2019 WAEC (WASSCE) Mathematics Past Questions

Questions

1. 1.

   Simplify, correct to three significant figures, (27.63)$^2$ - (12.37)$^2$

   1. A.614
   2. B.612
   3. C.611
   4. D.610

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   Answer: D. 610

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2. 2.

   Evaluate: $\frac{0.42 \div 2.5}{0.5 \times 2.05}$, leaving the answer in the standard form.

   1. A.1.639 x 10$^2$
   2. B.1.639 x 10$^1$
   3. C.1.639 x 10$^{-1}$
   4. D.1.639 x 10$^{-2}$

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   Answer: C. 1.639 x 10$^{-1}$

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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 m : n = 2 : 1, evaluate $\frac{3m^2 - 2n^2}{m^2 + mn}$

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

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

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6. 6.

   8, 18, 10,14, 18, 11, 13, 14, 13, 17, 15, 8, 16, and 13 The following are scores obtained by some students in a test. How many students scored above the mean score?

   1. A.10
   2. B.9
   3. C.8
   4. D.7

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   Answer: D. 7

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7. 7.

   The interior angles of a polygon are 3x$^o$, 2x$^o$, 4x$^o$, 3x$^o$ and 6x$^o$. Find the size of the smallest angle of the polygon.

   1. A.80$^o$
   2. B.60$^o$
   3. C.40$^o$
   4. D.30$^o$

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   Answer: B. 60$^o$

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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.

   From the top of a vertical cliff 20m high, a boat at sea can be sighted 75m away and on the same horizontal position as the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.

   1. A.56$^o$
   2. B.75$^o$
   3. C.16$^o$
   4. D.15$^o$

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   Answer: D. 15$^o$

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10. 10.

    Find the equation of a straight line passing through the point (1, -5) and having gradient of $\frac{3}{4}$

    1. A.3x + 4y - 23 = 0
    2. B.3x + 4y +23 = 0
    3. C.3x - 4y +23 = 0
    4. D.3x - 4y - 23 = 0

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    Answer: D. 3x - 4y - 23 = 0

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11. 11.

    The following are scores obtained by some students in a test. Find the median score    8 18 10 14 18 11 13 14 13 17 15 8 16 13

    1. A.14.5
    2. B.14.0
    3. C.13.5
    4. D.13.0

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    Answer: C. 13.5

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12. 12.

    Evaluate: (0.064)$^{-\frac{1}{3}}$

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

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    Answer: A. $\frac{5}{2}$

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13. 13.

    Evaluate; $\frac{\log_3 9 - \log_2 8}{\log_3 9}$

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

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    Answer: D. -$\frac{1}{2}$

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14. 14.

    A rectangular board has a length of 15cm and width x cm. If its sides are doubled, find its new area.

    1. A.60x cm$^2$
    2. B.45x cm$^2$
    3. C.30x cm$^2$
    4. D.15x cm$^2$

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    Answer: A. 60x cm$^2$

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15. 15.

    Find the angle at which an arc of length 22 cm subtends at the centre of a circle of radius 15cm.  [Take $\pi = \frac{22}{7}$]

    1. A.70$^o$
    2. B.84$^o$
    3. C.96$^o$
    4. D.156$^o$

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    Answer: B. 84$^o$

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16. 16.

    If (0.25)$^y$ = 32, find the value of y.

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

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    Answer: A. y = - $\frac{5}{2}$

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17. 17.

    Solve $4x^{2}$ - 16x + 15 = 0.

    1. A.x = 1$\frac{1}{2}$ or x = -2$\frac{1}{2}$
    2. B.x = 1$\frac{1}{2}$ or x = 2$\frac{1}{2}$
    3. C.x = 1$\frac{1}{2}$ or x = -1$\frac{1}{2}$
    4. D.x = -1$\frac{1}{2}$ or x -2$\frac{1}{2}$

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    Answer: B. x = 1$\frac{1}{2}$ or x = 2$\frac{1}{2}$

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18. 18.

    A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?

    1. A.$\frac{2}{3}$
    2. B.$\frac{3}{5}$
    3. C.$\frac{7}{20}$
    4. D.$\frac{12}{25}$

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    Answer: D. $\frac{12}{25}$

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19. 19.

    There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?

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

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

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20. 20.

    If 2$^{a}$ = $\sqrt{64}$ and $\frac{b}{a}$ = 3, evaluate a$^2 + b^{2}$

    1. A.250
    2. B.160
    3. C.90
    4. D.48

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    Answer: C. 90

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21. 21.

    Simplify: $\log_{10}$ 6 - 3 log$_{10}$  3 + $\frac{2}{3} \log_{10} 27$

    1. A.3 $\log_{10}^2$
    2. B.$\log_{10}^2$
    3. C.$\log_{10}^3$
    4. D.2 $\log_{10}^3$

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    Answer: B. $\log_{10}^2$

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22. 22.

    Simplify: $\frac{x^2 - 5x - 14}{x^2 - 9x + 14}$

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

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    Answer: D. $\frac{x + 2}{x - 2}$

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23. 23.

    Calculate the variance of 2, 4, 7, 8 and 9

    1. A.7.2
    2. B.6.8
    3. C.3.5
    4. D.2.6

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    Answer: B. 6.8

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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.

    Express, correct to three significant figures, 0.003597.

    1. A.0.359
    2. B.0.004
    3. C.0.00360
    4. D.0.00359

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    Answer: C. 0.00360

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26. 26.

    If 3p = 4q and 9p = 8q - 12, find the value of pq.

    1. A.12
    2. B.7
    3. C.-7
    4. D.-12

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    Answer: A. 12

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27. 27.

    If log$_x$ 2 = 0.3, evaluate log$_x$ 8.

    1. A.2.4
    2. B.1.2
    3. C.0.9
    4. D.0.6

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    Answer: C. 0.9

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28. 28.

    In XYZ, |YZ| = 32cm, < YXZ 53$^o$ and XZY = 90$^o$. Find, correct to the nearest centimetre, |XZ|

    1. A.31 cm
    2. B.25 cm
    3. C.20 cm
    4. D.13 cm

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    Answer: B. 25 cm

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29. 29.

    Make b the subject of the relation lb = $\frac{1}{2}$ (a + b)h

    1. A.$\frac{ah}{2l - h}$
    2. B.$\frac{2l - h}{al}$
    3. C.$\frac{al}{2l - h}$
    4. D.$\frac{al}{2 - h}$

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    Answer: A. $\frac{ah}{2l - h}$

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30. 30.

    The foot of a ladder is 6m from the base of an electric pole. The top of the ladder rest against the pole at a point 8m above the ground. How long is the ladder?

    1. A.14m
    2. B.12m
    3. C.10m
    4. D.7m

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    Answer: C. 10m

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31. 31.

    Which of these values would make $\frac{3p - 1}{p^{2} - p}$ undefined?

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

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    Answer: A. 1

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

33. 33.

    Evaluate: 2$\sqrt{28} - 3\sqrt{50} + \sqrt{72}$

    1. A.4$\sqrt{7} - 21 \sqrt{2}$
    2. B.4$\sqrt{7} - 11 \sqrt{2}$
    3. C.4$\sqrt{7} - 9 \sqrt{2}$
    4. D.4$\sqrt{7} + \sqrt{2}$

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    Answer: C. 4$\sqrt{7} - 9 \sqrt{2}$

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34. 34.

    Solve: $\frac{y + 1}{2} - \frac{2y - 1}{3}$ = 4

    1. A.y = 19
    2. B.y = -19
    3. C.y = -29
    4. D.y = 29

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    Answer: B. y = -19

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35. 35.

    The total surface area of a solid cylinder 165cm$^2$. Of the base diameter is 7cm, calculate its height. [Take $\pi = \frac{22}{7}$]

    1. A.7.5 cm
    2. B.4.5 cm
    3. C.4.0 cm
    4. D.2.0 cm

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    Answer: C. 4.0 cm

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36. 36.

    Bala sold an article for #6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600.00.

    1. A.5%
    2. B.10%
    3. C.12%
    4. D.13%

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    Answer: B. 10%

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37. 37.

    Eric sold his house through an agent who charged 8% commission on the selling price. If Eric received $117,760.00 after the sale, what was the selling price of the house?

    1. A.$130,000.00
    2. B.$128,000.00
    3. C.$125,000.00
    4. D.$120,000.00

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    Answer: B. $128,000.00

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38. 38.

    H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y.

    1. A.H = $\frac{p}{4y^2}$
    2. B.H = $\frac{2p}{y^2}$
    3. C.H = $\frac{p}{2y^2}$
    4. D.H = $\frac{p}{y^2}$

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    Answer: C. H = $\frac{p}{2y^2}$

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39. 39.

    If 6, P, and 14 are consecutive terms in an Arithmetic Progression (AP), find the value of P.

    1. A.9
    2. B.10
    3. C.6
    4. D.8

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    Answer: B. 10

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40. 40.

    If 7 + y = 4 (mod 8), find the least value of y, 10 $\leq y \leq 30$

    1. A.11
    2. B.13
    3. C.19
    4. D.21

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    Answer: B. 13

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41. 41.

    Factorize completely; (2x + 2y)(x - y) + (2x - 2y)(x + y)

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

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    Answer: A. 4(x - y)(x + y)

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42. 42.

    If 23$_y$ = 1111$_{\text{two}}$, find the value of y

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

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    Answer: C. 6

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

44. 44.

    A box contains 5 red, 6 green and 7 yellow pencils of the same size. What is the probability of picking a green pencil at random?

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

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    Answer: C. $\frac{1}{3}$

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45. 45.

    The fourth term of an Arithmetic Progression (A.P) is 37 and the first term is -20. Find the common difference.

    1. A.3
    2. B.57
    3. C.19
    4. D.17

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    Answer: C. 19

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46. 46.

    If T = {prime numbers} and M = {odd numbers} are subsets of $\mu$  = {x : 0 < x ≤ 10} and x is an integer, find (T$^{\prime}$ n M$^{\prime}$).

    1. A.{4, 6, 8, 10}
    2. B.{1. 4, 6, 8, 10}
    3. C.{1, 2, 4, 6, 8, 10}
    4. D.{1, 2, 3, 5, 7, 8, 9}

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    Answer: A. {4, 6, 8, 10}

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47. 47.

    An arc subtends an angle of 72$^o$ at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5 cm. [Take $\pi = \frac{22}{7}$]

    1. A.6.6 cm
    2. B.8.8 cm
    3. C.4.4 cm
    4. D.2.2 cm

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    Answer: C. 4.4 cm

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48. 48.

    The pie chart represents fruits on display in a grocery shop. If there are 60 oranges on display, how many apples are there?

    1. A.90
    2. B.80
    3. C.70
    4. D.40

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    Answer: B. 80

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49. 49.

    The following are scores obtained by some students in a test, Find the mode of the distribution   8 18 10 14 18 11 13 14 13 17 15 8 16 13

    1. A.18
    2. B.14
    3. C.13
    4. D.8

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    Answer: C. 13

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50. 50.

    If tan x = $\frac{3}{4}$, 0 < x < 90$^o$, evaluate $\frac{\cos x}{2 sin x}$

    1. A.$\frac{8}{3}$
    2. B.$\frac{3}{2}$
    3. C.$\frac{4}{3}$
    4. D.$\frac{2}{3}$

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

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