OBJECTIVE TEST

If r = $(\begin{matrix} 2 \\ -5 \end{matrix})$ and s = $(\begin{matrix} -2 \\ 5 \end{matrix})$ , calculate 2r - 3s.

$(\begin{matrix} -10 \\ -25 \end{matrix})$

$(\begin{matrix} -2 \\ -25 \end{matrix})$

$(\begin{matrix} 10 \\ -25 \end{matrix})$

$(\begin{matrix} 10 \\ 25 \end{matrix})$

Simplify 6(7a + 4) - 3(8a + 9)

18a - 3

18a + 51

42a - 27

66a -3

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

$\frac{1}{4}$

$\frac{1}{2}$

The base of an isosceles triangle is 7cm long. Each of the other two sides is x cm long. What will be the expression for its perimeter?

x + 7

x + 14

2x - 7

2x + 7

In the diagram, P and Q are two sets and U is the universal set.

Use the information to answer the question below

Find P ∩ Q.

{c, d, e}

{a, b}

{c, b, c, d, e}

{f, g, h}

If 3t – 2 (t + 12) = 11, find the value of t.

–35

–13

The product of three numbers is 1197. Two of the numbers are 3 and 19. Find the third number.

210

544

1175

simplify: 4a - 9b -2(2a - 3b).

8a + 3b

8a - 3b

-15b

-3b

If a trader made a profit of 10% in selling a shirt for GH₵ 44.00, find the cost price

GH₵ 39.60

GH₵ 38.50

GH₵ 48.40

GH₵ 40.00

10.

The diagram is a square of side 2 cm in which is inscribed a circle with center O.

Use the information to answer the question below.

Find the area of the shaded portion.

[Take π = $\frac{22}{7}$ ]

0.86 cm²

3.00 cm²

6.28 cm²

12.56 cm²

11.

Find the smallest number which is divisible by 16 and 20?

120

160

12.

If R = $\frac{1}{2}$ (a + b)k, find k in terms of R, a and b.

$\frac{a + b}{2R}$

$\frac{2R}{a + b}$

$\frac{2R - a}{b}$

$\frac{2R - b}{a}$

$\frac{R}{2(a + b)}$

13.

If the set A = {1, 2, 3, 4, 5} and the set B = {2, 4, 6}, find the number of members in the set A U B.

14.

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

Use it to answer the question below

Find the value of the angle marked X°.

30°

40°

100°

150°

15.

A mapping is defined by n → 2n – 3.

What is the image of –2 under the mapping?

–1

–5

–7

16.

In how many years will ₵5,000.00 yield a simple interest of ₵1,000.00 at a rate of 5% per annum.

4 years

5 years

10 years

25 years

30 years

17.

In a secondary school class, 23 pupils study Economics, 6 pupils study both Government and Economics. 48 pupils study either Government or Economics or both.

Use this information to answer the question below.

How many pupils study only Economics?

18.

In an enlargement, the area of the object was multiplied by 144 to get the area of the image. Find the scale factor of the enlargement.

144

19.

Find the GCF (HCF) of 2³ × 3² and 2³ × 3⁴.

648

20.

Which of the following is an infinite set?

{1, 2, ..., 5, 6, 7}

{4, 6, 8, 10, 12}

{2, 3, 5, 7, 11, ...}

{3, 6, ..., 18, 21, ...33, 36}

21.

Use the information below to answer the question below.

A rectangular tank has length 3 m, width 2 m and height 1.5 m.

The Alpha Water Company charges ₵40,000.00 for every 1 m³ of water.

Find how much it will cost to fill the tank completely.

₵180,000.00

₵240,000.00

₵300,000.00

₵360,000.00

22.

Find the value of x, if $\frac{x}{4}$ + 1 = 5.

23.

Find the simple interest on GH₵120,000.00 for 5 months at 12% per annum.

GH₵6,000.00

GH₵7,200.00

GH₵50,000.00

GH₵72,000.00

24.

Which of the following geometric figures is the plane shape of a cube?

Circle

Rectangle

Square

Triangle

25.

Write 1204_five as a number in base ten.

9996

179

26.

Express 72 as a product of prime factors.

2×3

2²×3²

2²×3³

2³×3²

27.

Factorize: 5ay - by + 15a - 3b.

(y + 3)(5a - b)

(y + 5)(3a - b)

(y - 3)(5a + b)

(y - 5)(3a + b)

28.

The cost of three items at a shop are GH₵ 72.00, GH₵ 1,105.00 and GH₵ 216.00.

If a customer bought all the three items and received a change of GH₵ 107.00, how much did he initially give the shopkeeper?

GH₵ 1,300.00

GH₵ 1,400.00

GH₵ 2,000.00

GH₵ 1,500.00

29.

In the triangle RST, ∠RST is 90°, |RS| = 4 cm and |ST| = 3 cm.

What is the length of RT?

2 cm

3 cm

4 cm

5 cm

7 cm

30.

If P = {7, 11, 13} and Q = {9, 11, 13}. Find P U Q.

{7}

{9}

{7, 9}

{7, 9, 11}

{7, 9, 11, 13}

31.

The bearing of P from Q is 060^o. Find the bearing of Q from P

120^o

150^o

210^o

240^o

32.

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

33.

In a class, there are 12 girls and 48 boys. Find the percentage of boys in the class.

20%

40%

60%

80%

34.

Find the least common multiple (LCM) of 12 and 20.

35.

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

36.

Convert 12.03 metres to centimetres.

0.1203 cm

120.3

1203 cm

12030 cm

37.

In the diagram above, AB is parallel to CD. Angles x and y are

alternate angles

corresponding angles

vertically opposite angles

co-interior angles

38.

Express 87_ten as a base five numeral.

302_five

322_five

3022_five

3202_five

39.

If u = $(\begin{matrix} 1 \\ 3 \end{matrix})$ and v = $(\begin{matrix} 4 \\ -2 \end{matrix})$ , find 2u + 3v.

$(\begin{matrix} 5 \\ 1 \end{matrix})$

$(\begin{matrix} 11 \\ 5 \end{matrix})$

$(\begin{matrix} 11 \\ 13 \end{matrix})$

$(\begin{matrix} 14 \\ 0 \end{matrix})$

$(\begin{matrix} 14 \\ 12 \end{matrix})$

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)

The pie chart shows the weight (in kg) of items Mrs. Mensah bought for her household.

(i)

What angle represents fish?

(ii)

If she bought a total of 20 kg of items,

(α)

what is the weight of flour bought?

(β)

express, correct to one decimal place, the weight of sugar as a percentage of the weight of rice.

(b)

In a class of 30 students, five wear glasses. If a student is selected at random from the class, what is the probability that the student does not wear glasses?

(a)

Antwiwaa bought 25 mangoes, 7 of which were unripe. What percentage of the mangoes were ripe?

(b)

The mapping shows the relationship between x and y. Find the:

(i)

rule for the mapping;

(ii)

values of m and n

(c)

A bus left town X at 6:30 am and arrived at town Y at 1:00 pm. If the bus travelled at an average speed of 100 km per hour, calculate the distance from town X to town Y.

(a)

In an examination, 50 candiates sat for either Mathematics or English Language.

60% passed in Mathematics and 48% passed in English Language. If each candiate passed in at least one of the subjects, how many candidates passed in:

(i)

Mathematics?

(ii)

English Language?

(b)

Illustrate the information given in (a) on a Venn diagram.

(c)

Using the Venn diagram, find the number of candidates who passed in:

(i)

both subjects;

(ii)

Mathematics only.

(d)

If a = $(\begin{matrix} 4 \\ -5 \end{matrix})$ and b = $(\begin{matrix} 2x \\ 3+y \end{matrix})$ are equal vectors, find the values of x and y.

(a)

Factorize: (x-y)(3m+n)-(x-y)(m-2n)

(b)

Given that

and

Find the value of (x + y)

(c)

(i)

Find the truth set of

(ii)

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

(a)

M is a set consisting of all positive integers between 1 and 10. P and Q are subsets of M such that P = {factors of 6}, Q = {multiples of 2}

(i)

List the elements of M, P and Q

(ii)

Represent M, P and Q on a Venn diagram

(iii)

Find P ∩ Q

(b)

(i)

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

(ii)

Illustrate your answer on the number line.

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	0	3	6	9	12

The mapping shows the relationship between x and y.

using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw two perpendicular axes 0x and 0y on a graph sheet for 1 ≤ x ≤ 5 and 0 ≤ x ≤ 14;

ii)

plot the point for each ordered pair, (x, y).

iii)

join the points with a straight line;

iv)

using the graph, find the gradient of the line in (a)(iii);

use the graph to find the equation of the line in (a)(iii).

Simplify: 32 x 8 x 4 x 2, leaving the answer in the form 2ⁿ