2016 General Mathematics WAEC SSCE (School Candidates) May/June: Difference between revisions

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=== Objective Test Questions ===
=== Objective Test Questions ===
<ol>
<ol>
     <li>Question 1
     <li>If 23<sub>x</sub> + 101<sub>x</sub> = 130<sub>x</sub>. Find the value of x.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>7</li>
             <li>Option b</li>
             <li>6</li>
             <li>Option c</li>
             <li>5</li>
             <li>Option d</li>
             <li>4</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 2
     <li>Simplify: <math>(\tfrac{3}{4}-\tfrac{2}{3}) \times 1\tfrac{1}{5} </math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>\tfrac{1}{60}</math></li>
             <li>Option b</li>
             <li><math>\tfrac{5}{72}</math></li>
             <li>Option c</li>
             <li><math>\tfrac{1}{10}</math></li>
             <li>Option d</li>
             <li><math>1\tfrac{7}{10}</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 3
     <li>Simplify: <math>(\tfrac{10\sqrt{3}}{\sqrt{5}}-\sqrt{15})^2 </math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>75.00</li>
             <li>Option b</li>
             <li>15.00</li>
             <li>Option c</li>
             <li>8.66</li>
             <li>Option d</li>
             <li>3.87</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 4
     <li>The distance, ''d'', through which a stone falls from rest varies directly as the square of the time, ''t'', taken. If the stone falls 45 cm in 3 seconds, how far will it fall in 6 seconds?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>90 cm</li>
             <li>Option b</li>
             <li>135 cm</li>
             <li>Option c</li>
             <li>180 cm</li>
             <li>Option d</li>
             <li>225 cm</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 5
     <li>Which of the following is a valid conclusion from the premise: 'Nigerian footballers are good footballers'?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>Joseph plays football in Nigeria therefore he is a good footballer.</li>
             <li>Option b</li>
             <li>Joseph is a good footballer therefore he is a Nigerian footballer.</li>
             <li>Option c</li>
             <li>Joseph is a Nigerian footballer therefore he is a good footballer.</li>
             <li>Option d</li>
             <li>Joseph plays good football therefore he is a Nigerian footballer.</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 6
     <li>On a map, 1 cm represents 5 km. Find the area on the map that represents 100 km².
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>2 cm²</li>
             <li>Option b</li>
             <li>4 cm²</li>
             <li>Option c</li>
             <li>8 cm²</li>
             <li>Option d</li>
             <li>16 cm²</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 7
     <li>Simplify: <math>\tfrac{3^{n-1}\times27^{n+1}}{81^n} </math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>3<sup>2n</sup></li>
             <li>Option b</li>
             <li>9</li>
             <li>Option c</li>
             <li>3<sup>n</sup></li>
             <li>Option d</li>
             <li>3<sup>n+1</sup></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 8
     <li>What sum of money will amount to ''D''10,400.00 in 5 years at 6% simple interest?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>''D''8,000.00</li>
             <li>Option b</li>
             <li>''D''10,000.00</li>
             <li>Option c</li>
             <li>''D''12,000.00</li>
             <li>Option d</li>
             <li>''D''16,000.00</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 9
     <li>Which of the following number lines illustrates the solution of the inequality 4 ≤ <math>\tfrac{1}{3}(2x-1) </math> < 5?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>[[File:WA2016 MATH P1Q009OA.jpg|center|thumb|229x229px]]</li>
             <li>Option b</li>
             <li>[[File:WA2016 MATH P1Q009OB.jpg|center|thumb|244x244px]]</li>
             <li>Option c</li>
             <li>[[File:WA2016 MATH P1Q009OC.jpg|center|thumb|245x245px]]</li>
             <li>Option d</li>
             <li>[[File:WA2016 MATH P1Q009OD.jpg|center|thumb|252x252px]]</li>
         </ol>
         </ol>
     </li>
     </li>
     <li>Question 10
     <li>The roots of a quadratic equation are <math>\tfrac{4}{3} </math> and <math>\tfrac{-3}{7} </math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>21x² - 19x - 12 = 0</li>
             <li>Option b</li>
             <li>21x² + 37x - 12 = 0</li>
             <li>Option c</li>
             <li>21x² - x + 12 = 0</li>
             <li>Option d</li>
             <li>21x² + 7x - 4 = 0</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 11
     <li>Find the values of y for which the expression <math>\tfrac{y^2-9y+18}{y^2+4y-2 1}</math> is undefined
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>6, -7</li>
             <li>Option b</li>
             <li>3, -6</li>
             <li>Option c</li>
             <li>3, -7</li>
             <li>Option d</li>
             <li>-3, -7</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 12
     <li>Given that 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>1</li>
             <li>Option b</li>
             <li>3</li>
             <li>Option c</li>
             <li>7</li>
             <li>Option d</li>
             <li>17</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 13
     <li>Simplify: <math>\tfrac{2}{1-x}-\tfrac{1}{x}</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>\tfrac{x+1}{x(1-x)}</math></li>
             <li>Option b</li>
             <li><math>\tfrac{3x-1}{x(1-x) }</math></li>
             <li>Option c</li>
             <li><math>\tfrac{3x+1}{x(1-x)}</math></li>
             <li>Option d</li>
             <li><math>\tfrac{x-1}{x(1-x)}</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 14
     <li>Make s the subject of the relation: p = s + <math>\tfrac{sm^2}{nr}</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>s = <math>\tfrac{mrp}{nr+m^2}</math></li>
             <li>Option b</li>
             <li>s = <math>\tfrac{nr+m^2}{nrp }</math></li>
             <li>Option c</li>
             <li>s = <math>\tfrac{nrp}{mr+m^2}</math></li>
             <li>Option d</li>
             <li>s = <math>\tfrac{nrp}{nr+m^2}</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 15
     <li>Factorize: (2x + 3y)² − (x − 4y)²
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>(3x − y)(x + 7y)</li>
             <li>Option b</li>
             <li>(3x + y)(2x − 7y)</li>
             <li>Option c</li>
             <li>(3x + y)(x − 7y)</li>
             <li>Option d</li>
             <li>(3x − y)(2x + 7y)</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 16
     <li>The curved surface area of a cylinder 5 cm high is 110 cm². Find the radius of its base.    [Take π = <math>\tfrac{22}{7}</math>]
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>2.6 cm</li>
             <li>Option b</li>
             <li>3.5 cm</li>
             <li>Option c</li>
             <li>3.6 cm</li>
             <li>Option d</li>
             <li>7.0 cm</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 17
     <li>The volume of a pyramid with height 15 cm is 90 cm³. If its base is a rectangle with dimensions x cm by 6 cm, find the value of x.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>3</li>
             <li>Option b</li>
             <li>5</li>
             <li>Option c</li>
             <li>6</li>
             <li>Option d</li>
             <li>8</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 18
     <li>[[File:WA2016 MATH P1Q018.jpg|center|thumb]]In the diagram, <math>\overrightarrow{YW}</math> is a tangent to the circle at X, /UV/ = /VX/ and <math>\ang</math>VXW = 50°. Find the value of <math>\ang</math>VXW
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>70°</li>
             <li>Option b</li>
             <li>80°</li>
             <li>Option c</li>
             <li>105°</li>
             <li>Option d</li>
             <li>110°</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 19
     <li>[[File:WA2016 MATH P1Q019.jpg|center|thumb]]In the diagram, <math>\overline{PF}</math>, <math>\overline{QT }</math>, <math>\overline{RG}</math> intersect at S and PQ / RG. If <math>\ang</math>SPQ = 113° and <math>\ang</math>RST = 22°, find <math>\ang</math>PSQ.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>22°</li>
             <li>Option b</li>
             <li>45°</li>
             <li>Option c</li>
             <li>67°</li>
             <li>Option d</li>
             <li>89°</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 20
     <li>[[File:WA2016 MATH P1Q020.jpg|center|thumb|188x188px]]In the diagram, O is the centre of circle, <math>\ang</math>XOZ = (10 m)° and <math>\ang</math>XWZ = m°. Calculate the value of m.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>30</li>
             <li>Option b</li>
             <li>36</li>
             <li>Option c</li>
             <li>40</li>
             <li>Option d</li>
             <li>72</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 21
     <li>Kweku walked 8 m up a slope and was 3 m above the ground. If he walks 12 m further up the slope, how far above the ground will be?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>4.5 m</li>
             <li>Option b</li>
             <li>6.0m</li>
             <li>Option c</li>
             <li>7.5 m</li>
             <li>Option d</li>
             <li>9.0 m</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 22
     <li>[[File:WA2016 MATH P1Q022.jpg|center|thumb|227x227px]]In the diagram, TS is a tangent to the circle at S, |PR| = |RS| and <math>\ang</math>PQR = 117°. Calculate <math>\ang</math>PST.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>54°</li>
             <li>Option b</li>
             <li>44°</li>
             <li>Option c</li>
             <li>34°</li>
             <li>Option d</li>
             <li>27°</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 23
     <li>[[File:WA2016 MATH P1Q023.jpg|center|thumb]]In the diagram, PR/SV/WY, TX/QY, <math>\ang</math>PQT = 48° and <math>\ang</math>TXW = 60°. Find <math>\ang</math>TQU
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>120°</li>
             <li>Option b</li>
             <li>108°</li>
             <li>Option c</li>
             <li>72°</li>
             <li>Option d</li>
             <li>60°
        </ol>
A straight line passes through the points P(1,2) and Q(5,8). ''Use this information to answers questions'' '''24''' and '''25.'''</li> </ol>
     </li>
     </li>
     <li>Question 24
     <li>Calculate the gradient of the line PQ
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>\tfrac{3}{5}</math></li>
             <li>Option b</li>
             <li><math>\tfrac{2}{3}</math></li>
             <li>Option c</li>
             <li><math>\tfrac{3}{2}</math></li>
             <li>Option d</li>
             <li><math>\tfrac{5}{3}</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 25
     <li>Calculate the length PQ
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>4\sqrt{11}</math></li>
             <li>Option b</li>
             <li><math>4\sqrt{10}</math></li>
             <li>Option c</li>
             <li><math>2\sqrt{17}</math></li>
             <li>Option d</li>
             <li><math>2\sqrt{13}</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 26
     <li>[[File:WA2016 MATH P1Q026.jpg|center|thumb]]In the diagram, TX is perpendicular to UW, |UX| = 1 cm and TX = |WX| = <math>\sqrt{3}</math> cm. Find<math>\ang</math>UTW.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>135°</li>
             <li>Option b</li>
             <li>105°</li>
             <li>Option c</li>
             <li>75°</li>
             <li>Option d</li>
             <li>60°</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 27
     <li>If cosθ = x and sin 60° = x + 0.5, 0° < θ < 90°, find correct to the nearest degree, the value of θ.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>66°</li>
             <li>Option b</li>
             <li>67°</li>
             <li>Option c</li>
             <li>68°</li>
             <li>Option d</li>
             <li>69°</li> </ol>
        </ol>
{| class="wikitable"
|+
|-
| Age (Years) || 13 || 14 || 15 || 16 || 17
|-
| Frequency || 10 || 24 || 8 || 5 || 3
|}
The table shows the ages of students in a club. ''Use it to answer questions '''28''' and '''29'''''
     </li>
     </li>
     <li>Question 28
     <li>How many students are in the club?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>50</li>
             <li>Option b</li>
             <li>55</li>
             <li>Option c</li>
             <li>60</li>
             <li>Option d</li>
             <li>65</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 29
     <li>Find the median age.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>13</li>
             <li>Option b</li>
             <li>14</li>
             <li>Option c</li>
             <li>15</li>
             <li>Option d</li>
             <li>16</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 30
     <li>[[File:WA2016 MATH P1Q030.jpg|center|thumb|197x197px]]The figure is a pie chart which represents the expenditure of a family in a year. If the total income of the family was Le 10,800,000.00, how much was spent on food?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>Le 2,250,000.00</li>
             <li>Option b</li>
             <li>Le 2,700,000.00</li>
             <li>Option c</li>
             <li>Le 3,600,000.00</li>
             <li>Option d</li>
             <li>Le 4,500,000.00</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 31
     <li>A fair die is thrown '''two''' times. What is the probability that the sum of the score is '''at least''' 10?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>\tfrac{5}{36}</math></li>
             <li>Option b</li>
             <li><math>\tfrac{1}{6}</math></li>
             <li>Option c</li>
             <li><math>\tfrac{5}{18}</math></li>
             <li>Option d</li>
             <li><math>\tfrac{2}{3}</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 32
     <li>The marks of eight students in a test are: 10, 4, 5, 3, 14, 16 and 7. Find the range.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>16</li>
             <li>Option b</li>
             <li>14</li>
             <li>Option c</li>
             <li>13</li>
             <li>Option d</li>
             <li>11</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 33
     <li>If log<sub>2</sub>(3x − 1) = 5, find x.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>2.00</li>
             <li>Option b</li>
             <li>3.67</li>
             <li>Option c</li>
             <li>8.67</li>
             <li>Option d</li>
             <li>11.00</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 34
     <li>A sphere of radius r cm has the same volume as a cylinder 3 cm and height 4 cm. Find the value of r.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>\tfrac{2}{3}</math></li>
             <li>Option b</li>
             <li>2</li>
             <li>Option c</li>
             <li>3</li>
             <li>Option d</li>
             <li>6</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 35
     <li>Express 1975 correct to 2 significant figures.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>20</li>
             <li>Option b</li>
             <li>1,900</li>
             <li>Option c</li>
             <li>1,980</li>
             <li>Option d</li>
             <li>2,000</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 36
     <li>[[File:WA2016 MATH P1Q036.jpg|center|thumb]]In the diagram, MOPQ is a trapezium with QP//MO, MQ//NP, NQ//OP, |QP| = 9 cm and the height of △QNP = 6 cm, calculate the area of the trapezium.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>96 cm²</li>
             <li>Option b</li>
             <li>90 cm²</li>
             <li>Option c</li>
             <li>81 cm²</li>
             <li>Option d</li>
             <li>27 cm²</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 37
     <li>The perimeter of a sector of a circle of radius 21 cm is 64 cm. Find the angle of the sector.  [Take π = <math>\tfrac{22}{7}</math>]
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>70°</li>
             <li>Option b</li>
             <li>60°</li>
             <li>Option c</li>
             <li>55°</li>
             <li>Option d</li>
             <li>42°</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 38
     <li>[[File:WA2016 MATH P1Q038.jpg|center|thumb]]Determine '''M''' <math>\cap</math> '''N''' from the Venn diagram.<ol type="a">
        <ol type="a">
             <li>{ ''f, g'' }</li><li>{ ''e'' }</li><li>{ ''c, f, g'' }</li><li>{ ''e, f, g'' }</li> </ol>
             <li>Option a</li>
            <li>Option b</li>
            <li>Option c</li>
            <li>Option d</li>
        </ol>
     </li>
     </li>
     <li>Question 39
     <li>If 20 (mod 9) is equivalent to y (mod 6), find y.
         <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 40
     <li>Simplify: <math>\tfrac{(p-r)^2-r^2}{2p^2- 4pr}</math>
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>\tfrac{1}{2}</math></li>
             <li>Option b</li>
             <li>p − 2r</li>
             <li>Option c</li>
             <li><math>\tfrac{1}{p-2r}</math></li>
             <li>Option d</li>
             <li><math>\tfrac{2p}{p-2r}</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 41
     <li>[[File:WA2016 MATH P1Q041.jpg|center|thumb|193x193px]]In the diagram, O is the centre of the circle, <math>\ang</math>QPS = 100°, <math>\ang</math>PSQ = 60° and <math>\ang</math>QSR = 80°. Calculate <math>\ang</math>SQR.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>20°</li>
             <li>Option b</li>
             <li>40°</li>
             <li>Option c</li>
             <li>60°</li>
             <li>Option d</li>
             <li>80°</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 42
     <li>A bag contains 5 red and 4 blue identical balls. If two balls are selected at random from the bag, one after the other, with replacement, find the probability that the first is red and the second blue.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>\tfrac{2}{9}</math></li>
             <li>Option b</li>
             <li><math>\tfrac{5}{18}</math></li>
             <li>Option c</li>
             <li><math>\tfrac{20}{81}</math></li>
             <li>Option d</li>
             <li><math>\tfrac{5}{9}</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 43
     <li>The relation y = x² + 2x + k passes through the point (2,0). Find the value of k.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>−8</li>
             <li>Option b</li>
             <li>−4</li>
             <li>Option c</li>
             <li>4</li>
             <li>Option d</li>
             <li>8</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 44
     <li>Find the next three terms of the sequence: 0 1, 1, 1, 2, 3, 5, 8....
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>13, 19, 23</li>
             <li>Option b</li>
             <li>9, 11, 13</li>
             <li>Option c</li>
             <li>11, 15, 19</li>
             <li>Option d</li>
             <li>13, 21, 34</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 45
     <li>[[File:WA2016 MATH P1Q045.jpg|center|thumb]]Find the lower quartile of the distribution illustrated by the cumulative frequency curve.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>17.5</li>
             <li>Option b</li>
             <li>19.0</li>
             <li>Option c</li>
             <li>27.5</li>
             <li>Option d</li>
             <li>28.0</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 46
     <li>The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>30</li>
             <li>Option b</li>
             <li>24</li>
             <li>Option c</li>
             <li>18</li>
             <li>Option d</li>
             <li>12</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 47
     <li>Halima is n years old. Her brother's age is 5 years more than half of her age. How old is her brother?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li><math>\tfrac{n}{2}+\tfrac{5}{2 }</math></li>
             <li>Option b</li>
             <li><math>\tfrac{n}{2}-5</math></li>
             <li>Option c</li>
             <li><math>5-\tfrac{n}{2}</math></li>
             <li>Option d</li>
             <li><math>\tfrac{n}{2}+5</math></li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 48
     <li>[[File:WA2016 MATH P1Q048.jpg|center|thumb|211x211px]]In the diagram, MN is a chord of a circle KMN centre O and radius 10 cm. If <math>\ang</math>MON = 140°, find correct to the nearest cm, the length of the chord MN.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>19 cm</li>
             <li>Option b</li>
             <li>18 cm</li>
             <li>Option c</li>
             <li>17 cm</li>
             <li>Option d</li>
             <li>12 cm</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 49
     <li>An object is 6 m away from the base of a mast. If the angle of depression of the object from the top of the mast is 50°, find; correct to 2 decimal places, the height of the mast.
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>8.60 m</li>
             <li>Option b</li>
             <li>7.83 m</li>
             <li>Option c</li>
             <li>7.51 m</li>
             <li>Option d</li>
             <li>7.15 m</li> </ol>
        </ol>
     </li>
     </li>
     <li>Question 50
     <li>[[File:WA2016 MATH P1Q050.jpg|center|thumb|238x238px]]From the diagram, which of the following is '''true'''?
         <ol type="a">
         <ol type="a">
             <li>Option a</li>
             <li>m + n + p = 180°</li>
             <li>Option b</li>
             <li>m + n = 180°</li>
             <li>Option c</li>
             <li>m − p + n</li>
             <li>Option d</li>
             <li>n = m + p</li> </ol>
        </ol>
     </li>
     </li>
</ol>
</ol>
Line 407: Line 363:
==== Section A ====
==== Section A ====
<ol>
<ol>
     <li>Question 1
     <li><ol type="a">
        <ol type="a">
             <li>Without using Mathematical tables or calculators, evaluate: <math>\tfrac{0.09\times1.21}{3.3\times 0.00025}</math>, leaving the answer in standard form (Scientific Notation) </li>
             <li>Sub-question a
             <li>A principal of GH¢5,600 was deposited for 3 years at compound interest. If the interest earned was GH¢1,200.00, find, correct to 3 significant figures, the interest rate per annum. </li> </ol>
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
             <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
        </ol>
     </li>
     </li>
     <li>Question 2
     <li><ol type="a">
        <ol type="a">
             <li>'''Solve:''' 7(x + 4) − <math>\tfrac{2}{3}</math>(x − 6) ≤ 2[x − 3(x + 5)] </li>
             <li>Sub-question a
             <li>A transport company has a total 20 vehicles made up of tricycles and taxicabs. Each tricycle carries 2 passengers while '''each''' taxicab carries 4 passengers. If the 20 vehicles carry a total of 66 passengers at a time, how many tricycles does the company have? </li> </ol>
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
        </ol>
     </li>
     </li>
     <li>Question 3
     <li><ol type="a">
        <ol type="a">
             <li>[[File:WA2016 MATH P2Q03OA.jpg|center|thumb]]In the diagram, <math>\ang</math>RTS = 28°, <math>\ang</math>VRM = 46°, MQ is a tangent to the circle VRSTU at the point R. Find <math>\ang</math>VUS. </li>
             <li>Sub-question a
             <li>A cylindrical tin, 7 cm high, is closed at one end. If its total surface area is 462 cm², calculate its radius.          [ Take π = <math>\tfrac{22}{7}</math>] </li> </ol>
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
        </ol>
     </li>
     </li>
     <li>Question 4
     <li>
        <ol type="a">
{| class="wikitable"
            <li>Sub-question a
|+
                <ol type="i">
|-
                    <li>Sub-question i</li>
| Scores || 1 || 2 || 3 || 4 || 5 || 6
                    <li>Sub-question ii</li>
|-
                    <li>Sub-question iii</li>
| Frequency || 25 || 30 || x || 28 || 40 || 32
                    <li>Sub-question iv</li>
|}
                    <li>Sub-question v</li>
The table shows the outcome when a die is thrown a number of times. If the probability of obtaining a 3 is 0.225:<ol type="a">
                </ol>
             <li>how many times was the die thrown? </li>
            </li>
             <li>calculate the probability that a trial chosen at random gives a score of an even number '''or''' a prime number. </li> </ol>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
        </ol>
     </li>
     </li>
     <li>Question 5
     <li><ol type="a">
        <ol type="a">
             <li>[[File:WA2016 MATH P2Q005OA.jpg|center|thumb]]In the diagram, PQST is a parallelogram, PR is a straight line, |TS| = 8 cm, |SM| = 6 cm and area of triangle PSR = 36 cm². Find the value of QR </li>
             <li>Sub-question a
             <li>A tree and a flagpole are on the same horizontal ground. A bird on top of the tree observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively. If the tree is 10.65 m high, calculate, correct to 3 significant figures, the height of the flagpole. </li> </ol>
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
        </ol>
     </li>
     </li>
</ol>
</ol>
Line 701: Line 395:
==== Section B ====
==== Section B ====
<ol start=6>
<ol start=6>
     <li>Question 6
     <li><ol type="a">
        <ol type="a">
             <li>Find the sum of the Arithmetic Progression (AP) 1, 3, 5, ... 101. </li>
             <li>Sub-question a
             <li>Out of the 95 travelers interviewed. 7 travelled by bus and train only, 3 by train and car only and 8 travelled by all three means of transport. The number, x, of travelers who travelled by bus only was equal to the number who travelled by bus and car only. If 47 people travelled by bus and 30 by train:
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
             <li>Sub-question e
                 <ol type="i">
                 <ol type="i">
                     <li>Sub-question i</li>
                     <li>represent this information in a Venn diagram;</li>
                     <li>Sub-question ii</li>
                     <li>calculate the
                    <li>Sub-question iii</li>
'''I.''' value of x;
                    <li>Sub-question iv</li>
'''II.''' number who travelled by '''at least''' two means.</li> </ol>
                    <li>Sub-question v</li>
             </li> </ol>
                </ol>
            </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
        </ol>
     </li>
     </li>
     <li>Question 7
     <li><ol type="a">
        <ol type="a">
             <li>Using completing the squares method, solve, correct to 2 decimal places, <math>\tfrac{x-2}{4}=\tfrac{x+2}{2x}</math> </li>
             <li>Sub-question a
            <li>[[File:WA2016 MATH P2Q007OB.jpg|center|thumb|209x209px]]In the diagram, PQRST is a circle with centre O. If PS is a diameter, RS/QT, |QR| = |RS| and <math>\ang</math>QTS = 52°, find:
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question b
                 <ol type="i">
                 <ol type="i">
                     <li>Sub-question i</li>
                     <li><math>\ang</math>SQT;</li>
                    <li>Sub-question ii</li>
                     <li><math>\ang</math>PQT.</li> </ol>
                    <li>Sub-question iii</li>
             </li> </ol>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                     <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
        </ol>
     </li>
     </li>
     <li>Question 8
     <li><ol type="a">
        <ol type="a">
             <li>[[File:WA2016 MATH P2Q008OA.jpg|center|thumb]]In the diagram, <math>\ang</math>KLM = x, <math>\ang</math>LMK = y, <math>\ang</math>KJH = r and <math>\ang</math>KGF = 110°. If 2x - r = y, find the value of x. </li>
             <li>Sub-question a
             <li>Ten boys and twelve girls collected donations for a project. The total amount collected by the boys was ₦600.00 greater than that collected by the girls. If the average collection of the boys was ₦100.00 greater than the average collection of the girls, how much was collected by the two groups? </li> </ol>
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
        </ol>
     </li>
     </li>
     <li>Question 9
     <li>The weight (in kg) of 50 contestants at a competition is as follows:
{| class="wikitable"
|+
|-
| 65 || 66 || 67 || 66 || 64 || 66 || 65 || 63 || 65 || 68
|-
| 64 || 62 || 66 || 64 || 67 || 65 || 64 || 66 || 65 || 67
|-
| 65 || 67 || 66 || 64 || 65 || 64 || 66 || 65 || 64 || 65
|-
| 66 || 65 || 64 || 65 || 63 || 63 || 67 || 65 || 63 || 64
|-
| 66 || 64 || 68 || 65 || 63 || 65 || 64 || 67 || 66 || 64
|}
         <ol type="a">
         <ol type="a">
             <li>Sub-question a
             <li>Construct a frequency table for the discrete data </li>
                <ol type="i">
             <li>Calculate, correct to 2 decimal places the:
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
             <li>Sub-question f
                 <ol type="i">
                 <ol type="i">
                     <li>Sub-question i</li>
                     <li>mean;</li>
                     <li>Sub-question ii</li>
                     <li>standard deviation of the data.</li> </ol>
                    <li>Sub-question iii</li>
             </li> </ol>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
        </ol>
     </li>
     </li>
     <li>Question 10
     <li>Using ruler and a pair of compasses only,
         <ol type="a">
         <ol type="a">
             <li>Sub-question a
             <li>construct:
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question f
                 <ol type="i">
                 <ol type="i">
                     <li>Sub-question i</li>
                     <li>△XYZ such that |XY| = 10 cm, <math>\ang</math>XYZ = 30° and <math>\ang</math>YXZ = 45°;</li>
                    <li>Sub-question ii</li>
                     <li>locus, l<sub>1</sub>, of points equidistant from Y and Z;</li>
                     <li>Sub-question iii</li>
                     <li>locus, l<sub>2</sub> of points parallel to  through Z.</li> </ol>
                     <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
             </li>
        </ol>
            <li>Locate point M, the point of intersection of l<sub>1</sub> and l<sub>2</sub> </li>
            <li>Measure <math>\ang</math>ZMY. </li> </ol>
     </li>
     </li>
     <li>Question 11
     <li><ol type="a">
        <ol type="a">
             <li>If <math>\tfrac{3p+4q}{3p-4q}</math> = 2, find p:q. </li>
             <li>Sub-question a
             <li>[[File:WA2016 MATH P2Q011OB.jpg|center|thumb]]The diagram shows the cross section of a bridge with a semi circular hollow in the middle, If the perimeter of the cross section is 34 m, calculate the:
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question d
                 <ol type="i">
                 <ol type="i">
                     <li>Sub-question i</li>
                     <li>length PQ;</li>
                     <li>Sub-question ii</li>
                     <li>area of the cross section      [ Take π = <math>\tfrac{22}{7}</math>]</li> </ol>
                    <li>Sub-question iii</li>
             </li> </ol>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
        </ol>
     </li>
     </li>
     <li>Question 12
     <li>
{| class="wikitable"
|+
|-
| x || 0° || 30° || 60° || 90° || 120° || 150° || 180° || 210° || 240° || 270° || 300° || 330° || 360°
|-
| y || 2.0 ||  ||  || 3.0 || 1.6 ||  || -2.0 ||  || -3.6 || -3.0 ||  ||  || 2.0
|}
         <ol type="a">
         <ol type="a">
             <li>Sub-question a
             <li>Copy and complete the table of values, correct to one decimal place, for the relation y = 3sin x + 2cos x for 0° ≤ x ≤ 360°. </li>
                <ol type="i">
             <li>Using scales of 2 cm to 30° on the x-axis and 2 cm to 1 unit on the x-axis, draw the graph of the relation x = 3sin x + 2cos x for 0° ≤ x ≤ 360°. </li>
                    <li>Sub-question i</li>
             <li>Use the graph to solve:
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
            <li>Sub-question b
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
             <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                 <ol type="i">
                 <ol type="i">
                     <li>Sub-question i</li>
                     <li>3sin x + 2cos x = 0;</li>
                    <li>Sub-question ii</li>
                     <li>2 + 2cos x + 3sin x = 0</li> </ol>
                    <li>Sub-question iii</li>
             </li> </ol>
                    <li>Sub-question iv</li>
                     <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
        </ol>
     </li>
     </li>
     <li>Question 13
     <li><ol type="a">
        <ol type="a">
             <li>Find the equation of a straight line which passes through the point (2, -3) and is parallel to the line 2x + y = 6. </li>
             <li>Sub-question a
             <li>The operation △ is defined on the set T = {2, 3, 5, 7} by x △ y = (x + y + xy) mod 8.
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
             <li>Sub-question b
                 <ol type="i">
                 <ol type="i">
                     <li>Sub-question i</li>
                     <li>Construct modulo 8. table for the operation △ on the set T.</li>
                     <li>Sub-question ii</li>
                     <li>Use the table to find:
                    <li>Sub-question iii</li>
'''I.''' 2 △(5 △ 7);
                    <li>Sub-question iv</li>
'''II.''' 2 △ n = 5 △ 7.</li> </ol>
                    <li>Sub-question v</li>
             </li> </ol>
                </ol>
            </li>
            <li>Sub-question c
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question d
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question e
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
            </li>
            <li>Sub-question f
                <ol type="i">
                    <li>Sub-question i</li>
                    <li>Sub-question ii</li>
                    <li>Sub-question iii</li>
                    <li>Sub-question iv</li>
                    <li>Sub-question v</li>
                </ol>
             </li>
        </ol>
     </li>
     </li>
</ol>
</ol>
[[Category:WAEC General Mathematics]]
[[Category:WAEC General Mathematics]]

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Objective Test Questions

  1. If 23x + 101x = 130x. Find the value of x.
    1. 7
    2. 6
    3. 5
    4. 4
  2. Simplify: 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}-\tfrac{2}{3}) \times 1\tfrac{1}{5} }
    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 \tfrac{1}{60}}
    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{5}{72}}
    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}{10}}
    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\tfrac{7}{10}}
  3. Simplify: 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{10\sqrt{3}}{\sqrt{5}}-\sqrt{15})^2 }
    1. 75.00
    2. 15.00
    3. 8.66
    4. 3.87
  4. The distance, d, through which a stone falls from rest varies directly as the square of the time, t, taken. If the stone falls 45 cm in 3 seconds, how far will it fall in 6 seconds?
    1. 90 cm
    2. 135 cm
    3. 180 cm
    4. 225 cm
  5. Which of the following is a valid conclusion from the premise: 'Nigerian footballers are good footballers'?
    1. Joseph plays football in Nigeria therefore he is a good footballer.
    2. Joseph is a good footballer therefore he is a Nigerian footballer.
    3. Joseph is a Nigerian footballer therefore he is a good footballer.
    4. Joseph plays good football therefore he is a Nigerian footballer.
  6. On a map, 1 cm represents 5 km. Find the area on the map that represents 100 km².
    1. 2 cm²
    2. 4 cm²
    3. 8 cm²
    4. 16 cm²
  7. Simplify: 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^{n-1}\times27^{n+1}}{81^n} }
    1. 32n
    2. 9
    3. 3n
    4. 3n+1
  8. What sum of money will amount to D10,400.00 in 5 years at 6% simple interest?
    1. D8,000.00
    2. D10,000.00
    3. D12,000.00
    4. D16,000.00
  9. Which of the following number lines illustrates the solution of the inequality 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 \tfrac{1}{3}(2x-1) } < 5?
  10. The roots of a quadratic equation 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{4}{3} } 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 \tfrac{-3}{7} }
    1. 21x² - 19x - 12 = 0
    2. 21x² + 37x - 12 = 0
    3. 21x² - x + 12 = 0
    4. 21x² + 7x - 4 = 0
  11. Find the values of y for which the expression 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{y^2-9y+18}{y^2+4y-2 1}} is undefined
    1. 6, -7
    2. 3, -6
    3. 3, -7
    4. -3, -7
  12. Given that 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?
    1. 1
    2. 3
    3. 7
    4. 17
  13. Simplify: 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{2}{1-x}-\tfrac{1}{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 \tfrac{x+1}{x(1-x)}}
    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{3x-1}{x(1-x) }}
    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{3x+1}{x(1-x)}}
  14. Make s the subject of the relation: p = s + 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{sm^2}{nr}}
    1. s = 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{mrp}{nr+m^2}}
    2. s = 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{nr+m^2}{nrp }}
    3. s = 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{nrp}{mr+m^2}}
    4. s = 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{nrp}{nr+m^2}}
  15. Factorize: (2x + 3y)² − (x − 4y)²
    1. (3x − y)(x + 7y)
    2. (3x + y)(2x − 7y)
    3. (3x + y)(x − 7y)
    4. (3x − y)(2x + 7y)
  16. The curved surface area of a cylinder 5 cm high is 110 cm². Find the radius of its base. [Take π = 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{22}{7}} ]
    1. 2.6 cm
    2. 3.5 cm
    3. 3.6 cm
    4. 7.0 cm
  17. The volume of a pyramid with height 15 cm is 90 cm³. If its base is a rectangle with dimensions x cm by 6 cm, find the value of x.
    1. 3
    2. 5
    3. 6
    4. 8
  18. In the diagram, 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 \overrightarrow{YW}} is a tangent to the circle at X, /UV/ = /VX/ 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 \ang} VXW = 50°. 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 \ang} VXW
    1. 70°
    2. 80°
    3. 105°
    4. 110°
  19. In the diagram, 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 \overline{PF}} , 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 \overline{QT }} , 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 \overline{RG}} intersect at S and PQ / RG. 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 \ang} SPQ = 113° 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 \ang} RST = 22°, find 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 \ang} PSQ.
    1. 22°
    2. 45°
    3. 67°
    4. 89°
  20. In the diagram, O is the centre of circle, 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 \ang} XOZ = (10 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 \ang} XWZ = m°. Calculate the value of m.
    1. 30
    2. 36
    3. 40
    4. 72
  21. Kweku walked 8 m up a slope and was 3 m above the ground. If he walks 12 m further up the slope, how far above the ground will be?
    1. 4.5 m
    2. 6.0m
    3. 7.5 m
    4. 9.0 m
  22. In the diagram, TS is a tangent to the circle at S, |PR| = |RS| 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 \ang} PQR = 117°. Calculate 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 \ang} PST.
    1. 54°
    2. 44°
    3. 34°
    4. 27°
  23. In the diagram, PR/SV/WY, TX/QY, 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 \ang} PQT = 48° 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 \ang} TXW = 60°. Find 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 \ang} TQU
    1. 120°
    2. 108°
    3. 72°
    4. 60° A straight line passes through the points P(1,2) and Q(5,8). Use this information to answers questions 24 and 25.
  24. Calculate the gradient of the line PQ
    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 \tfrac{3}{5}}
    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{2}{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 \tfrac{3}{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 \tfrac{5}{3}}
  25. Calculate the length PQ
    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 4\sqrt{11}}
    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 4\sqrt{10}}
    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 2\sqrt{17}}
    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 2\sqrt{13}}
  26. In the diagram, TX is perpendicular to UW, |UX| = 1 cm and TX = |WX| = 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 \sqrt{3}} cm. FindFailed 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 \ang} UTW.
    1. 135°
    2. 105°
    3. 75°
    4. 60°
  27. If cosθ = x and sin 60° = x + 0.5, 0° < θ < 90°, find correct to the nearest degree, the value of θ.
    1. 66°
    2. 67°
    3. 68°
    4. 69°
    Age (Years) 13 14 15 16 17
    Frequency 10 24 8 5 3

    The table shows the ages of students in a club. Use it to answer questions 28 and 29

  28. How many students are in the club?
    1. 50
    2. 55
    3. 60
    4. 65
  29. Find the median age.
    1. 13
    2. 14
    3. 15
    4. 16
  30. The figure is a pie chart which represents the expenditure of a family in a year. If the total income of the family was Le 10,800,000.00, how much was spent on food?
    1. Le 2,250,000.00
    2. Le 2,700,000.00
    3. Le 3,600,000.00
    4. Le 4,500,000.00
  31. A fair die is thrown two times. What is the probability that the sum of the score is at least 10?
    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 \tfrac{5}{36}}
    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}{6}}
  32. The marks of eight students in a test are: 10, 4, 5, 3, 14, 16 and 7. Find the range.
    1. 16
    2. 14
    3. 13
    4. 11
  33. If log2(3x − 1) = 5, find x.
    1. 2.00
    2. 3.67
    3. 8.67
    4. 11.00
  34. A sphere of radius r cm has the same volume as a cylinder 3 cm and height 4 cm. Find the value of r.
    1. 2
    2. 3
    3. 6
  35. Express 1975 correct to 2 significant figures.
    1. 20
    2. 1,900
    3. 1,980
    4. 2,000
  36. In the diagram, MOPQ is a trapezium with QP//MO, MQ//NP, NQ//OP, |QP| = 9 cm and the height of △QNP = 6 cm, calculate the area of the trapezium.
    1. 96 cm²
    2. 90 cm²
    3. 81 cm²
    4. 27 cm²
  37. The perimeter of a sector of a circle of radius 21 cm is 64 cm. Find the angle of the sector. [Take π = ]
    1. 70°
    2. 60°
    3. 55°
    4. 42°
  38. Determine M N from the Venn diagram.
    1. { f, g }
    2. { e }
    3. { c, f, g }
    4. { e, f, g }
  39. If 20 (mod 9) is equivalent to y (mod 6), find y.
    1. 1
    2. 2
    3. 3
    4. 4
  40. Simplify:
    1. p − 2r
  41. In the diagram, O is the centre of the circle, QPS = 100°, PSQ = 60° and QSR = 80°. Calculate SQR.
    1. 20°
    2. 40°
    3. 60°
    4. 80°
  42. A bag contains 5 red and 4 blue identical balls. If two balls are selected at random from the bag, one after the other, with replacement, find the probability that the first is red and the second blue.
  43. The relation y = x² + 2x + k passes through the point (2,0). Find the value of k.
    1. −8
    2. −4
    3. 4
    4. 8
  44. Find the next three terms of the sequence: 0 1, 1, 1, 2, 3, 5, 8....
    1. 13, 19, 23
    2. 9, 11, 13
    3. 11, 15, 19
    4. 13, 21, 34
  45. Find the lower quartile of the distribution illustrated by the cumulative frequency curve.
    1. 17.5
    2. 19.0
    3. 27.5
    4. 28.0
  46. The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?
    1. 30
    2. 24
    3. 18
    4. 12
  47. Halima is n years old. Her brother's age is 5 years more than half of her age. How old is her brother?
  48. In the diagram, MN is a chord of a circle KMN centre O and radius 10 cm. If MON = 140°, find correct to the nearest cm, the length of the chord MN.
    1. 19 cm
    2. 18 cm
    3. 17 cm
    4. 12 cm
  49. An object is 6 m away from the base of a mast. If the angle of depression of the object from the top of the mast is 50°, find; correct to 2 decimal places, the height of the mast.
    1. 8.60 m
    2. 7.83 m
    3. 7.51 m
    4. 7.15 m
  50. From the diagram, which of the following is true?
    1. m + n + p = 180°
    2. m + n = 180°
    3. m − p + n
    4. n = m + p

Theory

Section A

    1. Without using Mathematical tables or calculators, evaluate: , leaving the answer in standard form (Scientific Notation)
    2. A principal of GH¢5,600 was deposited for 3 years at compound interest. If the interest earned was GH¢1,200.00, find, correct to 3 significant figures, the interest rate per annum.
    1. Solve: 7(x + 4) − (x − 6) ≤ 2[x − 3(x + 5)]
    2. A transport company has a total 20 vehicles made up of tricycles and taxicabs. Each tricycle carries 2 passengers while each taxicab carries 4 passengers. If the 20 vehicles carry a total of 66 passengers at a time, how many tricycles does the company have?
    1. In the diagram, RTS = 28°, VRM = 46°, MQ is a tangent to the circle VRSTU at the point R. Find VUS.
    2. A cylindrical tin, 7 cm high, is closed at one end. If its total surface area is 462 cm², calculate its radius. [ Take π = ]
  1. Scores 1 2 3 4 5 6
    Frequency 25 30 x 28 40 32
    The table shows the outcome when a die is thrown a number of times. If the probability of obtaining a 3 is 0.225:
    1. how many times was the die thrown?
    2. calculate the probability that a trial chosen at random gives a score of an even number or a prime number.
    1. In the diagram, PQST is a parallelogram, PR is a straight line, |TS| = 8 cm, |SM| = 6 cm and area of triangle PSR = 36 cm². Find the value of QR
    2. A tree and a flagpole are on the same horizontal ground. A bird on top of the tree observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively. If the tree is 10.65 m high, calculate, correct to 3 significant figures, the height of the flagpole.

Section B

    1. Find the sum of the Arithmetic Progression (AP) 1, 3, 5, ... 101.
    2. Out of the 95 travelers interviewed. 7 travelled by bus and train only, 3 by train and car only and 8 travelled by all three means of transport. The number, x, of travelers who travelled by bus only was equal to the number who travelled by bus and car only. If 47 people travelled by bus and 30 by train:
      1. represent this information in a Venn diagram;
      2. calculate the I. value of x; II. number who travelled by at least two means.
    1. Using completing the squares method, solve, correct to 2 decimal places,
    2. In the diagram, PQRST is a circle with centre O. If PS is a diameter, RS/QT, |QR| = |RS| and QTS = 52°, find:
      1. SQT;
      2. PQT.
    1. In the diagram, KLM = x, LMK = y, KJH = r and KGF = 110°. If 2x - r = y, find the value of x.
    2. Ten boys and twelve girls collected donations for a project. The total amount collected by the boys was ₦600.00 greater than that collected by the girls. If the average collection of the boys was ₦100.00 greater than the average collection of the girls, how much was collected by the two groups?
  1. The weight (in kg) of 50 contestants at a competition is as follows:
    65 66 67 66 64 66 65 63 65 68
    64 62 66 64 67 65 64 66 65 67
    65 67 66 64 65 64 66 65 64 65
    66 65 64 65 63 63 67 65 63 64
    66 64 68 65 63 65 64 67 66 64
    1. Construct a frequency table for the discrete data
    2. Calculate, correct to 2 decimal places the:
      1. mean;
      2. standard deviation of the data.
  2. Using ruler and a pair of compasses only,
    1. construct:
      1. △XYZ such that |XY| = 10 cm, XYZ = 30° and YXZ = 45°;
      2. locus, l1, of points equidistant from Y and Z;
      3. locus, l2 of points parallel to through Z.
    2. Locate point M, the point of intersection of l1 and l2
    3. Measure ZMY.
    1. If = 2, find p:q.
    2. The diagram shows the cross section of a bridge with a semi circular hollow in the middle, If the perimeter of the cross section is 34 m, calculate the:
      1. length PQ;
      2. area of the cross section [ Take π = ]
  3. x 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330° 360°
    y 2.0 3.0 1.6 -2.0 -3.6 -3.0 2.0
    1. Copy and complete the table of values, correct to one decimal place, for the relation y = 3sin x + 2cos x for 0° ≤ x ≤ 360°.
    2. Using scales of 2 cm to 30° on the x-axis and 2 cm to 1 unit on the x-axis, draw the graph of the relation x = 3sin x + 2cos x for 0° ≤ x ≤ 360°.
    3. Use the graph to solve:
      1. 3sin x + 2cos x = 0;
      2. 2 + 2cos x + 3sin x = 0
    1. Find the equation of a straight line which passes through the point (2, -3) and is parallel to the line 2x + y = 6.
    2. The operation △ is defined on the set T = {2, 3, 5, 7} by x △ y = (x + y + xy) mod 8.
      1. Construct modulo 8. table for the operation △ on the set T.
      2. Use the table to find: I. 2 △(5 △ 7); II. 2 △ n = 5 △ 7.