2018 WAEC (WASSCE) Mathematics Past Questions

Questions

1. 1.

   Given that y varies inversely as the square of x. If x = 3 when y = 100, find the equation connecting x and y.

   1. A.$yx^2 = 300$
   2. B.$yx^2 = 900$
   3. C.y = $\frac{100x}{9}$
   4. D.$y = 900x^2$

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   Answer: B. $yx^2 = 900$

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2. 2.

   The diagonals of a rhombus WXYZ intersect at M. If |MW| = 5cm and |MX| = 12cm, calculate its perimeter

   1. A.42cm
   2. B.48cm
   3. C.52cm
   4. D.60cm

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   Answer: C. 52cm

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3. 3.

   If F = $\frac{9}{5}$C + 32, find C when F = 98.6

   1. A.30
   2. B.37
   3. C.39
   4. D.41

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   Answer: B. 37

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4. 4.

   If M and N are the points (-3, 8) and (5, -7) respectively, find |MN|

   1. A.8 units
   2. B.11 units
   3. C.15 units
   4. D.17 units

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   Answer: D. 17 units

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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.

   If P and Q are two statements, under what condition would p|q be false?

   1. A.If p is true and q is true
   2. B.If p is true and q is false
   3. C.If p is false and q is false
   4. D.If p is false and q is true

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   Answer: B. If p is true and q is false

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7. 7.

   A curve is such that when y = 0, x = -2 or x = 3. Find the equation of the curve.

   1. A.y = $x^2 - 5x - 6$
   2. B.y = $x^2 + 5x - 6$
   3. C.y = $x^2 + x - 6$
   4. D.y = $x^2 - x - 6$

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   Answer: D. y = $x^2 - x - 6$

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8. 8.

   If tan x = $\frac{4}{3}$, 0$^o$ < x < 90$^o$, find the value of sin x - cos x

   1. A.$\frac{1}{10}$
   2. B.$\frac{1}{5}$
   3. C.$\frac{5}{12}$
   4. D.1$\frac{2}{5}$

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   Answer: B. $\frac{1}{5}$

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9. 9.

   The volume of a cylindrical tank, 10m high is 385 m$^2$. Find the diameter of the tank. [Take $\pi = \frac{22}{7}$]

   1. A.14m
   2. B.10m
   3. C.7m
   4. D.5m

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   Answer: C. 7m

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10. 10.

    The surface area of a sphere is $\frac{792}{7} cm^2$. Find, correct to the nearest whole number, its volume. [Take $\pi = \frac{22}{7}$]

    1. A.113$cm^3$
    2. B.131$cm^3$
    3. C.311$cm^3$
    4. D.414$cm^3$

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    Answer: A. 113$cm^3$

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11. 11.

    Evaluate: $(64^{\frac{1}{2}} + 125^{\frac{1}{3}})^2$

    1. A.121
    2. B.144
    3. C.169
    4. D.196

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    Answer: C. 169

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12. 12.

    Solved the equation $2x^2 - x - 6$ = 0

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

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    Answer: A. x = $\frac{-3}{2}$ or 2

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13. 13.

    The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground as the foot of the tree is 30$^o$. Find the height of the tree.

    1. A.27m
    2. B.13.5 $\sqrt{3m}$
    3. C.13.5 $\sqrt{2m}$
    4. D.9$\sqrt{3m}$

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    Answer: D. 9$\sqrt{3m}$

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14. 14.

    If $\log_{10}$(6x - 4) - $\log_{10}$2 = 1, solve for x.

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

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    Answer: C. 4

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16. 16.

    Simplify: $\sqrt{108} + \sqrt{125} - \sqrt{75}$

    1. A.$\sqrt{3} + 5\sqrt{5}$
    2. B.$6 \sqrt{3} - 5 \sqrt{5}$
    3. C.$6 \sqrt{3} + \sqrt{2}$
    4. D.$6\sqrt{3} - \sqrt{2}$

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    Answer: A. $\sqrt{3} + 5\sqrt{5}$

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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.

    If y + 2x = 4 and y - 3x = -1, find the value of (x + y)

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

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    Answer: A. 3

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20. 20.

    Factorise completely the expression $(x + 2)^2$ - $(2x + 1)^2$

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

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    Answer: D. 3(x + 1)(1 - x)

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21. 21.

    The mean of 1, 3, 5, 7 and x is 4. Find the value of x

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

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    Answer: B. 4

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22. 22.

    The angles of a polygon are x, 2x, 2x, (x + $30^o$), (x + $20^o$) and (x - $10^o$). Find the value of x

    1. A.$45^o$
    2. B.$95^o$
    3. C.$84^o$
    4. D.$85^o$

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    Answer: D. $85^o$

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23. 23.

    M and N are two subsets of the universal set (U). If n(U) = 48, n(M) = 20, n(N) = 30 and n(MUN) = 40, find n(M $\cap$ N)

    1. A.18
    2. B.20
    3. C.30
    4. D.38

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    Answer: A. 18

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24. 24.

    The solution of x + 2 $\geq$ 2x + 1 is illustrated

    1. A.i
    2. B.ii
    3. C.iii
    4. D.iv

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    Answer: C. iii

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

27. 27.

    Find  the $n^{th}$ term of the sequence 2 x 3, 4 x 6, 8 x 9, 16 x 12...

    1. A.2$^n$ x 3(n + 1)
    2. B.2$^n$ x 3n
    3. C.2$^n$ x 3$^n$
    4. D.2$^n$ x 3$^n - 1$

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    Answer: B. 2$^n$ x 3n

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28. 28.

    If x : y : z = 3 : 3 : 4, evaluate $\frac{9x + 3y}{6z - 2y}$

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

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    Answer: B. 2

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29. 29.

    A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. [Take $\pi = \frac{22}{7}$]

    1. A.170$^o$
    2. B.177$^o$
    3. C.182$^o$
    4. D.192$^o$

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    Answer: B. 177$^o$

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30. 30.

    Find the value of x for which $32_{four} = 22_x$

    1. A.three
    2. B.five
    3. C.six
    4. D.seven

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    Answer: C. six

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31. 31.

    The equation of the line through the points (4,2) and (-8, -2) is 3y = px + q, where p and q are constants. Find the value of p.

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

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    Answer: A. 1

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33. 33.

    Find the inter-quartile range of 1, 3, 4, 5, 8, 9, 10, 11, 12, 14, 16

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

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    Answer: C. 8

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34. 34.

    Donations during the launching of a church project were sent in sealed envolopes. The table shows the distribution of the amount of money in the envelope. How much was the donation?

    1. A.N26,792.00
    2. B.N26,972.00
    3. C.N62.792.00
    4. D.N62,972.00

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    Answer: D. N62,972.00

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35. 35.

    Find the mean deviation of 20, 30, 25, 40, 35, 50, 45, 40, 20 and 45

    1. A.8
    2. B.9
    3. C.10
    4. D.12

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    Answer: B. 9

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36. 36.

    If  x : y = $\frac{1}{4} : \frac{3}{8}$ and y : z = $\frac{1}{3} : \frac{4}{9}$, find x : z

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

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    Answer: D. 1:2

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37. 37.

    The diagram shows a trapezium inscribed in a semi-circle. If O is the mid-point of WZ and |WX| = |XY| = |YZ|, calculate the value of m

    1. A.90$^o$
    2. B.60$^o$
    3. C.45$^o$
    4. D.30$^o$

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    Answer: B. 60$^o$

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38. 38.

    The graph of y = x$^2$ and y = x intersect at which of these points?

    1. A.(0,0), (1,1)
    2. B.(0,0), (0,1)
    3. C.(1, 0), (0, 0)
    4. D.(0, 0) (0, 0)

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    Answer: A. (0,0), (1,1)

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39. 39.

    There are 250 boys and 150 girls in a school, if 60% of the boys and 40% of the girls play football, what percentage of the school play football?

    1. A.40.0%
    2. B.42.2%
    3. C.50.0%
    4. D.52.5%

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    Answer: D. 52.5%

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40. 40.

    The table shows the distribution of goals scored by 25 teams in a football competition. Calculate the probability that a team selected at randon scored either 4 or 7 goals.

    1. A.$\frac{9}{25}$
    2. B.$\frac{1}{5}$
    3. C.$\frac{6}{25}$
    4. D.$\frac{2}{5}$

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

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41. 41.

    If 3x$^o$ 4(mod 5), find the least value of x

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

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    Answer: C. 3

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43. 43.

    Expression 0.612 in the form $\frac{x}{y}$, where x and y are integers and y $\neq$ 0

    1. A.$\frac{153}{250}$
    2. B.$\frac{68}{111}$
    3. C.$\frac{61}{100}$
    4. D.$\frac{21}{33}$

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    Answer: A. $\frac{153}{250}$

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44. 44.

    Given that Y is 20cm on a bearing of 300$^o$ from x, how far south of y is x?

    1. A.10cm
    2. B.15cm
    3. C.25cm
    4. D.30cm

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    Answer: A. 10cm

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45. 45.

    Simplify; $\frac{2 - 18m^2}{1 + 3m}$

    1. A.$2 (1 + 3m)$
    2. B.$2 (1 + 3m^2)$
    3. C.$2(1 - 3m)$
    4. D.$2(1 - 3m^2)$

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    Answer: C. $2(1 - 3m)$

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46. 46.

    Find the value of x for which $\frac{x - 5}{x(x - 1)}$ is undefined.

    1. A.0 or 5
    2. B.-5 or 5
    3. C.-11 or 5
    4. D.0 or 1

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    Answer: D. 0 or 1

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47. 47.

    Find the median of 2, 1, 0, 3, 1, 1, 4, 0, 1 and 2

    1. A.0.0
    2. B.0.5
    3. C.1.0
    4. D.1.5

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    Answer: C. 1.0

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48. 48.

    The table shows the distribution of goals scored by 25 teams in a football competition. Calculate the probability that a team selected at random scored at most 3 goals.

    1. A.$\frac{3}{25}$
    2. B.$\frac{1}{5}$
    3. C.$\frac{6}{25}$
    4. D.$\frac{2}{5}$

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

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49. 49.

    Simplify; 2$\frac{1}{4} \times 3\frac{1}{2} \div  4 \frac{3}{8}$

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

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    Answer: D. 1$\frac{4}{5}$

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50. 50.

    The total surface area of a hemispher is 75$\pi cm^2$. Find the radius.

    1. A.5.0 cm
    2. B.7.0 cm
    3. C.8.5 cm
    4. D.12.0 cm

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    Answer: A. 5.0 cm

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