A HOME OF HEALTH: 2017

1. Evaluate 21.05347 - 1.6324 x 0.43, to 3

decimal places.

A. 20.980 B. 20.351

C. 20.981 D. 20.352

2. Simplify

3 3

ö ç

æ a

A. 4a B.

a 8

C. 8A D.

a 4

3. Given that p = 1 + 2 and q = 1 - 2 ,

evaluate

q p

2 2

A. 2(2 + 2 ) B. –2(2 + 2 )

C. 2 2 D. -2 2 .

4. A car dealer bought a second-hand car for

#250,000.00 and spent #70,000.00

refurbishing it. He then sold the car for

#400,000.00. What is the percentage gain?

A. 60% B. 32% C. 25% D. 20%

5. If

- ¸

+ = 2

2 3

evaluate x

D C B .

6. Find the principal which amounts to #5,500

at simple interest in 5 years at 2% per

annum.

A. #4,900 B. #5,000

C. #4,700 D. #4,800

7. Evaluate ( )

) 02 . 0 ( 7

275 . 0 14 . 0 2

´ , correct to 3 decimal

places.

A. 0.039 B. 0.358

C. 0.033 D. 0.308.

8. Divide a3x

- 26a2x

+ 156ax

- 216

by a2x

– 24ax

+ 108.

A. ax

– 2 B. ax

+ 2

C. ax

– 18 D. ax

– 6

y+2x+2=0

2y-x-2=0

-2

-1

Triangle PST is the solution of the linear

inequalities

A. 2y – x – 2 £ 0, y + 2x + 2 ³ 0,

-2 £ x £ -1

B. –2 £ x £ 2, y ³ 0, y + 2x + 2 £ 0,

x £ 0

C. 2y – x – 2 £ 0, y + 2x + 2 £ 0, y ³ 0,

x £ 0

D. 2y – x – 2 ³ 0, y + 2x + 2 £ 0, x £ 0.

10.

Ä k L m

k l M k

l m K l

m k L m

The identity element with respect to the

multiplication shown in the table above is

A. 0 B. m C. l D. k

11. A man saves #100.00 in his first year of

work and each year saves #20.00 more than

in the preceding year. In how many years

will he save #5,800.00?

A. 100 years B. 58 years

C. 29 years D. 20 years

12. If P = ,

1 5 7

6 0 5

4 2 3

then, -2P is

- -

2 10 14

12 0 10

8 4 6

- -

- - -

- -

2 10 14

12 2 10

2 4 6

- -

1 5 14

6 0 10

8 4 6

- -

1 5 7

6 0 5

8 4 6

13. Given the matrix K = ,

4 3

1 2

the matrix K2

+ K + I where I is the 2 x 2 identity matrix, is

21 12

2 7

÷ ÷

ç ç

20 13

3 6

÷ ÷

ç ç

23 22

8 9

24 21

7 10

14. If two graphs y = px

+ q and

y = 2x

– 1 intersect at x = 2, find the value

of p in terms of q.

8 q

D q

C q

q + - - -

15. Find the integral values of x and y satisfying

the inequality 3y + 5x £ 15, given that y > 0,

y < 3 and x > 0.

A. (1, 1), (1, 2), (1, 3)

B. (1, 1), (2, 1), (1, 3)

C. (1, 1), (3, 1), (2, 2)

D. (1, 1), (1, 2), (2, 1)

16. Evaluate .

1 2 1

1 1 3

1 1 1

- - -

A. –12 B. –4 C. 4 D. –2

17. Solve the equations m2

+ n2

= 29;

m + n = 7.

A. (2, 3) and (3, 5) B. (2, 5) and (5, 2)

C. (5, 2) and (5, 3) D. (5, 3) and (3, 5)

18. An operation * is defined on the set of real

numbers by a * b = a + b + 1. If the identity

element is –1, find the inverse of the

element 2 under *.

A. 4 B. 0 C. –2 D. –4

19. The sixth term of an arithmetical

progression is half of its twelfth term. The

first term is equal to

A. zero

B. half of the common difference

C. double the common difference

D. the common difference.

20. Factorize 4x

– 9y2

+ 20x + 25

A. (2x – 3y + 5)(2x – 3y – 5)

B. (2x – 3y)(2x + 3y)

C. (2x – 3y + 5)(2x + 3y + 5)

D. (2x + 5)(2x – 9y + 5)

21. A sector of a circle of radius 7.2cm which

subtends an angle of 3000

at the center is

used to form a cone. What is the radius of

the base of the cone?

A. 8cm B. 6cm C. 9cm D. 7cm.

22. A point P moves such that it is equidistant

from points Q and R. Find /QR/ when /PR/

= 8cm and <PRQ = 300

A. 4 cm D cm C cm B cm 4 . 3 8 . 8 . 3

23.

Ö3t

t t

Find the value of q in the diagram above.

A. 1000

B. 1200

C. 300

D. 600

24. A straight line makes an angle of 300

with

the positive x-axis and cuts the y-axis at y

= 5. Find the equation of the straight line.

A. y = 5 10

+ x

B. y = x + 5

C. 3 5 3 + - = x y

D. 3 5 3 + = x y

25. Find the value of p if the line joining (p, 4)

and (6, -2) is perpendicular to the line

joining (2, p) and (-1, 3).

A. 4 B. 6 C. 3 D. 0

26. Find the number of sides of a regular

polygon whose interior angle is twice the

exterior angle.

A. 6 B. 2 C. 3 D. 8

27. P(-6, 1) and Q(6, 6) are the two ends of the

diameter of a given circle. Calculate the

radius.

A. 6.5 units B. 13.0 units

C. 3.5 units D. 7.0 units.

28. The bearings of P and Q from a common

point N are 0200

and 3000

respectively. If P

and Q are also equidistant from N, find the

bearing of P from Q.

A. 0400

B. 0700

C. 2800

D. 3200

29. A cylindrical tank has a capacity of 3080m3

What is the depth of the tank if the

diameter of its base is 14m?

A. 23m B. 25m C. 20m D. 22m

30. Find the locus of a point which moves such

that its distance from the line y = 4 is a

constant, k.

A. y = k ±4 B. y = 4 ± k

C. y = 4 + k D. y = k – 4

31. The chord ST of a circle is equal to the

radius, r, of the circle. Find the length of arc

ST.

D r

C r

r p p p p

32.

Q R

750

In the figure above, PQR is a straight line

segment, /PQ/ = /QT/. Triangle PQT is an

isosceles triangle, <SRQ is 750

and <QPT is

250

. Calculate the value of <RST.

A. 450

B. 550

C. 250

D. 500

33. If the gradients of the curve

y = 2kx

+ x + 1 at x = 1 is 9, find k.

A. 4 B. 3 C. 2 D. 1

34. Evaluate

ò - dx x 3

) 3 2 ( 2

A. k x + - 3

) 3 2 (

B. k x + - 3

) 3 2 (

C. 2x – 3 + k D. 2(2x – 3) + k.

35. Differentiate (2x + 5)

(x – 4) with respect to

A. 4(2x + 5)(x – 4)

B. 4(2x + 5)(4x – 3)

C. (2x + 5)(2x – 13)

D. (2x + 5)(6x – 11)

36. Find the area bounded by the curves

y = 4 – x

and y = 2x + 1.

A. units sq B units sq . 20 . . 20 3

C. units sq D units sq . 10 . . 10 3

37. Find the rate of change of the volume, V, of

a sphere with respect to its radius, r, when r

= 1.

A. 12 p p p p 8 . 24 . 4 . D C B

38. If y = xsinx, find .

= x when

. 1 . 1 .

p p

D C B -

39. Find the dimensions of the rectangle of

greatest area which has a fixed perimeter,

A. Square of sides p

B. Square of sides 2p

C. Square of sides

D. Square of sides

Use the table below to answer questions 40 and

Score 4 7 8 11 13 8

Frequency 3 5 2 7 2 1

40. Find the square of the mode.

A. 49 B. 121 C. 25 D. 64

41. The mean score is

A. 7.0 B. 8.7 C. 9.5 D. 11.0

42. Teams P and Q are involved in a game of

football. What is the probability that the

game ends in a draw?

D C B

43. If . , 6 1

6 6

+ = r r

P of value the find P

A. 30 B. 33 C. 35 D. 15

44.

5.5

10.5

15.5

20.5

25.5

30.5

Masses (Kg)

Cummulative

frequency

Q 1 Q 2 Q3

The graph above shows the cummulative

frequency of the distribution of masses of

fertilizer for 48 workers in one institution.

Which of the following gives the inter-

quartile range?

A. Q3 – Q2 B. ) ( 1 3 2

Q Q -

C. Q3 – Q1 D. Q2 – Q1

45.

0.5

2.5

4.5

6.5

8.5

10.5

12.5

No. of passengers

No. of taxis

The histogram above shows the distribution

of passengers in taxis of a certain motor

pack. How many taxis have more than 4

passengers?

A. 16 B. 17 C. 14 D. 15

46.

Colou

Blu

Blac

Yello

Whit

Brow

No. of

Beads

3 5 2 7 2

The distribution of colours of beads in a

bowl is given above. What is the probability

that a bead selected at random will be blue

or white?

D C B

47. Find the variance of 2, 6, 8, 6, 2 and 6.

A. 6 B. 5 C. 5 . 6 D

48.

Colour of cars

No. of cars

Yellow

White

Red

Green

Blue

Black

The bar chart above shows different colours of

cars passing a particular point of a certain street

in two minutes. What fraction of the total

number of cars is yellow?

D C B

49. Find the number o0f ways of selecting 8

subjects from 12 subjects for an

examination.

A. 490 B. 495 C. 496 D. 498.

50. Find the range of .

and

A. .

D C B

2001 Solutions

1. Option D.

2. Option D.

3. Option D.

4. Option C.

5. Option B.

6. Option B.

7. Option A.

8. Option A.

9. Option C.

10. Option B.

11. Option D.

12. Option A.

13. Option D.

15. Option D.

16. Option B.

17. Option B.

18. Option D.

19. Option D.

20. Option C.

21. Option B.

22. Option C.

23. Option B.

24. Option D.

25. Option A.

26. Option A.

27. Option A.

28. Option B.

29. Option C.

30. Option B.

31. Option D.

32. Option B.

33. Option C.

34. Option B.

35. Option D.

36. Option C.

37. Option B.

38. Option C.

39. Option D.

40. Option B.

41. Option B.

42. Option B.

43. Option A.

44. Option C.

45. Option B.

46. Option B.

47. Option B.

48. Option A.

49. Option B.

50. Option D.

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