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THEORY QUESTIONS

WAEC SYLLABUS

1. Find the domain of f(x) = ^x/_{3 - x}, where x E R. the set of real numbers.

A. {x: x E R, x ≠3}

B {x:x E R, x ≠ 1}

C.{x:x E R, x≠ 0}

D. {x:x E R, x≠ - 3}

2. Find the value of cos (60° + 45°) leaving your answer in surd form.

A. ^{(√6 + √2)}/₄

B. ^{(√3 + √6)}/₄

C. ^{(√2 - √6)}/₄

D. ^{(√3 - √6)}/₄

3. If ⁵/_√2 - ⁸/_√8 = m√2. where m is a constant find m

A. 1 ½

B. 1%

C.2 ¼

D. 2 ½

4. If I6^3x, = ¼ (32^x ^{- 1} ), find the value of x.

A. -1

B. - ¹/₃

C. – ³/₇

D. -⁵/₁₉

5. Simplify ^(log₅8)/_(log5√8)

A. -2

B. – ½

C. ½

D 2

ANSWERS

6. The coefficient of the 7th term in the binomial expansion of (2 – ^x/₃)¹⁰in ascending powers of x is

A. ⁵⁰⁰/₂₄₃

B. ⁸⁴¹/₂₄₃

C. ¹¹²⁰/₂₄₃

D. ⁴⁴⁸¹/₂₃₄

7. The roots of a quadratic equation are (3 - √3) and (3 + √ 3). Find its equation.

A. x² - 6x - 9 = 0

B. x² – 6x + 6 = 0

C. x² + 6x - 9 = 0

D. x² + 6x + 6 = 0

8. If (x - 3) is a factor of 2x² - 2x + p, find the value of constant p.

A. -12

B. -6

C.3

D. 6

9. If sin x = -sin 70⁰ , 0⁰< x < 360°, determine the two possible values of x.

A. 110⁰, 250⁰

B. 110⁰ 290⁰

C. 200⁰, 250⁰

D. 250⁰, 290⁰

ANSWERS

16. Given the P = ( x : x is a factor of 6) is the domain of g(x) = x² + 3x – 5, find the range of f(x)

A. (-1, 5, 13)

B. ( 5, 13, 49)

C. ( 1, 2, 3, 6)

D. ( -1, 5, 13, 40)

17. The third term of geometric progression (GP.) is 10 and the sixth term is 80. Find the common ratio.

A. 2

B. 3

C. x = 2

D. 7 = 2

18. Find the axis of symmetry of the curve y = x² – 4x – 12.

A. x = -2

B. y = -2

C. x = 2

D. y = 2

19. Find the equation of the tangent to the curve y = 4x² – 12x + 7 at point (2 -1).

A. y + 4x – 9 = 0

B. y – 4x – 9 = 0

C. y – 4x + 9 = 0

D. y + 4x + 9 = 0

20. If h (x) = x³ - (1/x³) , evaluate h(a) - h

A. - 1/a³

B. 0

C. 2a³ - (2/a³)

D. (2/a³) - 2a³

ANSWERS

21. The mean age of 15 pupils in a class is 14.2 years. One new pupil joined the class and the mean changed to 14.1 years. Calculate the age of the new pupil.

A. 12.4 years

B. 12.6 years

C. 13.2 years

D. 14. 1 years

22. The distance 3 metres of a particle from a fuel point at time 1 seconds is given by s = 7 + pt³ + t², where p is a constant if the acceleration at t = 3 seconds -s 8ms-2, find the value of p

A. 1/3

B. 4/9

C. 5/9

D.1

23. The probabilities that a husband and wife will be alive in 15 years time are m and n respectively. Find the probability that only one of them will be alive at that time.

A. mn

B. m + n

C. m + n - 2mn

D. 1 - mn

24. In a class of 50 pupils, 35 like Science and 30 like History. What is the probability of selecting a pupil who likes both Science and History?

A. 0.10

B. 0.30

C. 0.60

D. 0.70

25. P, Q, R, S are points in a plane such that PQ = 8i - 5j, QR = 5i + 7j, RS = 7i + 3j and PS = x i + y j. Find (x, y)-

A. (-6,-15)

B. (-6, 5)

C. (20, 5)

D. (20,15)

ANSWERS

26. Find the least value of n for which ³ⁿC₂ > 0, n E R.

A. 1/6

B. 1/3

C. 2/3

D. 1

27. If OA = 3i + 4j and OB = 5i - 6j where O is the origin and M is the mid-point of AB, find OM.

A. -2i – 10j

B. -2i + 2j

C. 4i –j

D. 4i + j

28. Find the direction cosines of the vector 4i - 3j.

A. 9/10, ²⁷/10

B. ^√17/₁₇, ^{- √17}/₁₇

C. ⁴/₅, - ³/₅

D.^3√10/₁₀, ^3√10/_10s

29. Yomi was asked to label four seats with letter S, R, P, Q. What is the probability that he labelled them in alphabetical order?

A. 1/24

B. 1/12

C. 1/6

D. 1/4

30. Two forces (2i - 5j) N and (-3i + 4j) N act on a body of mass 5kg. Find, in ms^-2, the magnitude of the acceleration of I body

A. ^{√ 2}/₅

B. 5 √ 2.

C. 2 √ 5

D. ^{5√ 2}/₂

ANSWERS

31. Two particles are fired together along a smooth horizont surface with velocities 4ms^-1 and 5ms^-1. If they move at 60 to each other, find the distance between them after 2 seconds.

A. 2 √ 61

B. 2 √41

C. 2 √21

D. 2 √10

32. Two forces F1 = (7i + 8j) N and F2 = (3i + 4j)N act on a particle. Find the magnitude and direction of (F1 - F2).

A. (4 √2N. 000°)

B. (4 √2N, 045°)

C. (4 √2N. 090°)

D. (4 √2N, 180°)

33. A stone is thrown vertically upwards and its height 1 time r seconds is h = 45t – 9t². Find the maximum height reached.

A. 45.25m

B. 45.50 m

C. 56.00 m

D.56.25m

34. Given that dy/dx = 3x² - 4 and y = 6 when x - 3, find y.

A. x³ - 4x - 9

B. x³ - 4x + 9

C. x³ + 4x – 9

D. x³ + 4x + 9

35. A company took delivery of 12 vehicles made up of 7 buses and 5 saloon cars for two of its Departments Personnel and General Administration. If the Personnel Department is to have at least 3 saloon cars, in how many ways can these vehicles be distributed equally between the Departments?

A. 350

B. 455

C. 462

D. 56. 25m

ANSWERS

36. A bicycle wheel of diameter 70cm covered a distance of 350 cm in 2 seconds. How many radians per second did turn?

A. 5

B. 7

C. 8

D. 10

37. The initial velocity of an object is u = (^-5₃) ms^-1. If the 3 Acceleration of the object is a = (³_-4) ms^-1 and it moved -4 For 3 seconds, find the final velocity.

A. (^-14₁₅) ms^-1

B. (^-2₁) ms^-1

C. (⁴₉) ms^-1

D. (¹⁴₉) ms^-1

38. Find the maximum value of 2 + sin (θ + 25°).

A.1

B.2

C.3

D.4

39. Simplify (1 + 2 √3)² - (1 - 2 √3)².

A.O

B. 8 √3