OBJECTIVE TEST

Which of the following statements about sets is true?

Every set is a subset of the null set.

The universal set is the subset of the null set.

The intersection of two sets is always null set.

The universal set is the union of all its subsets.

A farmer has 1853 pineapple suckers. He plants 17 pineapples in a row. How many rows can he plant?

109

190

Write ₵35,632.00 correct to the nearest thousand cedis.

₵40,000.00

₵36,000.00

₵35,600.00

₵35,000.00

₵30,000.00

Use the diagram below to answer the question below

Find the value of y.

68^o

75^o

112^o

124^o

The bar chart shows the mark distribution of pupils in a test. Use it to answer the question below

How many pupils took the test?

A certain number is subtracted from 12 and the result is multiplied by 3. If the answer is 21, find the number.

Express 0.625 as a fraction in its lowest term.

$\frac{7}{8}$

$\frac{3}{4}$

$\frac{5}{8}$

$\frac{1}{2}$

$\frac{1}{3}$

Simplify

-1

In an enlargement, PQ→P′Q′. |PQ| = 3 cm and |P′Q′| = 15 cm. Calculate the scale factor of the enlargement.

$\frac{1}{5}$

$\frac{2}{3}$

10.

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%

11.

Given that A = {a, e, i, o, u} and B = {r, s, t}, how many elements are in A∩B?

12.

Write in standard form 1342.

0.1342 x 10^-3

0.1342 x 10^-4

13.42 x 10²

1.342 x 10³

1.342 x 10⁴

13.

Round 8921465 to the nearest hundred.

8921000

8921400

8921460

8921500

14.

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

-10

-6

-3

15.

Solve: 3(x - 2) - $\frac{x}{3}$ + 6 > 0.

x < 0

x > 0

x > 3

x > $\frac{1}{8}$

16.

A man was 24 years old when his son was born. Now he is three times as old as his son. Find the age of the son.

6 years

12 years

18 years

36 years

17.

State the rule for the mapping

x	1	2	3	4
↓	↓	↓	↓	↓
y	15	30	46	60

x → 15x

x → 15 + x

x → $\frac{15}{x}$

x → 10 + 5x

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 figure above is made up of a rectangle and a triangle. The dimensions of the rectangle are 8 cm and 6 cm. The triangle has 6 cm as its base and 3 cm as its height.

Find the area of the figure.

33 cm²

48 cm²

51 cm²

57 cm²

66 cm²

20.

In the diagram above, KGM is a right-angled triangle and angle GKM = 62°. Find the angle of elevation of K from M.

28°

62°

90°

118°

21.

If 50 oranges cost ₵2,500.00 how many oranges can be bought for ₵15,000.00?

300

360

22.

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

23.

In the diagram below, K is an enlargement of J. Use it to answer the question below.

Calculate the scale factor

$\frac{1}{3}$

$\frac{1}{2}$

24.

If n² + 1 = 50, find n

24.5

$\sqrt{51}$

25.

If x + 5 = -7, find the value of $\frac{x}{6}$ .

-5 $\frac{5}{6}$

-2

- $\frac{1}{3}$

26.

Factorize 2pq + 6p -6q - 18.

2(p - 3)(q - 3)

2(p + 3)(q + 3)

2(p - 3)(q + 3)

2(p + 3)(q - 3)

27.

The circumference of a circular track is 15.4 m. Find the diameter of the track.

[Take π = $\frac{22}{7}$ ]

4.9 m

22 m

24 m

24.5 m

28.

Simplify: $\frac{5^{7} x 5^{-4}}{5^{3}}$ .

29.

Given that a = $(\begin{matrix} -3 \\ 4 \end{matrix})$ and b = $(\begin{matrix} 1 \\ 2 \end{matrix})$ .

Find b - a.

$(\begin{matrix} -2 \\ 6 \end{matrix})$

$(\begin{matrix} -4 \\ 2 \end{matrix})$

$(\begin{matrix} -3 \\ 8 \end{matrix})$

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

$(\begin{matrix} 4 \\ -2 \end{matrix})$

30.

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

a - 3

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

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

a + 3b

a - b

31.

The volume of water in a cuboid is 9 m³. The length of the cuboid is 3 m and the breadth is 2 m.

Calculate the depth of water in the cuboid.

0.15 m

0.18 m

1.5 m

1.8 m

6.0 m

32.

John walks for 22 $\frac{1}{2}$ minutes and runs 7 $\frac{1}{2}$ minutes to school. What percentage of the total time does he spend walking?

25%

30%

33%

75%

33.

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

34.

The number of boys in a school is 120. If the ratio of boys to girls is 5 : 7, find the total number of students in the school.

240

288

600

840

35.

Which of the following is the set of factors of 12?

{12, 6, 4, 3, 2, 1}

{12, 6, 4, 3, 2}

{12, 6, 4, 2}

{6, 4, 2, 1}

{6, 4, 3, 2}

36.

The pie chart above shows the distribution of 360 pupils to various houses in a school.

Use it to answer the question below

How many more students are in Yellow House than in Blue House?

100

37.

Write 1204_five as a number in base ten.

9996

179

38.

Which of the number lines below represents the inequality 2 < x ≤ 6?

39.

Use the mapping below to answer the question below.

( $\frac{1}{2}$ ) → (1) → (3.14)

(1) → (2) → (6.28)

(2) → (4) → (12.56)

(3) → (6) → (x)

(y) → (10) → (31.4)

Find the value of x

9.42

18.84

25.12

40.

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

If |PR| = 3.6 m, what is |P¹R¹|?

–7.2 m

–1.8 m

1.2 m

1.8 m

7.2 m

THEORY QUESTIONS

(a)

Given the sets A = {multiples of 3 less than 12}, B = {integers between 4 and 8} and C = {4,5,7}, find:

(i)

A∩B;

(ii)

(A∪B)∩C;

(ii)

(A∩B)∪C;

(b)

Simplify: 1 $\frac{3}{4}$ - 2 $\frac{5}{6}$ - 1 $\frac{9}{10}$ + 4 $\frac{7}{8}$ .

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)

Simplify $\frac{2a + 4b}{3}$ - $\frac{3(a - b)}{2}$

(b)

Solve 5(a – 5) – $\frac{1}{2}$ (2a + 6) = 4

(c)

If r = $(\begin{matrix} 3 \\ 1 \end{matrix})$ and q = $(\begin{matrix} -2 \\ 1 \end{matrix})$ , calculate 6(r + 2q).

(a)

The cost (P), in Ghana cedis, of producing n items is given by the formula,

P = $\frac{3}{4}$ n + 1800.

Find the:

(i)

cost of producing 2,000 items;

(ii)

number of items that will be produced with GH₵2,400.00;

(iii)

cost when no items are produced.

(b)

A passenger travelling by air is allowed a maximum of 20 kg luggage. A man has four bags weighing 3.5 kg, 15 kg, 2 kg and 1.5 kg.

(i)

Find the excess weight of his luggage.

(ii)

Express the excess weight as a percentage of the maximum weight allowed.

(a)

Evaluate $\frac{4000 x 0.35}{0.05}$ , leaving the answer in standard form.

(b)

Mr Boakye gets 10% commission on type P house he sells and 15% on type Q house.

He sells 3 type P houses at GH₵ 700,000.00 each and 4 type Q at GH₵ 1,400,000.00 each.

Calculate the total commissions he makes.

(a)

If r =

and m =

, find p given p = r - m.

(b)

The sum of two numbers is 81. If the second number is twice the first, find the second number

(c)

The floor of a rectangular hall is of length 9 m and width 4 m. How many tiles of 20 cm by 30 cm can be used to cover the floor completely.