2013 WAEC (WASSCE) Mathematics Past Questions

Questions

1. 1.

   If 9(2 - x) = 3, find x

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

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

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2. 2.

   When a number is subtracted from 2, the result equals 4 less than one-fifth of the number. Find the number

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

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   Answer: C. 5

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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.

   Simplify: $\frac{x^2 - y^2}{(x + y)^2} \div \frac{(x - y)^2}{(3x + 3y)}$

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

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   Answer: C. $\frac{3}{x - y}$

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5. 5.

   If 2 log x (3$\frac{3}{8}$) = 6, find the value of x

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

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

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

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

8. 8.

   A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume

   1. A.322m3
   2. B.448m3
   3. C.632m2
   4. D.840m2

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   Answer: B. 448m3

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9. 9.

   Which of the following is not a probability of Mary scoring 85% in a mathematics test?

   1. A.0.15
   2. B.0.57
   3. C.0.94
   4. D.1.01

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   Answer: D. 1.01

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10. 10.

    If Un = n(n2 + 1), evaluate U5 - U4

    1. A.18
    2. B.56
    3. C.62
    4. D.80

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    Answer: C. 62

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11. 11.

    The bearing of Y from X is 060º and the bearing of Z from Y = 060º. Find the bearing of X from Z

    1. A.300o
    2. B.240o
    3. C.180o
    4. D.120o

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    Answer: B. 240o

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12. 12.

    In what number base is the addition 465 + 24 + 225 = 1050?

    1. A.ten
    2. B.nine
    3. C.eight
    4. D.seven

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    Answer: D. seven

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

14. 14.

    The graph of the relation y = x2 + 2x + k passes through the point (2, 0). Find the values of k

    1. A.zero
    2. B.-2
    3. C.-4
    4. D.-8

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    Answer: D. -8

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

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

17. 17.

    The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used

    1. A.1: 1,000,000
    2. B.1: 500,000
    3. C.1: 100,000
    4. D.1: 10,000

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    Answer: A. 1: 1,000,000

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18. 18.

    Four oranges sell for Nx and three mangoes sell for Ny. Olu bought 24 oranges and 12 mangoes. How much did he pay in terms of x and y?

    1. A.N94x + 6y)
    2. B.N(6x + 4y)
    3. C.N(24x + 12y)
    4. D.N(12x + 24y)

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    Answer: B. N(6x + 4y)

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19. 19.

    A sales boy gave a change of N68 instead of N72. Calculate his percentage error

    1. A.4%
    2. B.5$\frac{5}{9}$%
    3. C.5$\frac{15}{17}$%
    4. D.7%

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    Answer: B. 5$\frac{5}{9}$%

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20. 20.

    Find the values of k in the equation 6k2 = 5k + 6

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

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    Answer: B. {$\frac{-2}{3}, \frac{3}{2}$}

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21. 21.

    A cube and cuboid have the same base area. The volume of the cube is 64cm$^3$ while that of the cuboid is 80cm$^3$. Find the height of the cuboid

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

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    Answer: C. 5cm

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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.

    Using the venn diagram, find n(x $\cap$ y1)

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

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    Answer: B. 3

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25. 25.

    Given that (x + 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M

    1. A.(x + 2)2
    2. B.x(x + 2)
    3. C.xv + 2
    4. D.x2 - x

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    Answer: D. x2 - x

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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.

    If y varies directly as the square root of (x + 1) and y = 6 when x = 3, find x when y = 9

    1. A.8
    2. B.7
    3. C.6
    4. D.5

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    Answer: A. 8

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28. 28.

    Solve the inequality: $\frac{2x - 5}{2} < (2 - x)$

    1. A.x > 0
    2. B.x < $\frac{1}{4}$
    3. C.x > 2$\frac{1}{2}$
    4. D.x < 2$\frac{1}{4}$

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    Answer: D. x < 2$\frac{1}{4}$

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29. 29.

    If $\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}$, find K

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

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    Answer: D. 2

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30. 30.

    If p = (y : 2y $\geq$ 6) and Q = (y : y -3 $\leq$ 4), where y is an integer, find p$\cap$Q

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

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    Answer: C. {3, 4, 5, 6, 7}

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31. 31.

    Simplify $\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}$

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

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

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32. 32.

    If x = 64 and y = 27, evaluate: $\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}$

    1. A.2$\frac{1}{5}$
    2. B.1
    3. C.$\frac{5}{11}$
    4. D.$\frac{11}{43}$

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    Answer: C. $\frac{5}{11}$

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33. 33.

    If $\frac{1}{2}$x + 2y = 3  and $\frac{3}{2}$x - 2y = 1, find (x + y)

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

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    Answer: A. 3

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34. 34.

    An object is 6m away from the base of a mast. The angle of depression of the object from the top pf the mast is 50o, Find, correct to 2 decimal places, the height of the mast

    1. A.8.60m
    2. B.7.51m
    3. C.7.15m
    4. D.1.19m

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    Answer: C. 7.15m

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35. 35.

    Express $\frac{2}{x + 3} - \frac{1}{x - 2}$ as a simple fraction

    1. A.$\frac{x - 7}{x^2 + x - 6}$
    2. B.$\frac{x - 1}{x^2 + x - 6}$
    3. C.$\frac{x - 2}{x^2 + x - 6}$
    4. D.$\frac{x - 27}{x^2 + x - 6}$

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    Answer: A. $\frac{x - 7}{x^2 + x - 6}$

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36. 36.

    A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord

    1. A.2$\sqrt{21}$cm
    2. B.$\sqrt{42}$cm
    3. C.2$\sqrt{19}$cm
    4. D.$\sqrt{21}$cm

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    Answer: A. 2$\sqrt{21}$cm

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37. 37.

    An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?

    1. A.15
    2. B.12
    3. C.9
    4. D.6

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    Answer: B. 12

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38. 38.

    What is the locus of the point X which moves relative to two fixed points P and M on a plane such that < PXM = 30o

    1. A.thebisector of the straight line joining P and M
    2. B.an arc of a circle with PM as a chord
    3. C.the bisector of angle PXM
    4. D.a circle centre X and radius PM

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    Answer: B. an arc of a circle with PM as a chord

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39. 39.

    Given that P = x2 + 4x - 2, Q = 2x - 1 and Q - p = 2, find x

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

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    Answer: B. -1

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40. 40.

    The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole number, the volume of the cone. ( Take $\pi = \frac{22}{7}$)

    1. A.48cm3
    2. B.47cm3
    3. C.38cm3
    4. D.12cm3

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    Answer: C. 38cm3

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41. 41.

    An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. calculate the arc of the sector (Take $\pi = \frac{22}{7}$)

    1. A.8800cm2
    2. B.8448cm2
    3. C.4400cm2
    4. D.4224cm2

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    Answer: A. 8800cm2

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42. 42.

    Multiply 2.7 x 10-4 by 6.3 x 106 and leave your answers in standard form

    1. A.1.7 x 103
    2. B.1.70 x 103
    3. C.1.701 x 103
    4. D.17.01 x 103

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    Answer: C. 1.701 x 103

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43. 43.

    The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. What percentage of the total number of textbooks belongs to science?

    1. A.12$\frac{1}{2}$%
    2. B.$\frac{205}{6}$%
    3. C.25%
    4. D.$\frac{412}{3}$%

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    Answer: A. 12$\frac{1}{2}$%

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45. 45.

    Given that $p^{\frac{1}{3}}$ = $\frac{\sqrt[3]{q}}{r}$, make q the subject of the equation

    1. A.q = p$\sqrt{r}$
    2. B.q = p3r
    3. C.q = pr3
    4. D.q = pr$\frac{1}{3}$

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    Answer: C. q = pr3

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46. 46.

    In the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?

    1. A.$\bigtriangleup$ ZYX = $\bigtriangleup$ OMN
    2. B.$\bigtriangleup$ YZX = $\bigtriangleup$ NOM
    3. C.$\bigtriangleup$ ZXY= $\bigtriangleup$ MON
    4. D.$\bigtriangleup$ XYZ= $\bigtriangleup$ NOM

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    Answer: D. $\bigtriangleup$ XYZ= $\bigtriangleup$ NOM

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47. 47.

    If sin x = $\frac{5}{13}$ and 0o $\leq$ x $\leq$ 90o, find the value of (cos x - tan x)

    1. A.$\frac{7}{13}$
    2. B.$\frac{12}{13}$
    3. C.$\frac{79}{156}$
    4. D.$\frac{209}{156}$

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    Answer: C. $\frac{79}{156}$

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48. 48.

    The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. How many textbooks are for the technical class?

    1. A.100
    2. B.150
    3. C.200
    4. D.250

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    Answer: B. 150

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