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FURTHER MATHEMATICS


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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2019

Objectives



1. Solve: 8x – 2 = 43x

A. -2

B. -1

C.1

D.


2. Evaluate tan 750, leaving the answer in surd form (radicals)

A. √3 + 2

B. √3 + 1

C. √3 - 1

D. √3 - 2


3. Solve. p/2 + k/3 = 5 and 2p – k = 6 simultaneously.

A. p = -6, k = - 6

B. p =-6, k = 6

C. p = 6, k = 6

D. p = 6, k = -6


4. Rationalise: 1/√2+1)

A. √2 - 1

B. 1 - √2

C. √2 -1/ 2


5. If nC2 = 15, find the value of n

A.8

B.7

C.6

D.5


ANSWERS

6. An operation (*) is defined on the set T = { - 1, 0, …,5} by x * y = x + y – xy. Which of the following operation(s) will give an image which is an element of T? I. 2(*)5 II. 3(*)2 III. 3(*)4

A. I only

B. II only

C. I and III

D. II and III only


7. Given that g: x → 3x and f:x → cosx, find the value of g0 f(200).

A. 0.50

B. 0.94

C. 2.60

D. 2.82


8. A linear transformation is defined by T: (x, y) → (-x + y, -4y). Find the image, Q’, of Q(-3,2) under T.

A. Q’(5, -8)

B. Q’(-8, 5)

C. Q’(5, 3)

D. Q’(-5, -8)


9. If g: r → 5 – 2r, r is a real number, find the image of -3.

A. 13

B. 11

C. -1

D. -9


10. Consider the following statements: p: Birds fly q: The sky is blue r: The grass is green. What is the symbolic representation of “If the grass is green and the sky is not blue, then the birds do not fly”?

A. (r⋀p) ⇒q

B. (r⋀q) ⟹∼p

C. (r⋀∼q) ⟹∼p

D. (r⋀∼p) ⇒∼q


ANSWERS

11. Given that 1/(x - 4) ≡ P/(x-2) + Q/(x-2), x ≠ ± 2 , find the value of (P + Q).

A. 3/2

B. 1

C. 1/2

D. 0


12. Find the sum of the first 20 term of the sequence -7, -3, 1,….

A. 620

B.660

C. 690

D. 1240


13. Find the value of x for which 6(√4x2 +1) = 13x, where x > 0.

A. 6/5

B. 25/24

C. 24/25

D. 5/6


14. Calculate the distance between points (-2, -5) and (-1 3).

A. √5 units

B. √17 units

C. √65 units

D. √73 units




ANSWERS

16. The second and fourth terms of an exponential sequence (G.P) are 2/9 and 8/81 respectively. Find the sixth term sequence.

A. 81/32

B. 9/8

C. 1/4

D. 32/729


17. Points X and Y are on the same horizontal base as the foot of a building such that X is 96cm due east of the building and Y is due west. If the angle of elevation of the top of the building from X is 300 and that of Y is 600, calculate the distance of Y from the base of the building.

A. 30m

B. 32m

C. 42m

D. 50m





19. If the mean of 2, 5, (x + 1), (x + 2), 7 and 9 is 6, find the median.

A. 6.5

B. 6.0

C. 5.5

D. 5.0


20. Calculate the mean deviation of 5, 8, 2, 9 and 6

A. 5

B. 4

C. 3

D.2


ANSWERS

A particles starts from rest and moves in a straight line such that its velocity, Vms-1, at time t seconds is given by V = 3t2 – 6t

Use the information to answer question 21 and 22


21. Calculate the distance in 4 seconds.

A. 12m

B. 16m

C. 64m

D. 96m


22. Calculate the acceleration in the 3rd second.

A. 0ms-2

B. 3ms-2

C. 6ms-2

D. 9ms-2


23. Find the constant term in the binomial expansion of (2x2 1/x2 )

A.10

B.12

C.24

D.42





24. Which of these inequalities is represented by the shaded portion of the graph?

A. 2y + x < 0

B. 2y – x – 3 < 0

C. 2y – x + 3 < 0

D. 2y + x + 3 < 0


25. A 35N force acts on a body of mass 5kg for 2 seconds. Calculate the change in momentum of the body.

A. 70kgms-1

B. 55kgms-1

C. 50kgms-1

D. 35kgms-1


ANSWERS

26. Solve, correct to three significant figures, (0.3)x = (0.5)8.

A. 4.61

B. 4.606

C. 0.461

D. 0.0130


27. Given that P and Q are two non – empty subsets of the universal set, U. find P∩(Q∪QI) A. P

B. PI

C.Q

D.QI


28. Find the coefficient of the third term in the binomial expansion of (2x + 3y/4 )3 In descending power of x.

A. 27/64(y2 )

B. 27/8(y2 )

C. 8y2

D.9y2


29. Find the coordinates of the centre of the circle 3x2 + 3y2- 6x + 9y – 5 = 0

A. (-3, 9/2 )

B. (-1, 3/2 )

C. (1, (-3)/2 )

D. (3, (-9)/2)


30. Evaluate ∫ 90 √x dx .

A. 3

B. 9

C.18

D. 27


ANSWERS

31. The function f: x→x2 + px + q has turning point when x = -3 and a remainder of -6 when divided by (x + 2). Find the value of q.

A. 6

B.2

C.-2

D.-8







34. Find, correct to the nearest degree, the angle between p = 12i – 5j and q = 4i + 3j.

A. 590

B. 600

C. 750

D. 760


35. Find the area between line y = x + 1 and the x – axis from x = -2 to x = 0.

A. 5 square units.

B. 4 square units.

C. 2 square units.

D. 1 square unit


ANSWERS

36. How many numbers greater than 200 can be formed from the digits 1,2, 3, 4, 5 if no digit is to be repeated in any particular number?

A. 50

B. 60

C. 288

D. 300


37. The probabilities that John and Jane will pass an examination are 0.9 and 0.7 respectively. Find the probability that at least one of them will pass the examination.

A. 0.28

B. 0.67

C. 0.72

D. 0.97


38. Given that X and Y are independent events such that P(X) = 0.5, P(Y) = m and P(XUY) = 0.75, find the value of m.

A. 0.6

B. 0.5

C. 0.4

D. 0.3


39. A uniform beam, PQ, is 100cm long and weighs 35N. it is placed on a support at a point 40cm from P. If weights of 54N and FN are attached at P and Q respectively in order to keep it in horizontal position, calculate, correct to the nearest whole number, the value of F

A. 69

B. 60

C.35

D.30





WASSCE JUNE 2019 FURTHER MATHEMATICS OBJECTIVE TEST

ANSWERS

1. A 2. A 3. C 4. A 5. C 6. B 7. D 8. A 9. B 10. C 11. D 12. A 13. A 14. C 15. C 16. D 17. B 18. D 19. A 20. D 21. B 22. C 23. C 24. A 26. A 27. A 28. B 29. C 30. C 31. B 32. C 33. D 34. A 35. D 36. C 37. B 39. D 40. D


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