2017 WAEC (WASSCE) Mathematics Past Questions

Questions

1. 1.

   Which of the following is true about parallelogram?

   1. A.opposite angles are supplementary
   2. B.opposite angles are complementary
   3. C.opposite angles are equal
   4. D.opposite angles are reflex angles

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   Answer: C. opposite angles are equal

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2. 2.

   The diagram shows a circle centre O. if <STR = 29º and < RST = 46º, Calculate the value of <STO.

   1. A.12$^o$
   2. B.15$^o$
   3. C.29$^o$
   4. D.34$^o$

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   Answer: B. 15$^o$

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3. 3.

   A sum of N18,100 was shared among 5 boys and 4 girls with each boy taking N20.00 more than each girl. Find a boy's share.

   1. A.N1,820.00
   2. B.2,000.00
   3. C.N2,020.00
   4. D.N2,040.00

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   Answer: C. N2,020.00

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4. 4.

   If 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.a $\alpha$ z$^2$
   4. D.x $\alpha$ $\frac{1}{z^2}$

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

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

7. 7.

   If M = {x : 3 $\leq$  x < 8} and N = {x : 8 <  x $\leq$ 12}, which of the following is true? i. 8 $\in$ M $\cap$ N ii. 8 $\in$ M $\cup$ N iii. M $\cap$ N = $\varnothing$

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

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   Answer: A. iii only

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8. 8.

   Water flows out of a pipe at a rate of 40$\pi cm^2$ per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds.

   1. A.10 cm
   2. B.14 cm
   3. C.16 cm
   4. D.20 cm

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   Answer: A. 10 cm

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9. 9.

   Calculate the variance of 2, 3, 3, 4, 5, 5, 5, 7, 7 and 9

   1. A.2.2
   2. B.3.4
   3. C.4.0
   4. D.4.2

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   Answer: D. 4.2

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10. 10.

    Solve: - $\frac{1}{4}$ < $\frac{3}{4}$ (3x - 2) < $\frac{1}{2}$

    1. A.-$\frac{5}{9}$ < x <$\frac{8}{9}$
    2. B.-$\frac{8}{9}$ < x <$\frac{7}{9}$
    3. C.-$\frac{8}{9}$ < x <$\frac{5}{9}$
    4. D.-$\frac{7}{9}$ < x <$\frac{8}{9}$

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    Answer: A. -$\frac{5}{9}$ < x <$\frac{8}{9}$

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11. 11.

    Simplify; 3x - (p - x) - (r - p)

    1. A.2x - r
    2. B.2x + r
    3. C.4x - r
    4. D.2x - 2p - r

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    Answer: C. 4x - r

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12. 12.

    Fig. 1 and Fig. 2 are the addition and multiplication tables respectively in modulo 5. Use these tables to solve the equation (n $\oplus 4$)

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

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    Answer: A. 1

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13. 13.

    Given that cos 30$^o$ = sin 60$^o$ = $\frac{3}{2}$ and sin 30$^o$ = cos 60$^o$ = $\frac{1}{2}$, evaluate $\frac{tan 60^o - 1}{1 - tan 30^o}$

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

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    Answer: C. $\sqrt{3}$

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14. 14.

    Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2)

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

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    Answer: A. -1

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15. 15.

    Two bottles are drawn with replacement from a crate containing 8 Coke, 12 Fanta, and 4 Sprite bottles. What is the probability that the first is coke and the second is not coke?

    1. A.$\frac{1}{12}$
    2. B.$\frac{1}{6}$
    3. C.$\frac{2}{9}$
    4. D.$\frac{3}{8}$

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    Answer: C. $\frac{2}{9}$

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16. 16.

    Three exterior angles of a polygon are 30$^o$, 40$^o$ and 60$^o$. If the remaining exterior angles are 46$^o$ each, name the polygon.

    1. A.decagon
    2. B.nonagon
    3. C.octagon
    4. D.hexagon

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    Answer: C. octagon

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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.

    One factor of $7x^2 + 33x - 10$ is

    1. A.7x + 5
    2. B.x - 2
    3. C.7x - 2
    4. D.x - 5

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    Answer: C. 7x - 2

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19. 19.

    If the simple interest on a certain amount of money saved in a bank for 5 years at 2$\frac{1}{2}$% annum is N500.00, calculate the total amount due after 6 years at the same rate

    1. A.N2,500.00
    2. B.N2,600.00
    3. C.N4,500.00
    4. D.N4,600.00

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    Answer: D. N4,600.00

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20. 20.

    Find the 6th term of the sequence $\frac{2}{3} \frac{7}{15} \frac{4}{15}$,...

    1. A.-$\frac{1}{3}$
    2. B.-$\frac{1}{5}$
    3. C.-$\frac{1}{15}$
    4. D.$\frac{1}{9}$

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    Answer: A. -$\frac{1}{3}$

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21. 21.

    Express 0.0000407, correct to 2 significant figures

    1. A.0.0
    2. B.0.00004
    3. C.0.000041
    4. D.0.0000407

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    Answer: C. 0.000041

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22. 22.

    A stationary boat is observed from a height of 100m. If the horizontal distance between the observer and the boat is 80m, calculate, correct to two decimal places, the angles of depression of the boat from point of observation

    1. A.36.87$^o$
    2. B.39.70$^o$
    3. C.51.34$^o$
    4. D.53.13$^o$

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    Answer: C. 51.34$^o$

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23. 23.

    Given that t = $2 ^{-x}$, find $2 ^{x + 1}$ in terms of t.

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

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

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24. 24.

    In what number base was the addition 1 + nn = 100, where n > 0, done?

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

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    Answer: B. n + 1

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25. 25.

    The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres

    1. A.4.55 litres
    2. B.7.50 litres
    3. C.8.10 litres
    4. D.9.55 litres

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    Answer: A. 4.55 litres

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26. 26.

    If x = $\frac{2}{3}$ and y = - 6, evaluate xy - $\frac{y}{x}$

    1. A.0
    2. B.5
    3. C.8
    4. D.9

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    Answer: B. 5

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27. 27.

    Evaluate $\frac{3\frac{1}{4} \times 1\frac{3}{5}}{11\frac{1}{3} - 5 \frac{1}{3}}$

    1. A.$\frac{14}{15}$
    2. B.$\frac{13}{15}$
    3. C.$\frac{4}{5}$
    4. D.$\frac{11}{15}$

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    Answer: B. $\frac{13}{15}$

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28. 28.

    The diagonal of a square is 60 cm. Calculate its peremeter

    1. A.20$\sqrt{2}$
    2. B.40$\sqrt{2}$
    3. C.90$\sqrt{2}$
    4. D.120$\sqrt{2}$

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    Answer: D. 120$\sqrt{2}$

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29. 29.

    A circular pond of radius 4m has a path of width 2.5m round it. Find, correct to two decimal places, the area of the path. [Take$\frac{22}{7}$]

    1. A.7.83$m^2$
    2. B.32.29$m^2$
    3. C.50.29$m^2$
    4. D.82.50$m^2$

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    Answer: D. 82.50$m^2$

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30. 30.

    Simplify the expression $\frac{a^2 b^4 - b^2 a^4}{ab(a + b)}$

    1. A.$a^2 - b^2$
    2. B.$b^2 - a^2$
    3. C.$a^2b - ab^2$
    4. D.$ab^2 - a^2b$

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    Answer: D. $ab^2 - a^2b$

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31. 31.

    Make x the subject of the relation d = $\sqrt{\frac{6}{x} - \frac{y}{2}}$

    1. A.x = $\frac{6 + 12}{d^2 + y}$
    2. B.x = $\frac{12}{d^2 - y}$
    3. C.x = $\frac{12}{y} - 2d^2$
    4. D.x = $\frac{12}{2d^2 + y}$

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    Answer: D. x = $\frac{12}{2d^2 + y}$

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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.

    Simplify; $\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}$

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

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    Answer: A. 4

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34. 34.

    Solve the equation: $\frac{1}{5x} + \frac{1}{x}$= 3

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

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

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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.

    The ages of Tunde and Ola are in the ratio 1:2. If the ratio of Ola's age to Musa's age is 4:5, what is the ratio of Tunde's age to Musa's age?

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

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    Answer: C. 2 : 5

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37. 37.

    Consider the statements: p it is hot, q: it is raining Which of the following symbols correctly represents the statement "It is raining if and only if it it is cold"?

    1. A.p $\iff$ $\sim$q
    2. B.p $\iff$ q
    3. C.$\sim$p $\iff$ $\sim$q
    4. D.q $\iff$ $\sim$p

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    Answer: D. q $\iff$ $\sim$p

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38. 38.

    Marks 0 1 2 3 4 5 Frequency 7 4 18 12 8 11 The table gives the distribution of marks obtained by a number of pupils in a class test. Using this information, Find the median of the distribution

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

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    Answer: B. 3

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39. 39.

    An arc of a circle of radius 7.5cm is 7.5cm  long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take $\pi = \frac{22}{7}$]

    1. A.29$^o$
    2. B.57$^o$
    3. C.65$^o$
    4. D.115$^o$

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    Answer: B. 57$^o$

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40. 40.

    The roots of a quadratic equation are $\frac{-1}{2}$ and $\frac{2}{3}$. Find the equation.

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

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    Answer: B. $6x^2 - x - 2 = 0$

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41. 41.

    The diagram shows a circle O. If < ZYW = 33$^o$ , find < ZWX

    1. A.33$^o$
    2. B.57$^o$
    3. C.90$^o$
    4. D.100$^o$

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    Answer: C. 90$^o$

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42. 42.

    In a class of 45 students, 28 offer chemistry and 25 offer Biology. If each student offers at least one of the two subjects, calculate the probability that a student selected at random from the class the class offers chemistry only.

    1. A.$\frac{2}{9}$
    2. B.$\frac{4}{9}$
    3. C.$\frac{5}{9}$
    4. D.$\frac{7}{9}$

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

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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.

    If P(2,3) and Q)2, 5) are points on a graph, calculate the length PQ

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

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    Answer: D. 2 units

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45. 45.

    Marks 0 1 2 3 4 5 Frequency 7 4 18 12 8 11 The table gives the distribution of marks obtained by a number of pupils in a class test. Using this information, find the first quartile

    1. A.1.0
    2. B.1.5
    3. C.2.0
    4. D.2.5

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    Answer: C. 2.0

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46. 46.

    Given that a = log 7 and b = $\log$ 2, express log 35 in terms of a and b.

    1. A.a + b + 1
    2. B.ab - 1
    3. C.a - b + 1
    4. D.b - a + 1

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    Answer: C. a - b + 1

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47. 47.

    A bearing of 320$^o$ expressed as a compass bearing is

    1. A.N 50$^o$ W
    2. B.N 40$^o$ W
    3. C.N 50$^o$ E
    4. D.N 40$^o$ E

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    Answer: B. N 40$^o$ W

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48. 48.

    The average age of a group of 25 girls is 10year. If one girl, aged 12 years and 4 months joins the group, find the new average age of the group

    1. A.10.1 years
    2. B.9.3 years
    3. C.8.7 years
    4. D.8 . 3 years

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    Answer: A. 10.1 years

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49. 49.

    If the total surface area of a solid hemisphere is equal to its volume, find the radius

    1. A.3.0cm
    2. B.4.5cm
    3. C.5.0cm
    4. D.9.0cm

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    Answer: B. 4.5cm

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