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FURTHER MATHEMATICS


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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2014

Objectives



1. If 1/5-y = 25(54 – 2y), find the value of y

A. 4

B. 2

C. -4

D. – 5


2. Simplify (1 - sinθ) (1 + sinθ)

A. - sin2θ

B. sec2θ

C. tan2θ

D. Cos2θ


3 . given that the lines 3x + 4y + 6 = 0 and 4x - by + 3 = 0 are perpendicular, find the value of b

A. 4

B. 3

C. l/3

D. 1/4


4. Given that x * y = x * y/2 ,x o y = x2/y and (3 * b) 0 48 =1/3 find b, where b > 0

A. 8

B . 6

C. 5

D. 4


5. If(x) = 3x3 + 8x2 + 6x + k, and f(2) = 1, find the value of k

A -67

B. - 61

C. 61

D. 67


ANSWERS

6. If 8x + (l/4)y = 1 and log2 (x - 2y) = 1, find the value of (x - y)

A. 5/4

B. 3/5

C. 1

D. 2/3 ​





8. Using the binomial expansion (1 + x)6 = 1 + 6x + 15x2 + 20x3 + 15x4 + 6x5 + x°, find, correct to three decimal places, the value of (1.98)6

A. 64.245

B. 61.255

C. 60.255

D. 60.245


9. If (x + 2) and (3x- 1) are factors of 6x3 + x2 - 19x + 6, find the third factor.

A. 2x- 3

B. 3x + 1

C. x-2

D. 3x + 2


10. If 2, (k + 1), 8, ... form an exponential sequence (GP), find the values of k

A. - 3 and 5

B. 5 and - 5

C. 3 and -3

D. - 5 and 3


ANSWERS

11. A box contains 5 red and k blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is 2/3, find the value of k.

A. 5

B. 6

C. 8

D. 10




ANSWERS

16. Find h-1 (1/2)

A. 6

B. 11/6

C. 11/4

D. 5/3


17. The radius of a sphere is increasing at a rate 3 cm s-1. Find the rate of increase in the surface area, when the radius is 2cm

A. 8π cm2 s-1

B. 16π cm2s-l

C. 24π cm2 s-1

D. 48π cm2 s-1


The table shows the distribution of the ages of members of a Cultural Troupe


Age (years) 10 - 14 15 - 19 20 - 24 25-29 30 - 34

Frequency ----6 --------8 -------14 -----10 ------12


Use it to answers Questions 18 to 20


18. What is the class-mark of the median class?

A. 19

B. 22

C. 24

D. 32


19. In which group is the upper quartile?

A. (15-19)

B. (20-24)

C. (25 - 29)

D. (30 - 34)


20. Find the mean of the distribution

A. 23.4

B. 23.6

C. 24.3

D. 24.6


ANSWERS

21. If Px2 + (P + 1 )x + P = 0 has equal roots, find the values of P

A. -land - 1/3

B. - 1 and 1/3

C. 1 and - 1/3

D. 1 and 1/3


22. Integrate (x -1/x)2 with respect of x

A. 1/3 (x - 1/x)3 + C

B. x3/3 - x - 1/x 3 + C

C. x3/3 -2x + 1/x3 + C

D. x3/3 - 2x - 1/x + C





24. Find the angle between (5i + 3j) and (3i - 5j)

A. 180°

B. 90°

C. 45°

D. 00


25. Find the coefficient of x3 in the binomial expansion of (3x + 4)4 in ascending powers of x

A. 432

B. 194

C. 144

D. 108


ANSWERS

26. If a fair coin is tossed four times, when is the probability of obtaining at least one head?

A. 1/2

B. 1/4

C. 13/16

D. 15/16


27. Forces 90 N and 120 N act in the directions 120° and 240° respectively. Find the resultant of these forces.

A. 45 √ 3i - 45j

B. - 60 √ 3i - 60j

C. 15 √ 3i + 105j

D. - 15 √ 3i - 105j


28. The deviations from the mean of a set of numbers are (k+ 3)2, (k + 7), - 2, k and (k + 2)2, where k is a constant. Find the value of k

A. 3

B. 2

C. -2

D. -3


29. Find the equation of a circle with centre (2, - 3) and radius 2 units

A. x2 + y2 - 4x + 6y + 9 = 0

B. x2 + y2 + 4x - 6y - 9 = 0

C. x2 + y2 + 4x+6y-9 = 0

D.x2 + y2 + 4x-6y + 9 = 0


30. The first term of a linear sequence is 9 and the common difference is 7. If the nth term is 380, find the value of n.

A. 45

B. 54

C. 56

D. 65


ANSWERS

31. For what values of m is 9y2 +my + 4 a perfect square?

A. ± 2 √ 3

B. ± 6 √ 2

C. ± 6

D. ± 12


32. A particle accelerates at 12 ms-2 and travels a distance of 250 m in 6 seconds. Find the initial velocity of the particle

A. 5.7ms-1

B. 6.0ms-1

C. 60.0ms-1

D. 77.5ms-1


33. In how many ways can 9 people be seated on a bench if only 3 places are available?

A. 1200

B. 504

C. 320

D. 204


34. Find the variance of 1, 2, 0, -3, 5, -2, 4

A. 52/7

B. 40/7

C. 32/7

D. 27/7


35. If the points (-1, t -1), (t, t - 3) and (t - 6, 3) lie on the same straight line, find the values of t

A. t = 2 and -3

B. t = 2 and 3

C. t = -2and 3

D. t = 2 and -3


ANSWERS

36. A ball is thrown vertical upward with a velocity of 15ms-1. Calculate the maximum height reached. [ Take g = 10 ms-2]

A. 15.25 m

B. 13.25 m

C. 11.25 m

D. 10.25


37. Find the distance between the points (2,5) and (5, 9)

A. 4 units

B. 5 units

C. 12 units

D. 14 units





WASSCE JUNE 2014 FURTHER MATHEMATICS OBJECTIVE TEST

ANSWERS

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


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