OBJECTIVE TEST

In the diagram above, length of PS = Length of SQ and angle SQR = 112^o.

Find the value of x.

68^o

56^o

46^o

44^o

Find the simple interest on GH₵ 600.00 saved for 2 years 8 months at 5% per anum.

GH₵ 64.00

GH₵ 80.00

GH₵ 84.00

GH₵ 92.00

Express 108 as a product of prime factors.

2² x 3³

2³ x 3²

2 x 3⁴

2³ x 3

P = {3, 6, 9, 12, 15}. Which of the following best describes the set P?

The set of multiples of 3 less than 18

The set of multiples of 3

The set of odd numbers

The set of odd numbers less than 16

A graph of a straight line AB is shown below.

Use it to answer the question below

Find the coordinates of the point at which the line cuts the y-axis.

(1, 0)

(0, 1)

(-1, 0)

(0, -1)

(0, 0)

Solve the equation $\frac{1}{5}$ (2 + y) = $\frac{1}{2}$ (y -1).

-3

- $\frac{3}{4}$

$\frac{5}{3}$

In the diagram, XYZ is a triangle. YW is a straight line. Angle XYZ = 52° and angle XZW = 125°.

Find angle YXZ.

35°

55°

73°

107°

Calculate the volume of a cylinder with radius 7 cm and height 10 cm.

[Take π = $\frac{22}{7}$ ]

220 cm³

440 cm³

1,540 cm³

3,080 cm³

Simplify $\frac{2^{2} x 3^{2}}{4^{2} x 3^{3}}$ .

$\frac{1}{12}$

$\frac{1}{6}$

$\frac{1}{4}$

$\frac{1}{3}$

10.

Which of the number lines below represents the inequality 2 < x ≤ 6?

11.

The diagram shows the graph of a linear relation of the form y = mx + c.

Use the graph to answer the question below

Find the equation of the relation.

y = -2x + 3

y = -2x + 2

y = 2x + 3

y = 2x - 3

12.

Find the missing number in the following binary operation:

	1	1	0	0	1	1	0
-	*	*	*	*	*	*	*
		1	1	1	0	1	1

111011

101001

100011

101110

101011

13.

Which property is illustrated by the statement a × (b + c) = a × b + a × c?

Inverse

Identity

Commutative

Distributive

Associative

14.

Find the GCF (HCF) of 2³ × 3² and 2³ × 3⁴.

648

15.

Simplify: 16 + 5.6 + 0.681

2.2281

22.281

222.81

2228.1

16.

In the diagram, QRS is a triangle. Angle QRS = 50° and angle RST = 120°. Find angle RQS.

60°

65°

70°

80°

17.

Find the truth set of 5x – 8 ≤ 2x + 4.

{x ≥ 4}

{x ≥ -4}

{x ≤ 4}

{x ≤ -4}

{x = 4}

18.

Remove the brackets: a – 2(b – 3c)

a – 2b – 3c

a – 2b - 6c

a – 2b + 6c

a + 2b + 6c

a – 2b + 3c

19.

Multiply 247 by 32.

6916

7804

7904

1235

20.

The bar chart shows the distances of 5 villages, P, Q, R, S and T from a market town.

Use it to answer the question below.

How much farther is village Q than village R from the market town?

2 km

3 km

4 km

5 km

6 km

21.

Write 1204_five as a number in base ten.

9996

179

22.

The bar chart shows the mark distribution of pupils in a test. Use it to answer the question below

How many pupils took the test?

23.

Express

as a decimal fraction.

0.3200

0.3125

0.3676

0.3222

24.

When twelve is subtracted from three times a certain number and the result is divided by four, the answer is eighteen. Find the number.

25.

If Y = {house, tree} and V = {cat, house, tree} which of the following is true of Y and V?

Y = V

Y ⊂ V

V ⊂ Y

V ∈ Y

Y ∈ V

26.

A car is travelling at 60 km per hour. How far does it travel in 2 $\frac{1}{2}$ hours?

30 km

60 km

120 km

150 km

27.

Express 72 as a product of prime factors.

2³ x 3²

2² x 3³

2² x 3²

2 x 3

28.

The least number in a set of real numbers is 24 and the greatest is 30. Which of the following is the correct interpretation of the statement?

24 ≤ x ≤ 30

24 < x < 29

23 < x < 29

24 < x < 30

23 ≤ x ≤ 29

29.

Factorize: 5ay - by + 15a - 3b.

(y + 3)(5a - b)

(y + 5)(3a - b)

(y - 3)(5a + b)

(y - 5)(3a + b)

30.

The diagram below shows a circle with centre O, S and T are points on the circle.

Use it to answer the question below

The line ST is called

an arc

a chord

a diameter

a radius

a segment

31.

Divide 1.612 by 0.4.

4.3

4.03

0.403

0.43

32.

In the diagrams above Fig. I is an enlargement of Fig. II. Find the side EF of Fig. II.

20 cm

5 cm

4 cm

3 cm

33.

A car travelled a distance of 50 km in an hour. What distance did it travel in 30 minutes at the same speed?

1,500 km

100 km

80 km

25 km

20 km

34.

If 2y = 6 – 3x, find y when x = 0

–3

–2

35.

Solve: 4x - 2(x + 5) = -10.

x = -10

x = 0

x = $\frac{1}{2}$

x = 2

36.

Find the rule for the mapping:

1	2	3	4	...	t
↓	↓	↓	↓	↓	↓
9	20	31	42	...	...

t → 10t - 1

t → 8t + 1

t → 11t - 2

t → 7t + 2

37.

Simplify: 7a – 3(b – a)

4a – 3b

6a – 3b

8a – 3b

10a – 3b

10a + 3b

38.

The diagram is a square of side 2 cm in which is inscribed a circle with center O.

Use the information to answer the question below.

Find the area of the shaded portion.

[Take π = $\frac{22}{7}$ ]

0.86 cm²

3.00 cm²

6.28 cm²

12.56 cm²

39.

Find the simple interest on ₵28,000.00 at 3 $\frac{1}{2}$ % per annum for 6 months.

₵490.00

₵560.00

₵980.00

₵4,000.00

₵5,880.00

40.

In the diagram below, ACD is an isosceles triangle in which |AD| = |AC| and DC is parallel to BE, find the value of the angle marked x.

55°

62.5°

110°

117.5°

125°

THEORY QUESTIONS

(a)

In a school of 255 students, 80 of them study Arabic only and 125 study French only. Each student studies at least one of the two subjects.

(i)

Draw a Venn diagram to represent the information.

(ii)

How many students study

(α)

both subjects?

(β)

French?

(b)

Make h the subject of v = $\frac{1}{3}$ πr²h.

(c)

A bookseller bought 80 copies of books at GH₵ 3.50 per copy. He sold each of them at GH₵ 4.20. Find

(i)

the total cost price;

(ii)

his percentage profit.

(a)

Given that ₵10,000 = GH₵ 1.00.

Complete the following table relating cedis (x) to Ghana cedis (y).

₵(x)	GH₵(y)
10,000	1
50,000
150,000
250,000
350,000
450,000	45

(b)

(i)

On a graph sheet, draw two perpendicular axes 0x and 0y.

(ii)

Using a scale of 2 cm to ₵50,000.00 on the 0x axis and 2 cm to GH₵ 5.00 on the 0y axis, mark 0x axis from 0 to ₵500,000.00 and 0y axis from 0 to GH₵ 50.00.

(c)

Plot the points and join them with a straight line.

(d)

From your graph, find the value of

(i)

GH₵ 8.00 in cedis (₵);

(ii)

GH₵ 35.00 in cedis(₵);

(iii)

₵260,000.00 in Ghana cedis (GH₵).

(a)

Given the vectors p = $(\begin{matrix} m + 3 \\ 2 - n \end{matrix})$ , q = $(\begin{matrix} 3m - 1 \\ n - 8 \end{matrix})$ and p = q, find the values of m and n.

(b)

A man shared an amount of money between his children Baaba and William in the ratio 6 : 5. Baaba received GH₵ 1,200.00

(i)

find the total amount shared.

(ii)

William invested his share in an account at the rate of 20% simple interest per annum for 2 years. Find the total amount in his account at the end of the 2 years.

Using a rule and a pair of compasses only, construct:

a triangle ABC with |BC| = 9 cm, |AC| = 8 cm and |AB| = 6 cm;

the perpendicular bisector of line BC;

iii

the bisector of angle ACB.

Label the point of intersection of the two bisectors as Y.

Draw a line to join B and Y.

Measure:

|BY|;

|YC|;

iii

the base angles of triangle BYC.

What type of triangle is BYC?

(a)

Using a pair of compasses and ruler only,

(i)

Construct the triangle ABC with |AB| = 8 cm, |BC| = 8cm and |AC| = 7cm.

(ii)

Bisect angle ABC and let the bisector meet AC at D. Produce |BD| to P such that |BD| = |DP|. Join AP and CP.

(b)

Measure

(i)

angle ADB;

(ii)

|AP|.

(c)

What kind of quadrilateral is ABCP?

(a)

Simplify:

(b)

Find the product of (2x - 3) and (2x + 3).

(c)

In the diagram, ABC is an equilateral triangle. Find the value of (x + y).