2014 General Mathematics WAEC SSCE (School Candidates) May/June

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Objective Test Questions

1. Simplify: $10{\tfrac {2}{5}}-6{\tfrac {2}{3}}+3$
   1. $6{\tfrac {4}{15}}$
   2. $6{\tfrac {11}{15}}$
   3. $7{\tfrac {4}{15}}$
   4. $7{\tfrac {11}{15}}$
2. If 23_x = 32₅, find the value of x.
   1. 7
   2. 6
   3. 5
   4. 4
3. The volume of a cube is 512 cm³. Find the length of its side.
   1. 6 cm
   2. 7 cm
   3. 8 cm
   4. 9 cm The bar chart below shows the scores of some students in a test. Use it answer questions 4 and 5 *Insert Image here*
4. How many students took the test?
   1. 18
   2. 19
   3. 20
   4. 22
5. If one student is selected at random, find the probability that he/she scored at most 2 marks.
   1. ${\tfrac {11}{18}}$
   2. ${\tfrac {11}{20}}$
   3. ${\tfrac {7}{22}}$
   4. ${\tfrac {5}{19}}$
6. Simplify: ${\sqrt {12}}({\sqrt {48}}-{\sqrt {3}})$
   1. 18
   2. 16
   3. 14
   4. 12
7. Which of the following number lines represents the solution to the inequality: -9 ≤${\tfrac {2}{3}}x$ < 5
   1. Option a
   2. Option b
   3. Option c
   4. Option d
8. *Insert Image here*In the diagram, the value of x + y = 220°. Find the value of n.
   1. 20°
   2. 40°
   3. 60°
   4. 80°
9. Given that x > y and 3 < y, which of the following is/are true? I. y > 3 II. x < 3 III. x > y > 3
   1. I only
   2. I and II only
   3. I and III only
   4. I, II and III
10. Three quarters of a number added to two and a half of that number gives 13. Find the missing number.
    1. 4
    2. 5
    3. 6
    4. 7
11. If X = {0, 2, 4, 6}, Y = {1, 2, 3, 4} and Z = {1, 3} are subsets of U = {x: 0 ≤ x ≤ 6}, find x $\cap$ (Y $\cup$ Z).
    1. {0, 2, 6}
    2. {1, 3}
    3. {0, 6}
    4. { }
12. Find the truth set of the equation x² = 3(2x + 9)
    1. {x : x = 3, x = 9}
    2. {x : x = -3, x = -9}
    3. {x : x = 3, x = -9}
    4. {x : x = -3, x = 9}
13. The coordinates of points P and Q are (4, 3) and (2, -1) respectively. Find the shortest distance between P and Q
    1. $10{\sqrt {2}}$
    2. $4{\sqrt {5}}$
    3. $5{\sqrt {2}}$
    4. $2{\sqrt {5}}$
14. Make u the subject of the formula, $E={\tfrac {m}{2g}}(v^{2}-u^{2})$
    1. $u={\sqrt {v^{2}-{\tfrac {2Eg}{m}}}}$
    2. $u={\sqrt {{\tfrac {v^{2}}{m}}-{\tfrac {2Eg}{4}}}}$
    3. $u={\sqrt {v-{\tfrac {2Eg}{m}}}}$
    4. $u={\sqrt {\tfrac {2v^{2}Eg}{m}}}$
15. *Insert Image here*In the diagram, $\angle$QPT = $\angle$PTS = 90°, $\angle$PQR = 110° and $\angle$TSR = 20°. Find the size of the obtuse angle QRS.
    1. 140°
    2. 130°
    3. 120°
    4. 110°
16. If x varies inversely as y and y varies directly as z, what is the relationship between x and z?
    1. x $\varpropto$ z
    2. $x\varpropto {\tfrac {1}{z}}$
    3. $x\varpropto z^{2}$
    4. $x\varpropto z^{\tfrac {1}{2}}$
17. Find the gradient of the line joining the points (2, -3) and (2, 5)
    1. 0
    2. 1
    3. 2
    4. undefined
18. If (x - a) is a factor of bx - ax + x² - ab, find the other factor.
    1. (x + b)
    2. (x - b)
    3. (a + b)
    4. (a - b)
19. The table shows the distribution of the height of plants in a nursery. Calculate the mean heights of the plants.

    Height	2	3	4	5	6
    Frequency	2	4	5	3	1

    1. 3.8
    2. 3.0
    3. 2.8
    4. 2.3
20. *Insert Image here*In the diagram, PQR is a straight line, (m + n) = 120° and (n + r) = 100°. Find (m + r)
    1. 110°
    2. 120°
    3. 140°
    4. 160° *Insert Image here* In the diagram, ${\overrightarrow {SR}}$ is parallel to ${\overrightarrow {UW}}$, $\angle$WVT = x°, $\angle$VUT = y°, $\angle$RSV = 45° and $\angle$VTU = 20°. Use this diagram to answer questions 21 and 22.
21. Find the value of x
    1. 20
    2. 45
    3. 65
    4. 135
22. Calculate the value of y
    1. 20
    2. 25
    3. 45
    4. 65
23. The area of a sector of a circle with a diameter 12 cm is 66 cm². If the sector is folded to form a cone, calculate the radius of the base of the cone. [Take π = ${\tfrac {22}{7}}$]
    1. 3.0 cm
    2. 3.5 cm
    3. 7.0 cm
    4. 7.5 cm
24. A chord, 7 cm long, is drawn in a circle with radius 3.7 cm. Calculate the distance of the chord from the centre of the circle.
    1. 0.7 cm
    2. 1.2 cm
    3. 2.0 cm
    4. 2.5 cm
25. Which of the following is a measure of dispersion?
    1. Range
    2. Percentile
    3. Median
    4. Quartile
26. A box contains 13 currency notes, all of which are either ₦50 or ₦20 notes. The total value of the currency notes is ₦530. How many ₦50 notes are in the box?
    1. 4
    2. 6
    3. 8
    4. 9 *Insert Image here* The graph below is for the relation y = 2x² + x - 1. Use it to answer questions 27 and 28.
27. What are the coordinates of the point S?
    1. (1, 0, 2)
    2. (1, 0, 4)
    3. (1, 2, 0)
    4. (1, 4, 0)
28. Find the minimum value of y.
    1. 0.00
    2. -0.65
    3. -1.25
    4. -2.10
29. A ship sails x km due east to a point E and continues x km due north to F. Find the bearing of F from the starting point.
    1. 045°
    2. 090°
    3. 135°
    4. 225°
30. If x : y = 3 : 2 and y : z = 5 : 4, find the value of x in the ratio x : y : z
    1. 8
    2. 10
    3. 15
    4. 20
31. A trader bought sachet water for GH¢ 55.00 per dozen and sold them at 10 for GH¢ 50.00. Calculate, correct to 2 decimal places, his percentage gain.
    1. 8.00%
    2. 8.30%
    3. 9.09%
    4. 10.00%
32. *Insert Image here*In the figure, PQ is a tangent to the circle at R and UT is parallel to PQ. If $\angle$TRQ = x°, find $\angle$URT in terms of x.
    1. 2x°
    2. (90 - x)°
    3. (90 + x)°
    4. (180 - 2x)°
33. Given that cos x = ${\tfrac {12}{13}}$, evaluate ${\tfrac {1-\tan x}{\tan x}}$
    1. ${\tfrac {5}{13}}$
    2. ${\tfrac {5}{7}}$
    3. ${\tfrac {7}{5}}$
    4. ${\tfrac {13}{5}}$
34. Approximate 0.0033780 to 3 significant figures.
    1. 338
    2. 0.338
    3. 0.00338
    4. 0.003
35. Simplify: ${\sqrt {\tfrac {8^{2}\times 4^{n}+1}{2^{2n}\times 16}}}$
    1. 16
    2. 8
    3. 4
    4. 1
36. If ${\tfrac {2}{x-3}}-{\tfrac {3}{x-2}}$ is equal to ${\tfrac {P}{(x-3)(x-2)}}$, find P.
    1. −x − 5
    2. −(x + 3)
    3. 5x − 13
    4. 5 − x
37. Subtract ${\tfrac {1}{2}}(a-b-c)$ from the sum of ${\tfrac {1}{2}}(a-b+c)$ and ${\tfrac {1}{2}}(a+b-c)$
    1. ${\tfrac {1}{2}}(a+b+c)$
    2. ${\tfrac {1}{2}}(a-b-c)$
    3. ${\tfrac {1}{2}}(a-b+c)$
    4. ${\tfrac {1}{2}}(a+b-c)$
38. A man's eye level is 1.7 m above the horizontal ground and 13 m from a vertical pole. If the pole is 8.3 m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes.
    1. 33°
    2. 32°
    3. 27°
    4. 26°
39. A chord subtends an angle of 120° at the centre of a circle of radius 3.5 cm. Find the perimeter of the minor sector containing the chord. [Take π = ${\tfrac {22}{7}}$]
    1. $14{\tfrac {1}{3}}$cm
    2. $12{\tfrac {5}{6}}$cm
    3. $8{\tfrac {1}{7}}$cm
    4. $7{\tfrac {1}{3}}$cm
40. In parallelogram, PQRS, ${\overrightarrow {QR}}$is produced to M such that |QR| = |RM|. What fraction of the area of PQMS is the area of PRMS?
    1. Option a
    2. Option b
    3. Option c
    4. Option d
41. Question 41
    1. Option a
    2. Option b
    3. Option c
    4. Option d
42. Question 42
    1. Option a
    2. Option b
    3. Option c
    4. Option d
43. Question 43
    1. Option a
    2. Option b
    3. Option c
    4. Option d
44. Question 44
    1. Option a
    2. Option b
    3. Option c
    4. Option d
45. Question 45
    1. Option a
    2. Option b
    3. Option c
    4. Option d
46. Question 46
    1. Option a
    2. Option b
    3. Option c
    4. Option d
47. Question 47
    1. Option a
    2. Option b
    3. Option c
    4. Option d
48. Question 48
    1. Option a
    2. Option b
    3. Option c
    4. Option d
49. Question 49
    1. Option a
    2. Option b
    3. Option c
    4. Option d
50. 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

6. 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
7. 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
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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