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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2013

Objectives





2. Solve: Sin β = tan θ.

A. 2000

B. 90°

C. 600

D. 00


3. Given C a 5/6 X a - 1/n = 1, solve for n.

A. -6.00

B. -1.20

C. 0.85

D. 1.20


4. Express log 1/8 + log 1/2 in terms of log 2.

A. 3 1 log 2

B. 4 log 2

C. -3 1og2 t

D. -4 1og 2


5. If f(x) = x2 and g (x) = Sin x, find g of.

A. Sin2x

B. Sinx2

C. (Sinx)x2

D. x Sinx


ANSWERS

6. Find the third term in the expansion of (a – b)6 in ascending powers of b.

A. -15 a4b2

B. 15 a4b2

C. -I5 a3b3

D. 15 a3b3


7. If √x + √(x + 1) = √(2x + 1), find the possible values of x

A. l and -1

B. -l and 2

C. l and 2

D. 0 and -1


8. If a and β are the roots of the equation 2x-2 – 6x + 5 = 0. evaluate β/α + a/β,

A. 24/5

B. 8/5

C. 5/8

D. 5/24


9. Given that f(x) = 2x3 - 3x2 - 11x + 6 and f( 3) = 0, factorize f(x).

A. (x - 3) (x - 2) (2x + 2)

B. (x + 3) (x - 2) (x – 1)

C. (x - 3)(x + 2)(2x - 1)

D. (x + 3) (x - 2) (2x – 1)


10. Find the equation of the line that is perpendicular to 2y +5x - 6 = 0 and bisects the line joining the points P(4,3) and Q(-6, 1).

A. y + 5x + 3 = 0

B. 2y – 5x – 9 = 0

C. 5y + 2x-8 = 0

D. 5y - 2x – 12 = 0


ANSWERS

11. Differentiate x2 + , xy - 5 = 0 with respect to x.

A. - (2a + y) / x

B. (2x - y) / x

C. x / 2x+y

D. (2x + 3) / x


12. The fourth term of an exponential sequence is 192 and its ninth term is 6. Find the common ratio of the sequence

A. 1/3

B. 1/2

C. 2

D. 3


13. Find the range of values of x for which x2 + 4x + 5 is less than 3x2 - a + 2

A. x >- ½ , x > 3

B. x < - ½ , x > 3

C. – ½ ≤ x ≤ 3

D. - ½ < x < 3


14. Given that dy/dx = √x , find y'.

A. 2 x 3/2 + c

B. 2/3 x 3/2 + c 3

C. 3/2 x 3/2 + c

D. 2/3 x2 + c




ANSWERS

16. An object is thrown vertically upwards from the top of a cliff with a velocity of 25 ms-l. Find the times, in seconds, when it is 20 metres above the cliff. [Take g = l0 ms-2]

A. 0 and 1

B. 0 and 4

C. 0 and 5

D. 1 and 4 2


17. Evaluate ∫24(8x – 4x2) dx. 0

A. -16

B. - 16/3

C. 16/3

D. 16 3


18. Find the coordinates of the point which divides the line joining P(- 2, 3) and Q(4, 9) internally in the ratio 2 : 3.

A. (5 2/5 , 2/5)

B. (2/5 - 5 2/5)

C. (2/5 – 22/5)

D. (-2/5 - 52/5 )


19. The angle subtended by an arc of a circle at the centre is π radians. If the radius of the circle is 12 cm. 3 calculate the perimeter of the major sector.'

A. 4(6 + 5π)

B. 4 (6 + 2π)

C. 4(3 + 3π)

D. 4 (3 + 5π)


20. The function f: R is define by f(x)= 3x+2:x>4, 3x - 2 : x = 4, 5x-3:x<4

Find f(4)- f(3) is defined bv fixy=

A. 28

B. 26

C. -26

D. -28


ANSWERS

21. A committee consists of 5 boys namely: Kofi, John, Ojo, Ozo and James and 3 girls namely Rose, Ugo and Ama. In many ways can a sub-committee consisting of 3 boys and 2 girls be chosen, if Ozo must be on the sub-committee?

A. 35

B. 30

C. 18

D. 12





23. The sales of five sales girls on a certain day are as follows GHc 26.00, GHc 39.00, GHc 33.00, GHc 25.00 and GHc 37.00. Calculate the standard deviation if the mean sale is GHc 32.00.
A. GHc 5.65
B. GHc 5.66
C. GHc 6.55
D. GHc 6.56

24. A circular ink blot on a piece of paper increases its area at the rate of 4 mm2/s. Find the rate of increase of the radius of the blot when the radius is 8mm. [Take π =22/7]
A. 0.25 mm/s
B. 0.20mm/s
C. 0.08 mm/s
D. 0.05 mm/s



ANSWERS

26. Two bodies of masses 3 kg and 5 kg moving with velocities 2 ms-1 and V ms-1 respectively in opposite direction collide. If they move together after collision with velocity 3.5 ms-1 in the direction of the 5 kg mass, FIND THE VALUE OF V,

A. 7.8 MS-1

B. 6.8 MS-1

C. 5.6 MS-1

D. 4.6 MS-1


27. The equation of a circle is x2 + y2 – 8x + 15 = 0. Find its radius.

A. √5

B. ½ √15

C. ½ √85

D. √85


28. A particle is acted upon by two forces 6 N and 3N inclined at an angle of 1200 to each other. Find the magnitude of the resultant force.

A. 18 √3 N

B. 27 N

C. 24 N

D. 3 √3 N


29. If s = 3i – j and t = 2i + 3j, find (t + 3s). (t – 3s).

A. -77

B. -71

C. – 53

D. -41


30. If 2 sin2θ = 1 + Cosθ. 00 ≤ θ ≤ 900, find θ.

A 300

B. 450

C. 600

D. 900


ANSWERS

31. Find the upper quartile of the following scores: 41, 29, 17, 2, 12,33, 45, 18 ,21, 43 and 5.

A. 45

B.41

C.33

D.21





35. If g(x) = x + 1 , (x ≠ - 2), find g-1 (2).

A. 3

B. 2

C. -2

D. -3


ANSWERS

36. Calculate the mean deviation of 1, 2, 3, 4, 5, 5, 6, 7, 8, 9.

A. 2

B. 3

C. 4

D. 5


37. If V= (-24 ) and U = (-15 ) , find [U + V].

A. 3 10

B. 82

C. 46

D. 2 5


38. Find the equation of the straight line that passes through (2, - 3) and perpendicular to the line 3x – 2y + 4 = 0.

A. 2y - 3x = 0

B. 3y - 2x + 5 = 0

C. 3y + 2r+5 = 0

D. 2y - 3x - 5 = 0


39. If (nC3) / (nP2) = 1, find the value of n.

A. 8

B. 7

C. 6

D. 5


40. A body is kept at rest by three forces F1 = (10 N, 0300). F2 = (10 N, 150°) and F3. Find F3.

A. (12 N, 0900)

B. (10 N. 2700)

C. (10 N. 1800)

D. (10IV, 120°)



WASSCE JUNE 2013 FURTHER MATHEMATICS OBJECTIVE TEST

ANSWERS

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


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