OBJECTIVE TEST

Arrange the following fractions from the lowest to the highest: $\frac{3}{4}$ , $\frac{2}{3}$ and $\frac{3}{5}$ .

$\frac{3}{5}$ , $\frac{2}{3}$ , $\frac{3}{4}$

$\frac{3}{5}$ , $\frac{3}{4}$ , $\frac{2}{3}$

$\frac{3}{4}$ , $\frac{2}{3}$ , $\frac{3}{5}$

$\frac{3}{4}$ , $\frac{3}{5}$ , $\frac{2}{3}$

$\frac{2}{3}$ , $\frac{3}{5}$ , $\frac{3}{4}$

Ama covered a distance of 100m in 12 seconds. Express her speed in kilometres per hour.

5km/h

10 km/h

20 km/h

30 km/h

Madam Nancy wants to know which of the teachers in her school is liked best by most of the students. Which of the following methods is most suitable for collecting the data?

Experiment

Database

Questionnaire

Observation

There are 15 females in a debating club. If the ratio of females to males is 3:2, how many members are in the club?

Use the mapping below to answer the question below.

( $\frac{1}{2}$ ) → (1) → (3.14)

(1) → (2) → (6.28)

(2) → (4) → (12.56)

(3) → (6) → (x)

(y) → (10) → (31.4)

Find the value of y

Use the mapping below to answer the question below.

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	-4	-2	0	2	m

Find m.

–4

Find the highest(greatest) common factor of 35 and 70.

Two interior angles of a triangle are (3x - 10)° and (4x + 20)°. Find an expression for the third angle.

(170 - 7x)°

(150 - 5x)°

(120 - 7x)°

(100 - 5x)°

The following are the angles formed at the centre of a circle: 30°, 70°, 120°, 2x and 5x. Find the value of x.

100

140

10.

In the diagram, line MN is parallel to line TU, line TS cuts line MN at O and ∠MOS = 115^o. Find ∠OTU.

65^o

55^o

45^o

25^o

11.

In a class, there are 12 girls and 48 boys. Find the percentage of boys in the class.

20%

40%

60%

80%

12.

There are 6 girls and 18 boys in a class. What percentage of the class are girls?

14.40%

25.00%

33.33%

66.67%

75.00%

13.

Use the following information to answer the question below.

The relation between the Celsius (C) and Fahrenheit (F) scale of temperature is given by:
C = $\frac{5}{9}$ (F - 32).

If C is 40, F will be

104.0

78.4

72.0

65.6

40.0

14.

The marks obtained by 10 boys in a test are 0, 1, 3, 3, 5, 7, 8, 9, 9, 9.

Use this information to answer the question below

Calculate the mean score.

4.4

5.4

6.0

6.4

9.0

15.

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

16.

Write 1101101_two in base ten

108

109

218

17.

A man travelled a distance of 1.5 km in 30 minutes. What distance can he cover in 50 minutes, travelling at the same speed?

2.2 km

2.5 km

2.8 km

3.2 km

18.

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

$\frac{1}{36}$

$\frac{1}{12}$

19.

Aba bought a carton of fish at GHC 80.00 and sold it at a profit of GHC 13.60. Find the selling price.

GH₵ 66.40

GH₵ 93.60

GH₵ 103.60

GH₵ 144.00

20.

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

Find the mean score.

4.50

5.75

6.00

8.75

10.00

21.

Using the following mapping, find the missing numbers p and q.

x	1	2	3	4	5	6
↓	↓	↓	↓	↓	↓	↓
y	3	5	p	9	11	q

p = 6, q = 12

p = 6, q = 13

p = 7, q = 12

p = 7, q = 13

22.

A story book contains 50 pages. If a student reads 10 pages per hour, find the relationship between the number of unread pages (N) and time (t).

N = 10t + 50

N = -10t + 50

N = - $\frac{1}{10}$ t + 5

N = 10t - 50

23.

In a class of 24 pupils, 10 study French only and 8 study English only. If each pupil studies at least one of the two subjects, how many study English?

24.

The ages in years of 10 children at a party are 2,3,3,3,4,4,5,5,5 and 6. If a child is chosen at random, what is the probability that he or she is not less than 5 years old?

$\frac{2}{3}$

$\frac{2}{5}$

$\frac{3}{10}$

$\frac{1}{2}$

25.

In the Venn diagram M and N are the subsets of the universal set U.

Use this information to answer the question below.

How many members are in the set N?

26.

An equilateral triangle has side 16cm. A square has the same perimeter as the equilateral triangle. What is the area of the square?

48 cm²

96 cm²

144 cm²

256 cm²

27.

The figure QPR is an equilateral triangle. If angle PRS = (2x - 10)^o, find the value of x.

28.

What is the value of x in the relation 5^x = 125?

29.

Which of the following is not a quadrilateral?

Hexagon

Kite

Rectangle

Trapezium

30.

Use the graph below to answer the question below.

The travel graph describes the journey of a cyclist from Town X to Town Y.

How many minutes did the cyclist spend at town Y?

15 minutes

20 minutes

30 minutes

45 minutes

60 minutes

31.

If $(\begin{matrix} 4 \\ 11 \end{matrix})$ = $(\begin{matrix} x - 3 \\ 11 \end{matrix})$ , find the value of x.

-1

32.

State the property used in the statement: p(q + r) = pq + pr

Associative

Commutative

Distributive

Identity

Universal

33.

What is the rule for this mapping?

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	1	3	5	7	9

x→2x - 1

x→2(x - 1)

x→2x + 1

x→2(x + 1)

x→2x - 1

34.

In the diagram above, AB is parallel to CD. Angles x and y are

alternate angles

corresponding angles

vertically opposite angles

co-interior angles

35.

Given that A = {b, c, i} and B = {a, e, f, i}, find A ∩ B.

{a, b, c, e, f, i}

{f, i}

{a}

{i}

36.

The figure below is a cuboid wih dimensions x cm by y cm by z cm. Find the area of the face PQRV.

xy cm²

yz cm²

x² cm²

xz cm²

37.

The pie chart shows the monthly expenditure of Mr. Awuah whose monthly income is ₵18,000.00.

Use the chart to answer the question below.

What fraction of Mr. Awuah's income is spent on food?

$\frac{1}{6}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{2}{5}$

$\frac{1}{2}$

38.

If c = $\frac{b^{2} + 4r}{2ar}$ , find c when b = 3, r = 4 and a = 5

$\frac{19}{40}$

$\frac{11}{20}$

$\frac{3}{8}$

$\frac{5}{8}$

39.

If x →3x – 4, what is the image of –2?

–10

–2

–1

40.

A man can take 12 hours to do a piece of work. How long will it take 6 men working at the same rate to do the work?

6 hours

3 hours

2 hours

72 hours

THEORY QUESTIONS

In the Venn diagram, M and N are intersecting sets in the universal set µ.

(a)

Express n(M) and n(N) in terms of x.

(b)

Given that n(M) = n(N), find the:

(i)

Value of x.

(ii)

n(µ)

(c)

Simplify: 2⁶ ÷ (2² x 2¹) ÷ 2⁵.

(a)

(i)

Using a pair of compasses and ruler only, construct triangle XYZ with XZ = 12cm, XY = 10cm and angle XYZ = 90°.

(ii)

Measure YZ.

(iii)

Calculate the area of triangle XYZ

(iv)

Measure angle ZXY.

(b)

An isosceles triangle has a perimeter of (9y – 15) cm.

What is the length of each of the two equal sides, if its third side is (3y – 7) cm?

Simplify: 5(6 - ab) + 2(-7 + 3ab)

The equation of a straight line is given by 3x - 2y - 6 = 0. Find the:
(i) gradient of the line;
(ii) y-intercept

Adwoa received a commission of 20% on bread she sold. In one week, Adwoa's commission was GH₵ 540.00.
(i) How much bread did she sell during that week?
(ii) Find her average daily commission.

(a)

Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes, OX and OY on a graph sheet.

(b)

On the graph sheet, mark the x-axis from –5 to 5 and the y-axis from –6 to 6

(c)

(i)

Plot on the same graph sheet the points A(1, 1 $\frac{1}{2}$ ), B(4, 1 $\frac{1}{2}$ ), C(1, 4).

(ii)

Join the points to form a triangle. What type of triangle have you drawn?

(d)

Draw the image triangle A₁B₁C₁ of ABC under a reflection in the y-axis, where A→A₁, B→B₁ and C→C₁. Label the vertices and the co-ordinates clearly.

(e)

Draw the image triangle A₂B₂C₂ of triangle ABC under an enlargement with scale factor –1 with the centre of enlargement as the origin (0,0), where A→A₂, B→B₂ and C→C₂. Show all lines of enlargement. Label the vertices and co-ordinates clearly

(f)

What single transformation maps A₁B₁C₁ onto A₂B₂C₂ where A₁→A₂, B₁→ B₂ and C₁→C₂?

The table below shows the marks scored out of 10 by some candidates in a test.

Mark	1	2	3	4	5	6	7	8
Number of candidates	2	3	5	7	8	13	7	5

(a)

From the table, find

(i)

the modal mark;

(ii)

how many candidates took the test;

(iii)

the mean mark for the test.

(b)

If 20% of the candidates failed,

(i)

how many failed?

(ii)

What is the least mark a candidate should score in order to pass?

(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)