OBJECTIVE TEST

A rectangle has a length of 8 cm and a breadth of 6 cm. How long is its diagonal?

At a meeting attended by 23 people, the females were 7 more than the males. How many males were there?

A bag contains 4 blue and 8 red balls. What is the probability of picking a blue ball at random from the bag?

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{3}{4}$

The table shows the marks of some students in a test. Use the information to answer the question below.

Marks	0	1	2	3	4	5	6	7	8	9	10
Number of students	3	4	5	4	5	4	7	3	4	2	2

What is the modal mark?

In an enlargement with scale factor k, which of the following statements is not true?

Each length is multiplied by k

Each angle remains the same

The shape of the figure does not change

The size of the figure does not change

Corresponding lines are parallel

Subtract (7x-3) from (5-3x).

10x-8

4x-8

8-10x

2-10x

Simplify -35 – (-15) + (-30)

–50

Use the following information to answer the question below.

The pie chart below shows how a man spends his monthly salary.

If the man earns ₵720,000.00 monthly, find how much he spends on food.

₵120,000.00

₵180,000.00

₵210,000.00

₵240,000.00

In the diagram below, |AE| = |ED| = |DC| = |CE|.

Calculate the size of the angle marked x.

150°

120°

90°

60°

30°

10.

Simplify 2ab² × 3a²b

5a³b³

5a²b²

6a³b³

5a²b²

36ab

11.

In a school of 940 pupils, the number of girls exceeds the number of boys by 150. How many girls are there in the school?

620

545

470

395

12.

A man was 24 years old when his son was born. Now he is three times as old as his son. Find the age of the son.

6 years

12 years

18 years

36 years

13.

A trader sold 90 oranges at 3 for GH₵ 0.75. How much did she get from selling all the oranges?

GH₵ 22.50

GH₵ 67.50

GH₵ 75.00

GH₵ 225.50

14.

The stem and leaf plot shows the marks scored by students in a French test. Use the information to answer the question below.

Stem	Leaf
2	0 2 5 7 8
3	2 7 9
4	3 5 5 5
5	4 6 6 8
6	3 5 7
7	0 6

What is the modal mark?

15.

Find the highest (greatest) common factor of 63 and 81.

16.

How long will the simple interest on GH₵ 550.00 AT 12% per annum be GH₵ 132.00?

1 year

2 years

4 years

12 years

17.

What is the place value of 7 in 24.376?

Unit

Ten

Tenth

Hundredth

18.

In the relation $\frac{1}{R}$ = $\frac{1}{R_{1}}$ + $\frac{1}{R_{2}}$ , if R₁ = 1 and R₂ = 3,
find R

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{3}{2}$

$\frac{4}{3}$

19.

The table below gives the ages of members of a juvenile club.

Use it to answer the question below

Age in years	8	9	10	11
Frequency	5	10	6	9

What is the modal age of the members of the club?

8 years

9 years

10 years

11 years

20.

Simplify 2² × 3² × 2³ × 3⁴.

2² × 3⁶

2⁴ × 3⁷

2⁵ × 3⁶

2⁶ × 3⁸

21.

Correct 0.003858 to three significant figures

0.00385

0.00386

0.0039

386

22.

The sum of the ages of Kwaku and Kojo is 30 years. Kwaku is 4 years older than Kojo. How old is Kojo?

23.

Which of the following statements about sets is true?

Every set is a subset of the null set.

The universal set is the subset of the null set.

The intersection of two sets is always null set.

The universal set is the union of all its subsets.

24.

Use the diagram below to answer the question below

Find the value of x.

68^o

75^o

112^o

124^o

25.

If the two figures ABCD and PQRS are similar, find the value of b.

60 cm

40 cm

33 cm

30 cm

26.

In the diagram below, K is an enlargement of J. Use it to answer the question below.

Find the value of x.

3.0 m

3.5 m

4.5 m

6.0 m

9.0 m

27.

Arrange the following fractions in descending order of magnitude: $\frac{1}{2}$ , $\frac{17}{20}$ , $\frac{3}{4}$

$\frac{3}{4}$ , $\frac{17}{20}$ , $\frac{1}{2}$

$\frac{17}{20}$ , $\frac{3}{4}$ , $\frac{1}{2}$

$\frac{1}{2}$ , $\frac{3}{4}$ , $\frac{17}{20}$

$\frac{1}{2}$ , $\frac{17}{20}$ , $\frac{3}{4}$

28.

Simplify: ( $\frac{2}{3}$ - $\frac{1}{2}$ ) ÷ $\frac{1}{6}$

$\frac{1}{36}$

$\frac{1}{12}$

29.

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

30.

Correct 0.024561 to three significant figures.

0.03

0.025

0.0245

0.0246

31.

Find the Lowest Common Multiple (LCM) of 2² x 3 x 5² and 2³ x 3² x 5.

2² x 3 x 5

2² x 3² x 5²

2³ x 3 x 5

2³ x 3² x 5²

32.

Describe the set of M = {2, 3, 5, 7, 11, 13, 17, 19} in words.

M = {odd numbers less than 20}

M = {factors of 19}

M = {prime numbers less than 20}

M = {whole numbers less than 20}

33.

There are 18 girls and 22 boys in a class. A prefect is to be chosen at random from the class. What is the probability that the prefect will be a girl?

$\frac{1}{18}$

$\frac{9}{20}$

$\frac{11}{20}$

$\frac{9}{11}$

34.

An angle which is more than 90° but less than 180° is

an acute angle

a right angle

an obtuse angle

a reflex angle

35.

Use the information below to answer the question below

The scores obtained by 8 pupils in a test are 2, 3, 4, 5, 7, 8, 8 and 9

What is the probability that a pupil chosen at random scores 8 marks?

$\frac{1}{8}$

$\frac{4}{23}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{2}$

36.

In the diagram below, the angle of elevation of K from M is

17°

73°

90°

107°

163°

37.

Find the value of x in the polygon below

12°

36°

60°

72°

38.

If p = $(\begin{matrix} 4 \\ 3 \end{matrix})$ and q = $(\begin{matrix} -2 \\ 7 \end{matrix})$ , find 4p - 2q.

$(\begin{matrix} 12 \\ -2 \end{matrix})$

$(\begin{matrix} 12 \\ 2 \end{matrix})$

$(\begin{matrix} 20 \\ -2 \end{matrix})$

$(\begin{matrix} 20 \\ 2 \end{matrix})$

39.

Simplify: 11 – (11 – 4) + 13.

–7

–17

40.

In an examination, 25% of the candidates failed to obtain the pass mark. The number of candidates who passed was 150. How many candidates failed?

113

100

THEORY QUESTIONS

(a)

E and F are subsets of the universal set U such that

U = {natural numbers less than 15}

E = {even numbers between 1 and 15} and

F = {multiples of 4 between 9 and 15}

(i)

List the elements of U, E and F.

(ii)

Draw a Venn diagram to show the sets U, E and F.

(b)

In a school, $\frac{7}{10}$ of the pupils like Mathematics. Half of those pupils who like Mathematics are girls. If there are 240 pupils altogether in the school, how many girls like Mathematics?

(c)

A typist charges 28 Gp for the first five sheets and 8 Gp for each additional sheet she types. How much will she earn, if she types 36 sheets?

Solve:

The ratio of boys to girls in a school is 12:25. If there are 120 boys.

i) how many girls are in the school?
ii) what is the total number of boys and girls in the school?

Simplify:

(a)

If r =

and m =

, find p given p = r - m.

(b)

The sum of two numbers is 81. If the second number is twice the first, find the second number

(c)

The floor of a rectangular hall is of length 9 m and width 4 m. How many tiles of 20 cm by 30 cm can be used to cover the floor completely.

(a)

The following are the ages in years of members of a group: 8, 11, 8, 10, 6, 7, 3x, 11, 11.

If the mean age is 9 years, find

(i)

(ii)

the modal age

(iii)

the median age.

(b)

Draw a bar chart for the distribution

(a)

Using a pair of compasses and ruler only, construct

(i)

triangle ABC with │AB│ = 10cm, angle ABC = 30° and angle CAB = 60° ;

(ii)

a perpendicular from the point C to meet the line AB at P.

(b)

(i)

Extend line CP to the point D such that │BC│ = │BD│.

(ii)

Join A to D and B to D.

(iii)

Measure │AC│ and │AD│.

(c)

What type of quadrilateral is ADBC?

(a)

A man travelled from Bakwa to Pabam. The distance between the two towns is 510 km. At Pabam he covered additional 40 km on official duties. He returned to Bakwa the next day.

(i)

Find the total distance covered by the man

(ii)

If the car used one litre of petrol to cover 20 km, find the amount of petrol used for the whole journey.

(iii)

If a litre of petrol cost ₵522.00, calculate the total cost of petrol used for the whole journey.

(b)

A woman sold an article for ₵200,000.00. She made a profit of 25%. Find the cost price of the article