OBJECTIVE TEST

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

Find the value of y.

43°

47°

54°

86°

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.

15 $\frac{1}{2}$ years

16 years

16 $\frac{1}{2}$ years

17 years

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

13 cm

20 cm

25 cm

31 cm

Find the nth term of the Geometric Progression (G.P): $\frac{1}{2}$ , $\frac{1}{4}$ , $\frac{1}{8}$ , ...

2^{n - 1}

2ⁿ

$\frac{1}{2^{n}}$

$\frac{1}{2^{n - 1}}$

Correct 0.00798516 to three significant figures.

0.0109

0.0800

0.00799

0.008

Given that P ∝ $\frac{v^{2}}{x}$ and x ∝ vt express P in terms of v and t.

P ∝ $\frac{t}{v}$

P ∝ $\frac{v}{t}$

P ∝ vt

P ∝ $\frac{1}{vt}$

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

- $\frac{5}{2}$

- $\frac{3}{2}$

$\frac{3}{2}$

$\frac{5}{2}$

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

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

p = 2, q = 5, r = 3

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

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

Find the value of x in the diagram.

10.

Express 0.0063075 correct to three significant figures.

0.006

0.0063

0.00631

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.

24 cm²

18 cm²

12 cm²

10 cm²

12.

If tan x = $\frac{3}{4}$ , 0 < x < 90, evaluate $\frac{cos x}{2sin x}$

$\frac{2}{3}$

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{8}{3}$

13.

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

15 cm

12 cm

10 cm

20 cm

14.

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

62°

42°

52°

32°

15.

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

How tall is the tree?

8 m

8 $\sqrt{3}$ m

14 m

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?

GH₵ 0.35

GH₵ 0.30

GH₵ 0.22

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?

₦92,800.00

₦252,800.00

₦320,000.00

₦332,000.00

18.

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

-7

-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 = $\frac{22}{7}$ ]

240 cm

552 cm

480 cm

595 cm

20.

Given that tan x = $\frac{12}{5}$ , find the value of (sin x cos x)

$\frac{165}{60}$

$\frac{169}{65}$

$\frac{60}{169}$

$\frac{65}{169}$

21.

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

22.

Solve: $\frac{x - 2}{4}$ - $\frac{2x - 4}{3}$ = $\frac{5}{6}$ .

x = 0

x = 5

x = 4

x = 2

23.

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

5x + 2y = 13

5x - 2y = 10

2x - 5y = 10

2x + 5y = 13

24.

Make m the subject of the relation k = $\sqrt{\frac{m - y}{m + 1}}$ .

m = $\frac{y - k^{2}}{1 - k^{2}}$

m = $\frac{y - k^{2}}{k^{2} + 1}$

m = $\frac{y + k^{2}}{1 - k^{2}}$

m = $\frac{y + k^{2}}{k^{2} + 1}$

25.

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

- $\frac{1}{20}$

$\frac{7}{20}$

- $\frac{3}{20}$

$\frac{1}{20}$

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?

$\frac{11}{20}$

$\frac{9}{20}$

$\frac{3}{10}$

$\frac{1}{4}$

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?

10.00 a.m.

11.00 a.m.

12.00 noon

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.

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.

18°

52°

60°

45°

30.

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

31.

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

Calculate its perimeter.

26 cm

24 cm

17 cm

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.

$955.38

$1,230.00

$1,129.09

$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.

8.2 cm

5.7 cm

4.1 cm

2.9 cm

34.

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

23^o

38^o

46^o

67^o

35.

If 101_two + 12_y = 23_five, find the value of y.

36.

Find the value of x for which $\frac{2x - 1}{x^{2} + 2x + 1}$ is not defined.

$\frac{1}{2}$

-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.

₦ 500,000.00

₦ 490,000.00

₦ 480,000.00

₦ 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.

₦60,000.00

₦120,000.00

₦24,000.00

₦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?

$120,000.00

$125,000.00

$128,000.00

$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|.

6 cm

12 cm

10 cm

8 cm

41.

The expresson $\frac{5x + 3}{6x(x + 1)}$ will be undefined when x equals

{-3, 0}.

{-3, -1}.

{0, -1).

{0, 1}.

42.

Simplify: $\frac{2x}{1 - x^{2}}$ + $\frac{1}{1 + x}$ .

$\frac{1}{1 - x}$

$\frac{1}{1 - x^{2}}$

$\frac{2x + 1}{1 - x^{2}}$

$\frac{2x + 1}{1 - x}$

43.

If 2^a = $\sqrt{64}$ and $\frac{b}{a}$ = 3, evaluate a² + b².

160

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.

45.

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

46.

Find the equation whose roots are - $\frac{1}{2}$ and 1 $\frac{1}{2}$ .

2x² -4x + 6 = 0

4x² -4x - 3 = 0

2x² +3x + 4 = 0

4x² -4x + 3 = 0

47.

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

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?

49.

Evaluate $\frac{53,000,000 x 0.002}{0.0004}$

6.65 x 10⁸

6.65 x 10⁷

6.65 x 10^-7

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

THEORY QUESTIONS

(a)

A company bids for two contracts G and H. The probabilities that it will win contracts G and H are $\frac{1}{5}$ and $\frac{3}{8}$ 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.

(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|.

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|.

(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.

The mean age of a second year class of a school is 18 $\frac{2}{5}$ . 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 $\frac{1}{3}$ .

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

(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?