OBJECTIVE TEST

Simplify 6p³ × p² ÷ 3p⁴

18p

2p²

The distance between two towns is 12875 km.

Express this distance in standard form.

1.2875 x 10³ km

1.2875 x 10⁴ km

12.875 x 10³ km

128.75 x 10² km

12.875 x 10⁴ km

Express 30 minutes as a percentage of 3 hours 20 minutes

12.5 %

15 %

16⅔ %

20 %

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

60 cm

40 cm

33 cm

30 cm

Factorize 3r²s – 9rs²

rs(3r – s)

3rs(s – 3r)

3rs(r - 3s)

r²s²(3r – 9s)

3r²s²(s – 3r)

Three boys weeded a piece of land in 4 hours. How long would it take 18 boys to weed the same piece of land weeding at the same rate?

$\frac{2}{3}$ hour

3 $\frac{1}{3}$ hours

4 $\frac{2}{3}$

22 hours

24 hours

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

Expand (a + 2b)(a - 2b)

a² - 4ab - 4b²

a² + 4ab - 4b²

a² - 4b²

a² + 4b²

Simplify: (7⁵x7³)÷7⁶

7⁹

7⁴

7³

7²

10.

The perimeter of rectangle is 24 cm. If the length is 7 cm, find its width.

3 cm

5 cm

10 cm

12 cm

11.

Kofi bought 4 books at an average price of ₵2,500.00. If the total cost of 3 of the books was ₵6,500.00, find the cost of the fourth book.

₵3,500.00

₵4,000.00

₵4,500.00

₵6,500.00

₵10,000.00

12.

A farmer left home at 4:35 am and arrived on his farm at 6:18 am. How long did he take to get to his farm?

1 hour 23 minutes

1 hour 43 minutes

2 hours 43 minutes

10 hours 53 minute

13.

Simplify:

14.

Given that E = $\frac{1}{2}$ mc², find E when m = 10 and c = 4

160

15.

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?

$\frac{1}{18}$

$\frac{9}{20}$

$\frac{11}{20}$

$\frac{9}{11}$

16.

Find x, if $\frac{1}{x}$ + $\frac{1}{3}$ = 1

- $\frac{3}{2}$

- $\frac{2}{3}$

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{3}{2}$

17.

Find the rule for the mapping:

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	4	2	0	-2	-4

y = 2x + 2

y = -2x + 2

y = 4x

y = -2x + 6

18.

Mary had a chance to select a number from 1 to 20 randomly. What is the probability that the number is divisible by 3?

19.

Find the value of x in the polygon below

12°

36°

60°

72°

20.

If the set P = {1, 2, 3, 4, 5} which of the following statements best describes P?

Set of whole numbers up to 6

Set of counting numbers less than 6

Set of counting numbers greater than 6

Set of integers less than 6

21.

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

22.

If $\frac{3}{15}$ is equivalent to $\frac{45}{a}$ , find a

225

150

135

23.

A write watch is priced GH₵2,000.00. A shopkeeper allows a discount of 2% on the cost price.

Find the discount on 20 of such wrist watches.

GH₵500.00

GH₵600.00

GH₵800.00

GH₵1,000.00

24.

What type of triangle is ∆PQR?

Equilateral

Isosceles

Scalene

Right-angled

Obtuse-angled

25.

A number is selected at random from: 25,26,27,28,...,35. Find the probability that the number selected is a prime number.

6⁄11

3⁄11

2⁄11

1⁄11

26.

What is the rule for the above mapping?

y = x + 4

y = 3x + 2

y = 4x + 1

y = 5x + 1

27.

Find the rule for the mapping:

1	2	3	4	5	...	n
↓	↓	↓	↓	↓	↓	↓
10	21	32	43	54	...	-

n → 10n

n → (10n + 1)

n → (11n - 1)

n → (7n + 3)

28.

A map is drawn to the scale 1:100,000. What distance in kilometres is represented by 5 cm on the map?

0.5 km

5.0 km

50.0 km

500.0 km

29.

The following are the scores obtained by girls in a beauty contest: 12, 16, 19, 14, 17, 8, 11, 19.

What is the probability of obtaining a score of 19?

$\frac{1}{9}$

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{19}{53}$

$\frac{19}{108}$

30.

The pie chart below shows the performance of Kate in her final examination.

Use the diagram to answer the question below.

What is the angle for French?

120^o

100^o

70^o

35^o

31.

Convert 206 to a base five numeral.

411_five

4011_five

3321_five

1311_five

1131_five

32.

A bag contains 6 white and 8 red balls. What is the probability that a ball picked at random will be a white ball?

$\frac{1}{7}$

$\frac{3}{7}$

$\frac{4}{7}$

$\frac{6}{7}$

33.

One of the factors of the expression 4m² + 12m - 8m - 24 is (4m - 8). Find the other factor.

m - 3

m + 3

2m + 3

2m - 3

34.

Express 120₅ as a number in base 10.

35.

In an office, $\frac{2}{3}$ of the telephone bill is paid by Tom, $\frac{1}{5}$ by Azuma and the remaining by Tina. What fraction is paid by Tina?

$\frac{2}{15}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{7}{15}$

36.

The pie chart above shows the distribution of 360 pupils to various houses in a school.

Use it to answer the question below

How many more students are in Yellow House than in Blue House?

100

37.

What is the rule for the following mapping?

x	0	1	2	3	4
↓	↓	↓	↓	↓	↓
y	5	9	13	17	21

y = x + 5

y = 4x + 5

y = 5x + 4

y = 6x + 1

38.

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}

39.

The simple interest on GH₵ 450.00 for 4 years is GH₵ 45.00, find the rate of interest

2.5 %

10 %

25 %

6.5 %

40.

The dimensions of a cuboid are 2 cm, P cm and 5 cm. Which of the following is an expression for the volume of the cuboid?

7P cm³

(7 + P) cm³

10P cm³

(10 + P) cm³

THEORY QUESTIONS

(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.

Using a ruler and a pair of compasses only,

(a)

construct a triangle ABC such that |BA| = 10 cm, angle ABC = 90° and angle BAC = 30°. Measure the length BC.

(b)

(i)

Bisect the angle ACB to meet BA at D.

(ii)

What type of triangle is CDA?

(c)

Calculate the area of triangle ABC

(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?

(a)

A fair die and a fair coin are thrown together once.

(i)

Write down the set of all possible outcomes.

(ii)

Find the probability of obtaining a prime number and a tail.

(b)

The map of a field is drawn to a scale of 1 : 100. If the width and area of the field on the map are 8 cm and 88 cm² respectively, find in m², the area of the actual field.

(c)

Copy and complete the 3 x 3 magic square such that the sum of the numbers in each row, column and diagonal is equal to 21.

10	3
	7

(a)

Factorize completely 6xy - 3y + 4x - 2.

(b)

The diagram shows a ladder AB which leans against a vertical wall PQ at B. If |PB| is 8 m and the other end of the ladder is 6 m away from the foot of the wall (at P), find the length of the ladder (AB).

(c)

Kojo had 1,800 bags of rice in stock for sale. In January, he sold $\frac{2}{3}$ of it. In February, he sold $\frac{3}{4}$ of what was left.

(i)

What fraction of the stock of rice did he sell

(α)

in February?

(β)

in January and February?

(ii)

How many bags of rice were left unsold by the end of February?

(a)

Mr. Jones used 173 units of electricity last month. If the charge for the first 110 units was ₵150 per unit and ₵200 per unit for the rest, calculate the total bill for Mr. Jones.

(b)

Express 4 hours in seconds leaving your answer in standard form.

(c)

Given the vectors r = $(\begin{matrix} 3 \\ -5 \end{matrix})$ and p = $(\begin{matrix} -7 \\ -9 \end{matrix})$ and q = 2p - r, find q.