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THEORY QUESTIONS

WAEC SYLLABUS

1 Which of the following sets is equivalent to (P ∪ Q) ∩ (P ∪ Q)

A. P

B. P ∩ Q

C. P ∪ Q

D. Ф

2. Simplify: (cos 2 θ - 1) / (Sin 2 θ)

A. -tan θ

B. -cos θ

C. tan θ

D. cos θ

3. Solve the inequality x² – 2x ≥ 3.

A. -1 ≤ x ≤ 3

B. x ≥ 3 or ≤ - 1

C. x ≥ 3 or < - 1

D. -1 ≤ x < 3

4. Given that √6, 3 √2, 3 √6, 9 √2 ……. are the first four terms of an exponential sequence (G. P) Find in its simplest form, the 8th term.

A. 27√2

B. 27√ 6

C. 81√ 2

D. 81√ 6

5. Given that sin x = - ^√3/_√2 and cos x > 0, find the value of x.

A. 300⁰

B. 240⁰

C. 120⁰

D. 60⁰

ANSWERS

17. A binary operation. Δ. is defined on the set of real numbers by a Δ b = a + b + 4. Find the identity element of the operation

A. 4

B. 2

C. I/4

D. -4

The marks obtained by 10 students in a test are as follows 3. 6.2. 8. 5. 9.1.4 and 10.

Use the information to answer questions 18 and 19.

18. Find the mean mark.

A. 4.50

B. 5.50

C. 6.50

D. 6.75

19. Find the variance.

A. 8.25

B. 8.50

C. 9.00

D. 9.17

20. If r denotes the correlation co-efficient between two variables, which of the following is always true?

A. 0 < r ≤ 1

B. -I ≤ r < 1

C. -1 < r ≤ 0

D. -1 ≤ r ≤ 1

ANSWERS

26. g o h is

A. one to one

B. one to one onto

C. a relation.

D. a series

27. In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the correct mean.

A.19

B. 21

C. 23

D. 24

28. Given that nPr = 90 and nCr= 15, find the value of r.

A. 2

B. 3

C. 5

D. 6

29. Which one of the following options is not a measure of Central Tendency?

A. Mode

B. Variance

C. Mean

D. Median

30. A fair die is tossed twice. Find the probability of obtaining a 3 and a 5.

A. ⁵/₁₂

B. ¹/₁₈

C. ²/₉

D. ¹/₃₆

ANSWERS

31. Find the values of x at the point of intersection of the curve y = x² + 2x - 3 and the line y + x = 1.

A. (1.-2)

B. (0.4)

C. (2.-3)

D. (1.-4)

32. If P(x - 3) + Q(x + 1) = 2x + 3. find the value of (P + Q).

A. 0

B. 1

C. -2

D. 3

33. Find the constant term in the binomial expansion of (2x - ³/_x)⁸

A. 90720

B. 1296

C. 1120

D. 672

34. NOT DRAWN TO SCALE The diagram above is a velocity-time graph of a moving object. Calculate the distance travelled when the acceleration is zero. A. 45 m B. 9 m C. 150 m D. 240 m

35. A straight line makes intercepts of-3 and 2 on the x and y axes respectively . Find the equation of the line. A. 2x + 3y + 6 = 0 B. 3x-2y-6 = 0 C. -3x + 2y - 6 = 0 D.-2x + 3y-6 = 0

ANSWERS

36. Find the number of different arrangements of the letters of the word IKOTITINA.

A. 30240

B.60840

C.120960

D. 362880

37. Find the acute angle between the lines 2x + y = 4 and 3x + y + 7= 0.

A. 40°

B. 44°

C. 45°

D. 54°

38. A box contains 4 red and 3 blue identical balls. If two balls are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.

A. ⁴/₇

B. ²/₇

C. ¹/₇

D. ¹/₁₂

39. The distance s in metres covered by a particle in t seconds is s = (3t²)/2 - 3t. Find its acceleration.

A. 1 ms^-2

B. 2 ms^-2

C. 3 ms^-2

D. 4 ms^-2

40. The angle of a sector of a circle is 0.9 radians. If the radius of the circle is 4 cm, find the length of the arc of the sector.

A. 3.6 cm

B. 7.6 cm