OBJECTIVE TEST

In the following diagram RS and WV are parallel lines. The value of the angle marked α is

38^o

52^o

58^o

64^o

The area of a trapezium is 36 cm². If the parallel sides are 10.5 cm and 9.5 cm, calculate the distance between the two parallel sides.

1.0 cm

1.8 cm

3.2 cm

3.6 cm

There are 20 identical balls in a box. Twelve are blue and the rest are green. If one ball is taken at random from the box, find the probability that the ball is green.

$\frac{1}{20}$

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{3}{4}$

The volume of a cube is 27 cm³. Find the area of one of its faces.

3 cm²

6 cm²

9 cm²

18 cm²

54 cm²

Which of the fractions $\frac{13}{20}$ , $\frac{3}{5}$ , $\frac{3}{4}$ and $\frac{7}{10}$ is greatest?

$\frac{3}{5}$

$\frac{3}{4}$

$\frac{7}{10}$

$\frac{13}{20}$

The ratio of mangoes to oranges in a basket is 3:2. If there are 36 mangoes, how many oranges are in the basket?

Arrange the following fractions from the lowest to the highest: $\frac{3}{4}$ , $\frac{2}{3}$ and $\frac{3}{5}$ .

$\frac{3}{5}$ , $\frac{2}{3}$ , $\frac{3}{4}$

$\frac{3}{5}$ , $\frac{3}{4}$ , $\frac{2}{3}$

$\frac{3}{4}$ , $\frac{2}{3}$ , $\frac{3}{5}$

$\frac{3}{4}$ , $\frac{3}{5}$ , $\frac{2}{3}$

$\frac{2}{3}$ , $\frac{3}{5}$ , $\frac{3}{4}$

The table below gives the number of goals scored by a football team in a league season:

Number of goals scored in a match	0	1	2	3	4	5
Frequency	1	7	6	4	1	1

Use it to answer the question below.

What is the total number of matches played in the league season?

What is the fifth term of the sequence $\frac{1}{3}$ , $\frac{2}{5}$ , $\frac{7}{15}$ ...?

$\frac{4}{9}$

$\frac{5}{11}$

$\frac{6}{13}$

$\frac{3}{5}$

10.

Which of the following numbers is the largest?

-70

-50

-3

-2

11.

Simplify $\frac{2a}{3}$ - $\frac{(a - b)}{2}$

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

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

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

$\frac{7a - 3b}{6}$

12.

A trader received a commission of 25% on the sales he made in a month. His commission was ₵180,000.00. Find his total sales for the month.

₵135,000.00

₵150,000.00

₵240,000.00

₵540,000.00

₵720,000.00

13.

Make T the subject of the relation l² = $\frac{4 π^{2} T}{g}$

T = $\frac{gl}{2π}$

T = $\frac{g l^{2}}{2π}$

T = $\frac{l^{2}}{4g π^{2}}$

T = $\frac{g l^{2}}{4 π^{2}}$

14.

Find the bearing of Q from P in the diagram above.

030°

060°

070°

090°

150°

15.

Given that

find,

16.

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

17.

What is the value of ‘4’ in the number 2,043,507?

Forty

Four hundred

Four thousand

Forty thousand

Four hundred thousand

18.

A trader sold 90 oranges at 3 for ₵50.00. How much did she get from selling all the oranges?

₵1,500.00

₵4,500.00

₵6,000.00

₵15,000.00

₵45,000.00

19.

The following addition is in base ten. Find the missing addend.

	2	3	4	5
+	1	0	4	5
	*	*	*	*
	5	1	1	0

1300

1720

2765

4065

9500

20.

A car is travelling at 40 km per hour. How far does it travel in 2 $\frac{1}{2}$ hours?

16 km

80 km

90 km

100 km

140 km

21.

In an examination, Abu answered nine questions in 2 hours. He spent 20 minutes on the first question and the same time on each of the remaining questions.

How many minutes did he spend on each of the other question?

8.0 minutes

10.0 minutes

12.0 minutes

12.5 minutes

22.

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.

Calculate OC₁.

7.5 cm

8 cm

9 cm

12 cm

23.

If the average of 5,6,7 and x is 8, find the value of x

24.

A van travels 154 km in 1 $\frac{3}{4}$ hours. Find its speed in km/h.

77 km/h

88 km/h

100 km/h

269.5 km/h

25.

Which of the following inequalities is / are true?

I: $\frac{5}{6}$ > $\frac{3}{4}$ II: $\frac{3}{4}$ > $\frac{3}{5}$ III: $\frac{3}{8}$ > $\frac{1}{2}$ .

I only

II only

III only

I and II only

I and III only

26.

If P¹(4,-5) is the image of P(x,y) translated by r = ( ^-2 ₃), find the values of x and y.

(-6,8)

(-6,-8)

(6,-8)

(6,8)

27.

Given that 117(12+18) = 117(15+k), find the value of k

- 15

-30

28.

The bearing of X from Y is 196^o. What is the bearing of Y from X?

016^o

074^o

106^o

244^o

29.

Arrange

and

in ascending order.

30.

If n² + 4 = 40, find n.

31.

Simplify: (2ab²)² x 3a³b.

6a⁴b⁵

12a³b⁴

12a⁶b⁴

12a⁵b⁵

32.

If r = $\frac{m + 1}{m - 2}$ , express m in terms of r.

m = $\frac{2r + 1}{r - 1}$

m = $\frac{2r + 1}{r + 1}$

m = $\frac{2r - 1}{r - 1}$

m = $\frac{2r - 1}{r + 1}$

33.

A tank in the form of a cuboid has length 6 m and breadth 4 m. If the volume of the tank is 36 m³, find the height.

0.67 m

1.5 m

1.8 m

5.0 m

34.

In the diagram, AB is parallel to CD, Angle AGE is 80^o, angle CFG = 5k and angle CFE = r.

Use the information to answer the question below.

What is the value of r?

16^o

20^o

80^o

160^o

35.

The pie chart shows the distribution of crops on a farm of area 250 hectares.

Use it to answer the question below.

What fraction of the farm is planted with pepper?

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{5}$

$\frac{2}{9}$

$\frac{7}{32}$

36.

Given that (3.14 x 18) x 17.5 = 3.14 x (3p x 17.5)

Find the value of p.

3.0

5.8

6.0

9.0

37.

What is the value of four in the number 7073.48?

four tenth

four

forty

four hundred

38.

Find the sum of 124.3, 0.275 and 74.06. (Correct your answer to one decimal place)

198.6

198.7

892.0

892.4

39.

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

40.

The diagram above shows the construction for:

Copying a given angle

Bisecting a line segment

Drawing a perpendicular to a given line

Bisecting a given angle

Drawing an angle of 30°

THEORY QUESTIONS

(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.

Olu bought a radio for ₵65,000.00. After one year the radio was valued at 75% of the cost price.

(a)

What was the price of the radio after one year?

(b)

If he sold the radio for ₵55,700.00, calculate his profit or loss over the cost price.

Copy and complete the table for the relation y = 12x - 9

x	-2	-1	0	1	2	3	4	5
y			-9				39

Using a scale of 2 cm to 1 unit on the x - axis to 10 units in the y - axis, draw on a graph sheet two perpendicular axes ox and oy.

ii)

Using the table, plot all the points of the relation y = 12x - 9 on the graph.

iii)

Draw a straight line through the points.

iv)

Use the graph to find:

(α) y when x = 2.5;

(β) x when y = 10.

List the integers within the interval 7 < x ≤ 14

(a)

Solve the inequality $\frac{2x - 1}{4}$ - $\frac{x - 2}{3}$ > 1

(b)

Find the value of the expression 2x - 3y if x = $\frac{1}{3}$ and y = - $\frac{1}{2}$ .

(c)

25 students in a class took an examination in Mathematics and Science. 17 of them passed in Science and 8 passed in both Mathematics and Science. 3 students did not pass in any of the subjects.

Find

(i)

how many passed in Mathematics;

(ii)

the probability of meeting a student who passed in one subject only.

Express 250 % as a fraction in its lowest term.

Use the diagram to find the value of x.

Simplify:

If q =

and r =

find (q + r).

(a)

Using a scale of 2 cm to 1 unit on both axes, draw on a graph sheet two perpendicular axes 0x and 0y for -5 ≤ x ≤ 5 and -5 ≤ y ≤ 5.

(i)

Plot, indicating the coordinates of all points P(1,1), Q(1,2),R(2,2) and S(2,1) on the graph sheet. Join the points to form square PQRS.

(ii)

Draw and indicate clearly all coordinates, the image P₁Q₁R₁S₁ of square PQRS under an enlargement from the origin with a scale factor of 2, where P → P₁,Q → Q₁, R → R₁ and S → S₁.

(iii)

Draw and indicate clearly all coordinates, the image P₂Q₂R₂S₂ of square P₁Q₁R₁S₁ under a reflection in the x-axis where P₁ → P₂,Q₁ → Q₂, R₁ → R₂ and S₁ → S₂.

(b)

Using the graph in (a), find the gradient of line R₂S.