OBJECTIVE TEST

List the members of the set {2 ≤ x ≤ 5}.

{2, 5}

{2, 3, 4}

{2, 3, 5}

{2, 3, 4, 5}

At a meeting attended by 23 people, the females were 7 more than the males. How many males were there?

Find the value of x in the equation $\frac{x}{4}$ = 2

Find the HCF of 3³ × 5² and 3² × 5⁴.

3^{2^{× 5²}}

3³ × 5²

3² × 5⁴

3⁵× 5⁶

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

Which of the following polygons does not have a line of symmetry?

Kite

Isosceles triangle

Trapezium

Rhombus

The angle formed by one complete revolution is equivalent to

one right angle

two right angles

three right angles

four right angles

A bag contains 12 mangoes of which 4 are not ripe. What is the chance of picking at random a ripe mango from the bag?

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

In the diagram below AC // DF. Angle CBT is 40° and angle DET is 140°

320°

280°

220°

100°

80°

10.

If r = $(\begin{matrix} 2 \\ 5 \end{matrix})$ and t = $(\begin{matrix} -2 \\ -3 \end{matrix})$ , evaluate r + t.

$(\begin{matrix} 0 \\ -2 \end{matrix})$

$(\begin{matrix} 0 \\ 2 \end{matrix})$

$(\begin{matrix} 4 \\ 2 \end{matrix})$

$(\begin{matrix} 4 \\ 8 \end{matrix})$

11.

In the diagram below, MNO is a triangle. Angle MON = 72° and angle OMN = 68°.

Find angle ONP.

40°

68°

72°

112°

140°

12.

Which of the following is illustrated on the number line above?

–1 < x < $\frac{3}{2}$

–1 ≤ x < $\frac{3}{2}$

–1 ≤ x ≤ $\frac{3}{2}$

–1 < x ≤ $\frac{3}{2}$

$\frac{3}{2}$ ≤ x ≤ –1

13.

Use the graph of the straight line below to answer the question below

Determine the value of x when y is 3.

$\frac{1}{2}$

1 $\frac{1}{2}$

14.

What is the Highest Common Factor (HCF) of 24, 32 and 64?

15.

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

-2

- $\frac{3}{5}$

$\frac{1}{2}$

16.

Find the value of m if 4(m + 4) = -8.

-6

-2

17.

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

18.

What is the H.C.F of 48, 30 and 18?

19.

Find the size of the angle marked a in the diagram above.

30°

60°

90°

120°

180°

20.

If P = {factors of 36} and Q = {multiples of 4 less than 40}, find the number of subsets in P∩Q

21.

In the figure PQR is a straight line. Angle TQP = x°, angle TQS = 102° and angle SQR = 2x°. Find the value of x.

22.

Find the circumference of a circle whose area is equal to 64 π cm².

32 π cm

16 π cm

8 π cm

4 π cm

23.

Simplify 2ab² × 3a²b

5a³b³

5a²b²

6a³b³

5a²b²

36ab

24.

Which of the following are the prime factors of 12?

{1, 3}

{2, 3}

{2, 4, 6, 12}

{2, 3, 4, 6}

25.

E is the point (4, 2) and F the point (2, 1). Calculate the gradient of the straight line EF.

- $\frac{1}{2}$

-2

$\frac{1}{2}$

26.

A survey shows that 28% of all the men in a village are vegetarian. What is the probability that a man selected at random from the village is a vegetarian?

$\frac{7}{25}$

$\frac{41}{50}$

$\frac{1}{2}$

27.

In triangle ABC, |AB| = |BC| = 5 cm, and |AC| = 8 cm.

Find |BD|.

3 cm

4 cm

9 cm

33 cm

41 cm

28.

Simplify 200 x 0.01 x 372 leaving your answer in standard form.

74.4 x 10¹

7.44 x 10¹

7.44 x 10²

7.44 x 10⁴

29.

Subtract (7x-3) from (5-3x).

10x-8

4x-8

8-10x

2-10x

30.

The volume of water in a rectangular tank is 30 cm³ .The length of the tank is 5 cm and its breadth is 2 cm. Calculate the depth of water in the tank.

4.0 cm

3.0 cm

5.0 cm

6.0 cm

31.

Given that p = {1,2,3,4,5,6,7,8,9,10,11,12}, what is the probability of selecting a prime number from the set?

⅔

7⁄12

5⁄12

32.

A boy bought 3 pairs of socks at GH₵17.50 per a pair and paid with two GH₵50.00 notes. How much change was he given?

GH₵27.50

GH₵37.50

GH₵47.50

GH₵48.50

33.

For what value of x is 3^x = 81?

34.

Find the rule of the mapping:

x	0	3	6	9	12
↓	↓	↓	↓	↓	↓
y	-2	4	10	16	22

y → $\frac{x}{2}$ - 2

y → x - 2

y → x² - 2

y → 2x - 2

35.

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

–4.0

1.0

2.0

3.0

4.0

36.

Make a subject of the relation P = 2(a + b)

a = $\frac{P - 2b}{2}$

a = $\frac{P + 2b}{2}$

a = $\frac{2b - P}{2}$

a = $\frac{P - b}{2}$

a = $\frac{P - 2}{b}$

37.

There are 20 beads in a box. Some are red and some green. The chance that one bead taken at random from the box is red is $\frac{1}{4}$ . Find the number of red beads in the box.

38.

Which of the following statements is true?

8+4 < 10

7+4 < 10

6+4 < 10

5+4 < 10

39.

Solve for y in the equation $\frac{1}{3}$ y + $\frac{1}{5}$ y = 8

40.

Name the geometrical figure shown in the diagram below.

Cuboid

Cone

Pyramid

Sphere

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.

(a)

A car runs on the average at 45 km to 5 litres of fuel. Calculate how many litres of fuel are required for a journey of 117 km.

(b)

(i)

Solve for x in the inequality $\frac{2}{3}$ (2x + 5) ≤ 8 $\frac{2}{3}$

(ii)

Illustrate the solution on the number line.

(c)

A factory increased its production by 22 $\frac{1}{2}$ % and produced 49,000 tonnes. How many tonnes was it producing before?

(a)

Given the vectors p = $(\begin{matrix} m + 3 \\ 2 - n \end{matrix})$ , q = $(\begin{matrix} 3m - 1 \\ n - 8 \end{matrix})$ and p = q, find the values of m and n.

(b)

A man shared an amount of money between his children Baaba and William in the ratio 6 : 5. Baaba received GH₵ 1,200.00

(i)

find the total amount shared.

(ii)

William invested his share in an account at the rate of 20% simple interest per annum for 2 years. Find the total amount in his account at the end of the 2 years.

(a)

Simplify: (4x + 2)(x - 2) - 3x²

(b)

The following are the angles formed at the center of a circle: 40^o, 60^o, 100^o, 3x^o and 5x^o.

Find the value of x.

(c)

The cost (C) in Ghana Cedis of producing a book of x pages is given by C = 25 + 0.6x.

(i)

Find the cost of producing a book with 220 pages.

(ii)

How many pages are in a book produced at a cost of GH₵ 145.00?

(a)

Simplify: $\frac{2}{3}$ of 6 $\frac{3}{4}$ ÷ $(2 \frac{4}{15} - 1 \frac{2}{3})$ .

(b)

Solve the equation $\frac{1}{3}$ (x + 3) - 2(x - 5) = 4 $\frac{1}{3}$ .

(c)

If 3y = 2x² - 3x + 7, find y, when x = 5

(a)

In a class of 70 students, 40 belong to the Red Cross Society, 27 belong to the Girls' Guide Society and 12 belong to both the Red Cross Society and the Girl's Guide Society. The remaining students do not belong to any of the two societies.

(i)

Illustrate the information on a Venn diagram.

(ii)

How many students belong to the Red Cross Society only?

(iii)

How many students do not belong to any of the two societies?

(b)

A farmer uses $\frac{1}{3}$ of his land to plant cassava, $\frac{2}{5}$ of the remaining land to plant maize and the rest vegetables.

If vegetables cover an area of 10 acres, what is the total area of the farmer's land.