OBJECTIVE TEST

Which of the following dimensions of a triangle form the sides of a right angled triangle?

3cm, 4cm, 6cm

3cm, 5cm, 7cm

5cm, 12cm, 13cm

5cm, 13cm, 17cm

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

Find |BD|.

3 cm

4 cm

9 cm

33 cm

41 cm

Simplify 2ab² × 3a²b

5a³b³

5a²b²

6a³b³

5a²b²

36ab

A car covered a distance of 150 km at a speed of 18 km/h. Find the time taken.

7 hours 33 minutes

7 hours 53 minutes

8 hours 13 minutes

8 hours 20 minutes

What is the value of 7 in the number 832713?

Seven thousand

Seven hundred

Seventy

Seven

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

If 2y = 6 – 3x, find y when x = 0

–3

–2

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}

If 2x = 5(x - 2) + 7, find the value of x.

-5 $\frac{2}{3}$

-1

5 $\frac{2}{3}$

10.

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

11.

Use the mapping below to answer the question below

x	1	2	3	4
↓	↓	↓	↓	↓
y	3	5	7	9

What is the rule for the mapping?

x→ 4 - x

x→ x - 2

x→2x

x→2x + 1

x→3x

12.

The pie chart shows how Kwaku spends his monthly salary.

Use this information to answer the question below.

What percentage of his salary does he spend on rent and utilities?

12.1%

12.5%

22.2%

33.3%

13.

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

14.

Simplify: (x - 1)² - 1.

x² - 2x

x² + 2x

x² - 2x - 1

x² - 2x + 1

15.

A trader bought 100 tubers of yam for GH₵ n each. All the yams were sold at GH₵ m each. Find the profit.

GH₵ 100(m - n)

GH₵ 100(m + n)

GH₵ 100(n - m)

GH₵ 100( nm )

16.

The hypotenuse and a side of a right-angled triangle are 13 cm and 5 cm respectively. Find the length of the third side.

8 cm

9 cm

12 cm

17 cm

17.

The pie chart shows the distribution of programmes offered by 720 students at Kofikrom.

Use this information to answer the question below.

How many more students offered science subjects than Arts subjects.

160

240

18.

A train is travelling at a speed of 60 km/h. What distance will it cover from 10.45 am to 12.15 pm?

75 km

87 km

90 km

150 km

19.

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

20.

Express 0.125 as a fraction in its lowest form.

$\frac{1}{8}$

$\frac{1}{9}$

$\frac{1}{12}$

$\frac{1}{16}$

21.

What is the rule for the mapping?

x→ 3x²-1

x→ 5x²-3

x→ x²+1

x→ 4x-2

22.

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

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

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

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

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

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

23.

Solve for x in the equation 15 – 2x = 6

–10.5

–4.5

4.5

10.5

24.

There are 18 girls and 22 boys in a class. A prefect is to be chosen at random from the class. What is the probability that the prefect will be a girl?

$\frac{1}{18}$

$\frac{9}{20}$

$\frac{11}{20}$

$\frac{9}{11}$

25.

The circumference of a circle is 440 m. Find the area of the circle.

[Take π = $\frac{22}{7}$ ]

14,400 m²

15,400 m²

16,400 m²

18,000 m²

26.

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%

27.

Expand (2x + y)(2x - y).

2x² - y²

4x² - y²

2x² + 4xy - y²

4x² + 4xy - y²

28.

Simplify $\frac{30}{5(-2)}$

-10

-6

-3

29.

A man spends GH₵ 560.0 out of his weekly wage of GH₵ 700.00 and saves the rest. What percentage did he save?

10%

15%

20%

25%

30.

Mr. Nkrumah saved ₵75,000.00 at a simple interest rate of 20% per annum for 3 years. Calculate the interest he earned on his savings

₵15,000.00

₵30,000.00

₵45,000.00

₵60,000.00

31.

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

32.

Which of these best describes the given construction?

Bisecting a line

Constructing the bisector of a line segment

Constructing the perpendicular to a line

Constructing a perpendicular to a given line from a point outside the line

Constructing a perpendicular to a given line through a point on the line

33.

What is the rule for the following mapping?

x	0	1	2	3	4
↓	↓	↓	↓	↓	↓
y	5	9	13	17	21

y = x + 5

y = 4x + 5

y = 5x + 4

y = 6x + 1

34.

The point Q(-2,3) is rotated anticlockwise about the origin through an angle of 90^o. Find the coordinates of its image.

(-3,-2)

(-3,2)

(3,-2)

(3,2)

35.

P = {2, 4, 6, 8} and Q = {even counting numbers less than 12}.

What is the relationship between P and Q?

P = Q

P ⊂ Q

P < Q

Q ⊂ P

P ∈ Q

36.

Two bells P and Q ring at intervals of 3 hours and 4 hours, respectively. After how many hours will the two bells first ring simultaneously (at the same time)?

6 hours

8 hours

12 hours

24 hours

37.

Given that vectors u = $(\begin{matrix} -3 \\ 5 \end{matrix})$ and v = $(\begin{matrix} 2 \\ -3 \end{matrix})$ , calculate 2v - u.

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

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

$(\begin{matrix} -7 \\ -11 \end{matrix})$

$(\begin{matrix} 7 \\ -11 \end{matrix})$

38.

A refrigerator was sold for GH₵ 200.00 at a loss of 10%. Find the cost price.

GH₵ 180.00

GH₵ 190.48

GH₵ 220.00

GH₵ 222.22

39.

The figure QPR is an equilateral triangle. If angle PRS = (2x - 10)^o, find the value of x.

40.

Solve $\frac{4k}{9}$ = 12.

THEORY QUESTIONS

The table shows the distribution of the ages (in years) of children in a nursery school.

Age (years)	1	2	3	4	5
Number of children	6	4	2	3	5

(a)

Find

(i)

the modal age

(ii)

the mean age

(b)

Draw a bar chart for the distribution.

(c)

What is the probability that a child chosen at random from the school is 4 years old?

(a)

The ratio of men to women in a village is 12 : 25. If there are 120 men,

(i)

how many women are there?

(ii)

what is the total number of men and women?

(b)

A bag contains 70 pencils out of which 15 are green and 30 blue.

(i)

How many pencils of other colours are in the bag?

(ii)

A pencil is selected from the bag at random. What is the probability that it is blue?

(c)

Solve $\frac{1}{3}$ (x - 1) - $\frac{1}{2}$ (x - 3) ≤ 1 $\frac{1}{4}$ and illustrate your answer on the number line.

(a)

The volume of a cylinder is 220 cm³. The radius of the cross-section is 2.5 cm. Find the height of the cylinder.

[Take π = $\frac{22}{7}$ ]

(b)

Each of the interior angles of a regular polygon is 140°. How many sides does it have?

(a)

(i)

Find the least Common Multiple (L.C.M.) of 9, 18 and 16.

(ii)

Arrange $\frac{8}{9}$ , $\frac{7}{18}$ and $\frac{10}{16}$ in ascending order of magnitude.

(b)

Using a ruler and a pair of compass only,

(i)

construct a triangle PQR with length PQ = 10 cm, angles QPR = 45^o and PQR = 60^o.

(ii)

Construct the perpendicular bisectors of PR and RQ to meet at T.

(iii)

Measure the length of TP.

(a)

Mansah earns a salary of ₵10,000.00 per month as a sales girl. In addition to the salary, she is given a commission of 1.5% of whatever sales she makes in a month. In January this year, she made sales of ₵7,500,000.00. What was the total amount Mansah earned at the end of January?

(b)

The diagram below shows a circle with centre O and radius 14 cm. The shaded region AOB is a sector with angle AOB = 72°.

Find:

(i)

The length of the minor arc AB

(ii)

The area of the shaded sector AOB

[Take π = $\frac{22}{7}$ ]

(a)

Using a ruler and a pair of compasses only, construct ∆PQR such that angle PQR = 90°, |PQ| = 5.5 cm and |QR| = 8 cm.

(b)

Construct a perpendicular of PR from Q.

(c)

Locate M, the intersection of the perpendicular and PR.

(d)

Measure:

(i)

|MR|;

(ii)

|QM|.

(e)

Calculate, correct to the nearest whole number, the area of triangle QMR.