OBJECTIVE TEST

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%

The following are the angles formed at the centre of a circle: 30°, 70°, 120°, 2x and 5x. Find the value of x.

100

140

Find the image of 3 under the mapping, x → 10 - 2x.

Find the truth set of $\frac{1}{4}$ (x + 3) ≤ 2x - 1.

{x:x ≤ -3}

{x:x ≤ -1}

{x:x ≥ 1}

{x:x ≥ -3}

E is the point (4, 2) and F the point (2, 1). Calculate the gradient of the straight line EF.

- $\frac{1}{2}$

-2

$\frac{1}{2}$

If 2n - 5 = $\frac{1}{2}$ n, find the value of n.

$\frac{1}{3}$

$\frac{1}{2}$

2 $\frac{1}{2}$

3 $\frac{1}{3}$

Solve: 4^x = 32.

2½

3½

Find the value of p² – 6p + 9 when p = -2

–7

8 girls can weed a plot of land in 10 days. How many days will 5 girls take to weed the same plot of land, working at the same rate?

6 days

8 days

12 days

16 days

10.

A boy walks on a bearing 070^o. Which of the following diagrams show his direction?

11.

In the diagram above, PQ is parallel to RS and |PR| = |QR|.

Use the diagram to answer the question below.

Find b.

105

12.

Use the mapping below to answer the question below

-2	-1	0	2	3	4	......	x
↓	↓	↓	↓	↓	↓		↓
y	-1	1	5	7	9	......	21

Find the value of x

–7

13.

An amount of money is shared between Kofi and Ama in the ratio 3 : 5. If Ama received ₵4,650.00, what is Kofi's share?

₵930.00

₵1,550.00

₵1,743.75

₵2,790.00

₵2,906.25

14.

In the diagram, ∠ QPR = 30° and |QR| = 5 cm.

[Take sin 30° = $\frac{1}{2}$ ].

Find the length of PQ.

2.5 cm

5.0 cm

12.0 cm

10.0 cm

15.

The diagram shows the conversion graph for miles and kilometres.

Use it to answer the question below

Find in kilometres, the equivalent of 4 miles.

2.5

3.5

6.4

16.

A mother has GH₵ 5.00 and gives each of her 3 children GH₵ 1.50 as pocket money. How much is left for her?

GH₵ 3.50

GH₵ 4.5

GH₵ 0.15

GH₵ 0.50

17.

Simplify 2² × 3² × 2³ × 3⁴.

2² × 3⁶

2⁴ × 3⁷

2⁵ × 3⁶

2⁶ × 3⁸

18.

The marks obtained by 5 girls in a test are: 10, 15, 8, 18, 12.

Find the median mark.

19.

Find the image of 4 under the following mapping.

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	4	7	10	k	16

20.

If 22% of a rope is 55 m long, find the full length of the rope.

12.1 m

25 m

121 m

250 m

2500 m

21.

If A = {2,6,8} and B = {4,6,8,10}, which of the following statements is true?

A ⊂ B

A ∩ B = {2,6,8}

A ∪ B = {2,4,6,8,10}

A ⊃ B

22.

In the diagram, square P¹Q¹R¹S¹ is an enlargement of square PQRS from centre O. The area of PQRS is 4 cm² and the area of P¹Q¹R¹S¹ is 9 cm².

Find the scale factor of the enlargement.

$\frac{2}{3}$

$\frac{4}{9}$

1 $\frac{1}{2}$

- $\frac{2}{3}$

2 $\frac{1}{4}$

23.

Convert 39_ten to a base five numeral.

100111

1110

234

124

103

24.

The least common multiple (L.C.M) of 16, 30 and 36 is

240

720

25.

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

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

$(\begin{matrix} 5 \\ -3 \end{matrix})$

$(\begin{matrix} 8 \\ -7 \end{matrix})$

$(\begin{matrix} 3 \\ -4 \end{matrix})$

26.

Which of the following best describes the construction below?

Constructing an angle of 60°

Constructing the perpendicular bisector of AB

Constructing a circle about the midpoint of AB

Constructing an angle of 180°

27.

Simplify:5² x 2² x 5² x 2

2² x 5²

2² x 5⁴

2³ x 5²

2³ x 5⁴

28.

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

29.

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.

30.

A box can take 12 pencils. If 156 pencils are packed into such boxes, how many boxes will be fully packed?

31.

Arrange the following in descending order:

32.

Given that p = {1,2,3,4,5,6,7,8,9,10,11,12}, what is the probability of selecting a prime number from the set?

⅔

7⁄12

5⁄12

33.

If Y = 595 and Z = 7071, find the sum of Y and Z.

6466

7566

7666

12,021

13,021

34.

Use the mapping below to answer the question below.

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	-4	-2	0	2	m

What is the rule for this mapping?

x→ 2(x - 3)

x→ x - 5

x→ 2(x - 2)

x→ 2x-3

35.

The pie chart shows how Kwaku spends his monthly salary.

Use this information to answer the question below.

Find the value of x.

65^o

75^o

85^o

100^o

36.

Simplify 200 x 0.01 x 372 leaving your answer in standard form.

74.4 x 10¹

7.44 x 10¹

7.44 x 10²

7.44 x 10⁴

37.

What set does the following graph represent?

{x:x < 2}

{x:x ≤ 2}

{x:x > 2}

{x:x ≥ 2}

38.

Multiply (2x + y) by (2x – y)

4x² – 4xy – y²

4x² + xy – y²

4x² – xy – y²

4x² + y²

4x² – y²

39.

A farmer left home at 4:35 am and arrived on his farm at 6:18 am. How long did he take to get to his farm?

1 hour 23 minutes

1 hour 43 minutes

2 hours 43 minutes

10 hours 53 minute

40.

What percentage of 5 is 0.25?

20%

25%

THEORY QUESTIONS

Solve:

Multiply 0.03858 by 0.02, leaving the answer in standard form.

A cylindrical container of height 28 cm and diameter 18 cm is filled with water. The water is then poured into another container with a rectangular base of length 27 cm and width 11 cm. Calculate the depth of the water in the container. (Take π = 22⁄7)

The sum of the interior angles of a regular polygon is 900^o. Find the number of sides of the polygon.

Using a ruler and a pair of compasses only, construct:

triangle XYZ such that length XY = 10 cm, angle XYZ = 30^o and length YZ = 9 cm;

perpendicular from Z to meet line XY at P;

iii

measure the:

length PZ;

angle XYZ.

calculate, correct to the nearest whole number, the area of triangle XYZ.

(a)

Using a ruler and a pair of compasses only,

(i)

construct triangle ABC with sides |AB| = 7 cm, |BC| = 8 cm and |AC| = 9 cm;

(ii)

draw the perpendicular bisectors of the three sides;

(iii)

locate the point of the intersection, O, of the perpendicular bisector;

(iv)

with center O and radius OA, draw a circle to pass through the vertices of the triangle.

(b)

Measure and write down the radius of the circle you have drawn in (a)(iv).

(c)

Find the product of (2x - 3) and (x -1).

(a)

Using a scale of 2 cm to 1 unit on both axes, draw on a graph sheet two perpendicular axes 0x and 0y for -5 ≤ x ≤ 5 and -5 ≤ y ≤ 5.

(i)

Plot, indicating the coordinates of all points P(1,1), Q(1,2),R(2,2) and S(2,1) on the graph sheet. Join the points to form square PQRS.

(ii)

Draw and indicate clearly all coordinates, the image P₁Q₁R₁S₁ of square PQRS under an enlargement from the origin with a scale factor of 2, where P → P₁,Q → Q₁, R → R₁ and S → S₁.

(iii)

Draw and indicate clearly all coordinates, the image P₂Q₂R₂S₂ of square P₁Q₁R₁S₁ under a reflection in the x-axis where P₁ → P₂,Q₁ → Q₂, R₁ → R₂ and S₁ → S₂.

(b)

Using the graph in (a), find the gradient of line R₂S.

The table shows the number of students in a JSS class who prepared various dishes for their practical.

Dishes	No. of students
Fufu and light soup	5
Banku and Okro stew	20
Fried rice	30
Fried plantain and beans	25
Boiled yam and palaver sauce	10

(a)

(i)

Draw a pie chart for the distribution above.

(ii)

What dish was prepared most?

(iii)

What percentage of students prepared fried rice

(b)

What is the probability that a student chosen at random cooked fried plantain and beans?

(a)

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

(b)

Find the value of the expression 2x - 3y if x = $\frac{1}{3}$ and y = - $\frac{1}{2}$ .

(c)

25 students in a class took an examination in Mathematics and Science. 17 of them passed in Science and 8 passed in both Mathematics and Science. 3 students did not pass in any of the subjects.

Find

(i)

how many passed in Mathematics;

(ii)

the probability of meeting a student who passed in one subject only.