OBJECTIVE TEST

P(2, 5) and Q(-2, 3) are points in the Cartesian plane, find the vector PQ→.

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

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

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

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

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

Write the vector $(\begin{matrix} 6 cm W \\ 4 cm S \end{matrix})$ using cartesian components.

$(\begin{matrix} -6 \\ -4 \end{matrix})$

$(\begin{matrix} -4 \\ -6 \end{matrix})$

$(\begin{matrix} -6 \\ 4 \end{matrix})$

$(\begin{matrix} 6 \\ -4 \end{matrix})$

Find the least number that can be added to 207 to make the sum divisible by 17.

The ages in years of 10 children at a party are 2,3,3,3,4,4,5,5,5 and 6. If a child is chosen at random, what is the probability that he or she is not less than 5 years old?

$\frac{2}{3}$

$\frac{2}{5}$

$\frac{3}{10}$

$\frac{1}{2}$

The ratio of mangoes to oranges in a basket is 3:2. If there are 36 mangoes, how many oranges are in the basket?

An angle which is greater than 180^o but less than 360^o is

a right angle.

an acute angle.

an obtuse angle.

a reflex angle.

A man travelled a distance of 1.5 km in 30 minutes. What distance can he cover in 50 minutes, travelling at the same speed?

2.2 km

2.5 km

2.8 km

3.2 km

The table below shows the day and night temperatures of a town during a week. Use it to answer the question below.

Week	Temperature (^oC)
Week	Day	Night
Monday	33	24
Tuesday	29	25
Wednesday	32	23
Thursday	34	26
Friday	32	24
Saturday	30	24
Sunday	30	25

Find, correct to one decimal place, the average day temperature for the week.

24.4 ^oC

30.2 ^oC

31.4 ^oC

32.2 ^oC

Find the rule of the mapping:

1	2	3	4	5	....	x
↓	↓	↓	↓	↓		↓
7	11	15	19	23	....	y

x → 4x - 3

x → 3 - 4x

x → 4x + 3

x → 4x + 5

10.

Find the image of Q(-4,5) when rotated anticlockwise through 90^o about the origin.

Q¹(-5,4)

Q¹(-5,-4)

Q¹(4,-5)

Q¹(4,5)

11.

How many lines of symmetry does a rectangle have?

12.

In a class of 20 pupils, 8 pupils read Mathematics, 13 read English and 3 read both Mathematics and English.

Use this information to answer the question below.

How many pupils read English only?

13.

Set A is called ...... of set B, when all the numbers of set A are also members of set B.

the universal set

the union set

the null set

a subset

an empty set

14.

Expand the expression 2(3a + 2b)

6a + 2b

5a + 4b

6a + 4b

10ab

12ab

15.

Find the total cost of 25 pens and 75 books if each pen costs GH₵ 0.20 and each book costs GH₵ 0.30.

GH₵ 22.50

GH₵ 23.50

GH₵ 27.50

GH₵ 50.00

16.

A bag contains 5 red and 7 black balls of the same size. What is the probability of picking a black ball?

17.

There are 12 boys and 18 girls in a class

Find the fraction of boys in the class.

⅖

⅗

⅔

18.

Solve: 5x - (7x - 3) ≤ 9.

x ≥ -3

x ≤ -3

x ≥ -6

x ≤ 3

19.

Adjoa and Ama share ₵600.00 between them in the ratio 3 : 2. Find Adjoa's share.

₵200.00

₵240.00

₵300.00

₵360.00

₵400.00

20.

Make P the subject of the relation, R = $\frac{(P+Q)}{2}$

P = Q - 2R

P = 2R - Q

P = 2R + Q

P = 2Q + R

21.

Convert 320_five to a base ten numeral.

22.

Name the geometrical figure shown in the diagram below.

Cuboid

Cone

Pyramid

Sphere

23.

If P = {multiples of 4 less than 16}, find P.

{4,8,10}

{4,8,12}

{1,4,8,12}

{4,8,12,16}

24.

Simplify: (x - 1)² - 1.

x² - 2x

x² + 2x

x² - 2x - 1

x² - 2x + 1

25.

Given that a = $(\begin{matrix} 5 \\ 2n \end{matrix})$ and b = $(\begin{matrix} 2n -1 \\ 6 \end{matrix})$ .

If a = b, find the value of n.

26.

Make m the subject of p = $\frac{3m + 1}{m}$ .

m = 3p + 1

m = p - 3

m = $\frac{1}{p - 3}$

m = $\frac{3p + 1}{p}$

27.

Ama is 9 years older than Kwame. If Kwame is 18 years old, find the ratio of the age of Kwame to that of Ama.

3 : 2

1 : 3

2 : 3

2 : 1

28.

In the diagram, QP is parallel to ST, angle QPR = 68^o and angle SRT = 40^o.

Use the information to answer the question below:

Find the value of angle PQR.

40^o

68^o

72^o

108^o

29.

In the figure PQR is a straight line. Angle TQP = x°, angle TQS = 102° and angle SQR = 2x°. Find the value of x.

30.

Round 8921465 to the nearest hundred.

8921000

8921400

8921460

8921500

31.

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 )

32.

The marks obtained by 10 children in a mental drill are: 0, 1, 3, 3, 5, 7, 8, 9, 9, 9.

Use this information to answer the question below.

What is the modal mark?

33.

Evaluate $\frac{0.54 x 0.7}{9}$

0.0042

0.042

0.42

4.2

34.

The sum of 5 and x divided by 4 is equal to 3.25. Find the value of x.

2 $\frac{1}{4}$

-3 $\frac{4}{13}$

35.

Given that (23 × 82) × 79 = 148,994, find the exact value of (2.3 × 82) × 7.9

14.8994

148.994

1489.94

14899.4

148994.0

36.

Find the simple interest on GH₵ 350.00 for 4 years at 5% per annum.

GH₵ 20.00

GH₵ 35.00

GH₵ 70.00

GH₵ 140.00

37.

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.

How much does Mr. Awuah spend on rent?

₵90.00

₵450.00

₵4,500.00

₵9,000.00

₵16,200.00

38.

Simplify $\frac{0.12 x 0.08}{2.40}$

0.4

0.04

0.004

0.0004

0.00004

39.

The diagram shows the graph of a linear relation of the form y = mx + c.

Use the graph to answer the question below

Find the slope of the relation.

-2

-1

40.

Express 134.78 correct to the nearest tenth

130.0

134.7

134.8

135.0

THEORY QUESTIONS

The table below shows the marks scored out of 10 by some candidates in a test.

Mark	1	2	3	4	5	6	7	8
Number of candidates	2	3	5	7	8	13	7	5

(a)

From the table, find

(i)

the modal mark;

(ii)

how many candidates took the test;

(iii)

the mean mark for the test.

(b)

If 20% of the candidates failed,

(i)

how many failed?

(ii)

What is the least mark a candidate should score in order to pass?

Using a ruler and a pair of compasses only,

(a)

draw |PQ| = 9 cm

(b)

construct a perpendicular to PQ at Q

(c)

construct angle QPS = 60° at the point P on PQ such that |PS| = 6.5cm

(d)

construct a line parallel to PQ through S. let the perpendicular through Q and the parallel through S, meet at R. Measure |PR|.

(a)

Copy and complete the table below for the relation: x + y = 180

x	0	30	60	90	120	150	180
y	180			90			0

(b)

(i)

Using a scale of 2 cm to 20 units on both axes, draw two perpendicular axes OX and OY.

(ii)

Mark both axes from 0 to 180.

(iii)

Plot all the seven points. Use a ruler to join all the points.

(c)

Using your graph, find

(i)

y when x = 100;

(ii)

x when y = 70.

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 data below shows the distribution of the ages of workers in a factory.

Ages (in years)	No. of workers
19	3
24	7
29	8
34	4
39	5
44	3

(i)

How many workers are there in the factory?

(ii)

What is the modal age of the distribution?

(iii)

Calculate the mean age of the workers, correct to one decimal place.

(b)

(i)

Make T the subject of the relation

I = $\frac{P x R x T}{100}$

(ii)

If I = ₵40,000.00, P = ₵64,000.00 and R = 25%, find the value of T in years.

(a)

Using a pair of compasses and ruler only, construct

(i)

triangle ABC with │AB│ = 10cm, angle ABC = 30° and angle CAB = 60° ;

(ii)

a perpendicular from the point C to meet the line AB at P.

(b)

(i)

Extend line CP to the point D such that │BC│ = │BD│.

(ii)

Join A to D and B to D.

(iii)

Measure │AC│ and │AD│.

(c)

What type of quadrilateral is ADBC?