2011 WAEC (WASSCE) Mathematics Past Questions

Questions

1. 1.

   The perimeter of a sector of a circle of radius 4cm is ($\pi + 8$)cm. Calculate the anle of the sector

   1. A.45o
   2. B.60o
   3. C.75o
   4. D.90o

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   Answer: A. 45o

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2. 2.

   A cylindrical container has a base radius of 14cm and height 18cm. How many litres of liquid can it hold? correct to the nearest litre [Take $\pi = \frac{22}{7}$]

   1. A.11
   2. B.14
   3. C.16
   4. D.18

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   Answer: A. 11

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3. 3.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

4. 4.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

5. 5.

   The height of a cylinder is equal to its radius. If the volume is 0.216 $\pi m^3$ Calculate the radius.

   1. A.0.46m
   2. B.0.60m
   3. C.0.87m
   4. D.1.80m

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   Answer: B. 0.60m

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6. 6.

   Using the cumulative frequency curve. What is the 80th percentile?

   

   1. A.45.5
   2. B.46.5
   3. C.47.5
   4. D.48.5

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   Answer: D. 48.5

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7. 7.

   Given that n(p) = 19, m(P $\cup$ Q) = 38 and n(P $\cap$ Q) = 7, Find n(C)

   1. A.26
   2. B.31
   3. C.36
   4. D.50

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   Answer: A. 26

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8. 8.

   If 27x = 9y. Find the value of $\frac{x}{y}$

   1. A.$\frac{1}{3}$
   2. B.$\frac{2}{3}$
   3. C.1$\frac{1}{2}$
   4. D.3

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   Answer: B. $\frac{2}{3}$

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9. 9.

   Find the smaller value of x that satisfies the equation x$^2$ + 7x + 10 = 0

   1. A.-5
   2. B.-2
   3. C.2
   4. D.5

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   Answer: A. -5

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10. 10.

    From the equation whose roots are x = $\frac{1}{2}$ and -$\frac{2}{3}$

    1. A.6x2 - x + 2 = 0
    2. B.6x2 - x - 2 = 0
    3. C.6x2 + x + 2 = 0
    4. D.6x2 + x - 2 = 0

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    Answer: D. 6x2 + x - 2 = 0

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11. 11.

    The perpendicular bisectors of the sides of an acute-angled triangle are drawn. Which of these statements is correct? They intersect

    1. A.on one of the vertices
    2. B.at a midpoint of a side
    3. C.inside the triangle
    4. D.outside the triangle

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    Answer: C. inside the triangle

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12. 12.

    The cross section section of a uniform prism is a right-angled triangle with sides 3cm. 4cm and 5cm. If its length is 10cm. Calculate the total surface area

    1. A.142cm2
    2. B.132cm2
    3. C.122cm2
    4. D.112cm2

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    Answer: B. 132cm2

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13. 13.

    The graph represents the relation y = xo2 - 3x - 3. Find the value of x for which x2 - 3x = 7

    1. A.-1.55, 4.44
    2. B.1.55, -4.55
    3. C.-1.55, -4.55
    4. D.1.55, 4.55

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    Answer: C. -1.55, -4.55

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14. 14.

    G varies directly as the square of H, If G is 4 when H is 3, find H when G = 100

    1. A.15
    2. B.25
    3. C.75
    4. D.225

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    Answer: A. 15

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15. 15.

    The length of a piece of stick is 1.75m. A girl measured it as 1.80m. Find the percentage error

    1. A.$\frac{28}{7}$%
    2. B.$\frac{29}{7}$%
    3. C.5%
    4. D.$\frac{20}{7}$%

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    Answer: D. $\frac{20}{7}$%

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16. 16.

    Using the cumulative frequency curve, estimate the median of the data represented on the graph.

    1. A.35.5
    2. B.36.5
    3. C.37.5
    4. D.38.5

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    Answer: B. 36.5

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17. 17.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

18. 18.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

19. 19.

    If N112.00 exchanges for D14.95, calculate the value of D1.00 in naira

    1. A.0.13
    2. B.7.49
    3. C.8.00
    4. D.13.00

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    Answer: B. 7.49

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20. 20.

    A rectangular garden measures 18.6m by 12.5m. Calculate, correct to three significant figures, the area of the garden

    1. A.230m2
    2. B.231m2
    3. C.232m2
    4. D.233m2

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    Answer: D. 233m2

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21. 21.

    A regular polygon of n sides has each exterior angle to 45o. Find the value of n

    1. A.6
    2. B.8
    3. C.12
    4. D.15

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    Answer: B. 8

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22. 22.

    Solve the equation; 3x - 2y = 7, x + 2y = -3

    1. A.x = 1, y = -2
    2. B.x = 1, y = 3
    3. C.x = -2, y = -1
    4. D.x = 4, y = -3

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    Answer: A. x = 1, y = -2

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23. 23.

    a boy looks through a window of a building and sees a mango fruit on the ground 50m away from the foot of the building. If the window is 9m from the ground, calculate, correct to the nearest degree, the angle of depression of the mango from the window

    1. A.9o
    2. B.10o
    3. C.11o
    4. D.12o

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    Answer: B. 10o

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24. 24.

    The height of a cylinder is equal to its radius. If the volume is 0.216 $\pi$ m$^3$. Calculate the radius.

    1. A.0.46m
    2. B.0.60m
    3. C.0.87m
    4. D.1.80m

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    Answer: B. 0.60m

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25. 25.

    Solve for x in the equation; $\frac{3}{5}$(2x - 1) = $\frac{1}{4}$(5x - 3)

    1. A.zero
    2. B.1
    3. C.2
    4. D.3

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    Answer: D. 3

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26. 26.

    Simplify $\frac{\log \sqrt{27}}{\log \sqrt{81}}$

    1. A.3
    2. B.2
    3. C.$\frac{3}{2}$
    4. D.$\frac{3}{4}$

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    Answer: D. $\frac{3}{4}$

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27. 27.

    Esther was facing S 20° W. She turned 90° in the clock wise direction. What direction is she facing?

    1. A.N 70o W
    2. B.S 70o W
    3. C.N 20o W
    4. D.S 20o E

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    Answer: A. N 70o W

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29. 29.

    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. A.7
    2. B.9
    3. C.11
    4. D.13

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    Answer: A. 7

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30. 30.

    The diagram shows a cyclic quadrilateral PQRS with its diagonals intersecting at K. Which of the following triangles is similar to triangle QKR?

    1. A.$\bigtriangleup$ PQK
    2. B.$\bigtriangleup$ PKS
    3. C.$\bigtriangleup$ SKR
    4. D.$\bigtriangleup$ PSR

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    Answer: C. $\bigtriangleup$ SKR

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31. 31.

    One of the factors of (mn - nq - n$^2$ + mq) is (m - n). The other factor is?

    1. A.(n - q)
    2. B.(q - n)
    3. C.(n + q)
    4. D.(q - m)

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    Answer: C. (n + q)

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32. 32.

    If $\sqrt{72} + \sqrt{32} - 3 \sqrt{18} = x \sqrt{8}$, Find the value of x

    1. A.1
    2. B.$\frac{3}{4}$
    3. C.$\frac{1}{2}$
    4. D.$\frac{1}{4}$

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    Answer: C. $\frac{1}{2}$

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33. 33.

    Given that cos xo = $\frac{1}{r}$, express tan x in terms of r

    1. A.$\frac{1}{\sqrt{r}}$
    2. B.$\sqrt{r}$
    3. C.$\sqrt{r^2 + 1}$
    4. D.$\sqrt{r^2 - 1}$

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    Answer: D. $\sqrt{r^2 - 1}$

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34. 34.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

35. 35.

    What must be added to (2x - 3y) to get (x - 2y)?

    1. A.5y - x
    2. B.y - x
    3. C.x - 5x
    4. D.x - y

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    Answer: B. y - x

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36. 36.

    The histogram shows the age distribution of members of a club. What is their modal age?

    1. A.44.5
    2. B.42.5
    3. C.41.5
    4. D.40.5

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    Answer: D. 40.5

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37. 37.

    Factorize the expression: am + bn - an - bm

    1. A.(a - b)(m + n)
    2. B.(a - b)(m - n)
    3. C.(a + b)(m - n)
    4. D.(a + b)(m + n)

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    Answer: B. (a - b)(m - n)

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38. 38.

    John pours 96 litres of red oil into a rectangular container with length 220cm and breadth 40cm. Calculate, correct to the nearest cm, the height of the oil in the container

    1. A.11cm
    2. B.18cm
    3. C.21cm
    4. D.34cm

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    Answer: A. 11cm

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39. 39.

    in a quiz competition, a student answers n questions correctly and was given D(n + 50) for each question correctly answered. If he gets D600.00 altogether, how many questions did he answer correctly?

    1. A.18
    2. B.15
    3. C.12
    4. D.10

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    Answer: D. 10

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40. 40.

    The histogram shows the age distribution of members of a club. How many members are in the club?

    1. A.52
    2. B.50
    3. C.48
    4. D.40

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    Answer: D. 40

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41. 41.

    Which of these angles can be constructed using ruler and a pair of compasses only?

    1. A.115o
    2. B.125o
    3. C.135o
    4. D.145o

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    Answer: C. 135o

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42. 42.

    The graph represents the relation y = x$^2$ - 3x - 3. What is the equation of the line of symmetry of the graph?

    1. A.y = 0.5
    2. B.x = 1.0
    3. C.x = 1.5
    4. D.y = 4.6

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    Answer: C. x = 1.5

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43. 43.

    Simplify 1$\frac{3}{4} - (2 \frac{1}{3} + 4)$

    1. A.3$\frac{5}{12}$
    2. B.2$\frac{7}{12}$
    3. C.-4 $\frac{7}{12}$
    4. D.-5 $\frac{7}{12}$

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    Answer: C. -4 $\frac{7}{12}$

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44. 44.

    What is the value of 3 in the number 42.7531?

    1. A.$\frac{3}{10000}$
    2. B.$\frac{3}{1000}$
    3. C.$\frac{3}{100}$
    4. D.$\frac{1}{10}$

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    Answer: B. $\frac{3}{1000}$

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45. 45.

    Simplify $\frac{m}{n} + \frac{(m - 1)}{5n} = \frac{(m - 2)}{10n}$ where n $\neq$ 0

    1. A.$\frac{m - 3}{10n}$
    2. B.$\frac{11m}{10n}$
    3. C.$\frac{m + 1}{10n}$
    4. D.$\frac{11m + 4}{10n}$

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    Answer: B. $\frac{11m}{10n}$

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46. 46.

    If a number is chosen at random from the set {x: 4 $\leq x \leq 15$}. Find the probability that it is a multiple of 3 or a multiple of 4

    1. A.$\frac{1}{2}$
    2. B.$\frac{5}{12}$
    3. C.$\frac{7}{12}$
    4. D.$\frac{11}{12}$

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    Answer: A. $\frac{1}{2}$

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