2014 WAEC (WASSCE) Mathematics Past Questions

Questions

1. 1.

   Which of the following is a measure of dispersion?

   1. A.range
   2. B.percentile
   3. C.median
   4. D.quartile

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   Answer: A. range

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2. 2.

   If $\frac{2}{x - 3} - \frac{3}{x - 2}$ is equal to $\frac{p}{(x - 3)(x - 2)}$, find p

   1. A.-x - 5
   2. B.-(x + 3)
   3. C.5x - 13
   4. D.5 - x

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   Answer: D. 5 - x

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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.

   If x = {0, 2, 4, 6}, y = {1, 2, 3, 4} and z = {1, 3} are subsets of u = {x:0 $\geq$ x $\geq$ 6}, find x $\cap$ (Y' $\cup$ Z)

   1. A.{0, 2, 6}
   2. B.{1, 3}
   3. C.{0, 6)
   4. D.{9}

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   Answer: C. {0, 6)

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

6. 6.

   Simplify: $\sqrt{12} ( \sqrt{48} - \sqrt{3}$)

   1. A.18
   2. B.16
   3. C.14
   4. D.12

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   Answer: A. 18

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7. 7.

   Make u the subject of formula, E = $\frac{m}{2g}$(v2 - u2)

   1. A.u = $\sqrt{v^2 - \frac{2Eg}{m}}$
   2. B.u = $\sqrt{\frac{v^2}{m} - \frac{2Eg}{4}}$
   3. C.u = $\sqrt{v- \frac{2Eg}{m}}$
   4. D.u = $\sqrt{\frac{2v^2Eg}{m}}$

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   Answer: A. u = $\sqrt{v^2 - \frac{2Eg}{m}}$

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

9. 9.

   In a cumulative frequency graph, the lower quartile is 18 years while the 60th percentile is 48 years. What percentage of the distribution is at most 18 years or greater than 48 years?

   1. A.15%
   2. B.35%
   3. C.65%
   4. D.85%

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   Answer: C. 65%

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10. 10.

    A chord subtends an angle of 120o at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord, [Take $\pi = \frac{22}{7}$]

    1. A.14$\frac{1}{3}$cm
    2. B.12$\frac{5}{6}$cm
    3. C.8$\frac{1}{7}$cm
    4. D.7$\frac{1}{3}$cm

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    Answer: A. 14$\frac{1}{3}$cm

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

12. 12.

    The radii of the base of two cylindrical tins, P and Q are r and 2r respectively. If the water level in p is 10cm high, what would be the height of the same quantity of water in Q?

    1. A.2.5cm
    2. B.5.0cm
    3. C.7.5cm
    4. D.20.0cm

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    Answer: A. 2.5cm

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13. 13.

    Find the truth set of the equation x2 = 3(2x + 9)

    1. A.{x : x = 3, x = 9}
    2. B.{x : x = -3, x = -9}
    3. C.{x : x = 3, x = -9}
    4. D.{x : x = -3, x = 9}

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    Answer: D. {x : x = -3, x = 9}

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14. 14.

    A man's eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes.

    1. A.33o
    2. B.32o
    3. C.27o
    4. D.26o

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    Answer: C. 27o

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15. 15.

    The volume of a cube is 512cm3. Find the length of its side

    1. A.6cm
    2. B.7cm
    3. C.8cm
    4. D.9cm

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    Answer: C. 8cm

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

17. 17.

    Simplify 10$\frac{2}{5} - 6 \frac{2}{3} + 3$

    1. A.6$\frac{4}{15}$
    2. B.6$\frac{11}{15}$
    3. C.7$\frac{4}{15}$
    4. D.7$\frac{11}{15}$

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    Answer: B. 6$\frac{11}{15}$

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18. 18.

    Subtract $\frac{1}{2}$(a - b - c) from the sum of $\frac{1}{2}$(a - b + c) and $\frac{1}{2}$ (a + b - c)

    1. A.$\frac{1}{2}$ (a + b + c)
    2. B.$\frac{1}{2}$ (a - b - c)
    3. C.$\frac{1}{2}$ (a - b + c)
    4. D.$\frac{1}{2}$ (a + b - c)

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    Answer: A. $\frac{1}{2}$ (a + b + c)

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20. 20.

    Simplify $\sqrt{\frac{8^2 \times 4^{n + 1}}{2^{2n} \times 16}}$

    1. A.16
    2. B.8
    3. C.4
    4. D.1

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    Answer: C. 4

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21. 21.

    The coordinates of points P and Q are (4, 3) and (2, -1) respectively. Find the shortest distance between P and Q.

    1. A.10$sqrt{2}$
    2. B.4$sqrt{5}$
    3. C.5$sqrt{2}$
    4. D.2$sqrt{5}$

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    Answer: D. 2$sqrt{5}$

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22. 22.

    The bar chart shows the scores of some students in a test. If one students is selected at random, find the probability that he/she scored at most 2 marks

    1. A.$\frac{11}{18}$
    2. B.$\frac{11}{20}$
    3. C.$\frac{7}{22}$
    4. D.$\frac{5}{19}$

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    Answer: A. $\frac{11}{18}$

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23. 23.

    In the figures, PQ is a tangent to the circle at R and UT is parallel to PQ. if < TRQ = xo, find < URT in terms of x

    1. A.2xo
    2. B.(90 - x)o
    3. C.(90 + x)o
    4. D.(180 - 2x)o

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    Answer: A. 2xo

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

25. 25.

    The area of a sector a circle with diameter 12cm is 66cm2. If the sector is folded to form a cone, calculate the radius of the base of the cone [Take $\pi = \frac{22}{7}$]

    1. A.3.0cm
    2. B.3.5cm
    3. C.7.0cm
    4. D.7.5cm

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    Answer: B. 3.5cm

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26. 26.

    If x : y = 3 : 2 and y : z = 5 : 4, find the value of x in the ratio x : y : z

    1. A.8
    2. B.10
    3. C.15
    4. D.20

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    Answer: C. 15

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27. 27.

    Find the number of term in the Arithmetic Progression(A.P) 2, -9, -20,...-141.

    1. A.11
    2. B.12
    3. C.13
    4. D.14

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    Answer: D. 14

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28. 28.

    If 23x = 325, find the value of x

    1. A.7
    2. B.6
    3. C.5
    4. D.4

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    Answer: A. 7

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29. 29.

    A chord, 7cm long, is drawn in a circle with radius 3.7cm. Calculate the distance of the chord from the centre of the circle

    1. A.0.7cm
    2. B.1.2cm
    3. C.2.0cm
    4. D.2.5cm

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    Answer: B. 1.2cm

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30. 30.

    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. A.i
    2. B.i and ii
    3. C.i and iii
    4. D.i, ii and iii

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    Answer: C. i and iii

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31. 31.

    approximate 0.0033780 to 3 significant figures

    1. A.338
    2. B.0.338
    3. C.0.00338
    4. D.0.003

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    Answer: C. 0.00338

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32. 32.

    If a number is selected at random from each of the sets p = {1, 2, 3} and Q = {2, 3, 5}, find the probability that the sum of the numbers is prime

    1. A.$\frac{5}{9}$
    2. B.$\frac{4}{9}$
    3. C.$\frac{1}{3}$
    4. D.$\frac{2}{9}$

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    Answer: B. $\frac{4}{9}$

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33. 33.

    F x varies inversely as y and y varies directly as Z, what is the relationship between x and z?

    1. A.x $\alpha$ z
    2. B.x $\alpha \frac{1}{z}$
    3. C.x $\alpha z^2$
    4. D.x $\alpha \frac{1}{z^2}\0

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    Answer: B. x $\alpha \frac{1}{z}$

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34. 34.

    If (x - a) is a factor pf bx - ax + x2, find the other factor.

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

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    Answer: A. (x + b)

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

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

37. 37.

    Given that cos x = $\frac{12}{13}$, evaluate $\frac{1 - \tan x}{\tan x}$

    1. A.$\frac{5}{13}$
    2. B.$\frac{5}{7}$
    3. C.$\frac{7}{5}$
    4. D.$\frac{13}{5}$

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    Answer: C. $\frac{7}{5}$

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38. 38.

    The bar chart shows the scores of some students in a test. How many students took the test?

    1. A.18
    2. B.19
    3. C.20
    4. D.22

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    Answer: D. 22

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39. 39.

    A box contains 13 currency notes, all of which are either N50 or N20 notes. The total value of the currency notes is N530. How many N50 notes are in the box?

    1. A.4
    2. B.6
    3. C.8
    4. D.9

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    Answer: D. 9

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40. 40.

    A ship sails x km due east to a point E and continues x km due north to F. Find the bearing the bearing of f from the starting point.

    1. A.045o
    2. B.090o
    3. C.135o
    4. D.225o

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    Answer: A. 045o

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41. 41.

    In parallelogram PQRS, QR is produced to M such that |QR| = |RM|. What fraction of the area of PQMS is the area of PRMS?

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

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

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42. 42.

    If log 5.957 = 0.7750, find log $3 \sqrt{0.0005957}$

    1. A.$\overline{4}$.1986
    2. B.$\overline{2}$.9250
    3. C.$\overline{1}$.5917
    4. D.$\overline{1}$.075

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    Answer: B. $\overline{2}$.9250

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43. 43.

    $\begin{array}{c|c}height & 2 & 3 & 4 & 5 & 6 \\ \hline frequency & 2 & 4 & 5 & 3 & 1 \end{array}$ The table shows the distribution of the height of plants in a nursery. Calculate the mean height of the plants.

    1. A.3.8
    2. B.3.0
    3. C.2.8
    4. D.2.3

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    Answer: A. 3.8

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44. 44.

    Three quarters of a number added to two and a half of the number gives 13. Find the number

    1. A.4
    2. B.5
    3. C.6
    4. D.7

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    Answer: A. 4

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45. 45.

    The probability of an event P happening is $\frac{1}{5}$ and that of event Q is $\frac{1}{4}$. If the events are independent, what is the probability that neither of them happens?

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

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    Answer: C. $\frac{3}{5}$

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46. 46.

    Each exterior angle of a polygon is 30o. Calculate the sum of the interior angles

    1. A.540o
    2. B.720o
    3. C.1080o
    4. D.1800o

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    Answer: D. 1800o

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48. 48.

    Find the gradient of the line joining the points (2, -3) and 2, 5)

    1. A.9
    2. B.1
    3. C.2
    4. D.undefined

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    Answer: D. undefined

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49. 49.

    In what modulus is it true that 9 + 8 = 5?

    1. A.mod 10
    2. B.mod 11
    3. C.mod 12
    4. D.mod 13

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    Answer: C. mod 12

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