2011 General Mathematics WAEC SSCE (School Candidates) May/June

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Objective Test Questions

1. If ₦112.00 exchanges for D14.94. Calculate the value of D1.00 in naira
   1. 0.13
   2. 7.49
   3. 8.00
   4. 13.00
2. Solve for x in the equation ${\tfrac {3}{5}}{\bigl (}2x-1)$ = ${\tfrac {1}{4}}{\bigl (}5x-3{\bigr )}$
   1. 0
   2. 1
   3. 2
   4. 3
3. Given that cos x° = ${\tfrac {1}{r}}$_’ express tan x° in terms of r.

   

   1. ${\tfrac {1}{\sqrt {r}}}$
   2. ${\sqrt {r}}$
   3. ${\sqrt {r^{2}+1}}$
   4. ${\sqrt {r^{2}-1}}$
4. The diagram shows a cyclic quadrilateral PQRS with its diagonals intersecting at K. Which of the following triangles is similar to triangle QKR?

   

   1. △ PQK
   2. △PKS
   3. △SKR
   4. △PSR
5. In the diagram, OP and OR are radii, |PQ| =|QR| and reflex $\angle$POR is 240°. Calculate the value of x.

   

   1. 60°
   2. 55°
   3. 50°
   4. 45°
6. If a number is chosen at random from the set (x: 4≤x≤15), find the probability that it is a multiple of 3 or a multiple of 4.
   1. ${\tfrac {1}{12}}$
   2. ${\tfrac {5}{12}}$
   3. ${\tfrac {1}{2}}$
   4. ${\tfrac {11}{12}}$
7. Solve the equations: ${\begin{cases}3x-2y=7\\x+2y=-3\end{cases}}$
   1. x = 1, y = -2
   2. x = 1, y = 3
   3. x = 2, y = -1
   4. x = 4, y = -3
8. One of the factors of (mn − nq − n² + mq) is (m − n). The other factor is:
   1. (n − q)
   2. (q − n)
   3. (n + q)
   4. (q − m)
9. A cylindrical container has a base radius of 14cm and height 18cm. How many litres, correct to the nearest litre, of liquid can it hold? [Take π = ${\tfrac {22}{7}}$ ]

   

   1. 11
   2. 14
   3. 16
   4. 18
10. Find the size of the angle marked x in the diagram.

    

    1. 108°
    2. 112°
    3. 128°
    4. 142°
11. A regular polygon of a n sides has each exterior angle equal to 45°. Find the value of n.
    1. 6
    2. 8
    3. 12
    4. 15
12. Esther was facing S 20° W. She turned 90° in the clockwise direction. What direction is she facing?

    

    1. N 70° W
    2. S 70° W
    3. N 20° W
    4. S 20° E

       

       The histogram shows the age distribution of members of a club. Use the information to answer questions 13 and 14.
13. How many members are in the club?
    1. 52
    2. 50
    3. 48
    4. 40
14. What is their modal age?
    1. 44.5
    2. 42.5
    3. 41.5
    4. 40.5
15. The cross section of a uniform prism is a right-angled triangle with sides 3, 4 and 5 cm. If its length is 10 cm, calculate the total surface area.
    1. 142 cm²
    2. 132 cm²
    3. 122 cm²
    4. 112 cm²
16. Form the equation whose roots are x = ${\tfrac {1}{2}}$ and −${\tfrac {2}{3}}$.
    1. 6x² − x + 2 = 0
    2. 6x² − x − 2 = 0
    3. 6x² + x + 2 = 0
    4. 6x² + x − 2 = 0
17. Simplify: ${\tfrac {\log {\sqrt {27}}}{\log {\sqrt {81}}}}$.
    1. 3
    2. 2
    3. ${\tfrac {3}{2}}$
    4. ${\tfrac {3}{4}}$
18. Which of these angles can be constructed using ruler and a pair of compasses only?
    1. 115°
    2. 125°
    3. 135°
    4. 145°
19. The perimeter of a sector of a circle of radius 4 cm is ( π + 8) cm. Calculate the angle of the sector.
    1. 45°
    2. 60°
    3. 75°
    4. 90°
20. The length of a piece of stick is 1.75 m. A girl measured it as 1.80 m. Find the percentage error.
    1. ${\tfrac {284}{7}}$%
    2. ${\tfrac {29}{7}}$%
    3. 5%
    4. ${\tfrac {20}{7}}$%
21. What is the value of 3 in the number 42.7531?
    1. ${\tfrac {3}{10000}}$
    2. ${\tfrac {3}{1000}}$
    3. ${\tfrac {3}{100}}$
    4. ${\tfrac {3}{10}}$
22. The height of a cylinder is equal to its radius. If the volume is 0.216πm³, calculate the radius.
    1. 0.46m
    2. 0.60m
    3. 0.87m
    4. 1.80m
23. In the diagram MN//OP, $\angle$NMQ = 65° and $\angle$QOP = 125°. What is the size of $\angle$MQR?

    

    1. 110°
    2. 120°
    3. 130°
    4. 160°
24. A circle is divide into two sectors in the ratio 3:7. If the radius of the circle is 7 cm, calculate the length of the minor arc of the circle.
    1. 18.85 cm
    2. 13.20 cm
    3. 12.30 cm
    4. 11.30 cm

       

       Use the cumulative frequency curve to answer questions 25 and 26.
25. Estimate the median of the data represented on the graph.
    1. 35.5
    2. 36.5
    3. 37.5
    4. 38.5
26. What is the 80th percentile?
    1. 45.5
    2. 46.5
    3. 47.5
    4. 48.5
27. From the diagram which of the following statements are true? I. m = q II. n = q III. n + p = 180° IV. p + m =180°

    

    1. I and III
    2. I and IV
    3. II and III
    4. II and IV
28. Factorize the expression am + bn − an − bm.
    1. (a − b)(m + n)
    2. (a − b)(m − n)
    3. (a + b)(m − n)
    4. (a + b)(m + n)

       

       The graph represents the relation y = x² − 3x − 3. Use it to answer questions 29 and 30.
29. Find the values of x for which x² − 3x = 7
    1. −1.55, 4.55
    2. 1.55, −4.55
    3. −1.55, −4.55
    4. 1.55, 4.55
30. What is the equation of the line of symmetry of the graph?
    1. x = 0.5
    2. x = 1.0
    3. x = 1.5
    4. x = 4.5
31. Simplify ${\tfrac {m}{n}}+{\tfrac {{\bigl (}m-1{\bigr )}}{5n}}-{\tfrac {{\bigl (}m-2{\bigr )}}{10n}}$ where n ≠ 0
    1. ${\tfrac {m-3}{10n}}$
    2. ${\tfrac {11m}{10n}}$
    3. ${\tfrac {m+1}{10n}}$
    4. ${\tfrac {11m+4}{10n}}$
32. If ${\sqrt {72}}+{\sqrt {32}}-3{\sqrt {18}}=x{\sqrt {8}}$ , find the value of x.
    1. 1
    2. ${\tfrac {3}{4}}$
    3. ${\tfrac {1}{2}}$
    4. ${\tfrac {1}{4}}$
33. G varies directly as the square of H. If G is 4 when H is 3, find H when G = 100.
    1. 15
    2. 25
    3. 75
    4. 225
34. Given that n(P) = 19, n(P$\cup$Q) =38 and n(P$\cap$Q) = 7, find n(Q).
    1. 26
    2. 31
    3. 36
    4. 50
35. What must be added to (2x − 3y) to get (x − 2y)?
    1. 5y − x
    2. y − x
    3. x − 5x
    4. x − y
36. Simplify $1{\tfrac {3}{4}}-{\bigl (}2{\tfrac {1}{3}}+4{\bigr )}$
    1. $3{\tfrac {5}{12}}$
    2. $2{\tfrac {7}{12}}$
    3. $-4{\tfrac {7}{12}}$
    4. $-5{\tfrac {5}{12}}$
37. In the diagram, STUV is a straight line. $\angle$TSY = $\angle$UXY = 40° and $\angle$VUW = 110°. Calculate $\angle$TYW.

    

    1. 150°
    2. 140°
    3. 130°
    4. 120°
38. Given that 124_x = 7(14_x), find the value of x.
    1. 12
    2. 11
    3. 9
    4. 8
39. Find the smaller value of x that satisfies the equation: x² + 7x + 10 = 0
    1. −5
    2. −2
    3. 2
    4. 5
40. The perpendicular bisectors of the sides of an acute-angled triangle are drawn. Which of these statements is correct? They intersect:
    1. on one of the vertices
    2. at a midpoint of a side
    3. inside the triangle
    4. outside the triangle
41. A rectangular garden measures 18.6 m by 12.5 m. Calculate correct to three significant figures, the area of the garden.
    1. 230 m²
    2. 321 m²
    3. 232 m²
    4. 233 m²
42. John pours 96 litres of red oil into a rectangular container with length 220 cm and breadth 40 cm. Calculate, correct to the nearest cm, the height of the oil in the container.
    1. 11 cm
    2. 18 cm
    3. 21 cm
    4. 34 cm
43. In a quiz competition, a student answers n questions correctly and was given D(n + 50) for each questions correctly answered. If he gets D600.00 altogether, how many questions did he answer correctly?
    1. 18
    2. 15
    3. 12
    4. 10
44. The Venn diagram shows the number of students in a class who like reading (R), dancing (D) and swimming (S). How many students like dancing and swimming?

    

    1. 7
    2. 9
    3. 11
    4. 13
45. A shopkeeper allows a discount of 15% on the marked price of a mobile phone. If a customer paid GH¢170.00 for a mobile phone, what was the marked price of the phone?
    1. GH¢144.50
    2. GH¢195.40
    3. GH¢200.00
    4. GH¢225.00
46. If 27^x = 9^y, find the value of ${\tfrac {x}{y}}$
    1. ${\tfrac {1}{3}}$
    2. ${\tfrac {2}{3}}$
    3. $1{\tfrac {1}{2}}$
    4. 3
47. In the diagram, PQ//TS, PR//TU, reflex angle QPS = 245°, angle PŜT = 115°, $\angle$STU = 65° and $\angle$RPS = x. Find the value of x.

    

    1. 80°
    2. 70°
    3. 60°
    4. 50°
48. Illustrate the inequality -1< 3x + 5 < 14 on a number line.

    

49. A boy looks through a window of a building and sees a mango fruit on the ground 50 m away from the foot of the building. If the window is 9 m from the ground, calculate, correct to the nearest degree, the angle of depression of the mango from the window.
    1. 9°
    2. 10°
    3. 11°
    4. 12°
50. If $E={\tfrac {MN}{S+N}}$ and E = 75, M = 120, N = 5000, find S.
    1. 1000
    2. 2000
    3. 3000
    4. 4000

Theory

Section A

1. 1. Simplify: ${\tfrac {{\tfrac {1}{2}}of{\tfrac {1}{4}}\div {\tfrac {1}{3}}}{{\tfrac {1}{6}}-{\tfrac {3}{4}}+{\tfrac {1}{2}}}}$
   2. Given that ${\sqrt {x}}$ = 10^1.6741, without using calculators, find the value of x.
2. 1. Make q the subject of the relation $t={\sqrt {{\tfrac {pq}{r}}-r^{2}q}}$
   2. If $9^{1-x}=27^{y}$ and $x-y=-1{\tfrac {1}{2}}$, find the value of x + y
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