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1. Given that the straight lines kx - 5y + 6 = 0 and mx +ny -1 = 0 are parallel, find a relationship connecting the constants m, n and k.

A. 5n-km =0

B. kn +5m = 0

C. 5n + km = 0

D. kn-5m = 0

2. Given that α and β are the roots of an equation such that α + β = 3 and α β = 2, find the equation

A. x² – 3x + 2 = 0

B. x²- 2x + 3 = 0

C. x² – 3x + 2 = 0

D. x² – 2 x - 3 = 0

3. Which of the following is the same as sin (270 + x)?

A. sin x

B. tan x

C. -sin x

D. -cos x

4. The sum of the first three terms of an Arithmetic Progression (A. P.) is 18. If the first term is 4. Find their product

A. 130

B.192

C. 210

D. 260

5. Two functions/and g are defined on the set R of real numbers by f: x ⇾ 2x -1 and

g: x ⇾ x² + 1. Find the value of f^-1og(3).

A. 12

B. 11

C. ¹¹/₁₂

D. ⁹/₂

ANSWERS

11. Find the fourth term of the binomial expansion of (x - k)⁵ in descending powers of x.

A. 10x ²k³

B. 5x³k^-2

C. -5x³k²

D.-l0x²k^-3

12. The tangent to the curve y = 4x³ + be - 6x + 4 at the point P (1, m) is parallel to the x - axis, where k and m are constants.

Use the information to answer Questions 12 and 13.

12. Find the value of k.

A. 3

B. 2

C. -2

D. -3

13. Determine the coordinates of P

A. (l,2)

B. (l . l)

C. (l. - l)

D. (l, - 2)

14. Two vectors m and n are defined by m = 3i + 4j and n = 2i -j. Find the angle between m and n.

A. 97.9⁰

B. 79.7⁰

C.63.4⁰

D. 36.4°

15. Find the Area of the circle whose equation is x² + y² -4x + 8y + 11 = 0

A. 3π

B. 6π

C. 9π

D. 12π

ANSWERS

16. Two bodies of masses 8 kg and 5 kg travelling in the same direction with speeds of x ms^-1 and 2 ms^-1 respectively collide. If after collision, they move together with a speed of 3.85 ms^-1. find, correct to the nearest whole number, the value of x.

A. 2

B.5

C. 8

D.13

17. Calculate in surd form, the value of tan 15°.

A.(2 + √3)

B.(l + √3)

C. ( √3-l)

D. (2 - √3)

18. Evaluate lim (x² -2x -3 )

----------------x ⇾ 3 -----x - 3

A. 4

B. 3

C. 2

D. 0

19. A bag contains 2 red and 4 green sweets of the same size and shape. Two boys pick a sweet each from the box, one after the other, without replacement. What is the probability that at least a sweet with a green wrapper is picked?

A. ¹/_⁵

B. ²/₅

C. ⁸/₁₅

D. ¹⁴/₁₅

20. If f(x) = mx² -6x -3 and f1(1) = 12, find the value of constant m

A. 9

B. 3

C. -3

D. -4

ANSWERS

21. A body is acted upon by two forces F1 = (5N. 060⁰) and F2 = (10N. 180⁰ Find the magnitude of the resultant force

A. I8.75N

B. 15.75N

C. 9.50N

D. 8.66N

22. The equation of a curve is given by = y = 2x² - 5x + k. If the curve has two intercepts on the x-axis. find the value(s) of constant k

A. k = ⁸/₂₅

B. k = ²⁵/₈

C. k < ²⁵/₈

D. k > ²⁵/₈

23. Find the value of p which will make (x² - x + p) a perfect

A. ^-1/₂

B. ¹/₄

C. ¹/₂

D. 1

24. The polynomial g(x)=2x³ +3x² + qx -1. has the same remainder when divided by (x + 2) and (x -1). Find the value of constant q?

A. 11

B. -9

C. -3

D. -l

The table shows the marks obtained by 100 pupils in a test.

Marks ----5 – 7 8 – 10 11 -13 14 – 16 17 - 19 20 – 22

Frequency 4 ......7 ........26 .......41 ........14 ........8

Use it to answer Questions 25 and 26

25. Find the upper class boundary of the class containing the third quartile

A. 13.0

B.16.0

C.16.5

D. 22.5

ANSWERS

26. Find the probability that a pupil selected at random had a mark of at least 14

A. 0.22

B. 0.41

C. 0.49

D. 0.63

27. How mam ways can 12 people be divided into three groups of 2, 7 and 3 in that order?

A. 7,930

B. 792

C. 187

D. 42

Given that P = (4 9) and Q = (^-1₃ ^-2₂)

Use this information to answer Questions 28 and 29.

28. Which of the following operations is possible?

A. QP

B. P²

C. Q²P

D. PQ

29. Evaluate /Q\P.

A. (16 36)

B. (8 18)

C. (8 0)

D. (l 2)

30. The equation of a circle is given by x² + y² - 4x - 2y -3 = 0. Find the radius and the coordinates of its center.

A. 3, (-1.2)

B. 2 √2. (2, -1)

C. 2√ 2, (2,1)

D. 9,(2,-l)

ANSWERS

31. Simplify ⁿP₃ + ⁿP₀

---------------------ⁿC₂

A. n -5

B. n -3

C. 2n -1

D. 2n -3

32. X and Y are two independent events. If P{X) = ¹/₅and P (X X) = ²/₁₅, find P(Y).

A. ²/₃

B. ²/₅

C. ¹/₃

D. ¹/₅

33. Given that p =4i + 3j. find the unit vector in the direction

A. ¹/₃(4i + 3j)

B. ¹/₃(3i + 4j)

C. ¹/₅(3i + 4j)

D. ¹/₅(4i + 3j)

34. A particle is projected vertically upwards with a speed of 40ms^-1 .At what times will it be 35m above its point of projections? [Take g = l0ms^-2]

A. 1 sec. and 7 sec.

B. 1 sec. and 8 sec.

C. 2 sec. and 5 sec.

D. 2 sec. and 7 sec.

35. Three students are working independently on a Mathematics problem. Their respective probabilities of solving the problem are 0.6, 0.7 and 0.8. What is the probability that at least one of them solve the problem?

A. 0.024

B. 0.336

C.0.664

D. 0.976

ANSWERS

36. Given that R = (4,180°) and S = (3,300°) find the dot product R. S.

A. -6 √3

B. -6

C. 6

D. 6 √3

37. Calculate, correct to one decimal place, standard deviation of the

numbers -1,5,0,2 and 9

A. 12

B. 6.6

C. 3.6

D. 3.2

38. A group of 5 boys and 4 girls is to be chosen from a class of 8 boys and 6 girls. In how many ways can this be done?

A. 840

B. 480

C. 408

D. 3802

39. A force of 30 N acts at an angle of 60° on a body of mass 6 kg initially at rest on a smooth horizontal plane. Find the distance covered in 10 seconds.

A. 125 √3m

B. 125m

C. 62.5m

D. 25 √3rn

40. Three forces F1 = (8N, 300°), F2 = (6N, 090°) and F3 = (4N, 180⁰) act on a particle. Find the vertical component of the resultant force

A. 2 N

B. 10N

C. (4+4 √3)N

D. (6 – 4 √3)N