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THEORY QUESTIONS

WAEC SYLLABUS

ANSWERS

6. If y = 4x – 1, list the range of the domain {-2 ≤ x ≤ 2}, where x is an integer

A. {-9, -l, 2, 3, 4,}

B. {-9, -2, 0, 1,7}

C. {-5, -4, -3, -2}

C. {-9, -5, -1,3, 7}

7. Factorize completely: x² + x²y + 3x- 10y + 3xy-10

A. (x + 2) (x +5) (y + 1)

B. (x + 2) (x- 5) (y + 1)

C. (x – 2) (x + 5) (y+1)

D. (x - 2) (x - 5) (y + 1)

8. If the solution set of x² + kx - 5 = 0 is {-1, 5), find the value of k

A. -6

B. -4

C. 4

D. 5

9. The remainder when x³ - 2x + m is divided by x -1 is equal to the remained when 2x³ + x - m is divided by 2x + 1. Find the value of m

A. ^-7/₈

B. ^-3/₈

C. ¹/₈

D. ⁵/₈

10. If (2t + 3s) (t – s) = 0, find ½

A. 3/8 or 1

B. 3/8 or - 1

C. 1/8

D. 5/8

ANSWERS

21. Evaluate cos 75°, leaving the answer in a surd form

A. ^√2/₂ (√3 + 1)

B. ^√2/₄(√3 - 1)

C. ^√2/₄(√3+ 1)

D. ^√2/₂(√3 - 1)

22. Given that tan x = 5/12 and tan y = 3/4, find tan (x + y)

A. ¹⁶/₃₃

B. ³³/₅₆

C. ³³/₁₆

D. ⁵⁶/₃₃

23. Find the equation of the line which passes through (-4, 3) and parallel to line y = 2x + 5 A. y = 2x +11

B. y = 3x + 11

C. y = 2x - 11

D. y = 3x - 5

24. Points E(-2, -1) and F(3, 2) are the ends of the diameter of a circle. Find the equation of the circle

A. x² + y² -5x + 3 = 0

B. x² + y² - 2x- 6y - 13 = 0

C. x² + y² - x + 5y - 6 = 0

D. x² + y² - x - y - 8 = 0

25. The lines 2y+ 3x - 16 = 0 and 7y - 2x - 6 = 0 intersect at point P. Find the coordinates of P

A. (4, 2)

B. (4, -2)

C. (-4, 2)

D. (-4, -2)

ANSWERS

27. Find the gradient of the normal to the curve y = x3 - x2, at the point where x = 2

A. - 1/8

B. - 1/24

C. 1/8

D. 1

28. Find the minimum value of y = 3x²- x - 6

A. -6 ¹/₆

B. -6 ¹/₁₂

C. -6

D. 0

29. The radius of a circle increases at a rate of 0.5 cms^-1. Find the rate of change in the area of the circle with radius 7cm. [Take π = ²²/₇]

A. 11 cm²s^-1

B. 22 cm²s^-1

C. 33 cm²s^-1

D. 44 cm²s^-1

30. Find an expression for y given that ^dy/_dx = x²cx dx

A. l/7x^2/7 + c

B. 2/7x^3/2 + c

C. 2/7x^7/2 + c

D. 3/7x^3/2 + c

ANSWERS

31. Given that n = 10 and Σd² - 20, calculate the spearman's rank correlation coefficient

A. 0.121

B. 0.733

C. 0.879

D. 0.979

32. Find the variance of 11, 12, 13, 14 and 15

A. 2

B. 3

C. 2√3

D. 10√2

33. A fair coin is tossed three times. Find the probability of obtaining two heads

A. 1/8

B. 3/8

C. 5/8

D. 7/8

34. A box contains 14 white ball and 6 black balls. Find the probability of first drawing a black ball and then a white ball without replacement.

A. 0.21

B. 0 22

C. 0.30

D. 0.70

35. Given that r = 3i + 4j and t = 5i + 12j, find the acute angle between them

A. 14.3°

B. 55.9°

C. 59.5°

D. 75.6°

ANSWERS

36. Find the unit vector in the direction of -2i + 5j

A. ¹/_√29 (2i + 5j)

B. ¹/_√29 (-2i + 5j)

C. ^l/_√29 (2i - 5j)

D. ^l/_√29 (-2i - 5j)

37. A body of mass 10 kg moving with a velocity of 5 ms^-1 collides with another body of mass 15 kg moving in the same direction as the first with a velocity of 2 ms^-1. After collision, the two bodies move together with a common velocity v ms^-1. Find the value of v.

A. 3.2

B. 5.3

C. 7.0

D. 8.0

38. A force 10 N acts in the direction 060° and another force 6 N in the direction 330°. Find the y component of their resultant force.

A. (3 + 3√3) N

B. (3 + 5√3)N

C. (5 + 3√3) N

D. (5 + 5√3) N

39. A man of mass 80 kg stands in a lift. If the lift moves upwards with acceleration 0.5 ms^-2, calculate the reaction from the floor of the lift on the man. [Take g = 10 ms^-2]

A. 760 N

B. 800 N

C. 805 N

D. 840 N

40. A ball falls from a height of 18 m above the ground. Find the speed with which the ball hits the ground. [Take g = 10ms^-2]

A. 9 ms^-1

B. 9.49 ms^-1

C. 13.42 ms^-1

D. 18.97 ms^-1