OBJECTIVE TEST

What name is given to a triangle which has all its sides equal?

Isosceles triangle

Scalene triangle

Equilateral triangle

Right-angle triangle

What is the image of 3 in the mapping x → 3x + 7?

Find the integers within the interval 5 < x < 9

{5,6,7}

{5,6,7,8}

{5,6,7,8,9}

{6,7,8}

{6,7,8,9}

In sharing 95 oranges with Dede, Fofo kept 45 of them and shared the rest equally with Dede. How many oranges did Dede get?

Calculate the length of QR in triangle PQR

Which of the following statements best describe the construction above?

Constructing 30°

Constructing 60°

Constructing 120°

Constructing 135°

Five times a number is four more than the number. Find the number.

$\frac{3}{2}$

$\frac{2}{3}$

$\frac{1}{2}$

-1

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

$(\begin{matrix} 8 \\ 9 \end{matrix})$

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

$(\begin{matrix} 4 \\ 0 \end{matrix})$

$(\begin{matrix} 4 \\ 9 \end{matrix})$

$(\begin{matrix} -4 \\ -9 \end{matrix})$

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 y

10.

Multiply 0.014 by 0.2

0.00028

0.0028

0.028

0.28

11.

200 bottles of equal capacity hold 350 litres of water. How much water does each bottle hold?

1750 litres

175 litres

17.5 litres

1.75 litres

0.17 litres

12.

Find the least number that must be added to 308 to make it divisible by 19.

13.

Find the vector which translate the point (2,6) to (5,4).

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

$(\begin{matrix} -1 \\ 4 \end{matrix})$

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

$(\begin{matrix} 7 \\ 10 \end{matrix})$

14.

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°

15.

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

16.

Arrange the following in ascending order of magnitude:

0.301,0.3,0.33,0.03.

0.03,0.3,0.301,0.33

0.03,0.301,0.3,0.33

0.33,0.3,0.301,0.03

0.33,0.301,0.3,0.03

17.

Divide $(1 \frac{1}{2} + \frac{1}{4})$ by $(1 \frac{1}{2} - \frac{1}{4})$

$\frac{5}{7}$

1 $\frac{2}{5}$

1 $\frac{3}{4}$

18.

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

19.

If the vector m = $(\begin{matrix} 3 \\ 2 \end{matrix})$ and n = $(\begin{matrix} -1 \\ 3 \end{matrix})$ , find m - 2n.

$(\begin{matrix} -1 \\ 4 \end{matrix})$

$(\begin{matrix} 1 \\ -4 \end{matrix})$

$(\begin{matrix} 5 \\ 4 \end{matrix})$

$(\begin{matrix} 5 \\ -4 \end{matrix})$

20.

Find the Least Common Multiple (L.C.M) of 2, 3 and 5.

21.

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

Find |BD|.

3 cm

4 cm

9 cm

33 cm

41 cm

22.

If P = {7, 9, 13}, Q = {1, 7, 13}. Find P ∩ Q.

{1, 7, 13}

{1, 9, 13}

{7, 13}

{7, 9, 13}

{13}

23.

A man travelled a distance of 1.2 km in 30 minutes. What distance can he cover in 55 minutes travelling at the same speed?

1.375 km

2.02 km

2.2 km

12.02 km

13.25 km

24.

Use the mapping below to answer the question below

5 → 10_five

10 → 20_five

20 → 40_five

40 → x_five

y → 310_five

Find the value of x

30_five

100_five

110_five

120_five

130_five

25.

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.

How many people are employed under all the trade?

325,000

485,000

650,000

875,000

26.

On a map, two towns P and Q are 15.5 cm apart. The scale of the map is 1 cm: 4 km. Calculate the actual distance between P and Q.

15.5 km

31 km

46 km

60 km

62 km

27.

Madam Nancy wants to know which of the teachers in her school is liked best by most of the students. Which of the following methods is most suitable for collecting the data?

Experiment

Database

Questionnaire

Observation

28.

In the diagram above, length of PS = Length of SQ and angle SQR = 112^o.

Find the value of x.

68^o

56^o

46^o

44^o

29.

Factorize x² – 5x + 6

(x + 3)(x – 2)

(x – 2)(x – 3)

(x + 1)(x –6)

(x + 2)(x + 3)

(x + 6)(x – 1)

30.

Adjoa travelled 12km due north and 5km due east. How much far was she from her starting point?

60km

17km

13km

7km

31.

In a school, 80 pupils wrote an examination and 64 of them passed. What is the percentage of pupils who passed?

16%

20%

64%

80%

32.

Find the value of x in the equation $\frac{x}{4}$ = 2

33.

Express 350 as a product of prime factors

2 × 5 × 7

2 × 5² × 7

2 × 5 × 7²

2² × 5 × 7

34.

If set N is a subset of set M, then

sets M and N have the same number of elements.

some members of set N can be found in set M

no member of set N is in set M.

all members of set N are in set M.

35.

The population of a town in 1990 was 88,000. The population increased by 20% in 1998. Find the population in 1998.

70,400

94,600

96,800

105,600

36.

Simplify $\frac{1}{3}$ - $\frac{1}{2}$ + $\frac{2}{5}$

$\frac{17}{30}$

$\frac{13}{30}$

$\frac{7}{30}$

- $\frac{7}{30}$

- $\frac{17}{30}$

37.

Given that t = p² + 1, find p when t = 10.

3.0

4.5

11.0

81.0

38.

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

39.

Simplify: 12 - 7 - (-5).

-10

-2

40.

The distance between two towns is 12875 km.

Express this distance in standard form.

1.2875 x 10³ km

1.2875 x 10⁴ km

12.875 x 10³ km

128.75 x 10² km

12.875 x 10⁴ km

THEORY QUESTIONS

(a)

If p = 4, a = 16, b = -5 and c = 3, evaluate p² - $\frac{(a - b)}{c}$

(b)

Solve the inequality 5x – 3(x – 1) ≥ 39. Illustrate your answer on the number line.

(c)

If x = $(\begin{matrix} -3 \\ 2 \end{matrix})$ and y = $(\begin{matrix} 4 \\ -1 \end{matrix})$ , find

(i)

x + 2y

(ii)

3x – y

(a)

E and F are subsets of the universal set U such that

U = {natural numbers less than 15}

E = {even numbers between 1 and 15} and

F = {multiples of 4 between 9 and 15}

(i)

List the elements of U, E and F.

(ii)

Draw a Venn diagram to show the sets U, E and F.

(b)

In a school, $\frac{7}{10}$ of the pupils like Mathematics. Half of those pupils who like Mathematics are girls. If there are 240 pupils altogether in the school, how many girls like Mathematics?

(c)

A typist charges 28 Gp for the first five sheets and 8 Gp for each additional sheet she types. How much will she earn, if she types 36 sheets?

(a)

A box has length 8.0 cm, width 5.0 cm and height 10.0 cm. Find the

(i)

total surface area of the box

(ii)

the volume of the box

(b)

(i)

Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular axes 0x and 0y 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.

(iii)

Plot and join the points A(0,3), B(2,3) and C(4,5) to form triangle ABC.

(iv)

Draw the image A₁B₁C₁ of triangle ABC under a translation by the vector $(\begin{matrix} -1 \\ -1 \end{matrix})$ .

(v)

Draw the image A₂B₂C₂ of triangle ABC under a reflection in the x-axis.

(a)

The marks obtained by 20 pupils in a test were as follows:

4	8	7	6	2
1	7	4	3	7
6	4	7	5	2
7	5	4	8	3

(i)

Construct a frequency distribution table for this data.

(ii)

What is the mode of the distribution?

(iii)

Calculate the mean mark.

(iv)

What percentage of the pupils passed, if the pass mark is 6?

(v)

What is the probability that a pupil selected at random scored not more than 5 marks?

(b)

Simplify 7 $\frac{2}{3}$ - 4 $\frac{5}{6}$ + 2 $\frac{3}{8}$

(a)

Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes OX and OY on a graph sheet. On the same graph sheet, mark the x-axis from –8 to 8 and the y-axis from –8 to 8

(i)

Plot P(-2, 3) and Q(6, 4). Join PQ

(ii)

Draw the image P₁Q₁ of PQ under an anticlockwise rotation through 90° about the origin, where P→P₁ and Q→Q₁. Indicate clearly all the co-ordinates.

(iii)

Draw the image P₂Q₂ of PQ under a clockwise rotation through 90° about the origin where P→P₂ and Q→Q₂. Indicate clearly all the co-ordinates

(b)

The base radius of a closed cylinder is 4 m. The height of the cylinder is 7 m. Calculate its total surface area.

[Take π = $\frac{22}{7}$ ]

(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.