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16. The mean age of n men in a club is 50 years. Two men aged 55 and 63, left the club and the mean age reduced by 1 year. Find the value of n

A. 30

B. 20

C. 18

D. 14

17. A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?

A. 15

B. 40

C. 70

D. 175

18. Simplify ⁿP₄

--------------------ⁿC₄

A. 24

B. 18

C. 12

D. 6

19. Which of the following matrices is a singular matrix?

A. (¹₀ ⁰₁)

B. (²₃ ¹₂)

C. (³₆ ⁸₁₆)

D. (⁰₁ ¹₀)

20. Simplify 8ⁿ x2²ⁿ 4 4³ⁿ

A. 2 ^-ⁿ

B. 2^{1 - n}

C. 2 ⁿ

D. 2 ^{n + 1}

ANSWERS

21. The area of a sector of a circle is 3cm². If the sector subtends an angle of 1.5 radians at the centre, calculate the radius of the circle

A. lcm

B. 72cm

C. 2cm

D.4cm

22. A particle of mass 2.5 kg is moving at a speed of 12 ms^-1. If a force of magnitude 10 N act against it, find how long it takes to come to rest

A. 1.5 s

B . 3.0 s

C. 4.0 s

D. 6.0 as

23. Calculate the standard deviation of the distribution below

Age (In years) 1 – 5 6 – 10 11 – 15

Frequency ------3 ------5 ---------2

A. 1.10

B. 2.36

C. 3.50

D. 7.50

24. In a firing contest, the probabilities that Kojo and Kwame hit the target are ²/₅and ¹/₃respectively. What is the probability that none of them will hit the target?

A. ¹/₅

B. ²/₅

C. ³/₅

D. ⁴/₅

25. The equation of the line of best fit for variables x and y is y = 19.33 + 0.42x, where x is the independent variable. Estimate the value of y when x = 15

A. 18.91

B. 19.74

C. 25.63

D. 3&23

ANSWERS

26. Find the coordinates of the point on the curve y =7 + 4x- 2, where the gradient is zero.

A. (-2,10)

B.(-2,2)

C. (-2, -2)

D.(-2, -6)

27. Find the least value of the function/fx) = 3.7+ 18x +32.

A. 5

B. 4

C. 3

D. 2

28. A force of 32 Newtons is applied to an object of mass m kg which is at rest on a smooth horizontal surface. If the acceleration produced is 8ms-2, find the value of m.

A. 16

B. 12

C. 6

D. 4

29. Given that (²₁^-3₄) (^-6_P) (³₂₆) find the value of P.

A. -8

B. -5

C. 4

D. 4

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

A. (-⁵/₄, ³/₄)

B. (³/₈,- ⁵/₈)

C. (⁵/₈,- ³/₈)

D. (⁵/₄,- ³/₄)

ANSWERS

31. A and B are, two independent events such that P(A) = ²/₁₅and P (A ∩ B) = ¹/₁₅. Find P(B).

A. 3/5

B. 1/3

C. ¼

D. 2/15

32. The parallelogram PQRS has vertices P(-2, 3), Q( 1,4) R(2,6) and S(-1,5). Find the coordinates of the point of intersection of the diagonals.

A. (-1,5)

B. (-¹/₂, 3¹/₂)

C. (0.4½ )

D. (l ½,5)

33. Find, in surd form, the value of cos 165°.

A. ¹/₄(√6 + √2)

B. ¹/₄(√6 - √2)

C. – ¹/₄(√6 - √2)

D. -¹/₄(√6 + √2)

34. The mean and median of integers x,y,z and t are 5 and z respectively. If x < y < z < r and y = 4, find (x +1).

A. 12

B. 11

C. 10

D. 8

ANSWERS

36. A lift moving upwards with a uniform acceleration of 5 ms^-2 carries a body of mass p kg. If the reaction on the floor is 480 N, find the value of p [Take g = 10 ms^-2]

A. 32

B. 36

C. 48

D. 64

37. Calculate, correct to one decimal place, the angle between 5i + 12i and 2j + 3j,

A. 54.8°

B. 56.3°

C. 66.4°

D. 76.3°

38. A particle is projected vertically upwards from a height 45 metres above the ground with a velocity of 40 ms"1. How long does it take to hit the ground? [Take g = 10 ms^-2]

A. 1s

B. 3s

C. 7s

D. 9s

39. Two forces, each of magnitude 16 N, are inclined to each other at an angle of 60⁰ . Calculate the magnitude of their resultant.

A. 16

B. 16√3

C. 18

D.18√3

40. ABCD is a square Forces of magnitude 14N, 4n, 2n and 2 √2.N

-------------------------------------------------------------- → ---→ → ----------→

act along the sides AB, BC, CD and DA respectively. Find in Newtons, the magnitude of the resultant of the forces.