OBJECTIVE TEST

PQR is a right-angled triangle. The area of the triangle is 6 cm² and |QR| = 3 cm.

Find |PR|.

2 cm

3 cm

5 cm

6 cm

Use the mapping below to answer the question below.

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	-4	-2	0	2	m

What is the rule for this mapping?

x→ 2(x - 3)

x→ x - 5

x→ 2(x - 2)

x→ 2x-3

Correct 0.024561 to three significant figures.

0.03

0.025

0.0245

0.0246

Simplify $\frac{1}{2}$ - $\frac{2}{3}$ + $\frac{3}{4}$

$\frac{11}{12}$

$\frac{7}{12}$

$\frac{1}{6}$

$\frac{5}{12}$

Find the value of x in the equation $\frac{x}{4}$ = 2

How many faces has a rectangular pyramid?

The pie chart shows the distribution of programmes offered by 720 students at Kofikrom.

Use this information to answer the question below.

Find the value of the angle marked y.

90°

100°

110°

120°

In the Venn diagram Q is the set of numbers inside the circle and R is the set of numbers inside the triangle.

Find Q ∩ R.

{1, 5}

{2, 3, 4}

{6, 7, 8}

{1,2,3,4,5}

{1,2,3,4,5,6,7,8}

Make k the subject of the relation, ky - k = y²

10.

The addition below was carried out in base x. Find x.

	2	4	3
	2	2	1
1	0	1	4	_x

Four

Five

Six

Seven

11.

Express 30 cm as a percentage of 2 m.

0.5%

1.5%

6.7%

15%

66.7%

12.

Make P the subject of the relation, R = $\frac{(P+Q)}{2}$

P = Q - 2R

P = 2R - Q

P = 2R + Q

P = 2Q + R

13.

Find the image of the point S(-2,2) when it is reflected in the y-axis.

(2,-2)

(2,2)

(-2,-2)

(-2,2)

14.

Find the next two numbers in the sequence 2, 5, 9, 14, 20, _ , _ .

26, 34

26, 35

27, 34

27, 35

15.

A simple interest of GH₵ 37,500.00 is earned on an amount of GH₵ 500,000.00 for 3 years. Calculate the percentage rate.

20.0 %

10.0 %

5.0 %

2.5 %

16.

In the diagram below, line PQ is parallel to RS and UV is a line drawn through PQ and RS.

Use the diagram to answer the question below.

Angle b and angle c are

alternate angles.

vertically opposite angles.

corresponding angles.

interior opposite angles.

17.

A man has three children whose ages are 9 years, 12 years and 24 years. Find the ratio of their ages.

1 : 2 : 3

1 : 2 : 4

2 : 3 : 6

3 : 4 : 8

3 : 6 : 8

18.

13	12	17
E	F	10
11	16	G

Use the magic square above to answer the question below

Find the value of F.

19.

Kofi, Kojo and Ama shared GH₵480,000.00 in the ratio 3:5:4.

How much did Ama receive?

GH₵160,000.00

GH₵200,000.00

GH₵218,181.81

GH₵342,859.14

20.

A woman bought a sewing machine for ₵800,000.00 and sold it for ₵920,000.00. Find the percentage profit

12%

13%

15%

16.4%

21.

Find the image of 3 under the mapping, x → 10 - 2x.

22.

The sum of three numbers is 28,542. Two of the numbers are 10,250 and 9,750. Find the third number.

8,452

8,542

9,452

9,542

23.

A box contains 30 identical balls of which 16 are white and the rest yellow. If a girl picks a ball at random from the box, what is the probability that it is a yellow ball?

$\frac{1}{16}$

$\frac{7}{15}$

$\frac{8}{15}$

$\frac{7}{8}$

24.

Esi bought a television set for GH₵ 1,500.00. If she sold it at a profit of 20%, find the selling price.

GH₵ 1,200.00

GH₵ 1,500.00

GH₵ 1,750.00

GH₵ 1,800.00

25.

A bag contains 5 red and 7 black balls of the same size. What is the probability of picking a black ball?

26.

A hall which is 8 m long is represented on a diagram as 4 cm long. What is the scale of the diagram?

1 : 200

1 : 250

1 : 400

1 : 800

27.

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

28.

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

Inverse

Identity

Commutative

Distributive

Associative

29.

An article costs ₵60,000.00. The price was increased by 10%. Find the new price.

₵54,000.00

₵61,000.00

₵66,000.00

₵70,000.00

30.

Evaluate 53 - (-7) + (-15).

31.

Expand – x(3 – 2x).

-2x² - 3x

2x² - 3x

-2x² + 3x

2x² + 3x

32.

The bearing of P from Q is 060^o. Find the bearing of Q from P

120^o

150^o

210^o

240^o

33.

In the diagram, square P¹Q¹R¹S¹ is an enlargement of square PQRS from centre O. The area of PQRS is 4 cm² and the area of P¹Q¹R¹S¹ is 9 cm².

Find the scale factor of the enlargement.

$\frac{2}{3}$

$\frac{4}{9}$

1 $\frac{1}{2}$

- $\frac{2}{3}$

2 $\frac{1}{4}$

34.

The diagram above shows the construction of :

the perpendicular bisector of the line

an angle of 45° at the point A

an angle of 45° at the point B

an angle of 90° at the point O

an angle of 90° at the point B

35.

A car uses 150 litres of petrol in 45 mins. How many litres of petrol will it use in 1 hour?

375 litres

230 litres

225 litres

200 litres

36.

Find the image of 5, under the mapping x → 4x - 7.

37.

In the figure below, triangle ABC is an enlargement of triangle ADE. If |AE| = 20 cm and |EC| = 10 cm. What is the scale factor of the enlargement?

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{5}{2}$

38.

Solve the inequality 2x + 10 ≥ $\frac{7}{2}$ x - 5.

x ≥ 10

x ≤ 10

x ≤ 40

x ≥ 40

39.

In an enlargement, XY → X₁Y₁.

If |XY| = 24 cm and |X₁Y₁| = 8 cm, calculate the scale factor of the enlargement.

$\frac{1}{32}$

$\frac{1}{24}$

$\frac{1}{8}$

$\frac{1}{3}$

40.

If y = k + ax², find y when k = $\frac{14}{5}$ , a = $\frac{4}{5}$ and x = 2.

7 $\frac{3}{5}$

THEORY QUESTIONS

(a)

Using a ruler and a pair of compasses only, construct

(i)

triangle ABC such that AB = 12cm, AC = 8cm and BAC = 30°;

(ii)

a perpendicular from C to meet AB at M.

(b)

Measure

(i)

angle ABC;

(ii)

|CM|.

(c)

Calculate the area of triangle ABC.

(a)

Using a pair of compasses and a ruler only,

(i)

construct triangle ABC such that |AB| = 10 cm, angle ABC = 30° and |BC| = 8 cm. Measure angle ACB.

(ii)

construct a perpendicular from C to meet line AB at D. Measure |CD|.

(b)

Calculate the area of triangle ABC.

(a)

A traffic survey gave the results shown in the table below.

Vehicle	Car	Lorry	Bus	Bicycle
Frequency	15	12	8	25

(i)

Represent the information on a pie chart.

(ii)

What percentage of the vehicles were lorries?

(b)

Akosua was granted a loan of GH₵ 96.00. The interest rate was 24% per annum.

Calculate the

(i)

interest at the end of the year

(ii)

total amount she had to pay at the end of the year

(iii)

amount she still owes, if Akosua was able to pay only GH₵ 60.00 at the end of the year.

Madam Esi used $\frac{1}{4}$ and $\frac{2}{3}$ of her x acres of land to cultivate mangoes and oranges respectively.

(a)

Express, in term of x, the number of acres of the land she used to cultivate:

(i)

mangoes;

(ii)

oranges.

(b)

If madam Esi used 20 more acres of land to cultivate oranges than mangoes, find the value of x.

(c)

How many acres of land was used to cultivate mangoes?

(d)

Calculate, correct to the nearest whole number, the percentage of the land that was not used.

The ages of 20 school children were recorded as follows:

13	9	15	17	13
9	11	9	11	15
17	15	11	9	9
11	15	11	11	11

(a)

Make a frequency table for the data using the ages of 9, 11, 13, ..........

(b)

Use your table to calculate the mean age (correct to the nearest whole number).

(a)

There are 30 boys in a sporting club. 20 of them play hockey and 15 play volley-ball. Each boy plays at least one of the two games.

(i)

Illustrate the information on a Venn diagram

(ii)

How many boys play volleyball only?

(b)

Factorize xy + 3x + 6y + 18

(c)

Multiply (3 + x) by (5 – 2x)