OBJECTIVE TEST

Express 24 as a product of prime factors.

2 × 3

2² × 3

2³ × 3

2² × 3²

2² × 3³

Write 78910 correct to the nearest thousand.

70,000

78,000

79,000

80,000

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

If a woman was paid ₵180,000.00 for working for 4 $\frac{1}{2}$ days, how much would she be paid for one day?

₵40,000.00

₵45,000.00

₵54,000.00

₵81,000.00

Simplify: 2 × 3² × 3⁴

2 × 3⁵

2 × 3⁶

2 × 3⁸

2 × 9⁶

2 × 9⁸

Make m the subject of the relation:

q = $\frac{1}{3}$ (m + n)h

m = $\frac{3q}{h}$ - n

m = 3q - hn

m = 3q + hn

m = $\frac{3q}{h}$ + n

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

Calculate the gradient of the straight line joining the points A(3,5) and B(–2,3).

$\frac{5}{2}$

$\frac{2}{5}$

- $\frac{2}{5}$

- $\frac{5}{2}$

Given the points S(5, -2) and T(3, 2), calculate the gradient of the line ST.

-2

- $\frac{3}{5}$

$\frac{1}{2}$

10.

Simplify: $\frac{27^{m + 1}}{3^{m + 2}}$

3^2m

3^{2m - 1}

3^{2m + 2}

3^{2m + 1}

11.

In the figure below, PQ and RS are straight lines. Find the value of the angle marked w°.

27°

53°

63°

127°

12.

Ama has 4 one cedi notes and orders an ice cream for GH₵ 1.75 and two toffees at 50 GP each.

How much does she have left?

GH₵ 1.25

GH₵ 1.75

GH₵ 2.25

GH₵ 2.75

13.

The marks obtained by 10 children in a mental drill are: 0, 1, 3, 3, 5, 7, 8, 9, 9, 9.

Use this information to answer the question below.

Find the median mark.

14.

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

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{5}{6}$

15.

Given that N = {x:x is a factor of 18} and M = {x:x is a multiple of 12}, find N ∩ M.

{1,2,3,6}

{1,2,3,6,12}

{2,3,6,12,18}

{}

16.

Simplify (2⁶ x 3⁴) ÷ (2⁴ x 3²)

2² x 3²

2² x 3⁶

2¹⁰ x 3²

2¹⁰ x 3⁶

17.

If the area of the figure above is 60 cm², find x.

8 cm

9 cm

12 cm

16 cm

20 cm

18.

Correct 0.024561 to three significant figures.

0.03

0.025

0.0245

0.0246

19.

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

Triangular prism

Square pyramid

Triangular pyramid

Cuboid

20.

Find the volume of a cylinder of height 3 cm and radius 2 cm.

6π cm³

12π cm³

18π cm³

24π cm³

21.

Use the information below to answer the question below.

A rectangular tank has length 3 m, width 2 m and height 1.5 m.

The Alpha Water Company charges ₵40,000.00 for every 1 m³ of water.

Find how much it will cost to fill the tank completely.

₵180,000.00

₵240,000.00

₵300,000.00

₵360,000.00

22.

If A = {1, 3, 5, 7, 9, 11, 13, 15} and B = {3, 6, 9, 12, 15}, find n(A∩B).

23.

Use the graph below to answer the question below.

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

State the period within which he travelled to town Y after his first rest?

1:00 – 2:00 pm

1:00 – 4:00 pm

1:15 – 1:30 pm

1:30 – 2:00 pm

2:00 – 4:00 pm

24.

Find the tangent of the angle marked y in the diagram below.

$\frac{3}{5}$

$\frac{3}{4}$

$\frac{4}{5}$

$\frac{4}{3}$

$\frac{5}{3}$

25.

A football match starts at 2.20 p.m. and lasts for 1 hour 50 minutes. At what time will the game end?

3.10 p.m.

4.10 p.m.

5.10 p.m.

6.10 p.m.

26.

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?

27.

A pineapple which was bought for GH₵1.00 was sold at GH₵1.30. Calculate the profit percent.

10%

20%

23%

30%

28.

Which of the following describes the relationship between the sets A and B in the Venn diagram below?

A ⊂ B

A ∩ B = 5

A ∩ B = ∅

A ∪ B = {1, 2, 3, 4, 5, 6, 7}

B ⊂ A

29.

A rod 200 cm long is broken into two parts. The shorter part is one-quarter of the length of the rod. Express the shorter part as a percentage of the longer part.

25%

30%

33.33%

66.67%

30.

Find the gradient of the line that joins the points A(-3,5) and B(7,-2).

31.

If w = 12, x = 5, y = 6 and z = 4, find the value of wx - yz.

32.

A cylinder has a radius 6 cm and height 7 cm. Find its volume.

[Take π = $\frac{22}{7}$ ]

132 cm³

264 cm³

294 cm³

792 cm³

924 cm³

33.

Kojo is 20% heavier than Afua. If Kojo weighs 6 kg, what is Afua’s weight?

4.8 kg

5.0 kg

6.0 kg

7.2 kg

34.

Which of the following expressions is illustrated on the number line.

x ≤ -2

x < -2

x ≥ -2

x > -2

35.

The marks obtained by 10 children in a mental drill are: 0, 1, 3, 3, 5, 7, 8, 9, 9, 9.

Use this information to answer the question below.

What is the modal mark?

36.

How many lines of symmetry has an equilateral triangle?

37.

Simplify $\frac{2^{10} x 3^{2}}{3^{6} x 2^{8}}$

$\frac{2^{2}}{3^{4}}$

$\frac{3^{4}}{2^{2}}$

3³ x 2⁴

$\frac{2^{4}}{3^{4}}$

38.

Esi and Kwasi are 12 and 8 years old respectively. They share 60 mangoes in the ratio of their ages. How many mangoes does Esi get?

39.

The point P(5,4) is reflected in the y-axis. Find its image.

(-5,4)

(5,-4)

(-4,5)

(4,-5)

40.

If set B is a subset of set A, then

sets A and B have the same number of elements.

some members of set B can be found in set A.

no member of set B is in set A.

all the members of set B are in set A.

THEORY QUESTIONS

(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

(a)

Solve $\frac{4x - 3}{2}$ = $\frac{8x - 10}{8}$ + 2 $\frac{3}{4}$

(b)

Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular lines OX and OY on a graph sheet for the x-axis from -5 to 5 and the y-axis from -6 to 6.

(i)

Plot the points A(2, 3) and B(-3, 4) and join them with a long straight line.

(ii)

Plot on the same graph sheet, the points C(4, 2) and D(-2, -3) and join them with a long straight line to meet the line through AB.

(iii)

Measure the angle between the lines through AB and CD.

(iv)

Find the coordinates of the point at which the lines through AB and CD meet.

Solve:

Multiply 0.03858 by 0.02, leaving the answer in standard form.

A cylindrical container of height 28 cm and diameter 18 cm is filled with water. The water is then poured into another container with a rectangular base of length 27 cm and width 11 cm. Calculate the depth of the water in the container. (Take π = 22⁄7)

(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?

Ama was granted a loan of ₵800,000.00 by a bank. The rate of interest was 42% per annum.

(a)

Calculate

(i)

the interest at the end of the year;

(ii)

the total amount Ama had to pay at the end of the year.

(b)

Ama was able to pay only ₵700,000.00 at the end of the year.

(i)

Find how much Ama still owed the bank.

(ii)

Express the amount Ama owed after paying the ₵700,000.00 to the bank as a percentage of the loan she took from the bank.

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.