OBJECTIVE TEST

Given that a = $(\begin{matrix} -2 \\ 3 \end{matrix})$ and b = $(\begin{matrix} 2 \\ -5 \end{matrix})$ , find a + 2b.

$(\begin{matrix} -2 \\ 3 \end{matrix})$

$(\begin{matrix} 2 \\ 13 \end{matrix})$

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

$(\begin{matrix} 6 \\ 13 \end{matrix})$

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

Convert 320_five to a base ten numeral.

If y = - $\frac{1}{2}$ x + 6, find y when x = 4.

-2

The ratio of the ages of two sisters is 4 : 3. The elder sister is 3 years older than the younger one. How old is the younger sister?

9 years

12 years

15 years

18 years

A bag contains 20 oranges of which 6 are bad. Find the probability of picking a good orange from the bag.

$\frac{1}{20}$

$\frac{3}{10}$

$\frac{1}{6}$

$\frac{7}{10}$

Remove the brackets: a – 2(b – 3c)

a – 2b – 3c

a – 2b - 6c

a – 2b + 6c

a + 2b + 6c

a – 2b + 3c

The total numbers of goals scored each month by a football team are:
3, 4, 8, 2, 4, 6, 4, 8, 7 and 6.
What is the mode?

If 4 - x = 3(4x + 5), find the value of x.

$\frac{11}{13}$

1 $\frac{6}{13}$

-1 $\frac{6}{13}$

$\frac{-11}{13}$

Express $\frac{5}{8}$ as a decimal fraction.

0.125

0.375

0.625

0.750

0.875

10.

Factorize x² – 5x + 6

(x + 3)(x – 2)

(x – 2)(x – 3)

(x + 1)(x –6)

(x + 2)(x + 3)

(x + 6)(x – 1)

11.

Simplify 5w + 7p² - 4w + 3p²

9w + 10p²

w + 10p²

w + 4p²

9w + 4p²

12.

A trader buys a dozen pens at GH₵ 4.80 and sells them at 48 Gp each. Find her percentage profit.

10%

15%

20%

13.

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

14.

Find the solution set of 2x + 4 > -6

{x = -5}

{x < 5}

{x > 5}

{x < -5}

{x > -5}

15.

A man travelled a distance of 1.5 km in 30 minutes. What distance can he cover in 50 minutes, travelling at the same speed?

2.2 km

2.5 km

2.8 km

3.2 km

16.

The scale of a map is 1 : 100,000. What is the distance (in km) between two towns 4 cm apart on the map?

0.04

0.4

4.0

400

17.

Simplify

⅓

⅙

⅔

18.

What is the image of 2 in the mapping x → 2x + 5?

19.

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

20.

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

$\frac{5}{2}$

$\frac{2}{5}$

- $\frac{2}{5}$

- $\frac{5}{2}$

21.

Find the solution set of n - $\frac{2}{3}$ > $\frac{1}{3}$ - n.

{n:n > -1}

{n:n = 0}

{n:n > $\frac{1}{3}$ }

{n:n > $\frac{1}{2}$ }

{n:n > 1}

22.

How many lines of symmetry has an equilateral triangle?

23.

Simplify 6(7a + 4) - 3(8a + 9)

18a - 3

18a + 51

42a - 27

66a -3

24.

How many faces has a cuboid?

25.

Arrange the following fractions in descending order of magnitude:

$\frac{2}{3}$ , $\frac{5}{7}$ , $\frac{2}{5}$ , $\frac{1}{2}$ .

$\frac{5}{7}$ , $\frac{2}{5}$ , $\frac{2}{3}$ , $\frac{1}{2}$

$\frac{5}{7}$ , $\frac{2}{3}$ , $\frac{1}{2}$ , $\frac{2}{5}$

$\frac{1}{2}$ , $\frac{2}{5}$ , $\frac{5}{7}$ , $\frac{2}{3}$

$\frac{1}{2}$ , $\frac{5}{7}$ , $\frac{2}{3}$ , $\frac{2}{5}$

26.

The pie chart shows how Kwaku spends his monthly salary.

Use this information to answer the question below.

Find the value of x.

65^o

75^o

85^o

100^o

27.

When a number is doubled and the result is decreased by 9, the answer is 19. Find the number.

28.

How many lines of symmetry has a square?

29.

Use the graph below to answer the question below.

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

How many minutes did the cyclist spend at town Y?

15 minutes

20 minutes

30 minutes

45 minutes

60 minutes

30.

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 probability that a child chosen at random scored 3 marks?

$\frac{2}{54}$

$\frac{3}{54}$

$\frac{2}{10}$

$\frac{3}{10}$

$\frac{1}{3}$

31.

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

Find the median mark.

32.

Simplify 35x⁵y³ ÷ 7xy²

5x⁶y⁵

5x⁴y

5x⁶y

5x⁴y⁵

5x⁴y

33.

Find the gradient of the line which passes through the points (2, 3) and (-4, 5).

-3

- $\frac{1}{3}$

$\frac{1}{3}$

34.

The area of a circle is 154 cm². Find the diameter.

(Take π = $\frac{22}{7}$ )

7 cm

14 cm

21 cm

49 cm

35.

In the diagram above, PQ is parallel to RS and |PR| = |QR|.

Use the diagram to answer the question below.

What is a?

134

36.

In the diagram, O is the centre of the circle and r is its radius.

Calculate the area of the shaded region.

$\frac{1}{6}$ πr²

$\frac{1}{5}$ πr²

$\frac{1}{3}$ πr²

$\frac{5}{6}$ πr²

$\frac{7}{12}$ πr²

37.

Use it to answer the question below.

How many pupils speak neither Twi nor Ga?

38.

Which property of arithmetic operation is illustrated by the statement: a × (b + c) = ab + ac?

Addition

Association

Commutative

Multiplication

Distributive

39.

A tank contains 400 litres of water. If 100 litres is used, what percentage is left?

25%

30%

40%

75%

40.

In the diagram, QP is parallel to ST, angle QPR = 68^o and angle SRT = 40^o.

Use the information to answer the question below:

Find the value of angle TSR.

40^o

68^o

72^o

112^o

THEORY QUESTIONS

Two consecutive odd numbers are such that seven times the smaller, sutracted from nine times the bigger, gives 144. Find the two numbers.

A paint manufacturing company has a machine which fills 24 tins with paint in 5 minutes.

How many tins will the machine fill in

1 minute, correct to the nearest whole number?

1 hour?

How many hours will it take to fill 1440 tins?

Given that s = $\frac{n}{2}$ [2a + (n - 1)d], a = 3,d = 4 and n = 10, find the value of s.

(a)

Using a ruler and a pair of compasses only, construct,

(i)

triangle PQR such that |PQ| = 8cm, angle QPR = 60° and angle PQR = 45°.

(ii)

Measure |QR|.

(b)

A rectangular water tank has length 60cm, width 45cm and height 50cm.

Find

(i)

the total surface area of the tank when closed

(ii)

the volume of the tank

(iii)

the height of the water in the tank, if the tank contains 81,000 cm³ of water.

(a)

Using a ruler and a pair of compasses only,

(i)

construct a triangle XYZ with length XY = 7 cm, length YZ = 5 cm and angle XYZ = 45^o.

(ii)

Measure and write down the length of XZ.

(b)

Given that the circumference of a circle is 44 cm, find

(i)

the radius of the circle;

(ii)

the area of the circle.

[Take π = $\frac{22}{7}$ ]

(a)

Given that P = {factors of 36} and Q = {factors of 54},

(i)

list the members in the sets P and Q.

(ii)

Find:

P∩Q

n(P∩Q)

The Highest Common Factor (HCF) of 36 and 54.

(b)

Write down the next two terms of the sequence 1,4,9,...,...

(c)

The median of the ordered set of observations 2,3,(4m-3),(3m+1),11 and 13 in ascending order is 6. Find the value of m.

Using a ruler and a pair of compasses only,

(a)

draw |PQ| = 9 cm

(b)

construct a perpendicular to PQ at Q

(c)

construct angle QPS = 60° at the point P on PQ such that |PS| = 6.5cm

(d)

construct a line parallel to PQ through S. let the perpendicular through Q and the parallel through S, meet at R. Measure |PR|.

(a)

Simplify: 7 $\frac{2}{3}$ - 4 $\frac{5}{6}$ + 2 $\frac{3}{8}$

(b)

The area of a trapezium is 31.5 cm². If the parallel sides are of lengths 7.3 cm and 5.3 cm, calculate the perpendicular distance between them.

(c)

The marks scored by four students in a Mathematics test are as follows:

Esi	-	92
Seth	-	85
Mary	-	65
Efe	-	x

(i)

Write down an expression for the mean (average) of the marks.

(ii)

If the mean is less than 80, write a linear inequality for the information.

(iii)

Find the possible marks Efe scored in the test. Represent your answer on the number line.