k</mi>
<mo>=</mo>
<mn>12</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X = 12} \right) = \left( {\begin{array}{*{20}{c}} {150} \\ {12} \end{array}} \right){\left( {0.08} \right)^{12}}{\left( {0.92} \right)^{138}}">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>=</mo>
<mn>12</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mn>150</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>12</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.08</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.92</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>138</mn>
</mrow>
</msup>
</mrow>
</math></span> <strong><em>(A1)</em></strong></p>
<p>0.119231</p>
<p>probability <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.119">
<mo>=</mo>
<mn>0.119</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \leqslant 11">
<mi>X</mi>
<mo>⩽</mo>
<mn>11</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p>0.456800</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X < 12) = 0.457">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo><</mo>
<mn>12</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.457</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Contestants in a TV gameshow try to get through three walls by passing through doors without falling into a trap. Contestants choose doors at random.<br>If they avoid a trap they progress to the next wall.<br>If a contestant falls into a trap they exit the game before the next contestant plays.<br>Contestants are not allowed to watch each other attempt the game.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The first wall has four doors with a trap behind one door.</p>
<p style="text-align: left;">Ayako is a contestant.</p>
</div>
<div class="specification">
<p>Natsuko is the second contestant.</p>
</div>
<div class="specification">
<p>The second wall has five doors with a trap behind two of the doors.</p>
<p>The third wall has six doors with a trap behind three of the doors.</p>
<p>The following diagram shows the branches of a probability tree diagram for a contestant in the game.</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>Write down the probability that Ayako avoids the trap in this wall.</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 probability that only one of Ayako and Natsuko falls into a trap while attempting to pass through a door <strong>in the first wall</strong>.</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><strong>Copy</strong> the probability tree diagram and write down the relevant probabilities along the branches.</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 contestant is chosen at random. Find the probability that this contestant fell into a trap while attempting to pass through a door in the second wall.</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>A contestant is chosen at random. Find the probability that this contestant fell into a trap.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>120 contestants attempted this game.</p>
<p>Find the expected number of contestants who fell into a trap while attempting to pass through a door in the third wall.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4}"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span> (0.75, 75%) <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{1}{4} + \frac{1}{4} \times \frac{3}{4}"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times \frac{3}{4} \times \frac{1}{4}"> <mn>2</mn> <mo>×</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their product <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4} \times \frac{3}{4}"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span> seen, and <em><strong>(M1)</strong></em> for adding their two products or multiplying their product by 2.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{3}{8}\,\,\,\,\left( {\frac{6}{{16}},\,\,0.375,\,\,37.5{\text{% }}} \right)"> <mo>=</mo> <mfrac> <mn>3</mn> <mn>8</mn> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>6</mn> <mrow> <mn>16</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>0.375</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>37.5</mn> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a), but only if the sum of their two fractions is 1.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct pair of branches. Follow through from part (a).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{2}{5}"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>2</mn> <mn>5</mn> </mfrac> </math></span> <em><strong>(M1)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for correct probabilities multiplied together.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{3}{{10}}\,\,\,\left( {0.3,\,\,30{\text{% }}} \right)"> <mo>=</mo> <mfrac> <mn>3</mn> <mrow> <mn>10</mn> </mrow> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>30</mn> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram or part (a).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{3}{4} \times \frac{2}{5} \times \frac{3}{6}"> <mn>1</mn> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>2</mn> <mn>5</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>6</mn> </mfrac> </math></span> <strong>OR </strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4} + \frac{3}{4} \times \frac{2}{5} + \frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mo>+</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>2</mn> <mn>5</mn> </mfrac> <mo>+</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>6</mn> </mfrac> </math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>6</mn> </mfrac> </math></span> and <em><strong>(M1)</strong></em> for subtracting their correct probability from 1, or adding to their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4} + \frac{3}{4} \times \frac{2}{5}"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mo>+</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>2</mn> <mn>5</mn> </mfrac> </math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{93}}{{120}}\,\,\,\,\left( {\frac{{31}}{{40}},\,\,0.775,\,\,77.5{\text{% }}} \right)"> <mo>=</mo> <mfrac> <mrow> <mn>93</mn> </mrow> <mrow> <mn>120</mn> </mrow> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>31</mn> </mrow> <mrow> <mn>40</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>0.775</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>77.5</mn> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6} \times 120"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>6</mn> </mfrac> <mo>×</mo> <mn>120</mn> </math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\,\,\,\,\left( {\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\,\,{\text{OR}}\,\,\frac{{27}}{{120}}\,\,{\text{OR}}\,\,\frac{9}{{40}}} \right)"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>6</mn> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>6</mn> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>OR</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mn>27</mn> </mrow> <mrow> <mn>120</mn> </mrow> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>OR</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mn>9</mn> <mrow> <mn>40</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> and <em><strong>(M1)</strong></em> for multiplying by 120.</p>
<p>= 27 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram or their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> <mo>×</mo> <mfrac> <mn>3</mn> <mn>6</mn> </mfrac> </math></span> from their calculation in part (d)(ii).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A manufacturer produces 1500 boxes of breakfast cereal every day.</p>
<p>The weights of these boxes are normally distributed with a mean of 502 grams and a standard deviation of 2 grams.</p>
</div>
<div class="specification">
<p>All boxes of cereal with a weight between 497.5 grams and 505 grams are sold. The manufacturer’s income from the sale of each box of cereal is $2.00.</p>
</div>
<div class="specification">
<p>The manufacturer recycles any box of cereal with a weight <strong>not </strong>between 497.5 grams and 505 grams. The manufacturer’s recycling cost is $0.16 per box.</p>
</div>
<div class="specification">
<p>A <strong>different </strong>manufacturer produces boxes of cereal with weights that are normally distributed with a mean of 350 grams and a standard deviation of 1.8 grams.</p>
<p>This manufacturer sells all boxes of cereal that are above a minimum weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<p>They sell 97% of the cereal boxes produced.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a diagram that shows this information.</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>(i) Find the probability that a box of cereal, chosen at random, is sold.</p>
<p>(ii) Calculate the manufacturer’s expected daily income from these sales.</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 manufacturer’s expected daily recycling cost.</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 value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="images/Schermafbeelding_2017-03-08_om_11.51.39.png" alt="N16/5/MATSD/SP2/ENG/TZ0/04.a/M"></p>
<p><strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for bell shape with mean of 502.</p>
<p>Award <strong><em>(A1) </em></strong>for an indication of standard deviation <em>eg </em>500 and 504.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.921{\text{ }}(0.920968 \ldots ,{\text{ }}92.0968 \ldots \% )">
<mn>0.921</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.920968</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>92.0968</mn>
<mo>…</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for a diagram showing the correct shaded region.</p>
<p> </p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1500 \times 2 \times 0.920968 \ldots ">
<mn>1500</mn>
<mo>×</mo>
<mn>2</mn>
<mo>×</mo>
<mn>0.920968</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = {\text{ }}(\$ ){\text{ }}2760{\text{ }}(2762.90 \ldots )">
<mo>=</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">$</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2760</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>2762.90</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from their answer to part (b)(i).</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1500 \times 0.16 \times 0.079031 \ldots ">
<mn>1500</mn>
<mo>×</mo>
<mn>0.16</mn>
<mo>×</mo>
<mn>0.079031</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1500 \times 0.16 \times {\text{ their }}(1 - 0.920968 \ldots )">
<mn>1500</mn>
<mo>×</mo>
<mn>0.16</mn>
<mo>×</mo>
<mrow>
<mtext> their </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mn>0.920968</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1500 - 1381.45) \times 0.16">
<mo stretchy="false">(</mo>
<mn>1500</mn>
<mo>−</mo>
<mn>1381.45</mn>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mn>0.16</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1500 - {\text{their }}1381.45) \times 0.16">
<mo stretchy="false">(</mo>
<mn>1500</mn>
<mo>−</mo>
<mrow>
<mtext>their </mtext>
</mrow>
<mn>1381.45</mn>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mn>0.16</mn>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = (\$ )19.0{\text{ (}}18.9676 \ldots )">
<mo>=</mo>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">$</mi>
<mo stretchy="false">)</mo>
<mn>19.0</mn>
<mrow>
<mtext> (</mtext>
</mrow>
<mn>18.9676</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="347{\text{ }}({\text{grams}}){\text{ }}(346.614 \ldots )">
<mn>347</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>grams</mtext>
</mrow>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>346.614</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(G2) </em></strong>for an answer that rounds to 346.</p>
<p>Award <strong><em>(G1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="353.385 \ldots ">
<mn>353.385</mn>
<mo>…</mo>
</math></span> seen without working (for finding the top 3%).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Jim writes a computer program to generate 500 values of a variable <em>Z</em>. He obtains the following table from his results.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>In this situation, state briefly what is meant by</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="indent2" style="margin-top:12.0pt;">Use a chi-squared goodness of fit test to investigate whether or not, at the 5 % level of significance, the N(0, 1) distribution can be used to model these results.</p>
<div class="marks">[12]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="indent2" style="margin-top:12.0pt;">a Type I error.</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 class="indent2" style="margin-top:12.0pt;">a Type II error.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img 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"> <em><strong>(A1)(A1)(A1)(A1)(A1)(A1)</strong></em></p>
<p><span class="mjpage"><math alttext="{\chi ^2} = \frac{{{{\left( {16 - 11.35} \right)}^2}}}{{11.35}} + \ldots " xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> </mrow> <mo>=</mo> <mfrac> <mrow> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>16</mn> <mo>−</mo> <mn>11.35</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </mrow> <mrow> <mn>11.35</mn> </mrow> </mfrac> <mo>+</mo> <mo>…</mo> </math></span> <em><strong>(M1)</strong></em></p>
<p>= 7.94 <em><strong> A1</strong></em></p>
<p>Degrees of freedom = 5 <em><strong> A1</strong></em></p>
<p>Critical value = 11.07 <em><strong> A1</strong></em></p>
<p>Or use of p-value</p>
<p>We conclude that the data fit the N(0, 1) distribution. <em><strong>R1 </strong></em></p>
<p>at the 5% level of significance <em><strong> A1</strong></em></p>
<p><em><strong>[12 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Type I error concluding that the data do not fit N(0, 1) when in fact they do. <em><strong>R2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Type II error concluding that data fit N(0, 1) when in fact they do not. <em><strong>R2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Casanova restaurant offers a set menu where a customer chooses <strong>one</strong> of the following meals: pasta, fish or shrimp.</p>
<p>The manager surveyed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn></math> customers and recorded the customer’s age and chosen meal. The data is shown in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> test was performed at the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>%</mo></math> significance level. The critical value for this test is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>605</mn></math>.</p>
</div>
<div class="specification">
<p>Write down</p>
</div>
<div class="specification">
<p>A customer is selected at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>H</mtext><mn>0</mn></msub></math>, the null hypothesis for this test.</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>Write down the number of degrees of freedom.</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>Show that the expected number of children who chose shrimp is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>31</mn></math>, correct to two significant figures.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mn>2</mn></msub></math> statistic.</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>the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value.</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>State the conclusion for this test. Give a reason for your answer.</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>Calculate the probability that the customer is an adult.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that the customer is an adult or that the customer chose shrimp.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the customer is a child, calculate the probability that they chose pasta or fish.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mtext>H</mtext><mn>0</mn></msub><mtext> :</mtext></mrow></mfenced></math> choice of meal is independent of age (or equivalent) <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept "not associated" or "not dependent" instead of independent. In lieu of "age", accept an equivalent alternative such as "being a child or adult".</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>69</mn><mn>150</mn></mfrac><mo>×</mo><mfrac><mn>67</mn><mn>150</mn></mfrac><mo>×</mo><mn>150</mn></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>69</mn><mo>×</mo><mn>67</mn></mrow><mn>150</mn></mfrac></math> <strong><em><span style="background-color: #ffffff;">(M1)</span></em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into expected frequency formula.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>.</mo><mn>82</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>30</mn><mo>.</mo><mn>8</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>31</mn></math> <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> Both an unrounded answer that rounds to the given answer and rounded answer must be seen for the <em><strong>(A1)</strong></em> to be awarded.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msubsup><mi>χ</mi><mtext>calc</mtext><mn>2</mn></msubsup><mi mathvariant="normal">=</mi></mrow></mfenced><mo> </mo><mn>2</mn><mo>.</mo><mn>66</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>2</mn><mo>.</mo><mn>657537</mn><mo>…</mo></mrow></mfenced><mo> </mo></math> <em><strong>(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>265</mn><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>264803</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(G1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(G0)(G2)</strong></em> if the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> statistic is missing or incorrect and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value is correct.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>265</mn><mo>></mo><mn>0</mn><mo>.</mo><mn>10</mn></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>66</mn><mo><</mo><mn>4</mn><mo>.</mo><mn>605</mn></math> <strong><em>(R1)</em>(ft)</strong></p>
<p>the null hypothesis is not rejected <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>OR</strong></p>
<p>the choice of meal is independent of age (or equivalent) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(R1)</em>(ft)</strong>) for a correct comparison of either their <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> statistic to the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math> critical value or their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>-value to the significance level.<br>Condone “accept” in place of “not reject”.<br>Follow through from parts (a) and (d).</p>
<p>Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>81</mn><mn>150</mn></mfrac><mo> </mo><mfenced><mrow><mfrac><mn>27</mn><mn>50</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>54</mn><mo>,</mo><mo> </mo><mn>54</mn><mo>%</mo></mrow></mfenced></math> <strong><em>(A1)</em><em>(A1)</em><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>116</mn><mn>150</mn></mfrac><mo> </mo><mfenced><mrow><mfrac><mn>58</mn><mn>75</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>773</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>773333</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>77</mn><mo>.</mo><mn>3</mn><mo>%</mo></mrow></mfenced></math> <strong><em>(A1)</em><em>(A1)</em><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>34</mn><mn>69</mn></mfrac><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>493</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>492753</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>49</mn><mo>.</mo><mn>3</mn><mo>%</mo></mrow></mfenced></math> <strong><em>(A1)</em><em>(A1)</em><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.489 seconds and standard deviation 0.07 seconds.</p>
</div>
<div class="specification">
<p>The participants in Group Y are 40 years or older. Their reaction times are normally distributed with mean 0.592 seconds and standard deviation <em>σ</em> seconds.</p>
</div>
<div class="specification">
<p>In the study, 38 % of the participants are in Group X.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A randomly selected participant has a reaction time greater than 0.65 seconds. Find the probability that the participant is in Group X.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ten of the participants with reaction times greater than 0.65 are selected at random. Find the probability that at least two of them are in Group X.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct work for P(group X and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> > 0.65) or P(group Y and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> > 0.65) (may be seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {{\text{group X}}} \right) \times {\text{P}}\left( {t > 0.65\left| {\text{X}} \right.} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>group X</mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
<mrow>
<mo>|</mo>
<mrow>
<mtext>X</mtext>
</mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {{\text{X}} \cap t > 0.65} \right) = 0.0107 \times 0.38\left( { = 0.004075} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>X</mtext>
</mrow>
<mo>∩</mo>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.0107</mn>
<mo>×</mo>
<mn>0.38</mn>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mn>0.004075</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>,</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {{\text{Y}} \cap t > 0.65} \right) = 0.396 \times 0.62">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>Y</mtext>
</mrow>
<mo>∩</mo>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.396</mn>
<mo>×</mo>
<mn>0.62</mn>
</math></span></p>
<p>recognizing conditional probability (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {\left. {\text{X}} \right|t > 0.65} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
<mrow>
<mtext>X</mtext>
</mrow>
<mo>|</mo>
</mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {\left. A \right|B} \right) = \frac{{{\text{P}}\left( {A \cap B} \right)}}{{{\text{P}}\left( B \right)}}">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
<mi>A</mi>
<mo>|</mo>
</mrow>
<mi>B</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<mi>B</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mi>B</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>valid approach to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {t > 0.65} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <img 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">, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {{\text{X and }}t > 0.65} \right) + {\text{P}}\left( {{\text{Y and }}t > 0.65} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>X and </mtext>
</mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>Y and </mtext>
</mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct work for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {t > 0.65} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.0107 × 0.38 + 0.396 × 0.62, 0.249595</p>
<p>correct substitution into conditional probability formula <strong><em> A1</em></strong></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.0107 \times 0.38}}{{0.0107 \times 0.38 + 0.396 \times 0.62}}">
<mfrac>
<mrow>
<mn>0.0107</mn>
<mo>×</mo>
<mn>0.38</mn>
</mrow>
<mrow>
<mn>0.0107</mn>
<mo>×</mo>
<mn>0.38</mn>
<mo>+</mo>
<mn>0.396</mn>
<mo>×</mo>
<mn>0.62</mn>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.004075}}{{0.249595}}">
<mfrac>
<mrow>
<mn>0.004075</mn>
</mrow>
<mrow>
<mn>0.249595</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.016327</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {\left. {\text{X}} \right|t > 0.65} \right) = 0.0163270">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
<mrow>
<mtext>X</mtext>
</mrow>
<mo>|</mo>
</mrow>
<mi>t</mi>
<mo>></mo>
<mn>0.65</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.0163270</mn>
</math></span> <em><strong>A1 N3</strong></em></p>
<p> </p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing binomial probability <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \sim B\left( {n,\,\,p} \right)">
<mi>X</mi>
<mo>∼</mo>
<mi>B</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>p</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){p^r}{q^{n - r}}">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>n</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mi>p</mi>
<mi>r</mi>
</msup>
</mrow>
<mrow>
<msup>
<mi>q</mi>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mi>r</mi>
</mrow>
</msup>
</mrow>
</math></span>, (0.016327)<sup>2</sup>(0.983672)<sup>8</sup>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {10} \\ 2 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mn>10</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X \geqslant 2} \right) = 1 - {\text{P}}\left( {X \leqslant 1} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>⩾</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
<mo>−</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>⩽</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - {\text{P}}\left( {X < a} \right)">
<mn>1</mn>
<mo>−</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo><</mo>
<mi>a</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, summing terms from 2 to 10 (accept binomcdf(10, 0.0163, 2, 10))</p>
<p>0.010994</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X \geqslant 2} \right) = 0.0110">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>⩾</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.0110</mn>
</math></span> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em> </p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>At Penna Airport the probability, P(<em>A</em>), that all passengers arrive on time for a flight is 0.70. The probability, P(<em>D</em>), that a flight departs on time is 0.85. The probability that all passengers arrive on time for a flight and it departs on time is 0.65.</p>
</div>
<div class="specification">
<p>The number of hours that pilots fly per week is normally distributed with a mean of 25 hours and a standard deviation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ<!-- σ --></mi>
</math></span>. 90 % of pilots fly less than 28 hours in a week.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that event <em>A</em> and event <em>D</em> are <strong>not</strong> independent.</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A \cap D'} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<msup>
<mi>D</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</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> Given that all passengers for a flight arrive on time, find the probability that the flight does <strong>not</strong> depart on time.</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="\sigma ">
<mi>σ</mi>
</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>All flights have two pilots. Find the percentage of flights where <strong>both</strong> pilots flew more than 30 hours last week.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>METHOD 1</strong></p>
<p>multiplication of P(<em>A</em>) and P(<em>D</em>) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 0.70 × 0.85, 0.595</p>
<p>correct reasoning for their probabilities <em><strong>R1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.595 \ne 0.65">
<mn>0.595</mn>
<mo>≠</mo>
<mn>0.65</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.70 \times 0.85 \ne {\text{P}}\left( {A \cap D} \right)">
<mn>0.70</mn>
<mo>×</mo>
<mn>0.85</mn>
<mo>≠</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<mi>D</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><em>A</em> and <em>D</em> are not independent <em><strong>AG N0</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>calculation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {D\left| A \right.} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>D</mi>
<mrow>
<mo>|</mo>
<mi>A</mi>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{13}}{{14}}">
<mfrac>
<mrow>
<mn>13</mn>
</mrow>
<mrow>
<mn>14</mn>
</mrow>
</mfrac>
</math></span>, 0.928</p>
<p>correct reasoning for their probabilities <em><strong>R1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.928 \ne 0.85">
<mn>0.928</mn>
<mo>≠</mo>
<mn>0.85</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.65}}{{0.7}}{\text{P}}\left( D \right)">
<mfrac>
<mrow>
<mn>0.65</mn>
</mrow>
<mrow>
<mn>0.7</mn>
</mrow>
</mfrac>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mi>D</mi>
<mo>)</mo>
</mrow>
</math></span></p>
<p><em>A</em> and <em>D</em> are not independent <em><strong>AG N0</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span style="background-color: #ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( A \right) - {\text{P}}\left( {A \cap D} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mi>A</mi>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<mi>D</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span></span> , 0.7 − 0.65 , correct shading and/or value on Venn diagram</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A \cap D'} \right) = 0.05">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mo>∩</mo>
<msup>
<mi>D</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.05</mn>
</math></span> <em><strong>A1 N2</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<p> </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">recognizing conditional probability (seen anywhere) <strong><em><span style="font-family: 'Verdana',sans-serif;">(M1)</span></em></strong></span></p>
<p><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">eg</span></em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{P}}\left( {D' \cap A} \right)}}{{{\text{P}}\left( A \right)}}">
<mfrac>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>D</mi>
<mo>′</mo>
</msup>
<mo>∩</mo>
<mi>A</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mi>A</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A\left| B \right.} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>A</mi>
<mrow>
<mo>|</mo>
<mi>B</mi>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">correct working <strong><em><span style="font-family: 'Verdana',sans-serif;">(A1)</span></em></strong></span></p>
<p><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">eg</span></em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.05}}{{0.7}}">
<mfrac>
<mrow>
<mn>0.05</mn>
</mrow>
<mrow>
<mn>0.7</mn>
</mrow>
</mfrac>
</math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">0.071428</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {D'\left| A \right.} \right) = \frac{1}{{14}}">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>D</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>|</mo>
<mi>A</mi>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>14</mn>
</mrow>
</mfrac>
</math></span> , 0.0714 <strong><em><span style="font-family: 'Verdana',sans-serif;">A1 N2</span></em></strong></span></p>
<p><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding standardized value for 28 hours (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = 1.28155">
<mi>z</mi>
<mo>=</mo>
<mn>1.28155</mn>
</math></span></p>
<p style="text-align: start;"><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;">correct working to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
<mi>σ</mi>
</math></span> <em><strong>(A1)</strong></em><br></span></p>
<p style="text-align: start;"><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.28155 = \frac{{28 - 25}}{\sigma }">
<mn>1.28155</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>28</mn>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{28 - 25}}{{1.28155}}">
<mfrac>
<mrow>
<mn>28</mn>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mrow>
<mn>1.28155</mn>
</mrow>
</mfrac>
</math></span></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.34091</span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma = 2.34">
<mi>σ</mi>
<mo>=</mo>
<mn>2.34</mn>
</math></span> <strong><em><span style="font-family: 'Verdana',sans-serif;">A1 N2</span></em></strong></span></p>
<p style="text-align: start;"><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X > 30} \right) = 0.0163429">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>></mo>
<mn>30</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.0163429</mn>
</math></span> <em><strong>(A1)</strong></em></p>
<p>valid approach (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left[ {{\text{P}}\left( {X > 30} \right)} \right]^2}">
<mrow>
<msup>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>></mo>
<mn>30</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span> , (0.01634)<sup>2</sup> , B(2, 0.0163429) , 2.67E-4 , 2.66E-4</p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">0.0267090</span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">0.0267 % <strong><em><span style="font-family: 'Verdana',sans-serif;">A2 N3</span></em></strong></span></p>
<p style="text-align: start;"><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[4 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the average body weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, and the average weight of the brain, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>, of seven species of mammal. Both measured in kilograms (kg).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_10.57.27.png" alt="M17/5/MATSD/SP2/ENG/TZ1/01"></p>
</div>
<div class="specification">
<p>The average body weight of grey wolves is 36 kg.</p>
</div>
<div class="specification">
<p>In fact, the average weight of the brain of grey wolves is 0.120 kg.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of the average body weights for these seven species of mammal.</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 data from these seven species calculate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, the Pearson’s product–moment correlation coefficient;</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>For the data from these seven species describe the correlation between the average body weight and the average weight of the brain.</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>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</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>Use your regression line to estimate the average weight of the brain of grey wolves.</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 percentage error in your estimate in part (d).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="529 - 3">
<mn>529</mn>
<mo>−</mo>
<mn>3</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 526{\text{ (kg)}}">
<mo>=</mo>
<mn>526</mn>
<mrow>
<mtext> (kg)</mtext>
</mrow>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.922{\text{ }}(0.921857 \ldots )">
<mn>0.922</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.921857</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(very) strong, positive <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 0.000986x + 0.0923{\text{ }}(y = 0.000985837 \ldots x + 0.0923391…)">
<mi>y</mi>
<mo>=</mo>
<mn>0.000986</mn>
<mi>x</mi>
<mo>+</mo>
<mn>0.0923</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>=</mo>
<mn>0.000985837</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>0.0923391</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.000986x">
<mn>0.000986</mn>
<mi>x</mi>
</math></span>, <strong><em>(A1) </em></strong>for 0.0923.</p>
<p>Award a maximum of <strong><em>(A1)(A0) </em></strong>if the answer is not an equation in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.000985837 \ldots (36) + 0.0923391 \ldots ">
<mn>0.000985837</mn>
<mo>…</mo>
<mo stretchy="false">(</mo>
<mn>36</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>0.0923391</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituting 36 into their equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.128{\text{ (kg) }}\left( {0.127829 \ldots {\text{ (kg)}}} \right)">
<mn>0.128</mn>
<mrow>
<mtext> (kg) </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.127829</mn>
<mo>…</mo>
<mrow>
<mtext> (kg)</mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(</em></strong><strong><em>A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (c). The final <strong><em>(A1) </em></strong>is awarded only if their answer is positive.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\frac{{0.127829 \ldots - 0.120}}{{0.120}}} \right| \times 100">
<mrow>
<mo>|</mo>
<mrow>
<mfrac>
<mrow>
<mn>0.127829</mn>
<mo>…</mo>
<mo>−</mo>
<mn>0.120</mn>
</mrow>
<mrow>
<mn>0.120</mn>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo>×</mo>
<mn>100</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for their correct substitution into percentage error formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6.52{\text{ }}(\% ){\text{ }}\left( {6.52442...{\text{ }}(\% )} \right)">
<mn>6.52</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>6.52442...</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (d). Do not accept a negative answer.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A biased four-sided die is rolled. The following table gives the probability of each score.</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 value of<em> k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected value of the score.</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>The die is rolled 80 times. On how many rolls would you expect to obtain a three?</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of summing to 1 <em><strong>(M1)</strong></em></p>
<p><em>eg </em>0.28 + <em>k</em> + 1.5 + 0.3 = 1, 0.73 + <em>k</em> = 1</p>
<p><em>k</em> = 0.27 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into formula for E (<em>X</em>) <em><strong>(A1)</strong></em><br>eg 1 × 0.28 + 2 × <em>k</em> + 3 × 0.15 + 4 × 0.3</p>
<p>E (<em>X</em>) = 2.47 (exact) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg np</em>, 80 × 0.15</p>
<p>12 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The Malvern Aquatic Center hosted a 3 metre spring board diving event. The judges, Stan and Minsun awarded 8 competitors a score out of 10. The raw data is collated in the following table.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The Commissioner for the event would like to find the Spearman’s rank correlation coefficient.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of the Pearson’s product–moment correlation coefficient, <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">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, interpret the relationship between Stan’s score and Minsun’s score.</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>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</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 your regression equation from part (b) to estimate Minsun’s score when Stan awards a perfect 10.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether this estimate is reliable. Justify your answer.</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><strong>Copy</strong> and complete the information in the following table.</p>
<p><img src="data:image/png;base64,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"></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 value of the Spearman’s rank correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r_s}">
<mrow>
<msub>
<mi>r</mi>
<mi>s</mi>
</msub>
</mrow>
</math></span>.</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>Comment on the result obtained for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r_s}">
<mrow>
<msub>
<mi>r</mi>
<mi>s</mi>
</msub>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Commissioner believes Minsun’s score for competitor G is too high and so decreases the score from 9.5 to 9.1.</p>
<p>Explain why the value of the Spearman’s rank correlation coefficient <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r_s}">
<mrow>
<msub>
<mi>r</mi>
<mi>s</mi>
</msub>
</mrow>
</math></span> does not change.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;">0.909 (0.909181…) <em><strong>A2</strong></em></p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;">(very) strong and positive <em><strong> A1A1</strong></em></p>
<p style="text-align: left;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for (very) strong <em><strong>A1</strong> </em>for positive.</p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 1.14x + 0.578\,\,\left( {y = 1.14033 \ldots x + 0.578183 \ldots } \right)">
<mi>y</mi>
<mo>=</mo>
<mn>1.14</mn>
<mi>x</mi>
<mo>+</mo>
<mn>0.578</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>y</mi>
<mo>=</mo>
<mn>1.14033</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>0.578183</mn>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong> A1A1</strong></em></p>
<p style="text-align: left;"><strong>Note</strong>: Award <em><strong>A1</strong> </em>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.14x">
<mn>1.14</mn>
<mi>x</mi>
</math></span>, <em><strong>A1</strong> </em>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.578">
<mn>0.578</mn>
</math></span>. Award a maximum of <em><strong>A1A0</strong></em> if the answer is not an equation in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;">1.14 × 10 + 0.578 <em><strong>M1</strong></em></p>
<p style="text-align: left;">12.0 (11.9814…) <em><strong>A1</strong></em></p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;">no the estimate is not reliable <em><strong>A1</strong></em></p>
<p style="text-align: left;">outside the known data range <em><strong>R1</strong></em><br><em><strong>OR</strong></em><br>a score greater than 10 is not possible <em><strong>R1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Do not award <em><strong>A1R0</strong></em>.</p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;"><img 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hLnQ45TfFf6L7XgoEu7nlvPg/Mh3jmVeSm3jTdhKMylbG0uWwc1Nm2JMhPAZtaU3ETC8MgA8QQoL8PvsMxSCkG3MG503wYzJpwTdr/IfJqjee9S1Due8d7IkF8ILkI2RiDsVu6bdgvF5t1YV2aztV9j13pjGWVfexA4CxNCmXpgBs+lzWa6KdrHC6XMNTeZh1LSeHqie1CDaigmNEyrzOOXvJjnEuuFis9V4+gppKQkMFAZAavMnBU9lscWz3TPiaUj5Jq7mbs4mfiBtbPDu9IkM9E9oATdlQyZfhfRHpNYmW+nqjHfRDA9h9zjHjmsnO1nyuuNOhrXmLiQtORpmNRRxaok6AfGk5y2kETV0FXFa+JfOK788V491IQqsxRmx2nhYVjBwfVvsdKq54ZrFcO/3k8XQZ+bLoXqApa+9IHbU1wvjV9vVnPq5MmGGihfs1i7wm0A+LyMNEzpt3uUEbu/U0b1V+/GPDeNrDyrN2qAw441L4flH3bDNFQL7dy3mhqvc2UC57ysNOYok+IrMxos8tyvfPNqYb1e15s6KlVQkreMtL+GclOTI0DrZPC7Dcepk6iTipWf5FRjjxO/06g5gbsQETeTReqsGQ2vdaXdf1xcUtsVq7ni/Oy4p75rTlQ0jNo4fuRkeQ3UVFDxw4VpDJ2cTqdTYdqpUyfcq36G2HcCZ5/v6PqZFh1F3PPfDmon63bpXL/PZf3jSqqbSMqce94/63P+dVd6GjTzyTZlGqAL8M3rdtHd28gbmdRdfVFTPtnm6h/cntO5nnfdm6tz5aVu3C/oP2gAUe04mOm86+2p78ZGcXqOeZdBrsnr26mTf7vpjmeift/pqeoNcPEyaJ+V9tNd0cd1rX+y61M21pmbVnEU/ZJxsQMY5P2Qw/nX//zr3lh9e55xF/aTbb66i+F3/tuaX53Bt3H4leBtIKzorr4DtgFJ/yoiUOs9UPVWWqfoLte6f92lzl1a3zZ/FqHecxdAShACQkAICAEhIASEgBBofwIa8Pi1PzQtn9H3rUDLejamm+guXoDG2oVW90l7l/au1bbdlF7S5l1tXjx+TbUQ2S8EhIAQEAJCQAgIAY0REMNPYxUq6ggBISAEhIAQEAJCoCkCYvg1RUb2CwEhIASEgBAQAkJAYwTE8NNYhYo6QkAICAEhIASEgBBoioAYfk2Rkf1CQAgIASEgBISAENAYATH8NFahoo4QEAJCQAgIASEgBJoiIIZfU2RkvxAQAkJACAgBISAENEZADD+NVaioIwSEgBAQAkJACAiBpgjUmcC5qUSyXwgIASEgBISAEBACQsB/CTidrgmcg3xV8Oz03SfrgUVAZjaX2fwDq8UH7ndb5VqXa12u9cAhoFzvnp+Eej0kZCkEhIAQEAJCQAgIAY0TEMNP4xUs6gkBISAEhIAQEAJCwENADD8PCVkKASEgBISAEBACQkDjBMTw03gFi3pCQAgIASEgBISAEPAQEMPPQ0KWQkAICAEhIASEgBDQOAEx/DRewaKeEBACQkAICAEhIAQ8BMTw85CQpRAQAkJACAgBISAENE5ADD+NV7CoJwSEgBAQAkJACAgBDwEx/DwkZCkEhIAQEAJCQAgIAY0TEMNP4xUs6gkBISAEhIAQEAJCwEPgrAw/h91KXtYipiUkkKD+TSP55bUUlVR4ynUtK0so2pzFH7Kt1NQ90kZbNdjz/uCS4cEsrOfnJG0kq6eYMvIWPUhCwoMsyivz7AzYpWOfGVOnTiifk6n/F/nkVsq1TMZhx7rhZZK919EcXt6wF7tDy0rX181Bxb581pifZLjaBn7DmrLq+om0u13xGS8Oj6T3izvRvtY/UbZzFU8Oj3Rf6/1IfNHCvoqAavCAg4qdGQzvNJwXd9Z7Zmq0pSs2w8d5q3k5+aEAfu6VY82aS0IHsFVabfg57J/y2rPPY7bYfG5U1dgLc8lcsIgsq+dRXYk1N4PMFRZsfmGQafSK69Bq/cj+7R+yuVEZBzDVdBPhjR7Tws5yrKteIPWdQ/RJziA7J5vlqUM5/n46f1h/kMB4FJazb81TjItOYImtN/9VfIQa5+tMMtT5hLgWKrsJHf7NztcXMzc/EF4AFWPndX73HtybU4LTeQLb6nF8O3c0w5LXURoYDd7VDiqKef2JdPKbaBWa211jZdW8VN4wr6bQrv3Xm8brz0GldQPLLKWNH27nva00/Kr4dvsHFCiVF2QkPnUZOTk5ZGc+xmC9crMuxWLeQkm7XcSd0cf9juy0eAzdwwmt/QZxO2OU050VAUcJ29d0582vTuB0Or1/NbY3udNwJ6aY7mdVrF9kqjlMcX4pRI/h3tgIdOgIueYORseEULbnAP/yCyXORcifKF2zgGGTd3L76q1sfP4hfjnAQCtvSOciwAXOq+j/FPf95RSDLrAk7XP6Y3z28cXMevoBBhh+BoTTZ9LjPD1vAGXmd7Ds/7F9xLjQZ3EcYk3ybP5C5IWWpP3O39lI4ls5rEoxEdx+Z+1QZ3Ic3UrGi4XQvWO81LZSihpOlbtd052vpE/PMBWuTn8rdw27ioLcg2A/wtHKUva/9BRmW5V6vMqSylSLHlPKcyQaQ6CyhE9zs3jN6zUMJdp0H/eMHYpR3wVQwqELMNsgevp/cY9uN++vtGBT7M3oXzJ35iT6qekUr/lRdvzlE6pvmsYV6lPDQWXJDiwb3iO30PMmbWBg/L2MN91GVEhTjxbPOcMZlXQXlRuzKbCDIX4R6ROv5seST8nNWoHFdsrVoIKiMU27h7EjjOiVIu15LEo2Y+MmpqeMQVe8jpWqfqFEj53JzIT+rnSNNEeXF/U1CuzBRMfPY+7E6whpJJ3mdlXquHbRQv6jr69f73vy33yVvVNfICa8qbrSAIlOIYQrN4EDn/PF0aHERXQBx785cqgKw5BeXKYBFc+kgqP0A5757Rqi09fx9KS+uO4kZ8qhrWOq/vPghZyHWB+bz1FtqdeINpcz4omH6u2/hOtjY4Bj9fZrdfMnStelM49Z5Dz6MbH5Nq0qKnr5EnAcYevyjfBAIncVvMoKtwnhm6S911v5ZO1MaLj7Fl21hWVLV5NXVEIlwURNTFW9fzkrHyU27AzFOo6Ql5HKEq/Rp6h8CpvFzPPLtnG0jrewCtuK50k1u4w+JWW1bT3P/eEDt1fRQcWONbxXY2J2vNFlLFVayc1Y6mP0KbnKKMxdSkaulcpmCdv5yLzC5dUkhKsjLwHFWn9maa3R5xIEi/l/WLb1SL2w3B5WpPqGwk9h25TRZPiu1ugDvWlW4Bh9CsOwPgyr7+Up34Nl1c95/N5bNRzmBXRXMmjMjQRV78ac9hZF9uMcXP8u269+gMdMV2vc8/U9+S+nYS7rx+28yzi1b18kw59cxc6yn5q9Qv0+geMQ655ZAi/MZcJVF/m9OmevQDUn/30Mhv2CmyMVL6C2f15jf/E4rjrDI1LbFAJNu9Mc3ZrNnxnHjBFXdpj7eiubXzBRpunER4cqJhj2wtWYMxcwIyGBaYuy2Pyx1d0x3UDcwqWkmPRqLQebUliVk6l6+xzfFvFX6ynQjyVleTY5OVlkJN2C4nqs3l/K9856DUM/mKQ0JaRcm44yG/v/pXQc1BEW+wgvzYrzevJqDn5OvhqKHkzyMqX8bJanjEWvyGt5B0uJywtZ7yx1Nz2yZWcw46aL+PaTj7FWB6E3zWd5Tg452S+SZFQYnGJ/6XHqihyEfmASaYpu3nTVjYfvTn7N+lfNqmdRP/gRnpraLzA8fXVp+2w5KC/OY1W/SYzvf4nPfi2udiEibiaLkwajt+eTmfwoCw8PZ5FPW9ai1qpOqnG/E8O00cSNX8jHziqObPlPeGEa4576QOP9vTxen8dYPEHrBn4zLVjp6vHuNyQ9Non+Z3IWNFOMXxz2NfZ7aN/I9Ys6aQchHUe3sfzP8MCMoUS00to6n+K1MtQLhFzHxKfT6LPtb2xZt97bWbPaZmGFzUL23+5n0dy7uaaJWKUuaiIv5UxEGeWz7ZOtlJ38Oxtzd7sGitRUUPGDg9q4TxCGYWMZEeXyMkbcfCu92M2ZHOSdLu9B7yCwVheQOfN7TFMG00N3NQ9nZrnDyM3hVM45mOvVkPDFhFyMy5s58TR2ayGf5G3m5N8t5CrGK1BzooIfFOeVt9irGDb+DrchGsHNsb3Ausd7tHalClvuGy5dgm5h3D0xTYaCa/Nofe0YxZZt9LtvGr070EVy/qgHExpxOVdER3PJARv/KFzOS1d117zX1/HPEnaXGeg3dAwj+7jC/IYRj/L0vI2MfGEJb8+8kycG1F5R549/+5esen3+1It3V0+gR0C08aYYKwbwK6RduYBtmjeAFV0z+NP1z7N6kmLsB+oAh6bagkb3qyHe/+XKJ+a4uvJ0IDVbb/gpwuv0GIdPVv9mUUFJUSG7iv6qhlerbZvYuPcOZsU20Y2z8h+sTX+BXE9fOV8YncMIu9j3btiZ8K4X1bpHuxuICgZ310HfnN51XcRQHn7yR95e9h6FdhuWFR4z8Q30A6cxe8YIr3fQm6nOiiu8WyuFg8qDH5C+8B21j2GdpEDnbmFcXGdnV7qGerB2prvBQDB7OKOfsfpLNn74NYMSA9zjp3qCenBfflRtnddhq6WN09iL3uLZnBAefu5pjBxwXRe5L5DRdRHz4yI1y8Bx8hgHCGHwJaE+OnYnxnQnhhfeY++h46BFw0/1+qzm+rSlDNC6h6uZS9VlAOtZtuJuzRvALl2vJm11jI+DoBlActjPCSgh3rf565X38N9G3z7sHUOtWvumJfJUFPHyNGXuvmnMWeuZciKMqNg4Jj6ahEm19crZ9fWRJubtq6LEssJl9OkHEp/0CCmZWW082qcLeuPdzMpcSc7yNJKTkkiabiI6SAlNr2SJ5VC9Pnn1FQ+mW5iP0eo4hOWV97Epod6Bk0l6KIXM7OXeMHb93K3aVkLKGY8xUJGtpWHoVp3AnxJ7wryjGdI7APo9VXzO20vzKb+1P30V77LqSV9EkhGsK9eyQ8NzmwVFXstgDlDwzXc+vg8dId26E8Il/PySuq9S/tSKzyjr0Z2sN+cwN+bS2jkrIyezEjgwN4YugTKvW8Vn/HHBVzywYj4j1BG+Z6Tm5werOVq0GfPmx4np2tld712InPwnIJ+5MV3p1PtFdooT0M/rub7437O34EvKLM+pXeFc8x3PcQ14rbKQOjWBB7PO1/zG9WVpuN06wy+sD7ExivVaTdnaleTstbuNqAoObljHFtWtFU7/vpF0bnguoJKjh10TVQRdcQODRtyB8bJjFOc34xFrtKzGdp7maN4Lromlk5dRdKoHsXFxxMWNYrDaL7GxPM3sq/yOw+rcQ8FcccMvGDHcyGX/+oL8z483k7G5w8FEjxuJMSKG+6YpfRwPsvbP/1tvcEtzZWjpuCfMOygwwrw/nOR4dW1XAbUmde6uAVqq1sZ0ibiBoXcaOPCXv/GF18D9kW+++IwDWp7GxzCJLJ9pi9QpjI6sZhrQK72Y086PNRvi9jaDii8xJ+fQff5jXqPPUfYRC36dxb46A/u8Ofx8JQjDpNe9U1W5pq06zZHV/wkMI734JM79TzDAEyTyc21FfA8BZZzDW64Br8q4APXvJZKigyHYRMqqHN5KNDZhJ3nKOH/LVja3S7ntvnswFpuxVtvY9Fwym+rJFhQ9lnH9ugGn3SOA7dRO57KY0TdcS1DhbqqtZmZPMbtyd9ejTANob9DHr17hzW52IWLQGEZu/BKL2mG+3hSZQbcwZlArR9aEXMUN0aEUWk9hNT+BS+QguuvDCeJYI338mhWyXgIfma0WPvzqdhI7oGu4ntBtvxlQYV7gshsYbAzFVvgeWbFRPBIbAfbPeG+jDf3Ix+mn5VCgrg/3ps1lVUw6T6TdSM6zI+m6fxNvrvqGpFfSGablaXza/srxmxIdZQVk/u43PL7ySzBn8msfyRXDd3Hr3BA+uWW14xNw8ENFBTXUUH7yR9VhJNV94Wqt1ex1EXHMfymFh+IH4hdo7VsAABTTSURBVBqz6xZemddu+mwWqwM7lGKD6TnkHsZ6PW3KSKZORIx4kCfv9+RVwqcJpCycw7hewVC9lyLriXOjEdKPxOcWk1xHPuU88SQvntn6Tpa6SEY8PIv7BxrcchkYeP9cFi6YQC/F91lcjNXrtThL0UOMxD98J/p2nwD7LOVt82yuMO/qMfdjCoQwr8JPF0nc7BQeM4VTlDmbKQkJTEl+n5qRjwfA6G4dYQMeJaf4eW7/NJHIzp3pOmw9+gU5ZKqd39u8gUmBF5qAEt5NiHcZfQ1kGcDkW69WZ3ZocEh2aICAMkfur3k4s4BqJVqYm8KUDvDZMg2APWsVOjkV37NiknXqpLqjz7okyagJAoHcDkT3uhMTaaJBt0CJQK33QNVbaRKiu1zrLbg1aCqJb5tvtcdPUyREGSEgBISAEBACQkAIBBABMfwCqLJFVSEgBISAEBACQiCwCYjhF9j1L9oLASEgBISAEBACAURADL8AqmxRVQgIASEgBISAEAhsAmL4BXb9i/ZCQAgIASEgBIRAABEQwy+AKltUFQJCQAgIASEgBAKbgBh+gV3/or0QEAJCQAgIASEQQATE8AugyhZVhYAQEAJCQAgIgcAmIIZfYNe/aC8EhIAQEAJCQAgEEAEx/AKoskVVISAEhIAQEAJCILAJ1PlkW2CjEO2FgBAQAkJACAgBIaBNAu4v9Nb9LrZnpzZVFq1aQsD3e34tSa+lNKK7fL9TS+25OV2kvUt7b66NaO14oLd5T31KqNdDQpZCQAgIASEgBISAENA4ATH8NF7Bop4QEAJCQAgIASEgBDwExPDzkJClEBACQkAICAEhIAQ0TkAMP41XsKgnBISAEBACQkAICAEPATH8PCRkKQSEgBAQAkJACAgBjRMQw0/jFSzqCQEhIASEgBAQAkLAQ0AMPw8JWQoBISAEhIAQEAJCQOMExPDTeAWLekJACAgBISAEhIAQ8BAQw89DQpZCQAgIASEgBISAENA4ATH8NF7Bop4QEAJCQAgIASEgBDwEgjwrLVuWkbdoAWZblSt5dBKZC+PQezMfp+jl+WQWlrv2BJtIWZ6I8Vgei5LN2LiJpMy5xOk7e3N02BW7R2Y9ppTnSDSGdFhRvYJ5ZfYjzl7hZUUICAEhIASEgBA43wTOzeN3wMY3FY5aGWuO8PUut9FXu1fWhECTBBz7zJg6dUL5hmL9v8gnt6Lp1uSwY93wMskJCSSof3N4ecNe7D6XVJPgNHPAQcW+fNaYn2S42gZ+w5qyas1o51Lk3+x88W469X6RnS1QreE1EcOTW7/XBpOKr1nzpMl9rfcjMaOAskBo744ydmZ52ngnOkUm8uJH+6jQRq02q4XDbuXjvNW8nPwQi/LKmk3vvwnKsWbNJeHBLKw1zWvhKFnLHO/9X3kO/IaXi443n/EcU5yb4Ve9lyLrCa8IjsP72ON2Bnp3Kiv6OBbm5JCT8zv/8PZ5ZM5OJd5wCeGhfuChrAPcXzZ+ZP/2D9ncqLgDmGq6ifBGj2lhZznWVS+Q+s4h+iRnkJ2TzfLUoRx/P50/rD9IIDwLoZx9a55iXHQCS2y9+a/iI9Q4X2eSoZWBiA7dHBxU7HyLJ+b+pYVS/ptdG9bUvSYMd2KK6d7C/B04meMQa9JWw69zcTpPYFs9jm8fj2f6iq813t7/zc4/pvIek8mpceI8+RWrp/6TuXdOJnnNIY3rDtRYWTUvlTfMqym0t+DNpwM34TOL5qDSuoFlltIzJ/MeLeerbZ9QxwwO6kessZs3xflaOcs7bDDXDbyRisKdFBftoyI2ljCq+HZXMWWEM2BgFF8W7sFrAzYWgvTZNz1lDLriday02KgmlOixM5mZ0B+9apZWUFL0ERty1tY2Gv1A4hPGY4qNwhWA9YSgITopjYVxBhevGitZM1KxVHlCn2DPSyfZvAeip5Byz88ofv9dLLZTEBTN2LkzSeinx2UNn8a+4yPyq6/j4Su6uMqrLKHIsoGc3ELs6p4g9AMnkjB+FLFRYU3UUY33nMGjpjOj0sLSgjIwxJOWPpGoH0v4NDeL11TdlSJCiTbdxz1jh2LUK+etzd+8zPVFOI296C2ezczHHmQkflEyE69pSs76edth21HC9jXdefOrEyT1rTXxFI/HmGH7tfGwawpjzWGK80uVBsu9sRFqmwu55g5Gx2wic88B/jXxGp8uFE0V4s/7f6J0zQKGTf4HU1dv5elJfelALbPNwDpK15F83/swyABHmy/WUbqVV/8Ywpu2H0jqc1HzGfwmhYPy/A84NPlRZvdxXet9Jkxj6p0r+PW2v3M0qS/uu7bfaNRiQct383HnaTydeLurjYf1ZVLKk8xbNZIX/rSFJyck0efcXDAtFuWCJOxsJPGtHKZYs5iRmn9BRGiPkzqObiXjxULoHgSnmj+j4+hnrNvyM+LT3mJiVHDzGdowxVk3N13f2xliCKJ619ccUlyajiPs2n4Ygvox8LaIVoi4hxWpz2P2Gj6nsG3KcHs9FAt6HRmZubVGn1KyvZDczKXkWs8hEGjLJjXV7DL6lDKrbWx67n9YX+I2Vys+5+33TjNu9gSMIQqmcqy5S8n0Gn1qJuyFuWRmrMNa2byPpuqjFS6jDwi6OpLLOUJeRipLvLorZZ7CZjHz/LJtHK1fZHMyK9m9v59qjT56YHrysY5l9ClyVuq4dtFCpvsYffA9+W++yt6pccSEn3Xz9FLosCudQghXbhAHPueLo6ddYjr+zZFDVRhu6sVlHVbwthHMUfoBz/x2DdHp/61Zow/HIdY9swReSOXR3i3pI/wj+y3vYC7L5anUV3h//U4NhUF1hI94lNkDLqltQBVHsO29jKRfDqA1T4zaAvxkLXwYT8x2G30ekcOvI3ZUL8+WLP2dgOMIW5dvhAcSuatFYxiq+PaTj7FWH2Rt1jts/tjarl18zv7JqjPQ56ZLoWof+w5XQeV3HFbcuL2iubZVD2zFa5ZE2vJscrJfJMkYqlhhlCleD37kYPEO1bsWNDCZZWq4+HVSTD2AUizmLZTUN45a3IAMDExKZXlODtkZSRhV3+cR9uw/5iohLJZZLz1KnMeT5/HQEM7A5KXkKLIsn49JHwT2zZgtLXHZ98CU8jo5Oat4fcYthHxbxF+tp0A/lhRF/5wsMpJuQRGlen8p3zvrK9OMzN7kNZzcv4lXl+Zjx8Dg5CeYaqz1qHmTXeiVsD4MG2Bwe1jdwpTvwbLq5zx+760aDvMCuisZNOZGgqp3Y057iyL7cQ6uf5ftVz/AY6ar6zK50PXU5uf/nvyX0zCX9eN23mWc2rcvkuFPrmJn2U9tfrYLU+BPlK5LZx6PsXhCr5bVZ/knvPlUripu2cq5xE+IYcCDS/lMM0w8NfETZTvX8OJj/80/n32bzElab+8evX2WjlP8+58wbNSNRJ79U9inQFm9cAROc3RrNn9mHDNGXNmya71iNxvWHlRFrrZZWPFGKnP++1322t1OgPOszFmGehWpQri6bx+CLEVs33WYkZHFFFcHqd6Ky2lpjFsp5yqGjb+DKNWrFsHNsb3Ausetdhcu79GDIOxUF2Yy87iJKYN7oOs5ncxsozsUfJaEDEMYP+IaV6g4wkhsr2CstjOU1elSevQOBWs5hZnzOG6ayOAeP6Pnwy+RbfSEh8+QXzlkGMTQ610GWEhIZ4iayEs5E1E6vm77ZCtlJ//OxtzdqL0gaiqo+MFBnfhXi2W2krvEqgoTZBzDPbe5QonNSNcBDjsoL85jVb9J5Pf38Qx0AMnaXoQuRMTNZDFZZJjzyUzOR3m5eXWW0m1C4z/VuN+JYdofiRv/a55/4jnKtj5HwshpjPs+lB1vTKKHnz8MVY/mPHhh29300LUgxqtUefgInj/i5PmKfWz9cANZs+aycuVvmRBk0AQTV6s+zJrE4UxeeUDdNLCNv4/pw+2Gn2m80ddVz7H/E97dO5rHzLdo/3qvq7rmthxHt7H8z/DAH4YSofuevS3RUHEsrcxhltJ9bPs2Psy2YLOtJ33ZZaTPjyPiPN//zqH4ToQZY4gJqqZs+0es/WQv1VzFkP6RLbN4vXC60jXUY392prvBQG20uwsRIx7kyfsHqv2dVMvYbMb8RirJU+bwct5BKr3lNLJyrAxP5LbB0fCuhHq174YhqhmPmC6SEQ/P4v6BSk8UJRybjdls5o3UZKYkLyWvpPnxWWp413tOJdT5D9YueogpyUrHVzNm3zBy5zDCLvZNrDwYWimz4jm0Wvjwq3MIiTcAdz53HKPYso1+9w2idz3Vz+dZL1zZwYRGXM4V0dFcFwTVhct5ae0/ztymL5ywbXZmxz9L2F1moN/QMYxU+3v9DMOIR3l63gDKzEt4e1fz11KbCXM+ClJDvKu5/t1nmdTjLAyasD6MuOcJsvbt5c1pN1JmfgfL/h/Ph6QXoMyrmJS1H+dJG5vTp8HK3xKbsJSdvrNDXACp2vWUSvt4fhVXvjKXCWfTPtpVWDnZGQmoId7/5confkNchHsswBkz1DsYEkXsnYksfH0R8dGhVFs/5pNvvaMj6iVuu81ze7yG9eSGXsFQ9r9YdpSDIYb+PWvNtjYRU6fHOH4Wmcqox7TZJCUlMd0UTRBlFJqXY2nSsmuTs9cpRKfvx/hZL5GTs4y05IdISpqCKToU7AWYl3zUbNi5c7cwLvaWWEWJZQW5ysASZbBK0iOkZGaxKsXkY/h6E7dyJQi96UkykgcTdM4h8Vae+lySq56gHtw3JKqVLw/nctILldc98Gb5aSbMfZpF6oUPttwXyMg7oumRfo6TxzhACD+/JNSnnrsTY7oTA4fZe+j8T2dw/mpdCfFm8Kfrk/mNb3+2szlh2I1MT5nNnXzOti9dw8nOppgOmSesD6OeeInseQMg/1O+OKKVEH9ztN3tI2IBz04IwBB3c3j86rgS4n2bv155D/Hn2pUq5Dp+mTgWAz7dzc4ji3Mz/OhO75siveI18Gh5j5zliuMIeakPkZAwjeSlRZzqeRtxcXHEjR5MtMdJqBZ9EV0vVQzOKg4UWV2DIhxHKXrvr5wpetsaqRxH80idpsyzM4elRafoGTucuLhRjB58ndonrzVludJWcvTwv9TVoCtuYNCIOzBedozifJ/R0K0v1J3jBsaNvZGI2yYyTekzWbaJP2/t6MaEJ8w7miG9tTSasYlKVAYPLc2n/Nb+9FW6OYRcx8SnF5FkBOvKtezQsAckKPJaBnOAgm++c3VrUBHpCOnWnRAu4eeX1L4eNUGvA+8+StH6D9g8N5au3rkpe7pCmwfmEtOlE71f3Omj95lV0V17M6N6XUW/qy89c0K/POox9v1S+LMQWpna53UWFN/FimdHYTjHp+9ZCCBZ2pTA9+wt+JIyy3PM8M7FN8f1gYsqC6lTE3gwy0oLpvNTpdJd1YebgsOJMnTY6Vw89ILp2T8GQ+5BdRqXmNg+an+FlirqKaXJpe7nDJowlI3WTdgLlpBcsKRO0iDjcAapHkYdUTdcS1DhbqqtZmZPMbvSddejjr1og6mDdBG3M2GkBaullILM2RTUkSQU45hYerbqQg47s8yN9fGrc84WbPjws27cyleDEtwjlFuQt92TeMK80wIjzPvDSY5XQ82JCn7A3ZVT5+7j2lZvK+1ehy08YcQNDL3TwMq//I0vftOfAWHKhfMj33zxGQf8fs46dygzy5eFu19bwW8o/voJBtR5afVN13Dd8c0XfNRrKkv6a7Hn50/8s2Q/ZcN+wc2RZxESb4irA+9xUPH1KpJf7cb8zJFuo+8nyram81TJZN5I6uvj/e7AaohoPgQMxC18izifPeCeWq5kmOurZa2YAlidB7n7MB67viUzANQ5aas3WmWqNFa6ruct6rQuyjQubT/xoI4QYwLPpSUTr/at80hgYGB8Motnj3B3gqzbFxCUkcLxJP/X/dzaCvCe0htfhmNMXEhacjwDFWvS81PCtMkpzI5rbd/GxmROIGXhHMYp4fN6k2N7Tte6pcJvPA8ro6BbPPK4dWdos9QBFeYFLruBwcZQqgvfI6voqBraddg/472NNvQj/4N+qjHUZnQ7VkG6PtybNpdh+ek8kbaFMofy9Y5NvLnqG5Je+U+GtWpWgI6lWsulcX/NI/K3rClVwpzuL5isyWef6u1Vttcw/7HPuC/zHg3M8+bR1/PFCsUQepfUp04w/+l76a/l9s5PlH32Go+OmI7ZPJ3ru3Z2f7kkmMiReVx/cwtHgra8cXXAlA5+qKighhrKT/6o6a4sDeEr09Jlk5zwEKlqNx4HlSU7yMvbQYk6DZyynccrS2wM+e0oos7ZKmsoQYM9TvcP8KzKMoAJXJh2UOM8sWW+s1fSauf/1Vw4+O2u+6mDzk9W/N459Ve/cv5K/Xvcmbl+j/O7C8Cg3XV3VjmPFK90zhtmUCYtcmKY5kzfbHOevADVf/51/9a5elovJ73SncWnPQoedxan3+XE8Khz9f9VOZ3OGufJr1Y4pxlw8eBO57w3NzqLjyjHzs/v/OvtK3eV88iW3zuHKXWt/hmcw+a96dxiO+GbqN3W20/3GufJ4j/66O3R3700zHduOdG+F3z76e6pziPOj34/3X2Pc9/rpq9wflntOd5+y/Ovu1vXOvrVOE99uco561cznM9+VOqscdY4T32z3vn7qT73/TX5zi+/++m8gvDVvZNyJsUaVL6T6l5tYBzKjsAhEMjtQHRXbwWB09jdmgZqvQeq3kq1i+5yrQfajc63zbeHUzHQ+Iq+QkAICAEhIASEgBDokATE8OuQ1SJCCQEhIASEgBAQAkKg7QmI4df2TKVEISAEhIAQEAJCQAh0SAJi+HXIahGhhIAQEAJCQAgIASHQ9gTE8Gt7plKiEBACQkAICAEhIAQ6JAEx/DpktYhQQkAICAEhIASEgBBoewJi+LU9UylRCAgBISAEhIAQEAIdkoAYfh2yWkQoISAEhIAQEAJCQAi0PQEx/NqeqZQoBISAEBACQkAICIEOSUAMvw5ZLSKUEBACQkAICAEhIATankCdT7a1ffFSohAQAkJACAgBISAEhMCFJuD5LG+QRxDPDs+2LIWAEBACQkAICAEhIAS0RUBCvdqqT9FGCAgBISAEhIAQEAJNEvh/yRhvGck3tpUAAAAASUVORK5CYII="> <em><strong>A1A1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>A1</strong> </em>for correct ranks for Stan. Award <em><strong>A1</strong> </em>for correct ranks for Minsun.</p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;">0.933 (0.932673…) <em><strong>A2</strong></em></p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;">Stan and Minsun strongly agree on the ranking of competitors. <em><strong>A1A1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>A1</strong> </em>for “strongly agree”, <em><strong>A1</strong> </em>for reference to a rank order.</p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;">decreasing the score to 9.1, does not change the rank of competitor G <em><strong>A1</strong></em></p>
<p style="text-align: left;"><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Lucy sells hot chocolate drinks at her snack bar and has noticed that she sells more hot chocolates on cooler days. On six different days, she records the maximum daily temperature, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>, measured in degrees centigrade, and the number of hot chocolates sold, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math>. The results are shown in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> can be modelled by the regression line with equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>a</mi><mi>T</mi><mo>+</mo><mi>b</mi></math>.</p>
</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> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the regression equation, estimate the number of hot chocolates that Lucy will sell on a day when the maximum temperature is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>°</mo><mtext>C</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p>eg correct value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> (or for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>r</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>962839</mn></math> seen in (ii))</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>84636</mn><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>221</mn><mo>.</mo><mn>592</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>85</mn><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>222</mn></math> <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0</mn><mo>.</mo><mn>981244</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>981</mn></math> <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into their equation <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>.</mo><mn>85</mn><mo>×</mo><mn>12</mn><mo>+</mo><mn>222</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>103</mn><mo>.</mo><mn>435</mn></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>103</mn><mo>.</mo><mn>8</mn></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>sf</mtext></math>)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>103</mn></math> (hot chocolates) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The aircraft for a particular flight has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> seats. The airline’s records show that historically for this flight only <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>%</mo></math> of the people who purchase a ticket arrive to board the flight. They assume this trend will continue and decide to sell extra tickets and hope that no more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> passengers will arrive.</p>
<p>The number of passengers that arrive to board this flight is assumed to follow a binomial distribution with a probability of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>9</mn></math>.</p>
</div>
<div class="specification">
<p>Each passenger pays <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>150</mn></math> for a ticket. If too many passengers arrive, then the airline will give <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>300</mn></math> in compensation to each passenger that cannot board.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The airline sells <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> tickets for this flight. Find the probability that more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> passengers arrive to board the flight.</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>Write down the expected number of passengers who will arrive to board the flight if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> tickets are sold.</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 maximum number of tickets that could be sold if the expected number of passengers who arrive to board the flight must be less than or equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math>.</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, to the nearest integer, the expected increase or decrease in the money made by the airline if they decide to sell <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> tickets rather than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math>.</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> be the number of passengers who arrive)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>></mo><mn>72</mn></mrow></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>≥</mo><mn>73</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>≤</mo><mn>72</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>74</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>9</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>74</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>00379</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>00379124</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong> </em></p>
<p><br><strong>Note:</strong> Using the distribution <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mfenced><mrow><mn>74</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></mfenced></math>, to work with the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>%</mo></math> that do not arrive for the flight, here and throughout this question, is a valid approach.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>9</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mo>.</mo><mn>8</mn></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>9</mn><mo>=</mo><mn>72</mn></math> <em><strong>(M1)</strong></em></p>
<p>80 <em><strong>A1</strong> </em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><strong>EITHER</strong></p>
<p>when selling <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> tickets</p>
<p><img src="data:image/png;base64,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"></p>
<p>top row <em><strong>A1A1</strong></em></p>
<p>bottom row <em><strong>A1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1A1</strong> </em>for each row correct. Award <em><strong>A1</strong> </em>for one correct entry and <em><strong>A1</strong> </em>for the remaining entries correct.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>I</mi></mfenced><mo>=</mo><mn>11100</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>9962</mn><mo>…</mo><mo>+</mo><mn>10800</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>00338</mn><mo>…</mo><mo>+</mo><mn>10500</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>000411</mn><mo>≈</mo><mn>11099</mn></math> <em><strong>(M1)A1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>income is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn><mo>×</mo><mn>150</mn><mo>=</mo><mn>11100</mn></math> <em><strong>(A1)</strong></em></p>
<p>expected compensation is</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>003380</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>×</mo><mn>300</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>0004110</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>×</mo><mn>600</mn><mo> </mo><mo> </mo><mo>(</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>26070</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> <em><strong>(M1)A1A1</strong></em></p>
<p>expected income when selling <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> tickets is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11100</mn><mo>-</mo><mn>1</mn><mo>.</mo><mn>26070</mn><mo>…</mo></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>11098</mn><mo>.</mo><mn>73</mn><mo>…</mo><mo> </mo><mo> </mo><mo>(</mo><mo>=</mo><mo>$</mo><mn>11099</mn><mo>)</mo></math> <em><strong>A1</strong> </em></p>
<p><br><strong>THEN</strong></p>
<p>income for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> tickets <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>72</mn><mo>×</mo><mn>150</mn><mo>=</mo><mn>10800</mn></math> <em><strong>(A1)</strong></em></p>
<p>so expected gain <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≈</mo><mn>11099</mn><mo>-</mo><mn>10800</mn><mo>=</mo><mo>$</mo><mn>299</mn></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> tickets sold, let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> be the compensation paid out</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>=</mo><mn>73</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>00338014</mn><mo>…</mo><mo>,</mo><mo> </mo><mo> </mo><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>=</mo><mn>74</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>000411098</mn><mo>…</mo></math> <em><strong>A1A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>C</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>003380</mn><mo>…</mo><mo>×</mo><mn>300</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>0004110</mn><mo>…</mo><mo>×</mo><mn>600</mn><mo> </mo><mo> </mo><mo>(</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>26070</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> <em><strong>(M1)A1A1</strong></em></p>
<p>extra expected revenue <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>300</mn><mo>-</mo><mn>1</mn><mo>.</mo><mn>01404</mn><mo>…</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>246658</mn><mo>…</mo><mo> </mo><mo> </mo><mfenced><mrow><mn>300</mn><mo>-</mo><mn>1</mn><mo>.</mo><mn>26070</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn></math> and <em><strong>M1</strong> </em>for the subtraction.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>$</mo><mn>299</mn></math> (to the nearest dollar) <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math> be the change in income when selling <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> tickets.</p>
<p><img src="data:image/png;base64,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"> <em><strong>(A1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for one error, however award <em><strong>A1A1</strong> </em>if there is no explicit mention that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>73</mn></math> would result in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mn>0</mn></math> and the other two are correct.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>≤</mo><mn>73</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>9962</mn><mo>…</mo><mo>,</mo><mo> </mo><mo> </mo><mtext>P</mtext><mfenced><mrow><mi>T</mi><mo>=</mo><mn>74</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>000411098</mn><mo>…</mo></math> <em><strong>A1A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>D</mi></mfenced><mo>=</mo><mn>300</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>9962</mn><mo>…</mo><mo>+</mo><mn>0</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>003380</mn><mo>…</mo><mo>-</mo><mn>300</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>0004110</mn></math> <em><strong>(M1)A1A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>$</mo><mn>299</mn></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><em><strong>[8 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a) Stronger candidates were able to recognize that they needed to use the binomial to find the probability. Some candidates confused binomialpdf and binomialcdf functions. Some did not understand that “more than 72” means “73 or 74” and how their GDC uses the lower boundary parameter.</p>
<p>In part (b) many candidates could find the expected number of passengers and the maximum number of tickets. This part was well attempted.</p>
<p>Part (c) was expected to challenge the strongest candidates and had little scaffolding. However, this may have been too much for this cohort and resulted in few marks being awarded. A variety of methods were used but few progressed beyond finding values of income minus compensation. Only a few candidates took probabilities into consideration.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The mass <em>M</em> of apples in grams is normally distributed with mean <em>μ</em>. The following table shows probabilities for values of <em>M</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The apples are packed in bags of ten.</p>
<p>Any apples with a mass less than 95 g are classified as small.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>k</em>.</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 <em>μ</em> = 106.</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 <em>P</em>(M < 95) .</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a bag of apples selected at random contains at most one small apple.</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 expected number of bags in this crate that contain at most one small apple.</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>Find the probability that at least 48 bags in this crate contain at most one small apple.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum {{p_i}} = 1">
<mo>∑</mo>
<mrow>
<mrow>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
</mrow>
</mrow>
<mo>=</mo>
<mn>1</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg k</em> + 0.98 + 0.01 = 1</p>
<p><em>k</em> = 0.01 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that 93 and 119 are symmetrical about <em>μ</em> <em><strong>(M1)</strong></em></p>
<p><em>eg μ</em> is midpoint of 93 and 119</p>
<p>correct working to find <em>μ</em> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{119 + 93}}{2}">
<mfrac>
<mrow>
<mn>119</mn>
<mo>+</mo>
<mn>93</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<p><em>μ</em> = 106 <em><strong>AG N0</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding standardized value for 93 or 119 <em><strong> (A1)</strong></em><br><em>eg</em> <em>z</em> = −2.32634, <em>z</em> = 2.32634</p>
<p>correct substitution using <strong>their</strong> <em>z</em> value <em><strong>(A1)</strong></em><br><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{93 - 106}}{\sigma } = - 2.32634,\,\,\frac{{119 - 106}}{{2.32634}} = \sigma ">
<mfrac>
<mrow>
<mn>93</mn>
<mo>−</mo>
<mn>106</mn>
</mrow>
<mi>σ</mi>
</mfrac>
<mo>=</mo>
<mo>−</mo>
<mn>2.32634</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>119</mn>
<mo>−</mo>
<mn>106</mn>
</mrow>
<mrow>
<mn>2.32634</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mi>σ</mi>
</math></span></p>
<p>σ = 5.58815 <em><strong>(A1)</strong></em></p>
<p>0.024508</p>
<p>P(<em>X</em> < 95) = 0.0245 <em><strong> A2 N3</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of recognizing binomial <strong><em>(M1) </em></strong></p>
<p><em>eg </em>10, <em>anana</em><em>Cpqn</em>−=××and 0.024B(5,,)<em>pnp</em>= </p>
<p>valid approach <strong><em>(M1) </em></strong></p>
<p><em>eg </em>P(1),P(0)P(1)<em>XXX</em>≤=+= </p>
<p>0.976285 </p>
<p>0.976 <strong><em>A1 N2 </em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing <strong>new</strong> binomial probability <em><strong>(M1)</strong></em><br><em>eg </em> B(50, 0.976)</p>
<p>correct substitution <em><strong>(A1)</strong></em><br><em>eg</em> <em>E(X) = </em>50 (0.976285)</p>
<p>48.81425</p>
<p>48.8 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> P(X ≥ 48), 1 − P(X ≤ 47)</p>
<p>0.884688</p>
<p>0.885 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2}{{\text{e}}^{3x}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mn>3</mn>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span>, <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="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> has a horizontal tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. Find <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">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>choosing product rule <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="uv' + vu'"> <mi>u</mi> <msup> <mi>v</mi> <mo>′</mo> </msup> <mo>+</mo> <mi>v</mi> <msup> <mi>u</mi> <mo>′</mo> </msup> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {{x^2}} \right)^\prime }\left( {{{\text{e}}^{3x}}} \right) + {\left( {{{\text{e}}^{3x}}} \right)^\prime }{x^2}"> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mrow> <mo>)</mo> </mrow> <mi mathvariant="normal">′</mi> </msup> </mrow> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> </mrow> <mo>)</mo> </mrow> <mi mathvariant="normal">′</mi> </msup> </mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </math></span></p>
<p>correct derivatives (must be seen in the rule) <em><strong>A1A1</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2x"> <mn>2</mn> <mi>x</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{3}}{{\text{e}}^{3x}}"> <mrow> <mtext>3</mtext> </mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = 2x{{\text{e}}^{3x}} + 3{x^2}{{\text{e}}^{3x}}"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <mi>x</mi> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> <mo>+</mo> <mn>3</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> </math></span> <em><strong>A1 N4</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid method <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = 0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </math></span>, <img src="data:image/png;base64,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">, <img src="data:image/png;base64,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"></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - 0.667\left( { = - \frac{2}{3}} \right)"> <mi>a</mi> <mo>=</mo> <mo>−</mo> <mn>0.667</mn> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mo>−</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 0.667"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>0.667</mn> </math></span>) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W">
<mi>W</mi>
</math></span>, of newborn babies in Australia are normally distributed with a mean 3.41 kg and standard deviation 0.57 kg. A newborn baby has a low birth weight if it weighs less than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> kg.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that 5.3% of newborn babies have a low birth weight, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</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>A newborn baby has a low birth weight.</p>
<p>Find the probability that the baby weighs at least 2.15 kg.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = - 1.61643">
<mi>z</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1.61643</mn>
</math></span>, <img src="images/Schermafbeelding_2017-03-06_om_06.21.13.png" alt="N16/5/MATME/SP2/ENG/TZ0/05.a/M"></p>
<p>2.48863</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w = 2.49{\text{ (kg)}}">
<mi>w</mi>
<mo>=</mo>
<mn>2.49</mn>
<mrow>
<mtext> (kg)</mtext>
</mrow>
</math></span> <strong><em>A2 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct value or expression (seen anywhere)</p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.053 - {\text{P}}(X \leqslant 2.15),{\text{ }}0.039465">
<mn>0.053</mn>
<mo>−</mo>
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>⩽</mo>
<mn>2.15</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.039465</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p>evidence of conditional probability <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{P}}(2.15 \leqslant X \leqslant w}}{{{\text{P}}(X \leqslant w)}},{\text{ }}\frac{{0.039465}}{{0.053}}">
<mfrac>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>2.15</mn>
<mo>⩽</mo>
<mi>X</mi>
<mo>⩽</mo>
<mi>w</mi>
</mrow>
<mrow>
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>⩽</mo>
<mi>w</mi>
<mo stretchy="false">)</mo>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>0.039465</mn>
</mrow>
<mrow>
<mn>0.053</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.744631</p>
<p>0.745 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> has the following probability distribution.</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 an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> which gives the largest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the largest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of summing probabilities to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>+</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup><mo>+</mo><mi>p</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>7</mn><mo>-</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><mo> </mo><mn>1</mn><mo>-</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup><mo>-</mo><mi>p</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>7</mn><mo>+</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo>-</mo><mi>p</mi></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math> formula <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>3</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mo>+</mo><mn>1</mn><mo>×</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>×</mo><mi>p</mi><mo>+</mo><mn>3</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>7</mn><mo>-</mo><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup></mrow></mfenced></math></p>
<p>valid approach to find when <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math> is a maximum <em><strong>(M1)</strong></em></p>
<p>eg max on sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mi>p</mi><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>×</mo><mfenced><mrow><mo>-</mo><mn>8</mn><mi>p</mi></mrow></mfenced><mo>=</mo><mn>0</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><mrow><mn>2</mn><mo>×</mo><mfenced><mrow><mo>-</mo><mn>8</mn></mrow></mfenced></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><mo> </mo><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>125</mn></mrow></mfenced></math> (exact) (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac></math>) <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>225</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>89</mn><mn>40</mn></mfrac></math> (exact), <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>23</mn></math> <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(i) valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{5 + 17}}{2}">
<mfrac>
<mrow>
<mn>5</mn>
<mo>+</mo>
<mn>17</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = 11">
<mi>c</mi>
<mo>=</mo>
<mn>11</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p>(ii) valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>period is 12, per <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{2\pi }}{b},{\text{ }}9 - 3">
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mi>b</mi>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>9</mn>
<mo>−</mo>
<mn>3</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = \frac{{2\pi }}{{12}}">
<mi>b</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</mfrac>
</math></span> <strong><em>A1</em></strong></p>
<p><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> <strong><em>AG N0</em></strong></p>
<p>(iii) <strong>METHOD 1</strong></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5 = a\sin \left( {\frac{\pi }{6} \times 3} \right) + 11">
<mn>5</mn>
<mo>=</mo>
<mi>a</mi>
<mi>sin</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mo>×</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>11</mn>
</math></span>, substitution of points</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - 6">
<mi>a</mi>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{17 - 5}}{2}">
<mfrac>
<mrow>
<mn>17</mn>
<mo>−</mo>
<mn>5</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span>, amplitude is 6</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - 6">
<mi>a</mi>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 2.5">
<mi>k</mi>
<mo>=</mo>
<mn>2.5</mn>
</math></span> <strong><em>A1 N1</em></strong></p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = - 6\sin \left( {\frac{\pi }{6}(x - 2.5)} \right) + 11">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
<mi>sin</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>2.5</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>11</mn>
</math></span> <strong><em>A2 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <strong>METHOD 1 </strong>Using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span></p>
<p>recognizing that a point of inflexion is required <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>sketch, recognizing change in concavity</p>
<p>evidence of valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g''(x) = 0">
<msup>
<mi>g</mi>
<mo>″</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0</mn>
</math></span>, sketch, coordinates of max/min on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g'}">
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w = 8.5">
<mi>w</mi>
<mo>=</mo>
<mn>8.5</mn>
</math></span> (exact) <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2 </strong>Using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span></p>
<p>recognizing that a point of inflexion is required <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>sketch, recognizing change in concavity</p>
<p>evidence of valid approach involving translation <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = w - k">
<mi>x</mi>
<mo>=</mo>
<mi>w</mi>
<mo>−</mo>
<mi>k</mi>
</math></span>, sketch, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6 + 2.5">
<mn>6</mn>
<mo>+</mo>
<mn>2.5</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w = 8.5">
<mi>w</mi>
<mo>=</mo>
<mn>8.5</mn>
</math></span> (exact) <strong><em>A1 N2</em></strong></p>
<p>(ii) valid approach involving the derivative of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> (seen anywhere) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'(w),{\text{ }} - \pi \cos \left( {\frac{\pi }{6}x} \right)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>w</mi>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mi>π</mi>
<mi>cos</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, max on derivative, sketch of derivative</p>
<p>attempt to find max value on derivative <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \pi \cos \left( {\frac{\pi }{6}(8.5 - 2.5)} \right),{\text{ }}f'(6)">
<mo>−</mo>
<mi>π</mi>
<mi>cos</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>8.5</mn>
<mo>−</mo>
<mn>2.5</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span>, dot on max of sketch</p>
<p>3.14159</p>
<p>max rate of change <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \pi ">
<mo>=</mo>
<mi>π</mi>
</math></span> (exact), 3.14 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A jar contains 5 red discs, 10 blue discs and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> green discs. A disc is selected at random and replaced. This process is performed four times.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that the first disc selected is red.</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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> be the number of red discs selected. Find the smallest value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{Var}}(X{\text{ }}) < 0.6">
<mrow>
<mtext>Var</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">)</mo>
<mo><</mo>
<mn>0.6</mn>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P(red)}} = \frac{5}{{15 + m}}">
<mrow>
<mtext>P(red)</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mn>5</mn>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
</math></span> <strong><em>A1 N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing binomial distribution <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X \sim B(n,{\text{ }}p)">
<mi>X</mi>
<mo>∼</mo>
<mi>B</mi>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>p</mi>
<mo stretchy="false">)</mo>
</math></span></p>
<p>correct value for the complement of <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> (seen anywhere) <strong><em>A1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{5}{{15 + m}},{\text{ }}\frac{{10 + m}}{{15 + m}}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mn>5</mn>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>10</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
</math></span></p>
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{Var}}(X) = np(1 - p)">
<mrow>
<mtext>Var</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>n</mi>
<mi>p</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mi>p</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4\left( {\frac{5}{{15 + m}}} \right)\left( {\frac{{10 + m}}{{15 + m}}} \right),{\text{ }}\frac{{20(10 + m)}}{{{{(15 + m)}^2}}} < 0.6">
<mn>4</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>10</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
<mrow>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>20</mn>
<mo stretchy="false">(</mo>
<mn>10</mn>
<mo>+</mo>
<mi>m</mi>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>15</mn>
<mo>+</mo>
<mi>m</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo><</mo>
<mn>0.6</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m > 12.2075">
<mi>m</mi>
<mo>></mo>
<mn>12.2075</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m = 13">
<mi>m</mi>
<mo>=</mo>
<mn>13</mn>
</math></span> <strong><em>A1 N3</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br>