OBJECTIVE TEST

PQR is a right-angled triangle. The area of the triangle is 6 cm² and |QR| = 3 cm.

Find |PR|.

2 cm

3 cm

5 cm

6 cm

In an examination, 60% of the candidates passed. The number that passed was 240. How many candidates failed?

140

160

360

400

600

The point K(3, 4) is rotated through 180° about the origin. Find its image.

(-3, 4)

(-4, 3)

(-3, -4)

(3, -4)

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.

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

What is the modal mark?

Arrange the following fractions in ascending order: 4 $\frac{1}{4}$ , 4 $\frac{1}{2}$ , 4 $\frac{1}{3}$

4 $\frac{1}{4}$ , 4 $\frac{1}{3}$ , 4 $\frac{1}{2}$

4 $\frac{1}{3}$ , 4 $\frac{1}{2}$ , 4 $\frac{1}{4}$

4 $\frac{1}{2}$ , 4 $\frac{1}{3}$ , 4 $\frac{1}{4}$

4 $\frac{1}{4}$ , 4 $\frac{1}{2}$ , 4 $\frac{1}{3}$

If 5 boys took 14 days to cultivate a piece of land, how long will it take 7 boys working at the same rate to cultivate the land?

14 days

12 days

10 days

8 days

A car is travelling at 60 km per hour. How far does it travel in 2 $\frac{1}{2}$ hours?

30 km

60 km

120 km

150 km

Make k the subject of the relation, ky - k = y²

10.

Esi and Kwasi are 12 and 8 years old respectively. They share 60 mangoes in the ratio of their ages. How many mangoes does Esi get?

11.

What is the value of the digit 8 in the number 78000?

8 ten thousands

8 thousands

8 hundreds

8 tens

12.

Which of the following sets is well defined?

{Man, Kofi, Red, 14}

{Ink, Mango, Green, Nail}

{Car, Road, Glass, Book}

{Seth, Mary, Jacob, Evelyn}

13.

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

-6

-2

14.

Simplify 6p³ × p² ÷ 3p⁴

18p

2p²

15.

If 2x – 1 = 5, find the value of x.

16.

In the diagram, Q is the set of numbers inside the circle and T is the set of numbers inside the triangle. Find Q U T.

{5}

{6, 7}

{3, 4, 5}

{5, 6, 7}

{3, 4, 5, 6, 7}

17.

The pie chart shows the monthly expenditure of Mr. Awuah whose monthly income is ₵18,000.00.

Use the chart to answer the question below.

What is the size of the angle that represents savings?

40°

60°

130°

230°

320°

18.

A square of side 6cm has the same area as a rectangle of length 9 cm. Find the breadth of the rectangle.

3 cm

4 cm

6 cm

24 cm

36 cm

19.

Use the mapping below to answer the question below.

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	-4	-2	0	2	m

Find m.

–4

20.

Tins of milk each of volume 77 cm³ and weight 170 g were packed into an empty carton of volume 1540 cm³ and weight 500 g.

What is the weight of the carton when packed with the tins of milk?

2.06 kg

2.94 kg

3.90 kg

8.50 kg

21.

A labourer worked for 20½ hours. If he was paid GH₵ 2.50 per hour, what was his total wage?

GH₵ 51.00

GH₵ 51.25

GH₵ 512.00

GH₵ 512.25

22.

Simplify: 7(y + 1) – 2(2y + 3)

3y – 5

3y – 2

3y + 1

3y + 4

3y + 13

23.

A man deposited an amount of ₵50,000.00 at a bank for 2 years at a rate of 20%. Find the simple interest.

₵1,000.00

₵2,000.00

₵10,000.00

₵20,000.00

₵200,000.00

24.

Find the rule for the mapping:

1	2	3	4	...	t
↓	↓	↓	↓	↓	↓
9	20	31	42	...	...

t → 10t - 1

t → 8t + 1

t → 11t - 2

t → 7t + 2

25.

The marks obtained by 10 boys in a test are 0, 1, 3, 3, 5, 7, 8, 9, 9, 9.

Use this information to answer the question below

Find the median score.

26.

L = $(\begin{matrix} 3 \\ -1 \end{matrix})$ and K = $(\begin{matrix} -4 \\ 2 \end{matrix})$ .

Find L + K.

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

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

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

$(\begin{matrix} 7 \\ -1 \end{matrix})$

$(\begin{matrix} 7 \\ 1 \end{matrix})$

27.

Find the value of 124.3 + 0.275 + 74.06, correcting your answer to one decimal place.

198.6

198.7

892.0

892.4

28.

Change 10111_two to base ten.

29.

Find the image of the point (2,5) under the transformation $(\begin{matrix} x \\ y \end{matrix})$ → $(\begin{matrix} x \\ 2 - y \end{matrix})$ .

(2,-3)

(2,2)

(2,3)

(2,7)

30.

Use the diagram below to answer the question below.

What is the value of c°?

68°

75°

105°

112°

124°

31.

The table below shows the distribution of workers in some trades.

Trade	Shoe making	Mining	Road transport	Agriculture	Manufacturing goods
Number of workers	300,000	25,000	160,000	225,000	165,000

Use this information to answer the question below.

Which trade employed the most number of workers?

Agriculture

Manufacturing

Shoe making

Road transport

32.

If P = {4, 8, 12, 16, 20}, Q = {16, 4, 12, k, 20} and P = Q, find the value of k.

33.

A car used 8 hours to travel from town A to town B at a speed of 18 km/h.

Find the distance travelled.

22.5 km

135 km

140 km

144 km

34.

The instrument used to measure the angle between two lines that meet at a point is known as a

pair of compasses.

set-square.

protractor.

pair of dividers.

35.

In the diagram, P→P¹, Q→Q¹, R→R¹, where P¹Q¹R¹ is an enlargement.

What is the scale factor of this enlargement?

–2

$\frac{1}{3}$

$\frac{1}{2}$

36.

Kojo can buy 15 shirts at GH₵4.00 each. If the price is increased to GH₵5.00, how many shirts can he now buy?

37.

Make d the subject of the relation n = 2d + 3

d = $\frac{3n}{2}$

d = $\frac{n + 3}{2}$

d = $\frac{n - 3}{2}$

d = $\frac{3 - n}{2}$

38.

In the diagram, XYZ is a triangle. YW is a straight line. Angle XYZ = 52° and angle XZW = 125°.

Find angle YXZ.

35°

55°

73°

107°

39.

The area of the trapezium above is

120 cm²

180 cm²

256 cm²

360 cm²

40.

Solve the inequality 2x + 10 ≥ $\frac{7x}{2}$ - 5

x ≤ 10

x ≥ 10

x ≤ 40

x ≥ 40

THEORY QUESTIONS

(a)

(i)

Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes OX and OY on a graph sheet.

(ii)

On the same graph sheet, mark the x-axis from –5 to 5 and the y-axis from –6 to 6.

(b)

Plot the points,

(i)

P(1, -2) and Q(4, 5)

(ii)

P′ the image of P under a translation by the vector $(\begin{matrix} -5 \\ 0 \end{matrix})$ and Q′, the image of Q by the same vector.

(c)

(i)

Join PQQ′P′.

(ii)

Measure angles PQQ′ and PP′Q′.

(d)

(i)

Find the vectors PQ→ and P′Q'→

(ii)

What is the shape of PQQ′P′?

(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 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.

Plot, indicating the coordinates of all perpendicular points A(2,3) and B(-3,4). Draw a straight line passing through the points A and B.

Plot on the same graph sheet, indicating the coordinates of the points C(4,2) and D(-2,-3). Draw a straight line passing through the points to meet line AB.

Using the graphs in (a):

find the values of y when x = -2;

measure the angle between the lines AB and CD.

If m = $(\begin{matrix} 2x + 1 \\ 2 - 3y \end{matrix})$ , n = $(\begin{matrix} 6 \\ -8 \end{matrix})$ and (m + n) = $(\begin{matrix} 9 \\ -12 \end{matrix})$ , find the:

values of x and y;

components of m.

Solve the inequality:

$\frac{3}{4}$ (x + 1) + 1 ≤ $\frac{1}{2}$ (x -2) + 5.

Illustrate the answer in b(i) on a number line.

In the diagram, AB is parallel to CD.

Find the value of:

(a)

Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes, OX and OY on a graph sheet.

(b)

On the graph sheet, mark the x-axis from –5 to 5 and the y-axis from –6 to 6

(c)

(i)

Plot on the same graph sheet the points A(1, 1 $\frac{1}{2}$ ), B(4, 1 $\frac{1}{2}$ ), C(1, 4).

(ii)

Join the points to form a triangle. What type of triangle have you drawn?

(d)

Draw the image triangle A₁B₁C₁ of ABC under a reflection in the y-axis, where A→A₁, B→B₁ and C→C₁. Label the vertices and the co-ordinates clearly.

(e)

Draw the image triangle A₂B₂C₂ of triangle ABC under an enlargement with scale factor –1 with the centre of enlargement as the origin (0,0), where A→A₂, B→B₂ and C→C₂. Show all lines of enlargement. Label the vertices and co-ordinates clearly

(f)

What single transformation maps A₁B₁C₁ onto A₂B₂C₂ where A₁→A₂, B₁→ B₂ and C₁→C₂?

(a)

(i)

Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes OX and OY on a graph sheet.

(ii)

On the same graph sheet, mark the x-axes from –5 to 5 and the y-axis from –6 to 6.

(b)

On the same graph sheet, plot the points A(2, 5), B(4, 3) and C(1, 1). Join the points A, B and C to form a triangle.

(c)

Reflect triangle ABC in the y-axis such that A→A₁, B→B₁ and C→C₁. Label the vertices of triangle A₁B₁C₁

(d)

Translate triangle A₁B₁C₁ by the vector $(\begin{matrix} 3 \\ -4 \end{matrix})$ such that A₁→A₂, B₁→B₂, and C₁→C₂. Label the vertices of triangle A₂B₂C₂

(e)

Join the vertices A₁B₁B₂ and C. Name the figure formed.

(f)

Find A₁B₁→