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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2018

Objectives



1. Simplify: √108 + √l25 - √ 75

(a) √3 + 5 √5

(b) 6√5 - 5√5

(c) 6√3 + √2

(d) 6√3 - √2


2. Evaluate: (641/2 + 1251/3)2

(a) 121

(b) 144

(c) 169

(d) 196


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

(a) yx2 = 300

(b) yx2 = 900

(c) y = 100x

(d) y = 900x2 / 9


4. Find the value of x for which 32four = 22x

(a) three

(b) five

(c) six

(d) seven


5. Simplify: 21/4 x 31/2 ÷ 43/8

(a) 5/9

(b) 11/5

(c) 11/4

(d) 14/5​


ANSWERS

6. 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?

(a) 40.0%

(b) 42.2%

(c) 50.0%

(d) 52.5%


7. If log10 (6x - 4) - log102 = 1, solve for x.

(a) 2

(b) 3

(c) 4

(d) 5


8. If F = 9/5 C + 32, find C when F = 98.6.

(a) 30

(b) 37

(c) 39

(d) 41


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

(a) 3

(b) 2

(c) 1

(d) -1


10. If x:y:z = 2 : 3 : 4, evaluate 9x + 3y/6z – 2y

(a) 11/2

(b) 2

(c) 21/2

(d)3


ANSWERS

11. Simplify: 2-18m2 / 1 + 3m

(a) 2 (1 + 3m)

(b) 2(2 + 3m2)

(c) 2(1 -3m)

(d) 2(1 - 3m2)


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

(a) y = x2-5x-6

(b) ) y = x2+5x-6

(c) y = x2 + x-6

(d) y = x2-x-6


13. The volume of a cylindrical tank, 10m high is 385m3. Find the diameter of the 22 tank. [ Take n = 7 ]

(a) 14m

(b) 10m

(c) 7m

(d) 5m


14. The surface area of a sphere is — 792/7 cm2-. Find, correct to the nearest whole number, its volume. [ Take rr = 22/7 ]

(a) 113cm3

(b) 131cm3

(c) 311cm3

(d)414cm3


15. 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 n = 22/7 ]

(a) 170°

(b) 177°

(c)182°

(d) 192°


ANSWERS



16. In the diagram, which of the following Ratios is equal |PN|/|PQ|

(a) |PN|/|PR|

b |PM|/|PQ|

c |PM|/|PR|

d |PR|/|PQ|





17. In the diagram PS and RS are tangents to the circle centre O. < PSR = 700 , <POR = m and

< PQR = n, Find (m+n)

(a) 110°

(b) 135°

(c) 165°

(d) 225°





Find the value of t in the diagram

(a) 110°

(b) 135°

(c) 165°

(d) 225°





In the diagram, PR is a tangent to the circle at Q, QT//RS, < SQR = 35° and < RSQ = 50°. Find the value of < QST

(a) 40°

(b) 65°

(c) 85°

(d) 95°


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

(a) 45°

(b) 84°

(c) 85°

(d) 95°


ANSWERS

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

(a) 8 units

(b) 11 units

(c) 15 units

(d) 17 units


22. 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.

(a) 1

(b) 2

(c) 3

(d) 9


23 The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground at the foot of the tree is 300. Find the height of the tree,

(a) 27m

(b) 13.5 √3m

(c) 13.5 √2M

(d) 9√3m 4


24. If tan x = 4/3 0° < x < 90°, find the value of sin x - cos x.

(a) 1/10

(b) 1/5

(c) 5/12

(d) 12/5


25. Given that Y is 20m on a bearing of 300° from X. how far south of Y is X?

(a) 10m

(b) 15m

(c) 25m

(d) 30m


ANSWERS

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

(a) 2

(b) 4

(c) 6

(d) 8


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

(a) 0.0

(b) 0.5

(c) 1.0

(d) 1.5


Number of goals 1 2 3 4 5 6 7

Number of teams 3 1 6 6 4 2 3


The table shows the distribution of goals scored by 25 teams in a football competition.

Use it to answer questions 28 and 29.


28. Calculate the probability that a team selected at random scored at most 3 goals. 3 1 4 2

(a) 3/25

(b) 1/5

(c) 4/25

(d) 2/5


29. Find the probability that a team selected at random scored either 4 or 7 goals.

(a) 9/25

(b) 11/25

(c) 2/5

(d) 18/25





In the diagram, WXYZ is a rectangle with dimension 8cm by 6cm. P, Q, R and S are the midpoints of the sides of the rectangle as shown. Use this information to answer questions 30 and 31.


30. What type of quadrilateral is the shaded region?

(a) Trapezium

(b) Prism

(c) Rectangle

(d) Rhombus


ANSWERS

31. Calculate the area of the part of the rectangle that is not shaded.

(a) 25cm2

(b) 24cm2

(c) 16cm2

(d) 12cm2


32. The total surface area of a hemisphere is 75ncm2. Find the radius.

(a) 5.0cm

(b) 7.0cm

(c) 8.5cm

(d) 12.0cm


33. Find the value of x for which x - 5/x(x – 1) is undefined.

(a) 0 or 5

(b) -5 or 5

(c) -1 or 5

(d) 0 or 1


34. Solved the equation 2x2 - x - 6 = 0.

(a) x = -3/2 or 2

(b) x = -2 or 2

(c) x = -3 or 2

(d) x = 3 or -2


35. Factories completely the expression (x + 2)2 - (2x + 1 )2.

(a) (3x + 2)(1 - x)

(b) (3x + 2)(2x + 1)

(c) 3(x + 2)2

(d) 3(x + 1)(1 -x)


ANSWERS

36. Find the nth term of the sequence 2 x 3, 4 x 6,8 x 9, 16 x 12....

(a) 2n x 3(n + 1)

(b) 2n x 3n

(c) 2n x 3n

(d) 2n x 3n-1


37. If 3x0 4 (mod 5), find the least value of x.

(a) 1

(b) 2

(c) 3

(d) 4





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

(a) If p is true and q is true

(b) If p is true and q is false

(c) If p is false and q is false

(d) If p is false and q is true





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.

(a) 90°

(b) 60°

(c) 45°

(d) 30l!


ANSWERS

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

(a) 6

(b) 7

(c) 8

(d) 9


42. Donations during the launching of a church project were sent in sealed envelopes. The table shows the distribution of the amount of money in the envelope

NO. OF ENVELOPS -:4 -----:7 --:20 ---:9 --:4 ---:5 -:5 :1 :2

AMOUNT (N) -------: 5000 2000 1000 700 500 100 50 2 10


How much was the total donation?

(a) N26.792.00

(b) N26, 972.00

(c) N62, 792.00

(d)-N 62,972.00





43 In the diagram, PQ is a straight line, (m +n) = 110°, (n + r) = 130°and (m + r) = 120°. Find the ratio of m : n : r.

(a) 2:3:4

(b) 3:4:5

(c) 4:5:6

(d) 5:6:7


44. If x:y = 1/4 : 3/8 and y : z = 1/3 : 4/9 , find x:z.

(a) 2:3

(b) 3:4

(c) 3:8

(d) 1:2


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

(a) 8

(b) 9

(c) 10

(d) 12


ANSWERS

46. 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(MnN)'.

(a) 18

(b) 20

(c) 30

(d) 38


47. Expression 0.612 in the form x/y, where x and y are integers and y ≠ 0.

(a) 153/250

(b) 68/111

(c) 61/100

(d) 21/33





(a) x = 240° - y - z

(b) x =180° - y - z

(c) x = 360° + y - z

(d) x = 360° - y - z


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

(a) 42cm

(b) 48cm

(c) 52cm

(d) 60cm


50. The graphs of y = x2 and y=x intersect at which of these points?

(a) (0,0), (1,1)

(b) (0,0), (0,1)

(c)(1,0),(0,0)

(d) (0,0), (0,0)



WASSCE JUNE 2018 MATHEMATICS OBJECTIVE TEST

ANSWERS

​1. A 2. C 3. B 4. C 5. D 6. D 7. C 8. B 9. A 10. C 11. C 12. C 13. C 14. A 15. B 16. C 17. A 18. C 19. D 20. C 21. D 22. A 23. D 24. B 25. A 26. B 27. C 28. D 29. A 30. D 31. B 32. A 33. D 34. A 35. D 36. B 37. C 38. A 39. B 40. B 41. C 42. D 43. D 44. D 45. B 46. D 47. A 48. D 49. C 50. A


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