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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2017

Objectives



1. Express 0.0000407, correct to 2 significant figures.

A. 0.0

B.0.00004

C. 0.000041

D. 0.0000407


2. If x varies inversely as y and y varies directly as z, what is the relationship between x and z?

A. x a z.

B. x a ½

C. x a z2

D. x a ½2​







4. Fig 1 Fig 2 Fig. 1 and Fig. 2 are the addition and multiplication tables respectively in modulo 5. Use these tables to solve the equation (n©4)© 3 = 0 (mod 5)

A-1

B.2

C3

D.4


5. 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?

A. 1:4

B. 1 :5

C. 2:5

D. 5:2


ANSWERS

6. lf M = (x:3 ≤ x < 8}and N = {x:8 < x ≤ 12} Which of the following is true?

I. 8⋲ M⋂N II. 8⋲ M⋃N III. M⋂N = 0

A. III only

B.I and II only

C. Hand III only

D.I, II and III


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

A. a + b + 1

B. ab – 1

C. a – b + 1

D. b – a + 1


8. If x = 2/3 and y = 6, evaluate xy – y/x

A. 0

B. 5

C. 8

D. 9


9. Solve the equation 1/5x + 1/x = 3

A. 1/5

B. 2/5

C. 3/5

D. 4/5


10. A sum of N18,100.00 was shared among 5 boys and r girls with each boy taking N20.00 more than each girl, find a boy’s share.

A. N1,820.00

B. N2,000.00

C. N2,020.00

D. N2,040.00


ANSWERS

11. One factor of 7x2 + 33x – 10 is

A. 7X + 5

B. x – 2

C. 7x – 2

D. x – 5


12. Solve the equation: - 1/4 < 3/4 (3x -2) < 1/2

A. 5/9 < x < 8/9

B. - 8/9 < x < 7/9

C. - 8/9 < x < 5/9

D. - 7/9 < x < 8/9


13. Simplify: 3x – (p – x) – (r – p)

A. 2x – r

B. 2x + r

C. 4x – r

D. 2x – 2p-r


14. An arc of a circle of radius 7.5 cm is 7.5 cm long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take π = 22/7]

A. 29o

B. 57°

C. 65°

D. 115°


15. Water flows out of a pipe at a rate of 40π cm3 per second into an empty cylindrical container of base radius 4 cm Find the height of water in the container after 4 second.

A. 10 cm

B. 14 cm

C 16 cm

D. 20 cm


ANSWERS

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

A. 4.55 liters

B. 7.50 liters

C. 8.10 liters

D. 9.55 Liters


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

A. 3.0 cm

B. 4.5 cm

C 5.0 cm

D. 9.0 cm


18. Which of the following is true about parallelograms?

A. Opposite angles are supplementary

B. Opposite angles are complementary

C. Opposite angles are equal

D. Opposite angle are reflex angels


19. The diagram shows a circle centre 0. If ∠STR = 29° and ∠RST = 46o. calculation value of of STO







20. In the diagram, XY is a straight line, ∠POX = ∠POQ and ∠ROY = ∠QOR, find the value of ∠POQ + ∠ROY

A. 60°

B. 90 0

C. 100O

D. 120°


ANSWERS



21. The diagram shows a circle centre O. If ∠ZYW = 330, find ∠ZWX

A. 330

B. 570

C. 900

D. 1000





22. In the diagram, PQ and PS are tangents to the circle centre O. If ∠PSO = m, ∠SPQ = n and ∠SQR = 33°, find the value of (m + n)

A. 103°

B. 123°

C. 133°

D. 143°


23. Calculate the gradient (slope) of the line joining point(-1,1) and (2,-2).

A. -1

B.- ½

C. 1/2

D. 1


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

A. 6 units

B. 5 units

C.4 units

D. 2 units


25. A bearing of 320° expressed as a compass bearing is

A. N 50° W

B. N40°W

C. N50°E

D. N 40° E


ANSWERS

26. Given that cos 30° = sin 60° = 2 and sin 30° = cos 60° = 1/2, evaluate tan 60° -1/1 - tan 30°

A. √3-2

B. 2 √ - 3

C. √3

D. - 2


27. A stationary boat is observed from a height of 1 00 m. If the horizontal distance between the observer and the boat is 80 m, calculate, correct to two decimal places, the angle of depression of the boat from the point of observation.

A. 36.87°

B. 39.70°

C. 51.34°

D. 53.13°


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

A. 10.1 Years

B. 9.3 years

C. 0 8.7 years

D. 8.3 years





29. The bar chart shows the statistics of the number of passes and failures in an examination in a school from 2001 to 2004. What is the ratio of the total number of passes to the total number of failures?

A. 60:13

B. 10:3

C. 5:1

D. 40:13


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. Use this information to answer questions 30 and 31.


30. Find the median of the distribution

A. 4

B. 3

C. 2

D. 1


ANSWERS

31. Find the first quartile

A. 1.0

B. 1.5

C.2.0

D. 2.5


32. 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 offers Chemistry only

A. 2/9

B. 4/9

C. 5/9

D. 7/9


33. In what number base was the addiction 1+ m = 100 where n > 0, done?

A. n – 1

B. n

C. n + 1

D. n - 2


34. Simplify: √2 (√6 + 2 √2) - 2 √3

A. 4

B. 3 + 4

C. 4 √2

D. 4 √3 + 4


35. Three exterior angles of a polygon are 300, 400 and 600. If the remaining exterior angles are 460 each, name the polygon.

A. Decagon

B. Nonagon

C. Octagon

D. Hexagon


ANSWERS



36. In the diagram NQ/TS, ∠RTS = 500 and ∠PRT = 1000. Find the value of ∠NPR.

A. 1100

B. 1300

C. 1400

D. 1500


37. Simplify the expression (a2b4 - b2a4) / (ab(a + b))

A. a2 - b2

B. b2 - a2

C. a2b - ab2

D. ab2 - a2b


38. Find the 6th term of the sequence 2/3 , 7/15 , 4/15

A. - 1/3

B. - l3/5

C. 1/15

D. 1/5


39. The diagonal of a square is 60 cm. Calculate its perimeter

A. 20√ 2

B. 40√2

C. 90√ 2

D. 120√ 2


40. The roots of a quadratic equation are – ½ and 2/3. Find the equation

A. 6x2 - x + 2 = 0

B. 6x2 - x - 2 = 0

C. 6x2 + x – 2 = 0

D. 6x2 + x + 2 = 0


ANSWERS



42. Consider the statements: p: it is hot q : it is raining. Which of the follow symbols correctly represents the statement "it is raining if and only if it is cold?

A. p⇔ ∼ q

B. q ⇔ p

C. ∼p ⇔ ∼ q

D. ⇔ ∼ p


43. Given that t = 2- *, find 2*+1 in term of t

A. 2/t

B. t/6

C. 1/2t

D. 2t





44. Find the value of m in the diagram

A. 72°

B.68°

C.44°

D. 34°


45. Two bottle 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?

A. 2/1

B. 1/2

C. 2/9

D.3/8


ANSWERS

46. If the simple interest on a certain amount of money saved in a bank for 5 years at 21/2 % per annum is N500.00, calculate the total amount due after 6 years at the same rate.

A. N 2,500.00

B. N 2,600.00

C. N 4,500.00

D. N 4,600.00


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

A. 2.2

B. 3.4

C.4.0

D.4.2.


48. A circular pond of radius 4 m has a path of width 2.5 m round it. Find, correct to two decimal places, the area of the path. [Take π = 22/7]

A. 7.83 m2

B. 32.29 m2

C. 50.29 m2

D. 82.50 m2​





49. The graph of y = ax2 + bx + c is shown in the diagram. Find the minimum value of y

A. -2.0

B. -2.1

C. -2.3

D. -2.5





50. In the diagram. RP is a diameter of the circle RSP. RP is produced to T and TS is a tangent to the circle at S. If ∠PRS = 24°, T calculate the value of ∠STR

A. 24°

B.420

C. 48°

D. 66°



WASSCE JUNE 2017 MATHEMATICS OBJECTIVE TEST

ANSWERS

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


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