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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2015

Objectives



1. If {ᵡ:2< 18 ᵡ ƭ integer} and 7 + ᵡ = 4(mod 9), find the highest value of ᵡ

A. 2

B. 5

C. 15

D. 18


2. The sum of 110112’ 111112 and 100002 is 10m 10n02’. Find the values of m and n.

A. m=0,n=02

B. m=l,n=02

C. m=0,n=l

D. m=l,n=l


3. 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?

A. N250, 000.00

B. N200, 000.00

C. 150,000.00

D. N100, 000.00


4. If (〖27〗^x x 3^(1-x))/9^2x = 1, find the value of x.

A. 1

B. ½

C. - ½

D -1


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

A. 37

B. 48

C. 50

D. 63


ANSWERS

6. Given that logx 64=3, evaluate x log28.

A. 6

B. 9

C. 12

D. 24


7. If 2n = y, Find 2(2+n/3)

A. 4y1/3

B.4y-3

C. 2y1/3

D. 2y-3


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

A. (2a–3b)(4x+y)

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

C. (3a–4b)(2x+3y)

D. (2a+3b)(4x–3y)


9. Find the equation whose roots are ¾ and - 4.

A. 4x2 – 13x + 12=0

B. 4x2 – 13x – 12=0

C. 4x2 + 13x – 12=0

D. 4x2 – 13x + 12=0


10. If m=4, n=9 and r=16, evaluate m/n – ⁡〖1 7/9+ 〗 ⁡〖n/r〗 A. 1


ANSWERS

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

A. 14

B. 13

C. 7

D. 6


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

A. x2 – x – 30 = 0

B. x2–3x–1=0

C. x2 3x–3=0

D. x2+3x–1=0


13. The volume of a cone of height 3 cm is 38½ cm3. Find the radius of its base. [Take x = ᴫ 22 7


14. A sector of a circle with radius 6cm subtends an angle of 600 at the centre. Calculate its perimeter in terms of ᴫ

A. 2(ᴫ+6)cm

B. 2(ᴫ+3)cm

C. 2(ᴫ + 2)cm

D. (ᴫ+12)cm


15. The dimensions of a rectangular tank are 2 m by 7 m by 11 m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take = ᴫ 22 ]

A. 14m

B. 7m

C. 3 1/2m

D. 1 3/4 m.


ANSWERS

16. In the diagram, 0 is the centre of the circle. If PQ// RS and < 1400, find the size of < POM,

A. 400

B. 500

C. 600

D. 800.





17. In the diagram, PTR is a tangent to the circle centre 0. If angle TON = 1080, calculate the size of angle PTN.

A. 1320

B. 1200

C. 1080

D. 1020.





18. In the diagram, PQ/RT,QR,SU, < PQR 480 and < RTS x. find the value of x.

A. 1340

B. 1320

C. 960

D. 480





19. In the diagram, 0 is the centre of the circle, RT is a diameter, < PQT 330 and < TQS 760 . Use the diagram to answer questions 19 and 20.

A. 730

B. 670

C. 570

D. 370





20. Find the size of angle PRS.

A. 760

B710

C. 380

D. 330


ANSWERS



Use it to answer questions 21 and 22


21. Find the gradient of the line.

A. 1

B. 2

C. 3

D. 4


22. What is the value of y when x =2?

A. 5

B. 7

C. 9

D. 11





24. PQRS is a square. If X is the midpoint of PQ, calculate, correct to the nearest degree, ZPX.

A. 530

B. 550

C. 630

D. 650


25. The angle of elevation of an aircraft from a point K on the horizontal ground is 300 if the aircraft is 800m above the ground, how far is it from K?

A. 400.00m

B. 692.82m

C. 923.76m

D. 1,600.00m


ANSWERS

26. 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.

A. 320

B. 450

C. 600

D. 750


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

A. 62

B. 63

C. 64

D. 65



28





The table shows the distribution of the scores of some students in test. Calculate the mean score.

A. 5.6

B. 6.2

C. 6.6

D. 7.0


29. The probabilities that Kebba, Ebou and Omar will hit a target are 2/5, 3/4 and 4/5 respectively. Find the probability that only Kebba will hit the target.

A. 2/5

B. 7/60

C. 1/30

D. 1/60





30. In the diagram. VW//YZ,/WX/ = 6cm, /XY/ = 16CM,/YZ/ = 20cm and /ZY/ = 12cm. Calculate /VX/

A. 3cm

B. 4cm

C. 6cm

D. 8cm


ANSWERS

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

A. (30 – n) years

B. (20 – n) years

C. (25 – n) years

D. (30 + n) years.


32. If (√(2 ) + √3)/√3 is simplified as m + n√6, find the value of (m + n)

A. 1⁄3

B. 2⁄3

C. 1 1⁄3

D. 1 2⁄3





33. In the diagram above, QT and PR are straight lines, < ROS = (3n-200). < POT = 2m, < SOT = n, < POL = m and < QOL is a right angle. Find the value of n.

A. 350

B. 400

C. 550

D. 600



34. Make k the subject of the relation T = (Tk -H )/(k - H)

A. K = H(T²-1)/(T²-T)

B. K= HT/((T-1)²)

C. K= H(T²-1)/T

D. K= H(T-1)/T


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

A. bar chart

B. frequency polygon

C. Ogive

D. Histogram


ANSWERS

36. The area of a rhombus is 110cm2. If the diagonals are 20cm and (2x+1) cm long, find the value of x.

A. 5.0

B. 4.0

C. 3.0

D. 2.5







39. A farmer uses 2/5 of his land to grow cassava, 1/3 of the remainder for yam and the rest for maize. Find the part.

A. 2/15

B. 2/5

C. 4/5


40. 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?

A. 221/2 km

B. 30 km

C. 333/4 km

D. 45 km


ANSWERS

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

A. 20% profit

B. 20% loss

C. 25% profit

D. 25% loss





42. Describe the shaded portion in the diagram.

A. P’nQnR’

B. (PnR)’nQ

C. P’nQnR

D. (PuQ)’nR.


43. Find the value of p if. 1/4p+ 3q =10 and 2p – 1/3q =7.

A. 4

B. 3

C. – 3

D. – 4


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

A. 0.0

B. 2.0

C. 2.5

D. 3.0





45. In the diagram, the shaded part is a carpet laid in a room with dimensions 3.5m by 2.2m leaving a margin of 0.5m round it. Find the area of the margin.

A. 4.7m2

B. 4.9m2

C. 5.7m2

D. 5.9m2


ANSWERS

46. Two angles of a pentagon are in the ration 2.3. The others are 600 each. Calculate the smaller of the two angles.

A. 720

B. 1000

C. 1200

D. 1440


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

A. 9/13

B. 11/26

C. 4/13

D. 1/26


48. In a circle radius r cm, a chord 16√3 cm long is 10 cm from the centre of the circle. Find, correct to the nearest cm, the value of r.

A. 22cm

B. 17cm

C. 16cm

D. 15cm


49. Consider the following statements:

X: Locally manufactured tyres are attractive.

Y: Many locally manufactured tyres do not last long.

Denoting locally manufactured tyres by M, attractive tyres by R and long-lasting Tyres by L, which of these Venn diagrams below illustrates the statements? A. B. C. D. In the diagram, OX bisects







50. In the diagram above, OX bisects < YXZ= 680, calculate the ‘value of < XOZ.

A. 680

B. 720

C. 1120

D. 1240



WASSCE 2015 MATHEMATICS OBJECTIVE TEST

ANSWERS

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


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