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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2017

Objectives



1. If logy ⅛ = 3, find the value of y

A. -2

B. -1/2

C. 1/2

D.2


2. A binary operation A is defined on the set of real numbers, R, by a Δ b = a + b /√ ab Where a ≠ 0, b ≠ 0. Evaluate -3 Δ -1

A. - 4 √3

B. – 4/3 3

C. √-¾ 3

D. ¾ √3


3. Simplify: 1/(1- √3)2

A. 1- ½ √3

B. 1+1/2 √3

C. √3

D. 1 + √3


4. If x2 - kx + 9 = 0 has equal roots, find the values of k

A. 3,4

B. ± 3

C. ± 5

D. ± 6


5. Find the coordinates of the centre of the circle 3x2 + 3y2 - 4x - 8y - 2 = 0

A. (-2,4)

B. ( - ⅔, ⁴∕₃ )

C. ( ⅔, -⁴∕₃ )

D. (2, -4)


ANSWERS

6. The function f: x →√( 4 - 2x) is defined on the set of real numbers R. Find the domain of f.

A. x<2

B. x ≤ 2

C. x = 2

D. x > - 2


7. Given that f(x) = (x + 1)/2, find f -1 (-2)

A. -5

B. -3

C. 3

D. 5





9. Find the coefficient of x4 in the expansion of (1 - 2x)6.

A. - 320

B. - 240

C. 240

D. 320


10. Find the 21st term of the Arithmetic Progression (A.P): -4, - 1. 5, 1, 3. 5

A. 43.5

B.46

C. 48.5

D. 51


ANSWERS

11. How many ways can six students be seated around a circular table?

A. 36

B. 48

C. 72

D. 120


12. If (²₄ ¹₃) (⁵₄) = k (¹⁷∙⁵₄₀.₀), find the value of k

A. 0.20

B. 0.40

C. 0.80

D. 1.25


13. Express Cos 150° in surd form

A. - √3

B. -√³/₂

C. - ½

D. √²/₂


14. 4 straight line parallel to 2x + 3y = 6, passes through the point (-1, 2). Find the equation of the line

A. 2x- 3y = 2

B.2x + 3y = -2

C.2x + 3y = -4

D.2x + 3y = 4


α and β are the roots of the equation 2x2 - 3x + 4 = 0.


USE THIS INFORMATION TO ANSWER QUESTIONS 15 AND 16.


15. Find (α + β)

A. -2

B. - ³/₂

C. ³/₂

D. 2


ANSWERS

16. Find [α/β + β/α]

A. -9/8

B. -7/8

C. 7/8

D.9/8


17. If B = (21 53) , find B-1

A. (-31 -52)

B. 3 -5

C (31 -52)

D (-31 5-2)


18. Given that sin x = 5/13 and sin y = 8/17 where x and y are acute. Find the

value of cos (x + y)

A 130/221

B. 140/221

C. 140/204

D. 220/23


19. A circle with centre (4, 5) passes through the y – intercept of the line 5x – 2y + 6 = 0. Find its equation.

A. x2 + y2 + 8x – 10y + 21 = 0

B. x2 + y2 + 8x – 10y – 21 = 0

C. x2 + y2 - 8x - 10y-21 =0

D. x2 + y2 - 8x - 10y + 21 =0


20. Given that f(x) = 5x2- 4x + 3, find the coordinates of the point where the gradient is 6

A. (4, 1)

B. (4, -2)

C. (1, 4)

D. (1, -2)


ANSWERS







24. There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys.

A.1638

B. 2730

C. 6006

D.7520


25. The 3rd and 7th terms of a Geometric Progression (G. P) are 81 and 16 respectively. Find the 5th term

A. 4/729

B. 16/81

C. 27

D. 36


ANSWERS

26. Differentiate (5x3 + x2 )/x , x ≠ 0 with respect to x

A. 10x + 1

B. 10x + 2

C. x(15x+1)

D. x(15x + 2)


27. A curve is given by y = 5 - x - 2x2. Find the equation of its line of symmetry.

A. x = - 41/8

B. x=- 1/4

C. x= l /4

D. x = 41/8


28. In a class of 10 boys and 15 girls, the average score in a Biology test is 90. If the average score for the girls is x, find the average score for the boys in terms of x.

A. 200- 2/3 x

B.225-3/2x

C. 250 - 2x

D. 250 - 3x


29. A fair die is tossed twice. What is the sample size?

A. 6

B. 12

C. 36

D. 48


30. Given that a = 2 and b = - 1 3 4 evaluate (2a - ¼ b). A. 17 B 17 C. 17 D. 17 4 4 4 4 7 5 3 2 The table shows the results of tossing a fair die 150 times FACE 1 2 3 4 5 6 FREQUENCY 12 18 Y 30 2Y 45




ANSWERS



Use this information to answer questions 31 and 32.


31. Find the probability of obtaining a 5

A. l/10

B. l/6

C. 1/5

D. 3/10


32. Find the mode

A. 3

B. 4

C. 5

D. 6


33. Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a - 8b)

A. 9i+44j

B. -9i+44j

C. -9i-44j

D. 9i-44j


34. A force (10i + 4j) N acts on a body of mass 2 kg which is at rest. Find the velocity after 3 seconds

A. [5/3 i + 2/3 j ] ms-1

B. [10/3 i + 4/3 j ] ms-1

C. (5i + 2j) ms-1

D. (15i + 6j) ms-1


35. Find the magnitude and direction of the vector p = (5i- 12j)

A. (13, 113.38°)

B. (13,067.38°)

C. (13,025.38°)

D. (13,157.38°)


ANSWERS

36. Solve: 32x - 3x-2 = 3x+1-27

A. 1 or 0

B. 1 or 2

C. 1 or -2

D. -1 or 2


37. The velocity, V, of a particle, in MS'1, after t seconds, V = 3t2 + 2t -1. Find the acceleration of the particle after 2 seconds.

A. 10 ms-2

B. 13 ms-2

C. 14ms-2

D. 17ms-2


38. Given that f(x) = 2x2 - 3 and g(x) = x+1, where x ϵ R, find gof(x)

A. 2(x2-1)

B. 2x2 + 4x-1

C. 2x2+6x-1

D. 3(x2-1)


39. If (2x2 - x - 3) is a factor of f(x) = 2x3 - 5x2 - x + 6, find the other factor

A. (x-2)

B. (x-1)

C. (x + 1)

D. (x+ 1/2)


40. If P = (n2 + 1: n = 0, 2, 3} and Q = {n + 1 : n = 2, 3, 5}, find PnQ

A. {5, 10}

B.{4, 6}

C. {1, 3}

D. {0, 1 }



WASSCE JUNE 2017 FURTHER MATHEMATICS OBJECTIVE TEST

ANSWERS

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


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