KUULCHAT
S.H.S MATHEMATICS MOCK

OBJECTIVE TEST

1.

The diagram shows a circle centre O. Use it to answer the question below.

Find the value of y.

A.

43°

B.

47°

C.

54°

D.

86°

2.

The table shows the distribution of the ages of members of a school choir.

Use the table to answer the question below

Age(years) 15 16 17 18
No. of students 5 6 3 1

Find the median age.

A.

15 1 2 years

B.

16 years

C.

16 1 2 years

D.

17 years

3.

In ∆XYZ, |YZ| = 32 cm, ∠ YXZ = 52° and ∠ XZY = 90°. Find, correct to the nearest centimetre, |XZ|.

A.

13 cm

B.

20 cm

C.

25 cm

D.

31 cm

4.

Find the nth term of the Geometric Progression (G.P): 1 2 , 1 4 , 1 8 , ...

A.

2n - 1

B.

2n

C.

1 2n

D.

1 2n - 1

5.

Correct 0.00798516 to three significant figures.

A.

0.0109

B.

0.0800

C.

0.00799

D.

0.008

6.

Given that P v2 x and xvt express P in terms of v and t.

A.

P t v

B.

P v t

C.

Pvt

D.

P 1 vt

7.

If (0.25)y = 32, find the value of y.

A.

- 5 2

B.

- 3 2

C.

3 2

D.

5 2

8.

If 1 2 and -3 are the roots of px2 + qx + r = 0, find the values of p, q and r.

A.

p = 2, q = -5, r = 3

B.

p = 2, q = 5, r = 3

C.

p = 2, q = 5, r = -3

D.

p = -2, q = 5, r = 3

9.

Find the value of x in the diagram.

A.

41

B.

37

C.

35

D.

31

10.

Express 0.0063075 correct to three significant figures.

A.

0.006

B.

0.0063

C.

0.00631

D.

0.0060

11.

In triangle XYZ, |XY| = 8 cm and Z is equidistant from X and Y.

If Z is 5 cm from X, find the area of the triangle.

A.

24 cm2

B.

18 cm2

C.

12 cm2

D.

10 cm2

12.

If tan x = 3 4 , 0 < x < 90, evaluate cos x 2sin x

A.

2 3

B.

4 3

C.

3 4

D.

8 3

13.

If the area of the trapezium MNOP is 300 cm2, find the value of x.

A.

15 cm

B.

12 cm

C.

10 cm

D.

20 cm

14.

In the diagram, O is the centre of the circle WXY. |WX| = |XZ| and ∠ ZXY = 26°. Find ∠ XYZ.

A.

62°

B.

42°

C.

52°

D.

32°

15.

From a height of 2 m above the ground and at a horizontal distance of 12 3 m from a tree, the angle of elevation of the top of the tree is 30°.

How tall is the tree?

A.

8 m

B.

8 3 m

C.

14 m

D.

18 m

16.

A woman buys 3 exercise books at GH₵ 0.4 each and 9 exercise books at GH₵ 0.2 each. What is the average cost of an exercise book?

A.

GH₵ 0.35

B.

GH₵ 0.30

C.

GH₵ 0.22

D.

GH₵ 0.25

17.

A man bought a car which costs ₦5,000,000.00 from a dealer on hire purchase. He pays a deposit of ₦3,000,000.00 and agrees to pay the balance at 8% compound interest per annum. If he pays ₦1,000,000.00 at the end of each year, how much will be remaining to be paid after two years?

A.
₦92,800.00
B.
₦252,800.00
C.
₦320,000.00
D.
₦332,000.00

18.

If (x + 2) is a factor of x2 + px - 10, find the value of p.

A.

-7

B.

7

C.

-3

D.

3

19.

A woman pours 85 litres of kerosene into a cylindrical container with radius 7 cm.

Calculate, correct to the nearest cm, the depth of the kerosene in the container.

[Take π = 22 7 ]

A.

240 cm

B.

552 cm

C.

480 cm

D.

595 cm

20.

Given that tan x = 12 5 , find the value of (sin x cos x)

A.

165 60

B.

169 65

C.

60 169

D.

65 169

21.

The fourth term of an Arithmetic Progression (A.P) is 37 and the first term is -20. Find the common difference.

A.

17

B.

19

C.

57

D.

63

22.

Solve: x - 2 4 - 2x - 4 3 = 5 6 .

A.

x = 0

B.

x = 5

C.

x = 4

D.

x = 2

23.

Find the equation of the line passing through P(4,1) and parallel to 2x + 5y = -10.

A.

5x + 2y = 13

B.

5x - 2y = 10

C.

2x - 5y = 10

D.

2x + 5y = 13

24.

Make m the subject of the relation k = m - y m + 1 .

A.

m = y - k2 1 - k2

B.

m = y - k2 k2 + 1

C.

m = y + k2 1 - k2

D.

m = y + k2 k2 + 1

25.

Given that sin A = 3 5 , 0° ≤ A ≤ 90°, find the value of (tan A - cos A)

A.

- 1 20

B.

7 20

C.

- 3 20

D.

1 20

26.

A box contains 40 identical balls of which 10 are red and 12 are blue. If a ball is selected at random from the box, what is the probability that it is neither red nor blue?

A.

11 20

B.

9 20

C.

3 10

D.

1 4

27.

Two buses start from the same station at 9.00 am and travel in opposite directions along the same straight road. The first bus travels at a speed of 72 km/h and the second at 48 km/h.

At what time will they be 240 km apart?

A.

10.00 a.m.

B.

11.00 a.m.

C.

12.00 noon

D.

1.00 p.m.

28.

The first of a Geometric Progression (G.P) is 3 and the 5th term is 48. Find the common ratio.

A.

16

B.

8

C.

4

D.

2

29.

In the diagram, RT is a tangent to the circle at R, ∠ PQR = 70°, ∠ QRT = 52°, ∠ QSR = y and ∠ PRQ = x.

Use the diagram to answer the question below.

Find the value of y.

A.

18°

B.

52°

C.

60°

D.

45°

30.

The graph of y = x2 - 5x + k passes through the point (3, 1). Find the value of k.

A.

2

B.

3

C.

7

D.

5

31.

The diagonal of a rhombus are 12 cm and 5 cm.

Calculate its perimeter.

A.

26 cm

B.

24 cm

C.

17 cm

D.

34 cm

32.

In the first year, Mr. Kwakye's annual salary was $1,560.00. His salary was increased each year by a constant value, y until it was $13,980.00 in the 13th year. Calculate the value of y.

A.

$955.38

B.

$1,230.00

C.

$1,129.09

D.

$1,035.00

33.

A chord of a circle with radius 5 cm subtends an angle of 70° at the centre.

Find, correct to one decimal place, the length of the chord.

A.

8.2 cm

B.

5.7 cm

C.

4.1 cm

D.

2.9 cm

34.

In the diagram, O is the centre of the circle PQR, |PS| = |PQ| and ∠RQS = 23o. Find the value of x.

A.

23o

B.

38o

C.

46o

D.

67o

35.

If 101two + 12y = 23five, find the value of y.

A.

5

B.

6

C.

7

D.

8

36.

Find the value of x for which 2x - 1 x2 + 2x + 1 is not defined.

A.

1 2

B.

1

C.

2

D.

-1

37.

An amount of ₦ 550,000.00 was realized when a principal, x was saved at 2% simple interest for 5 years. Find the value of x.

A.

₦ 500,000.00

B.

₦ 490,000.00

C.

₦ 480,000.00

D.

₦ 470,000.00

38.

A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of ₦ 22,800.00 was paid as import duty, calculate the cost of the engine.

A.

₦60,000.00

B.

₦120,000.00

C.

₦24,000.00

D.

₦18,000.00

39.

Eric sold his house through an agent who charged 8% commission on the selling price. If Eric received $117,760.00 after the sale, what was the selling price of the house?

A.

$120,000.00

B.

$125,000.00

C.

$128,000.00

D.

$130,000.00

40.

In the diagram, ∆PQR is similar to ∆PWY. WY||QR, |QR| = 15 cm, |WY| = 6 cm and |WP| = 4 cm.

Find |WQ|.

A.

6 cm

B.

12 cm

C.

10 cm

D.

8 cm

41.

The expresson 5x + 3 6x(x + 1) will be undefined when x equals

A.

{-3, 0}.

B.

{-3, -1}.

C.

{0, -1).

D.

{0, 1}.

42.

Simplify: 2x 1 - x2 + 1 1 + x .

A.

1 1 - x

B.

1 1 - x2

C.

2x + 1 1 - x2

D.

2x + 1 1 - x

43.

If 2a = 64 and b a = 3, evaluate a2 + b2.

A.

48

B.

90

C.

160

D.

250

44.

Number of subjects 1 2 3 4 5 6 7 8
Number of students 2 1 4 3 8 5 4 3

The table shows the number of subjects registered by a class of students for an examination.

Use the information to answer the question below

Calculate the mean of the distribution.

A.

2

B.

3

C.

8

D.

5

45.

If 17 = 3 mod x, find the least value of x.

A.

3

B.

5

C.

7

D.

9

46.

Find the equation whose roots are - 1 2 and 1 1 2 .

A.

2x2 -4x + 6 = 0

B.

4x2 -4x - 3 = 0

C.

2x2 +3x + 4 = 0

D.

4x2 -4x + 3 = 0

47.

Find the value of x that satisfies the equation: 2 3 (x + 5) = 1 - x - 7 2 .

A.

1

B.

4

C.

3

D.

2

48.

The following are scores obtained by some students in a test:

8 18 10 14 18 11 13
14 13 17 15 8 16 13

Use this information to answer the question below

How many students scored above the mean score?

A.

7

B.

8

C.

9

D.

10

49.

Evaluate 53,000,000 x 0.002 0.0004

A.

6.65 x 108

B.

6.65 x 107

C.

6.65 x 10-7

D.

6.65 x 10-8

50.

A man will be (x + 10) years old in 8 years time. If 2 years ago he was 63 years, find the value of x

A.

55

B.

63

C.

57

D.

67

THEORY QUESTIONS

1.

(a)

A company bids for two contracts G and H. The probabilities that it will win contracts G and H are 1 5 and 3 8 respectively.

Find the probability that the company wins:

(i)

both contracts;

(ii)

only one contract.

(b)

Amaka drove a car from Samoa to Mepeasem at an average speed of 60 km/h in 135 minutes. On her return journey, she took 3 minutes less to arrive at Samoa.

Find correct to one decimal place the:

(i)

distance between Samoa and Mepeasem;

(ii)

the return speed.

2.

(a)

Using ruler and a pair of compasses only, construct:

(i)

the quadrilateral ABCD such that |AB| = 6.5 cm, |BC| = 9 cm, |AD| = 4 cm, ∠ ABC = 60° and ∠ BAD = 120°;

(ii)

the perpendicular bisectors of BC and CD.

(b)

Locate the point of intersection, T, of the two bisectors in (a(ii).

(c)

With the point T in (b) as centre, draw a circle to pass through the vertices B, C and D.

(d)

Measure:

(i)

|BT|;

(ii)

|CD|.

3.

In the diagram, ABD is a triangle, |AC| = 50 cm and |CD| = d cm.

Find, correct to one decimal place,:

(a)

the value of d;

(b)

|BD|.

4.

(a)

From the top, X of a building 320 m high, the angles of depression of the top, Y and bottom, Z of another building on the same horizontal ground are 29° and 41° respectively.

(i)

Illustrate the information in a diagram.

(ii)

Calculate, correct to the nearest metre, the height of the other building.

(b)

The time taken to travel a distance of 120 km was reduced by 30 minutes when the speed was increased by 20 km/h. Calculate the initial speed.

5.

The mean age of a second year class of a school is 18 2 5 . At the end of the promotion examination, 3 students aged 20, 19 and 19 years were repeated. The new mean age of the class became 18 1 3 .

Calculate the number of students who were in the class before the promotion examination.

6.

(a)

Copy and complete the following table for the relation: y = 2(x + 2)2 - 3 for -5 ≤ x ≤ 2.

x -5 -4 -3 -2 -1 0 1 2
y -1 -3 5

(b)

Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of the relation y = 2(x + 2)2 - 3 for -5 ≤ x ≤ 2.

(c)

Use the graph to find the solution of:

(i)

2(x + 2)2 = 3;

(ii)

2(x + 2)2 = 5.

(d)

For what values of x, from the graph is y increasing in the interval?