2015 General Mathematics WAEC SSCE (School Candidates) May/June: Difference between revisions

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=== Objective Test Questions ===
=== Objective Test Questions ===
<ol>
<ol>
     <li>If {x :2 x 18; x € integer} and 7 + x = 4 (mod 9), find the highest value of x.  
     <li>If <math>\{x:2 \leq x \leq 18; x \epsilon\}</math> and <math>7 + x = 4\pmod{9}</math>, find the highest value of <math>x</math>.  
         <ol type="a">
         <ol type="a">
             <li>2</li>
             <li>2</li>
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         </ol>
         </ol>
     </li>
     </li>
     <li>The sum of 11011<sub>2</sub>, 11111<sub>2</sub>, and 10000<sub>2</sub> is, 10''m''10''n''0<sub>2</sub>. Find the values of m and n.
     <li>The sum of <math>11011_2, 11111_2,</math> and <math>10000_2</math> is <math>10_m10_n0_2</math>. Find the values of <math>m</math> and <math>n</math>.
         <ol type="a">
         <ol type="a">
             <li>m = 0,n = 0</li>
             <li>m = 0,n = 0</li>
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         </ol>
         </ol>
     </li>
     </li>
     <li>A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to #1.00, how much did the engine cost in naira?
     <li>A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to #1.00, how much did the engine cost in naira?  
         <ol type="a">
         <ol type="a">
             <li>#250,000.00</li>
             <li>#250,000.00</li>
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         </ol>
         </ol>
     </li>
     </li>
     <li>If  
     <li>If <math>{27^x \times3^{1-x}\over 9^{2x}}- = 1, </math> find the value of <math>x</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>1</math></li>
             <li>Option b</li>
             <li><math>\tfrac{1}{2}</math></li>
             <li>Option c</li>
             <li><math>-\tfrac{1}{2}</math></li>
             <li>Option d</li>
             <li><math>-1</math></li>
         </ol>
         </ol>
     </li>
     </li>
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         </ol>
         </ol>
     </li>
     </li>
     <li>Question 6
     <li>Given that <math>log{}_x^{64} = 3,</math> evaluate <math>x log_2^8 </math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>6</li>
             <li>Option b</li>
             <li>9</li>
             <li>Option c</li>
             <li>12</li>
             <li>Option d</li>
             <li>24</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 7
     <li>If <math>2^n = y,</math> find 2<sup><math>(2+_3^n )</math></sup>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>4y</math><sup><math>^1_2 </math></sup></li>
             <li>Option b</li>
             <li><math>4y </math><sup><math>-3</math></sup></li>
             <li>Option c</li>
             <li><math>2y^3</math></li>
             <li>Option d</li>
             <li><math>2y</math><sup><math>-3</math></sup></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Factorize completely: 6ax—12by—9ay+8bx.
     <li>Factorize completely: <math>6xa-12by-9ay+8bx</math>.
         <ol type="a">
         <ol type="a">
             <li>(2a 3b)(4x + 3y)</li>
             <li><math>(2a-3b)(4x+3y)</math></li>
             <li>(3a + 4b)(2x - 3y)</li>
             <li><math>(3a+4b)(2x-3y)</math></li>
             <li>(3a 4b)(2x + 3y)</li>
             <li><math>(3a-4b)(2x+3y)</math></li>
             <li>(2a + 3b)(4x 3y)</li>
             <li><math>(2a+3b)(4x-3y)</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Find the equation whose roots are 3/4 and -4.
     <li>Find the equation whose roots are <math>\tfrac{3}{4}</math> and <math>-4</math>.
         <ol type="a">
         <ol type="a">
             <li>4x<sup>2</sup> — 13x + 12 = 0</li>
             <li><math>4x^2 - 13x + 12 = 0 </math></li>
             <li>4x<sup>2</sup> — 13x -12 = 0</li>
             <li><math>
             <li>4x<sup>2</sup> + 13x -12 = 0</li>
4x^2 - 13x - 12 =0</math></li>
             <li>4x<sup>2</sup> +13x + 12 = 0</li>
             <li><math>
4x^2 + 13x - 12 = 0</math></li>
             <li><math>
4x^2 +13x + 12 = 0</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 10
     <li>If <math>m=4</math>, <math>n=9</math> and <math>r=16</math>, evaluate <math>{m \over n}-4{7 \over 9}+{n \over r}</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>1 {5 \over 16}</math></li>
             <li>Option b</li>
             <li><math>1{1 \over 16}</math></li>
             <li>Option c</li>
             <li><math>{5 \over 16}</math></li>
             <li>Option d</li>
             <li><math>{37 \over 48}</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 11
     <li>. Adding 42 to a given positive number gives the same result as squaring the number. Find the number.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>14</li>
             <li>Option b</li>
             <li>13</li>
             <li>Option c</li>
             <li>7</li>
             <li>Option d</li>
             <li>6</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 12
     <li>Ada draws the graphs of <math>y=x^2-x-2</math> and <math>y=2x-1</math> on the same axes. Which of these equations is she solving?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>x^2-x-3=0</math></li>
             <li>Option b</li>
             <li><math>x^2 -3x-1=0</math></li>
             <li>Option c</li>
             <li><math>x^2-3x-3=0</math></li>
             <li>Option d</li>
             <li><math>x^2+3x-1=0</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 13
     <li>The volume of a cone of height <math>3 {cm}</math> is <math>38\tfrac{1}{2} {cm^3}</math>. Find the radius of its base. [Take <math>\pi</math> = 22/7].
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>3.0{cm}</math></li>
             <li>Option b</li>
             <li><math>3.5{cm}</math></li>
             <li>Option c</li>
             <li><math>4.0{cm}</math></li>
             <li>Option d</li>
             <li><math>4.5{cm}</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 14
     <li>A sector of a circle with radius <math>6{cm}</math> subtends an angle of <math>60^\circ</math> at the center. Calculate its perimeter in terms of <math>\pi</math>.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>2(\pi+6) {cm}</math></li>
             <li>Option b</li>
             <li><math>2(\pi+3){cm}</math></li>
             <li>Option c</li>
             <li><math>2(\pi+2){cm}</math></li>
             <li>Option d</li>
             <li><math>(\pi+12) {cm}</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 15
     <li>The dimensions of a rectangular tank are <math>2m</math> by <math>7m</math> by <math>11m</math>. if its volume is equal to that of a cylindrical tank of height <math>4m</math>, calculate the base radius of the cylindrical tank. [Take <math>\pi</math> = 22/7]
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>14m</math></li>
             <li>Option b</li>
             <li><math>7m</math></li>
             <li>Option c</li>
             <li><math>3\tfrac{1}{2} m</math></li>
             <li>Option d</li>
             <li><math>1\tfrac{3}{4}{m}</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 16
     <li>[[File:WA2015 MATH P1Q016.jpg|alt=WA2015 MATH P1Q016|left|thumb|180x180px]]<p></p><p></p><p></p><p></p><p>In the diagram above, O is the center of the circle. If PQ//RS and <math>\angle</math>ONS = 140°, find the size of <math>\angle</math>POM.</p>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>40°</li>
             <li>Option b</li>
             <li>50° </li>
             <li>Option c</li>
             <li>60°</li>
             <li>Option d</li>
             <li>80°</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 17
     <li>[[File:WA2015 MATH P1Q017.jpg|alt=Image|left|thumb|180x180px]]<p></p><p></p><p></p><p></p><p>In the diagram, PTR is a tangent to the circle center O. If angle TON = 108°, calculate the size of angle PTN.</p>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>132°</li>
             <li>Option b</li>
             <li>126°</li>
             <li>Option c</li>
             <li>108°</li>
             <li>Option d</li>
             <li>102°</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 18
     <li>[[File:WA2015 MATH P1Q018.jpg|alt=Image|left|thumb|180x180px]]<p> </p><p> </p><p> </p><p> </p><p> </p><p> In the diagram, PQ//RT, QR//SU, <math>\angle</math>PQR = 48° <math>\angle</math>RTS = <math>x^\circ</math>. Find the value of <math>x^\circ</math></p><ol type="a">
        <ol type="a">
             <li><math>134^\circ</math></li>
             <li>Option a</li>
             <li><math>132^\circ</math></li>
             <li>Option b</li>
             <li><math>96^\circ</math></li>
             <li>Option c</li>
             <li><math>48^\circ</math>[[File:WA2015 MATH P1Q019.jpg|alt=Image|left|thumb|180x180px]]</li>
             <li>Option d</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 19
     <p>In the diagram above, O is the center of the circle, line RT is a diameter <math>\angle</math>PQT =  <math>33^\circ</math>and <math>\angle</math>TOS = <math>76^\circ</math>. '''''Use the diagram to answer question 19 and 20'''''</p>
<li>Calculate the value of angle PTR.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>73^\circ</math></li>
             <li>Option b</li>
             <li><math>67^\circ</math></li>
             <li>Option c</li>
             <li><math>57^\circ</math></li>
             <li>Option d</li>
             <li><math>37^\circ</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 20
     <li>Find the size of angle PRS
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>76^\circ</math></li>
             <li>Option b</li>
             <li><math>71^\circ</math></li>
             <li>Option c</li>
             <li><math>38^\circ</math></li>
             <li>Option d</li>
             <li><math>33^\circ</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 21
<p>The table below shows values for a linear graph</p>
{| class="wikitable"
|+
!Scores
!<math>x</math>
!<math>0</math>
!<math>1\tfrac{1}{4}</math>
!<math>2</math>
!<math>4</math>
|-
|Frequency
|<math>y</math>
|<math>3</math>
|<math>5\tfrac{1}{2}</math>
|
|
|}
<p>'''''Use it to answer questions 21 and 22'''''</p>
     <li>Find the gradient of the line
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>1</li>
             <li>Option b</li>
             <li>2</li>
             <li>Option c</li>
             <li>3</li>
             <li>Option d</li>
             <li>4</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 22
     <li>What is the value of <math>y</math> when <math>x=22</math>?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>5</li>
             <li>Option b</li>
             <li>7</li>
             <li>Option c</li>
             <li>9</li>
             <li>Option d</li>
             <li>11</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 23
     <li>Given that <math>\tan x= 2/3 </math>, where  <math>0^\circ\leq x \leq90^\circ</math>, find the value of <math>2\sin x</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>{2\sqrt{13} \over 13}</math></li>
             <li>Option b</li>
             <li><math>{3\sqrt{13} \over 13}</math></li>
             <li>Option c</li>
             <li><math>{4\sqrt{13} \over 13}</math></li>
             <li>Option d</li>
             <li><math>{6\sqrt{13} \over 13}</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 24
     <li>PQRS is a square. If <math>x</math> is the midpoint of PQ, calculate correct to the nearest degree, <math>\angle</math>PXS
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>53^\circ</math></li>
             <li>Option b</li>
             <li><math>55^\circ</math></li>
             <li>Option c</li>
             <li><math>63^\circ</math></li>
             <li>Option d</li>
             <li><math>65^\circ</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 25
     <li>The angle of elevation of an aircraft from point <math>k</math> on the horizontal ground is <math>30^\circ</math>, If the aircraft 800m above the ground, how far is it from <math>k</math>?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>400 .00m</math></li>
             <li>Option b</li>
             <li><math>692 .82m</math></li>
             <li>Option c</li>
             <li><math>923.76m</math></li>
             <li>Option d</li>
             <li><math>1,600.00m</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 26
     <li>The population of students in a school is <math>810</math>. If this is represented on a pie chart, calculate the sectoral angle for a class of <math>72</math> students.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>32^\circ</math></li>
             <li>Option b</li>
             <li><math>45^\circ</math></li>
             <li>Option c</li>
             <li><math>60^\circ</math></li>
             <li>Option d</li>
             <li><math>75^\circ</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 27
     <li>The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 54, 58, 59, 60, 61, 62, 63, 65, 67, 70, 73, 75. Find the third quartile.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>62</li>
             <li>Option b</li>
             <li>63</li>
             <li>Option c</li>
             <li>64</li>
             <li>Option d</li>
             <li>65</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 28
{| class="wikitable"
        <ol type="a">
|+
             <li>Option a</li>
!Scores
             <li>Option b</li>
!0 - 4
             <li>Option c</li>
!5 - 9
             <li>Option d</li>
!10 - 14
|-
|Frequency
|2
|1
|2
|}
      
<li>The table above shows the distribution of the scores of some students in a test. Calculate the mean score.
<ol type="a">
             <li>5.6</li>
             <li>6.0</li>
             <li>6.6</li>
             <li>7.0</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 29
     <li>The probabilities that Kenna, Ebou and Omar will hit a target are 2/3, 3/4, and 4/5 respectively. Find the probability that only Kenna will hit the target.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>2/5</li>
             <li>Option b</li>
             <li>7/60</li>
             <li>Option c</li>
             <li>1/30</li>
             <li>Option d</li>
             <li>1/60</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 30
     <li>[[File:WA2015 MATH P1Q030.jpg|alt=Image|left|thumb|180x180px]]In the diagram VW//YZ, |WX| = <math>6cm</math>, |XY| = <math>16cm</math>, |YZ| = <math>20cm</math> and |ZX| = <math>12cm</math>. Calculate |VX|.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>3cm</math></li>
             <li>Option b</li>
             <li><math>4cm</math></li>
             <li>Option c</li>
             <li><math>6cm</math></li>
             <li>Option d</li>
             <li><math>8cm</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 31
     <li>Tom will be <math>25</math> years old in <math>n</math> year’s time. If he is <math>5</math> years younger than Bade, find Bade’s present age.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>(30 - n) years</math></li>
             <li>Option b</li>
             <li><math>(20-n) years</math></li>
             <li>Option c</li>
             <li><math>(25 - n) years</math></li>
             <li>Option d</li>
             <li><math>(30 + n) years</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 32
     <li>If <math>{\sqrt{2} + \sqrt{3}\over\sqrt{3}}</math> is simplified as <math>m+n\sqrt{6} </math>, find the value of <math>(m+n)</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>\tfrac{1}{3}</math></li>
             <li>Option b</li>
             <li><math>\tfrac{2}{3}</math></li>
             <li>Option c</li>
             <li><math>1\tfrac{1}{3}</math></li>
             <li>Option d</li>
             <li><math>1\tfrac{2}{3}</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 33
     <li>[[File:WA2015 MATH P1Q033.jpg|alt=Image|left|thumb|180x180px]]<p> </p><p> </p><p> </p><p>In the diagram, line QT and line PR are straight lines, <math>\angle</math>ROS = (<math>3n ^\circ</math> - <math>20^\circ</math>), <math>\angle</math>POT = <math>2m^\circ</math>, <math>\angle</math>SOT = <math>n^\circ</math>, <math>\angle</math>POL = <math>m^\circ</math> and <math>\angle</math>QOL is a right angle. Find the value of <math>n^\circ</math> </p>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>35^\circ</math></li>
             <li>Option b</li>
             <li><math>40^\circ</math></li>
             <li>Option c</li>
             <li><math>55^\circ</math></li>
             <li>Option d</li>
             <li><math>60^\circ</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 34
     <li>Make <math>k</math> the subject of the relation
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>k= {H (T^2-1)\over T^2-T} </math></li>
             <li>Option b</li>
             <li><math>k= {HT\over (T-1)^2} </math></li>
             <li>Option c</li>
             <li><math>k= {H (T^2+1)\over T} </math></li>
             <li>Option d</li>
             <li><math>k= {H (T-1)\over T} </math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 35
     <li>Which of the following is used to determine the mode of a grouped data?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>Bar chart</li>
             <li>Option b</li>
             <li>Frequency polygon</li>
             <li>Option c</li>
             <li>Ogive</li>
             <li>Option d</li>
             <li>Histogram</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 36
     <li>The area of a rhombus is <math>110 {cm} ^2 </math>. If the diagonals are <math>20</math> and <math>(2x+1) {cm}</math> long, find the value of <math>x</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>5.0</math></li>
             <li>Option b</li>
             <li><math>4.0</math></li>
             <li>Option c</li>
             <li><math>3.0</math></li>
             <li>Option d</li>
             <li><math>2.5</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 37
     <li>Simplify: <math>{3x-y \over xy}-{2x+3x \over 2xy}+{1 \over 2}</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>{4x+5y-xy\over2xy} </math></li>
             <li>Option b</li>
             <li><math>{5y-5x+xy\over2xy}</math></li>
             <li>Option c</li>
             <li><math>{5x+5y-xy\over2xy}</math></li>
             <li>Option d</li>
             <li><math>{4x-5y+xy\over2xy} </math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 38
     <li>Illustrate graphically, the solution of <math>\tfrac{y}{2} +\tfrac{1}{8} +\tfrac{5y}{8}</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>[[File:WA2015 MATH P1Q038OA.jpg|alt=Image|left|thumb|230x230px]]</li>
             <li>Option b</li>
             <li>[[File:WA2015 MATH P1Q038OB.jpg|alt=Image|left|thumb|230x230px]]</li>
             <li>Option c</li>
             <li>[[File:WA2015 MATH P1Q038OC.jpg|alt=Image|left|thumb|230x230px]]</li>
             <li>Option d</li>
             <li>[[File:WA2015 MATH P1Q038OD.jpg|alt=Image|left|thumb|230x230px]]</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 39
     <li>A farmer uses 2/5 of his land to grow cassava, 1/3 of the remainder for yam and the rest for maize. Find the part of the land used for maize.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>2/15</math></li>
             <li>Option b</li>
             <li><math>2/5</math></li>
             <li>Option c</li>
             <li><math>2/3</math></li>
             <li>Option d</li>
             <li><math>4/5</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 40
     <li>The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If <math>4</math> litres of petrol is consumed on a distance of <math>15km</math>, how far would the vehicle go on <math>9</math> litres of petrol?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>22\tfrac{1}{2}{km}</math></li>
             <li>Option b</li>
             <li><math>30 {km}</math></li>
             <li>Option c</li>
             <li><math>33\tfrac{3}{4}{km}</math></li>
             <li>Option d</li>
             <li><math>45{km}</math></li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 41
     <li>A trader bought 100 oranges at 5 for #40.00 and sold them at 20 for #120.00. Find the profit or loss percent.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>20%</math> profit</li>
             <li>Option b</li>
             <li><math>20%</math> loss</li>
             <li>Option c</li>
             <li><math>25%</math> profit</li>
             <li>Option d</li>
             <li><math>25%</math> loss</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 42
     <li>[[File:WA2015 MATH P1Q042.jpg|alt=Image|left|thumb|180x180px]]
        <ol type="a">
<ol type="a"> <br> <br> <br><br> <br> <br><br><br>
<p>Describe the shaded portion in the
diagram above.</p>
             <li>Option a</li>
             <li>Option a</li>
             <li>Option b</li>
             <li>Option b</li>
             <li>Option c</li>
             <li>Option c</li>
             <li>Option d</li>
             <li>Option d</li>
         </ol>
         </ol> <br> <br> <br>
     </li>
     </li>
     <li>Question 43
     <li>Question 43

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Objective Test Questions

  1. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{x:2 \leq x \leq 18; x \epsilon\}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7 + x = 4\pmod{9}} , find the highest value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} .
    1. 2
    2. 5
    3. 15
    4. 18
  2. The sum of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 11011_2, 11111_2,} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10000_2} is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10_m10_n0_2} . Find the values of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} .
    1. m = 0,n = 0
    2. m = 1,n = 0
    3. m = O, n = 1
    4. m = 1, n = 1
  3. A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to #1.00, how much did the engine cost in naira?
    1. #250,000.00
    2. #200,000.00
    3. #150,000.00
    4. #100,000.00
  4. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {27^x \times3^{1-x}\over 9^{2x}}- = 1, } find the value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tfrac{1}{2}}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\tfrac{1}{2}}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -1}
  5. Find the 7th term of the sequence: 2, 5, 10, 17, 26...
    1. 37
    2. 48
    3. 50
    4. 63
  6. Given that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle log{}_x^{64} = 3,} evaluate Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x log_2^8 }
    1. 6
    2. 9
    3. 12
    4. 24
  7. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2^n = y,} find 2Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (2+_3^n )}
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4y} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^1_2 }
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2y^3}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2y} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3}
  8. Factorize completely: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6xa-12by-9ay+8bx} .
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (2a-3b)(4x+3y)}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (3a+4b)(2x-3y)}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (3a-4b)(2x+3y)}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (2a+3b)(4x-3y)}
  9. Find the equation whose roots are Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tfrac{3}{4}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -4} .
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4x^2 - 13x + 12 = 0 }
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4x^2 - 13x - 12 =0}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4x^2 + 13x - 12 = 0}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4x^2 +13x + 12 = 0}
  10. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m=4} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n=9} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=16} , evaluate Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {m \over n}-4{7 \over 9}+{n \over r}}
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 {5 \over 16}}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1{1 \over 16}}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {5 \over 16}}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {37 \over 48}}
  11. . Adding 42 to a given positive number gives the same result as squaring the number. Find the number.
    1. 14
    2. 13
    3. 7
    4. 6
  12. Ada draws the graphs of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=x^2-x-2} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=2x-1} on the same axes. Which of these equations is she solving?
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2-x-3=0}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 -3x-1=0}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2-3x-3=0}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2+3x-1=0}
  13. The volume of a cone of height is . Find the radius of its base. [Take = 22/7].
  14. A sector of a circle with radius subtends an angle of at the center. Calculate its perimeter in terms of .
  15. The dimensions of a rectangular tank are by by . if its volume is equal to that of a cylindrical tank of height , calculate the base radius of the cylindrical tank. [Take = 22/7]
  16. WA2015 MATH P1Q016

    In the diagram above, O is the center of the circle. If PQ//RS and ONS = 140°, find the size of POM.

    1. 40°
    2. 50°
    3. 60°
    4. 80°
  17. Image

    In the diagram, PTR is a tangent to the circle center O. If angle TON = 108°, calculate the size of angle PTN.

    1. 132°
    2. 126°
    3. 108°
    4. 102°
  18. Image

    In the diagram, PQ//RT, QR//SU, PQR = 48° RTS = . Find the value of

    1. Image
  19. In the diagram above, O is the center of the circle, line RT is a diameter PQT = and TOS = . Use the diagram to answer question 19 and 20

  20. Calculate the value of angle PTR.
  21. Find the size of angle PRS
  22. The table below shows values for a linear graph

    Scores
    Frequency

    Use it to answer questions 21 and 22

  23. Find the gradient of the line
    1. 1
    2. 2
    3. 3
    4. 4
  24. What is the value of when ?
    1. 5
    2. 7
    3. 9
    4. 11
  25. Given that , where , find the value of
  26. PQRS is a square. If is the midpoint of PQ, calculate correct to the nearest degree, PXS
  27. The angle of elevation of an aircraft from point on the horizontal ground is , If the aircraft 800m above the ground, how far is it from ?
  28. The population of students in a school is . If this is represented on a pie chart, calculate the sectoral angle for a class of students.
  29. The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 54, 58, 59, 60, 61, 62, 63, 65, 67, 70, 73, 75. Find the third quartile.
    1. 62
    2. 63
    3. 64
    4. 65
  30. Scores 0 - 4 5 - 9 10 - 14
    Frequency 2 1 2
  31. The table above shows the distribution of the scores of some students in a test. Calculate the mean score.
    1. 5.6
    2. 6.0
    3. 6.6
    4. 7.0
  32. The probabilities that Kenna, Ebou and Omar will hit a target are 2/3, 3/4, and 4/5 respectively. Find the probability that only Kenna will hit the target.
    1. 2/5
    2. 7/60
    3. 1/30
    4. 1/60
  33. Image
    In the diagram VW//YZ, |WX| = , |XY| = , |YZ| = and |ZX| = . Calculate |VX|.
  34. Tom will be years old in year’s time. If he is years younger than Bade, find Bade’s present age.
  35. If is simplified as , find the value of
  36. Image

    In the diagram, line QT and line PR are straight lines, ROS = ( - ), POT = , SOT = , POL = and QOL is a right angle. Find the value of

  37. Make the subject of the relation
  38. Which of the following is used to determine the mode of a grouped data?
    1. Bar chart
    2. Frequency polygon
    3. Ogive
    4. Histogram
  39. The area of a rhombus is . If the diagonals are and long, find the value of
  40. Simplify:
  41. Illustrate graphically, the solution of
    1. Image
    2. Image
    3. Image
    4. Image
  42. A farmer uses 2/5 of his land to grow cassava, 1/3 of the remainder for yam and the rest for maize. Find the part of the land used for maize.
  43. The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If litres of petrol is consumed on a distance of , how far would the vehicle go on litres of petrol?
  44. A trader bought 100 oranges at 5 for #40.00 and sold them at 20 for #120.00. Find the profit or loss percent.
    1. profit
    2. loss
    3. profit
    4. loss
  45. Image








      Describe the shaded portion in the diagram above.

    1. Option a
    2. Option b
    3. Option c
    4. Option d



  46. Question 43
    1. Option a
    2. Option b
    3. Option c
    4. Option d
  47. Question 44
    1. Option a
    2. Option b
    3. Option c
    4. Option d
  48. Question 45
    1. Option a
    2. Option b
    3. Option c
    4. Option d
  49. Question 46
    1. Option a
    2. Option b
    3. Option c
    4. Option d
  50. Question 47
    1. Option a
    2. Option b
    3. Option c
    4. Option d
  51. Question 48
    1. Option a
    2. Option b
    3. Option c
    4. Option d
  52. Question 49
    1. Option a
    2. Option b
    3. Option c
    4. Option d
  53. Question 50
    1. Option a
    2. Option b
    3. Option c
    4. Option d

Theory

Section A

  1. Question 1
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  2. Question 2
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  3. Question 3
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  4. Question 4
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  5. Question 5
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v

Section B

  1. Question 6
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  2. Question 7
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  3. Question 8
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  4. Question 9
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  5. Question 10
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  6. Question 11
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  7. Question 12
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
  8. Question 13
    1. Sub-question a
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    2. Sub-question b
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    3. Sub-question c
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    4. Sub-question d
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    5. Sub-question e
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v
    6. Sub-question f
      1. Sub-question i
      2. Sub-question ii
      3. Sub-question iii
      4. Sub-question iv
      5. Sub-question v