OBJECTIVE TEST

Kwame and Ama shared an amount of money in the ratio 5:4 respectively. If Kwame had GH₵ 9.00, how much did they share?

GH₵ 16.20

GH₵ 36.00

GH₵ 45.00

GH₵ 81.00

Convert 11001_two to a decimal numeral.

Solve 25x + 450 ≤ 3000.

x ≥ 102

x ≤ 102

x ≥ 138

x ≤ 138

How many faces has a cuboid?

Study the triangle of odd numbers and use it to answer the question below.

13		b		c		19
	7		9		a
		3		5
			1

Evaluate: 13 + b + c + 19.

Given that vectors u = $(\begin{matrix} -3 \\ 5 \end{matrix})$ and v = $(\begin{matrix} 2 \\ -3 \end{matrix})$ , calculate 2v - u.

$(\begin{matrix} 1 \\ -1 \end{matrix})$

$(\begin{matrix} -1 \\ 1 \end{matrix})$

$(\begin{matrix} -7 \\ -11 \end{matrix})$

$(\begin{matrix} 7 \\ -11 \end{matrix})$

If u = $(\begin{matrix} 1 \\ 3 \end{matrix})$ and v = $(\begin{matrix} 4 \\ -2 \end{matrix})$ , find 2u + 3v.

$(\begin{matrix} 5 \\ 1 \end{matrix})$

$(\begin{matrix} 11 \\ 5 \end{matrix})$

$(\begin{matrix} 11 \\ 13 \end{matrix})$

$(\begin{matrix} 14 \\ 0 \end{matrix})$

$(\begin{matrix} 14 \\ 12 \end{matrix})$

There are 12 red and 8 blue balls in a bag. If a ball is selected at random from the bag, what is the probability that it is red?

$\frac{2}{5}$

$\frac{2}{3}$

$\frac{3}{5}$

$\frac{4}{5}$

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

10.

Ama is three times as old as Kofi. The sum of their ages is 40. How old is Ama?

10 years

30 years

37 years

43 years

11.

Factorize completely the expression 2xy – 6y + 7x – 21

(x – 3)(2y + 7)

(x + 3)(2y – 7)

(y – 3) (2x +7)

(y + 3) (2x – 7)

12.

P = {3, 6, 9, 12, 15}. Which of the following best describes the set P?

The set of multiples of 3 less than 18

The set of multiples of 3

The set of odd numbers

The set of odd numbers less than 16

13.

Kofi deposited ₵500,000.00 with a bank for 2 years at a rate of 10% per annum. Find the simple interest

₵10,000.00

₵20,000.00

₵50,000.00

₵100,000.00

14.

It takes 6 students 1 hour to sweep their school compound. How long will it take 15 students to sweep the same compound?

24 minutes

12 minutes

3 hours

2 hours

15.

Make m the subject of the relation $\frac{1}{m}$ = $\frac{1}{p}$ + $\frac{1}{r}$ .

m = $\frac{pr}{r + p}$

m = $\frac{pr}{r - p}$

m = $\frac{r - p}{pr}$

m = $\frac{r + p}{pr}$

16.

The area of circle, centre O, is 120 cm². Angle AOB is 60°. Find the area of sector AOB.

2 cm²

3 cm²

6 cm²

20 cm²

60 cm²

17.

Kwame gets a commission of 20% on bread sold. In one week, Kwame's commission was ₵45,000.00. How much bread did he sell during that week?

₵205,000.00

₵220,000.00

₵225,000.00

₵235,000.00

18.

Find in base ten the value of 4 in 143_five.

19.

Write 1930.54 in standard form.

1.93054 X 10³

1.93054 X 10^-3

1.93054 X 10^-2

1.93054 X 10²

20.

The length of a rectangular fence is 25 m. The ratio of the length to the width is 5:3. Find the width of the rectangular fence.

9 m

13 m

15 m

16 m

21.

Simplify 2ab² × 3a²b

5a³b³

5a²b²

6a³b³

5a²b²

36ab

22.

Solve the equation: 2x -3(x - 1) = 6

-3

-7

-9

23.

The table below gives the distribution of ages of students in a class.

Use it to answer the question below.

Ages (years)	13	14	15	16	17
Number of students	3	10	6	7	4

If a student is selected at random from the class, what is the probability that the student is 15 years old?

$\frac{1}{5}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

24.

Simplify: (46 x 102) + (102 x 54)

1,020

10,200

102,000

1,020,000

25.

Evaluate $\frac{1}{2}$ [(4 – 1) – (5 – 6)]

–4.0

1.0

2.0

3.0

4.0

26.

State the rule for the mapping

x	1	2	3	4
↓	↓	↓	↓	↓
y	15	30	46	60

x → 15x

x → 15 + x

x → $\frac{15}{x}$

x → 10 + 5x

27.

The height of a cylinder is 5 cm and the radius 7 cm. Find the volume of the cylinder.

[Take π = $\frac{22}{7}$ ]

770 cm³

700 cm³

154 cm³

110 cm³

28.

The diagram below shows a circle with centre O, S and T are points on the circle.

Use it to answer the question below

What name is given to the shaded region?

sector

segment

radii

arc

cone

29.

What is the median of the following numbers:
4,16,13,18,3,20,6,7,15,2,10,12?

30.

In the figure below, triangle ABC is an enlargement of triangle ADE. If |AE| = 20 cm and |EC| = 10 cm. What is the scale factor of the enlargement?

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{5}{2}$

31.

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

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{5}{6}$

32.

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?

33.

Use the diagram below to answer the question below.

Find the angle marked b.

150^o

140^o

110^o

100^o

34.

If a = $(\begin{matrix} 2 \\ 1 \end{matrix})$ and b = $(\begin{matrix} 3 \\ -4 \end{matrix})$ , find 2a + b.

$(\begin{matrix} 7 \\ -2 \end{matrix})$

$(\begin{matrix} 5 \\ -3 \end{matrix})$

$(\begin{matrix} 8 \\ -7 \end{matrix})$

$(\begin{matrix} 3 \\ -4 \end{matrix})$

35.

Use the mapping below to answer the question below

x	1	2	3	4
↓	↓	↓	↓	↓
y	3	5	7	9

What is the rule for the mapping?

x→ 4 - x

x→ x - 2

x→2x

x→2x + 1

x→3x

36.

How many faces has a cuboid?

37.

In the figure below, MN and PQ are straight lines. Find the value of the angle marked x in the figure.

65°

75°

85°

155°

38.

Simplify: 3x - 2(3 + 2x) + x(2x + 4).

2x² + 11x - 6

2x² + 3x - 6

2x² - 4x - 6

2x² + 4x - 6

39.

Ama is N years old now. How old will she be in 10 years?

(N – 10) years

(N + 10) years

(10 – N) years

10 N years

$\frac{10}{N}$ years

40.

If (3.14 × 18) × 17.5 = 3.14 × (3a × 17.5). Find the value of a.

3.0

5.8

6.0

9.0

18.0

THEORY QUESTIONS

(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)

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 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)

(i)

Express 8 x 32 x 4 x 2 in the form 2^m.

(ii)

Using your answer in (a)(i), state the value of m.

(b)

(i)

Factorize the expression πn²k - $\frac{1}{4}$ πn²Q.

(ii)

Use your answer in (b)(i) to find the value of the expression when π = $\frac{22}{7}$ , n = 2, k = 19 and Q = 20.

(c)

Gifty and Justina shared an amount of GH₵ 418.00. If Gifty had 20% more than Justina, how much did Justina receive?

(a)

Solve the inequality $\frac{5x - 3}{6}$ - $\frac{2x - 4}{4}$ < 2

(b)

(i)

Copy and complete the table of values for he relation, y = 2x + 1

x	-3	-2	-1	0	1	2	3	4
y	-5	-3		1			7

(ii)

Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, plot the ordered pairs (x, y) on a graph sheet.

(iii)

Use a ruler to join the joints plotted.

(iv)

Use your graph to find

(α)

x when y = 4

(β)

y when x = -2.5

(a)

Using a pair of compasses and ruler only,

(i)

Construct the triangle ABC with |AB| = 8 cm, |BC| = 8cm and |AC| = 7cm.

(ii)

Bisect angle ABC and let the bisector meet AC at D. Produce |BD| to P such that |BD| = |DP|. Join AP and CP.

(b)

Measure

(i)

angle ADB;

(ii)

|AP|.

(c)

What kind of quadrilateral is ABCP?