OBJECTIVE TEST

A trader received a commission of 5% on goods sold at GH₵ 25,000.00. Find the commission.

GH₵ 1,250.00

GH₵ 1,200.00

GH₵ 1,100.00

GH₵ 1,000.00

What is the probability of obtaining a prime number when a fair die is thrown once?

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{5}{6}$

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

$\frac{19}{40}$

$\frac{11}{20}$

$\frac{3}{8}$

$\frac{5}{8}$

If q = ut + $\frac{1}{2}$ ft, find q when u = 20, t = 10 and f = 15

350

275

237.5

42.5

A quadrilateral with one pair of opposite sides parallel is called

kite.

rectangle.

square.

trapezium.

The cost of three items at a shop are GH₵ 72.00, GH₵ 1,105.00 and GH₵ 216.00.

If a customer bought all the three items and received a change of GH₵ 107.00, how much did he initially give the shopkeeper?

GH₵ 1,300.00

GH₵ 1,400.00

GH₵ 2,000.00

GH₵ 1,500.00

A rectangular tank is 4 m long, 3 m wide and 2.5 m high. What is the volume of the tank?

24 m³

30 m³

36 m³

48 m³

60 m³

In the diagram, G₁OH₁ is an enlargement of triangle GOH with scale factor k. If |GG₁| = 5cm, |GO| = 2 cm and |G₁H₁| = 1 cm, what is the value of k?

- $\frac{5}{2}$

- $\frac{3}{2}$

- $\frac{2}{5}$

$\frac{2}{3}$

$\frac{3}{2}$

A van travels 154 km in 1 $\frac{3}{4}$ hours. Find its speed in km/h.

77 km/h

88 km/h

100 km/h

269.5 km/h

10.

State the rule of the following mapping:

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	1	4	9	16	25

x→x

x→2x

x→3x

x→x²

x→x³

11.

If 7.2 and 7.9 are two points on a number line, find the number in the middle of these points.

7.35

7.45

7.55

7.65

12.

The volume of a cylinder is 20 π cm³. If the height of the cylinder is 5 cm, find the base radius.

1 cm

2 cm

3 cm

4 cm

13.

If 22% of a rope is 55 m long, find the full length of the rope.

12.1 m

25 m

121 m

250 m

2500 m

14.

A sales girl receives a 5 % commission on all she sells. Find how much she has to sell to receive GH₵ 15.00.

GH₵ 750.00

GH₵ 300.00

GH₵ 75.00

GH₵ 30.00

15.

A shop is rented at GH₵ 9.00 per month. How much money is paid in 1½ years?

GH₵ 162.00

GH₵ 135.00

GH₵ 6.00

GH₵ 13.00

16.

If 2y = 5 - 3x, find x when y = 1.

-2 $\frac{1}{3}$

-1

17.

Express 0.125 as a fraction in its lowest form.

$\frac{1}{8}$

$\frac{1}{9}$

$\frac{1}{12}$

$\frac{1}{16}$

18.

Multiply 247 by 32.

6916

7804

7904

1235

19.

Which of the following statements best describe the construction above?

Constructing 30°

Constructing 60°

Constructing 120°

Constructing 135°

20.

Find the volume of a cube of side 5 cm.

10 cm³

15 cm³

25 cm³

125 cm³

21.

Which of the following is the set of prime factors of 12?

{2, 3}

{1, 2, 3}

{1, 2, 4, 6}

{2, 3, 4, 6}

22.

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

23.

A woman bought 210 oranges for ₵650.00. She sold all of them at 3 for ₵20.00. How much profit did she make?

₵350.00

₵450.00

₵550.00

₵650.00

₵750.00

24.

In the diagram above, KGM is a right-angled triangle and angle GKM = 62°. Find the angle of elevation of K from M.

28°

62°

90°

118°

25.

If the bearing of A from B is 240^o, find the bearing of B from A

040^o

060^o

120^o

300^o

26.

Use the diagram below to answer the question below.

Find the angle marked b.

150^o

140^o

110^o

100^o

27.

The table below shows the distribution of workers in some trades.

Trade	Shoe making	Mining	Road transport	Agriculture	Manufacturing goods
Number of workers	300,000	25,000	160,000	225,000	165,000

Use this information to answer the question below.

How many people are employed under all the trade?

325,000

485,000

650,000

875,000

28.

Find 12 $\frac{1}{2}$ % of GH₵ 80.00

GH₵ 8.00

GH₵ 10.00

GH₵ 12.00

GH₵ 12.50

29.

Write the vector $(\begin{matrix} 6 cm W \\ 4 cm S \end{matrix})$ using cartesian components.

$(\begin{matrix} -6 \\ -4 \end{matrix})$

$(\begin{matrix} -4 \\ -6 \end{matrix})$

$(\begin{matrix} -6 \\ 4 \end{matrix})$

$(\begin{matrix} 6 \\ -4 \end{matrix})$

30.

Use the diagram below to answer the question below.

Find the size of angle y.

75°

80°

100°

105°

31.

Which of the following best describes the statement: "The locus of points 6 cm from a fixed point O?"

A parallel line 6 cm from O

A vertical line 6 cm from point O

A horizontal line 6 cm from point O

An equilateral triangle of side 6 cm

A circle with centre O and radius 6 cm

32.

The pie chart shows the distribution of crops on a farm of area 250 hectares.

Use it to answer the question below.

Find the area of the plot with corn.

48.6

55.3

62.5 ha

83.3 ha

125.0 ha

33.

In a secondary school class, 23 pupils study Economics, 6 pupils study both Government and Economics. 48 pupils study either Government or Economics or both.

Use this information to answer the question below.

What is the total number of pupils who study Government?

34.

Write in standard form 1342.

0.1342 x 10^-3

0.1342 x 10^-4

13.42 x 10²

1.342 x 10³

1.342 x 10⁴

35.

Which of the following can be made from the net below?

Triangular prism

Square pyramid

Triangular pyramid

Cuboid

36.

A straight line passes through the points P(-5,-3) and Q(-4,-7). Find the gradient of the line PQ.

-4

- $\frac{1}{4}$

$\frac{1}{4}$

37.

Solve: 4^x = 32.

2½

3½

38.

If P = {multiples of 4 less than 16}, find P.

{4,8,10}

{4,8,12}

{1,4,8,12}

{4,8,12,16}

39.

Simplify 3a² × 2ab × 4bc

9a³b²c

12a²b²c

24a²b²c

24a³b²c

40.

What is the rule for the mapping below?

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	2	4	8	16	32

y = 2x + 2

y = 2^x

y = x + 2

y = x + 1

y = 2x

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.

The diagram above is a plane figure made up of a rectangle of sides 50 cm by 28 cm and an equilateral triangle of height 24.25 cm. A circle is cut out of the rectangle as shown. If the circle touches three sides of the triangle,

Calculate

(a)

the perimeter of the figure;

(b)

the area of the remaining portion of the figure.

[Take π = $\frac{22}{7}$ ]

(a)

Simplify 2 $\frac{3}{4}$ ÷ $(3 \frac{3}{8} - 1 \frac{1}{12})$

(b)

A ribbon of length 3 m is to be cut into strips of length 14 cm.

(i)

How many strips of length 14 cm were cut?

(ii)

What length of ribbon remained?

(c)

One-fourth of a number is added to one-fifth of the same number. If the result is 18, find the number.

(a)

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

(b)

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

(c)

Plot on the same graph sheet the points A(1, 1), B(4, 3) and C(2, 5). Join the points A, B and C to form a triangle.

(d)

Using the y-axis as the mirror line, draw the image A₁B₁C₁ of the triangleABC, such that A→A₁, B→B₁ and C→C₁. Write down the co-ordinates of A₁, B₁ and C₁.

(e)

Using the x-axis as the mirror line, draw the image A₂B₂C₂ of triangle ABC where A→A₂, B→B₂ and C→C₂.

Using a ruler and a pair of compasses only,

(a)

construct triangle PQR in which |PQ| = 8 cm, angle QPR = 45° and angle PQR = 90°. Measure |QR|

(b)

construct the mediator of line PQ to meet line PR at the point S.

(c)

With S as the centre and radius 3 cm, construct a circle

(a)

Anita bought 51 tubers of yam at 3 for GH₵10.00. If she sold them and made a loss of 40%, how much did she sell each tuber of yam?

(b)

The volume of a cylinder closed at one end is 1056 cm³. If its height is 21 cm, find its:

(i)

diameter;

(ii)

total surface area.

[Take π = $\frac{22}{7}$ ]