OBJECTIVE TEST

In a class of 20 pupils, 8 pupils read Mathematics, 13 read English and 3 read both Mathematics and English.

Use this information to answer the question below.

How many pupils read English only?

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

How many students took the test?

In the diagram, MNO is a right angled triangle. |MO| = 13 cm and |MN| is 5 cm.

Find the value of x.

Given that x = 8, what type of angle is (9x + 8)^o?

Straight angle

Obtuse angle

Acute angle

Right angle

In the diagram, ABCD is a parallelogram; BC and AF are straight lines. Angle ABC = 110° and angle DEF = 40°. Find the angle marked θ.

30°

40°

50°

70°

110°

If x ∈ {2, 3, 4, 5}, find the truth set of 2x + 1 < 8

{2, 3, 4}

{2, 3}

{3, 4}

{4, 5}

If 60% of the pupils in a school is 240, find the total enrolment in the school.

144

160

360

384

400

Simplify 2² × 3² × 2³ × 3⁴.

2² × 3⁶

2⁴ × 3⁷

2⁵ × 3⁶

2⁶ × 3⁸

Aba bought a carton of fish at GHC 80.00 and sold it at a profit of GHC 13.60. Find the selling price.

GH₵ 66.40

GH₵ 93.60

GH₵ 103.60

GH₵ 144.00

10.

Express 3.75 as a mixed fraction.

3 $\frac{1}{5}$

3 $\frac{1}{4}$

3 $\frac{1}{3}$

3 $\frac{3}{4}$

11.

A point (2, 1) is reflected in the y-axis. Find its image.

(-1, 2)

(1, -2)

(-2, 1)

(2, -1)

12.

The ratio 8 : 12 is equivalent to y : 9. What is the value of y.

13.

find the value of n.

0.0105

0.105

105

1050

14.

Find the truth set of the inequality 2y + 5 < 4y - 5.

{y:y > 5}

{y:y < 5}

{y:y > 1}

{y:y > 0}

15.

In the following diagram, rectangle OABC is enlarged into rectangle OA₁B₁C₁ from center O. OC = 5 cm, OA = 2 cm and AA₁ = 1 cm.

Use the diagram to answer the question below.

Find the scale factor of the enlargement.

1.5

2.5

16.

Find the least number that can be added to 207 to make the sum divisible by 17.

17.

If p = $(\begin{matrix} 4 \\ 3 \end{matrix})$ and q = $(\begin{matrix} -2 \\ 7 \end{matrix})$ , find 4p - 2q.

$(\begin{matrix} 12 \\ -2 \end{matrix})$

$(\begin{matrix} 12 \\ 2 \end{matrix})$

$(\begin{matrix} 20 \\ -2 \end{matrix})$

$(\begin{matrix} 20 \\ 2 \end{matrix})$

18.

Express $\frac{3}{8}$ as a percentage.

0.373%

12%

25%

37 $\frac{1}{2}$ %

40%

19.

Elias bought five books. Their mean price was GH₵ 3.25. The total cost for four of the books was GH₵ 11.75. What was the cost of the fifth book?

GH₵ 3.50

GH₵ 4.00

GH₵ 4.20

GH₵ 4.50

20.

Calculate the length of QR in triangle PQR

21.

Multiply 0.014 by 0.2

0.00028

0.0028

0.028

0.28

22.

Find the simple interest on GH₵ 600.00 saved for 2 years 8 months at 5% per anum.

GH₵ 64.00

GH₵ 80.00

GH₵ 84.00

GH₵ 92.00

23.

Expand and simplify: 2(3a + 1) - 3(4a - 3).

11 - 5a

11 - 6a

11 + 5a

11 + 6a

24.

Given that vector a = $(\begin{matrix} -5 \\ 12 \end{matrix})$ and b = $(\begin{matrix} 10x \\ 12 \end{matrix})$

Find the value of x if a = b.

-2

- $\frac{1}{2}$

$\frac{1}{2}$

25.

Simplify 5(3t + 1) – 6(t – 1).

9t + 11

9t + 7

9t + 1

9t – 5

26.

Given the vectors m = $(\begin{matrix} 5 \\ -1 \end{matrix})$ and n = $(\begin{matrix} -4 \\ 2 \end{matrix})$ , find 2m + n.

$(\begin{matrix} 6 \\ 0 \end{matrix})$

$(\begin{matrix} -6 \\ 0 \end{matrix})$

$(\begin{matrix} 0 \\ 6 \end{matrix})$

$(\begin{matrix} 0 \\ -6 \end{matrix})$

27.

Expand and simplify: (a-2)(2a+3)

a² - a + 6

2a² + 7a - 6

2a² - a - 6

2a² - 12a + 6

28.

A 3.6 m long string is to be cut into pieces, each of length 40 cm. How many pieces can be cut from the string?

29.

Use the diagram below to answer the question below.

What is the value of b°?

68°

75°

105°

112°

124°

30.

A tank contains 250 litres of water. If 96 litres are used, what percentage of the original quantity is left?

61.6%

60.5%

59.0%

54.2%

38.4%

31.

From the diagram below, calculate the bearing of point X from Y.

035°

045°

135°

145°

225°

32.

Solve the equation 13x – 2(3x + 4) = 22.

$\frac{18}{7}$

$\frac{26}{7}$

$\frac{30}{7}$

33.

Find the product of 4xy⁴ and x²yz.

4x³y⁴z

4x³y⁵z

4x²y⁴z

4x²y⁴

34.

Peter had GH₵ 200.00 and spent GH₵ 83.00. What percentage of the money is left?

29.06%

70.94%

58.50%

41.50%

35.

Write 2340000 in standard form.

2.34 x 10^-6

2.34 x 10^-5

2.34 x 10⁶

2.34 x 10⁷

36.

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

-2

37.

Simplify: $\frac{2a}{3}$ - $\frac{a - b}{2}$ .

a - 3

$\frac{a - 3b}{6}$

$\frac{a + 3b}{6}$

a + 3b

a - b

38.

If S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, find the probability that a number selected at random from S is odd.

$\frac{3}{8}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{5}{8}$

39.

The product of 2x and 3 is 138. Find x

138

40.

Use the mapping below to answer the question below.

2³ → 8

2² → 4

2¹ → 2

2⁰ → a

2^-1 → b

What is the value of b?

–2

$\frac{1}{4}$

$\frac{1}{2}$

THEORY QUESTIONS

(a)

The ratio of the sheep to goats on a farm is 4 : 7. If there are 1,428 sheep, find how many goats are on the farm.

(b)

Using a ruler and a pair of compasses only, construct a triangle ABC with |AB| = 6cm, |AC| = 8 cm and angle BAC = 30°. Construct the bisector of angle ACB to meet line AB at D.

(i)

Measure |AD| and |BD|.

(ii)

Write down the ratio |AD|:|BD|

(a)

There are 30 boys in a sporting club. 20 of them play hockey and 15 play volley-ball. Each boy plays at least one of the two games.

(i)

Illustrate the information on a Venn diagram

(ii)

How many boys play volleyball only?

(b)

Factorize xy + 3x + 6y + 18

(c)

Multiply (3 + x) by (5 – 2x)

(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)

Copy and complete the table for the relation y = $\frac{x}{20}$ , where y is the cost(in Ghana cedis) and x is the weight (in grammes) of rice sold in a market.

x (weight in grammes)	50	100	150	200	250	300
y (cost in GH₵)		5.00			12.50

(b)

(i)

On a graph sheet, draw two perpendicular axes OX and OY.

(ii)

Using a scale of 2 cm to 50 grammes on the x-axis and 2 cm to GH₵ 2.00 on the y-axis draw the graph of the relation y = $\frac{x}{20}$ .

(c)

Using the graph, find

(i)

the cost of 175 grammes of rice;

(ii)

the weight of rice that can be bought with GH₵ 14.00

(a)

(i)

Factorize completely the expression 2xy – 8x + 3y – 12

(ii)

Evaluate the expression in (i) if x = 5 and y = 7

(b)

Make q the subject of the equation t = $\frac{1}{p}$ + $\frac{1}{p}$

(c)

Given that U = $(\begin{matrix} -5 \\ 9 \end{matrix})$ and V = $(\begin{matrix} 8 \\ 12 \end{matrix})$ , find 3(U + $\frac{1}{2}$ V).

The table below shows the scores of some students in an examination.

Scores	0	1	2	3	4	5	6	7	8	9	10
Frequency	3	5	3	2	7	6	5	4	2	2	1

From the table, find

(a)

how many students wrote the examination;

(b)

the modal score;

(c)

the number of students that scored 7 or more;

(d)

the mean score correct to one decimal place.