2015 WAEC (WASSCE) Mathematics Past Questions

Questions

1. 1.

   In the given diagram, $\bar{QT}$ and $\bar{PR}$ are straight lines, < ROS = (3n - 20), < SOT = n, < POL = m and < QOL is a right angle. Find the value of n.

   1. A.35o
   2. B.40o
   3. C.55o
   4. D.60o

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   Answer: D. 60o

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2. 2.

   A farmer uses $\frac{2}{5}$ of his land to grow cassava, $\frac{1}{3}$ of the remaining for yam and the rest for maize. Find the part of the land used for maize

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

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

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3. 3.

   If 2n = y, Find 2$^{(2 + \frac{n}{3})}$

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

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   Answer: A. 4y$^\frac{1}{3}$

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4. 4.

   The volume of a cone of height 3cm is 38$\frac{1}{2}$cm3. Find the radius of its base. [Take $\pi = \frac{22}{7}$]

   1. A.3.0cm
   2. B.3.5cm
   3. C.4.0cm
   4. D.4.5cm

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   Answer: B. 3.5cm

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5. 5.

   The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15km. how far would the vehicle go on 9 litres of petrol?

   1. A.22$\frac{1}{2}$km
   2. B.30km
   3. C.33$\frac{1}{2}$km
   4. D.45km

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   Answer: A. 22$\frac{1}{2}$km

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6. 6.

   The dimension of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take $\pi = \frac{22}{7}$]

   1. A.14cm
   2. B.7m
   3. C.3$\frac{1}{2}$m
   4. D.1$\frac{3}{4}$m

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   Answer: C. 3$\frac{1}{2}$m

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

8. 8.

   The probability that kebba, Ebou and Omar will hit a target are $\frac{2}{3}$, $\frac{3}{4}$ and $\frac{4}{5}$ respectively. Find the probability that only Kebba will hit the target.

   1. A.$\frac{2}{5}$
   2. B.$\frac{7}{60}$
   3. C.$\frac{1}{30}$
   4. D.$\frac{1}{60}$

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   Answer: C. $\frac{1}{30}$

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9. 9.

   A letter is selected from the letters of the English alphabet. What is the probability that the letter selected is from the word MATHEMATICS?

   1. A.$\frac{9}{13}$
   2. B.$\frac{11}{26}$
   3. C.$\frac{4}{13}$
   4. D.$\frac{1}{26}$

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   Answer: C. $\frac{4}{13}$

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10. 10.

    Simplify: $\frac{3x - y}{xy} - \frac{2x + 3y}{2xy} + \frac{1}{2}$

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

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    Answer: D. $\frac{4x - 5y + xy}{2xy}$

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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.

    Find the value of p if $\frac{1}{4}$p + 3q = 10 and 2p - $\frac{1}{3}$q = 7

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

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    Answer: A. 4

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13. 13.

    The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 53, 54, 58, 59, 60, 61, 63, 65, 67, 70, 73, 75. Find the third quartile.

    1. A.62
    2. B.63
    3. C.64
    4. D.65

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    Answer: C. 64

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

15. 15.

    The area of a rhombus is 110 cm$^2$. If the diagonals are 20 cm and (2x + 1) cm long, find the value of x.

    1. A.5.0
    2. B.4.0
    3. C.3.0
    4. D.2.5

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    Answer: A. 5.0

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16. 16.

    If {X: 2 d- x d- 19; X integer} and 7 + x = 4 (mod 9), find the highest value of x

    1. A.2
    2. B.5
    3. C.15
    4. D.18

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    Answer: C. 15

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17. 17.

    Make K the subject of the relation T = $\sqrt{\frac{TK - H}{K - H}}$

    1. A.K = $\frac{H(T^2 - 1)}{T^2 - T}$
    2. B.K = $\frac{HT}{(T - 1)^2}$
    3. C.K = $\frac{H(T^2 + 1)}{T}$
    4. D.K = $\frac{H(T - 1)}{T}$

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    Answer: A. K = $\frac{H(T^2 - 1)}{T^2 - T}$

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18. 18.

    Factorize completely: 6ax - 12by - 9ay + 8bx

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

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    Answer: B. (3a + 4b)(2x - 3y)

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19. 19.

    Find the 7th term of the sequence: 2, 5, 10, 17, 26,...

    1. A.37
    2. B.48
    3. C.50
    4. D.63

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    Answer: C. 50

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20. 20.

    If m = 4, n = 9 and r = 16., evaluate $\frac{m}{n}$ - 1$\frac{7}{9}$ + $\frac{n}{r}$

    1. A.1$\frac{5}{16}$
    2. B.1$\frac{1}{16}$
    3. C.$\frac{5}{16}$
    4. D.- $\frac{37}{48}$

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    Answer: D. - $\frac{37}{48}$

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

22. 22.

    In a circle radius rcm, a chord 16$\sqrt{3}cm$ long is 10cmfrom the centre of the circle. Find, correct to the nearest cm, the value of r

    1. A.22cm
    2. B.17cm
    3. C.16cm
    4. D.15cm

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    Answer: B. 17cm

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

24. 24.

    Which of the following is used to determine the mode of a grouped data?

    1. A.Bar chart
    2. B.Frequency polygon
    3. C.Ogive
    4. D.Histogram

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    Answer: D. Histogram

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25. 25.

    Find the equation whose roots are $\frac{3}{4}$ and -4

    1. A.4x2 - 13x + 12 = 0
    2. B.4x2 - 13x - 12 = 0
    3. C.4x2 + 13x - 12 = 0
    4. D.4x2 + 13x + 12 = 0

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    Answer: C. 4x2 + 13x - 12 = 0

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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.

    Adding 42 to a given positive number gives the same result as squaring the number. Find the number

    1. A.14
    2. B.13
    3. C.7
    4. D.6

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    Answer: C. 7

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28. 28.

    The sum 11011$_2$, 11111$_2$ and 10000$_2$ is 10m10n0$_2$. Find the value of m and n.

    1. A.m = 0, n = 0
    2. B.m = 1, n = 0
    3. C.m = 0, n = 1
    4. D.m = 1, n = 1

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    Answer: C. m = 0, n = 1

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

30. 30.

    Calculate the mean deviation of 5, 3, 0, 7, 2, 1

    1. A.0.0
    2. B.2.0
    3. C.2.5
    4. D.3.0

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    Answer: B. 2.0

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31. 31.

    Score 0 - 4 5 - 9 10 - 14 Frequency 2 1 2 The table shows the distribution of the scores of some students in a test. Calculate the mean scores.

    1. A.5.6
    2. B.6.2
    3. C.6.6
    4. D.7.0

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    Answer: D. 7.0

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32. 32.

    If $\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1$, find the value of x.

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

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

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33. 33.

    A trader bought 100 oranges at 5 for N40.00 and sold them at 20 for N120.00. Find the profit or loss percent

    1. A.20% profit
    2. B.20% loss
    3. C.25% profit
    4. D.25% loss

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    Answer: D. 25% loss

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34. 34.

    A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is$0.075 to N1.00, how much did the engine cost in Naira?

    1. A.N250,000.00
    2. B.N200,000.00
    3. C.N150,000.00
    4. D.N100,000.00

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    Answer: B. N200,000.00

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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.

    PQRS is a square. If x is the midpoint of PQ, calculate correct to the nearest degree, <PXS.

    1. A.53o
    2. B.55o
    3. C.63o
    4. D.65o

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    Answer: C. 63o

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37. 37.

    The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 72 students

    1. A.32o
    2. B.45o
    3. C.60o
    4. D.75o

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    Answer: A. 32o

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38. 38.

    Tom will be 25 years old in n years' time. If he is 5 years younger than Bade, find Bade's present age.

    1. A.(30 - n)years
    2. B.(20 - n)years
    3. C.(25 - n)years
    4. D.(30 + n)years

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    Answer: A. (30 - n)years

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

40. 40.

    Two angles of a pentagon are in the ratio 2:3. The others are 60o each. Calculate the smaller of the two angles

    1. A.72o
    2. B.100o
    3. C.120o
    4. D.144o

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    Answer: D. 144o

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41. 41.

    If $\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3}}$ is simplified as m + n$\sqrt{6}$, find the value of (m + n)

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

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

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

43. 43.

    Given that logx 64 = 3, evaluate x log$_2$8

    1. A.6
    2. B.9
    3. C.12
    4. D.24

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    Answer: C. 12

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44. 44.

    The angle of elevation of an aircraft from a point K on the horizontal ground 30$\alpha$. If the aircraft is 800m above the ground, how far is it from K?

    1. A.400.00m
    2. B.692.82m
    3. C.923.76m
    4. D.1,600.00m

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    Answer: D. 1,600.00m

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45. 45.

    Ada draws the graph of y = x2 - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?

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

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    Answer: B. x2 - 3x - 1 = 0

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