OBJECTIVE TEST

Simplify

⅓

⅙

⅔

Use the diagram above to answer the question below.

Find the angle MON.

48°

52°

58°

65°

75°

Illustrate 3 < x < 5 on the number line, where x ∈ {rational numbers}.

Write 78910 correct to the nearest thousand.

70,000

78,000

79,000

80,000

Find the highest common factor of 15 and 21.

Simplify

What is the probability that a number greater than 5 shows up when a die is thrown?

5/6

1/6

2/3

1/3

A man can take 12 hours to do a piece of work. How long will it take 6 men working at the same rate to do the work?

6 hours

3 hours

2 hours

72 hours

Evaluate 0.25 x 0.006, correct to three decimal places

0.001

0.002

0.015

0.075

0.105

10.

Two sides of a rectangle are 10 cm and 6 cm. Calculate the area of a square with the same perimeter as that of the rectangle.

16 cm²

30 cm²

60 cm²

64 cm²

11.

Ama is facing east. Through how many degrees should she turn clockwise to face north?

90°

135°

180°

225°

270°

12.

Use the mapping below to answer the question below.

2³ → 8

2² → 4

2¹ → 2

2⁰ → a

2^-1 → b

The value of a is

$\frac{1}{2}$

13.

An article costs ₵60,000.00. The price was increased by 10%. Find the new price.

₵54,000.00

₵61,000.00

₵66,000.00

₵70,000.00

14.

Factorize: kx+2xt-4k-8t.

(k-2t)(x+4)

(k+2t)(x+4)

(k+t)(x-4)

(k+2t)(x-4)

15.

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

16.

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

8a + 3b

8a - 3b

-15b

-3b

17.

Which property of arithmetic is used in a(x+y) = ax + ay.

Associative

Commutative

Distributive

Initiative

18.

A labourer worked for 20½ hours. If he was paid GH₵ 2.50 per hour, what was his total wage?

GH₵ 51.00

GH₵ 51.25

GH₵ 512.00

GH₵ 512.25

19.

Convert 133_five to a base ten numeral.

20.

Find the equation of the straight line passing through the points (-3,5) and (6,8)

y = ⅓^x

y = ⅓^x+6

y = ⅓^x-10

y = ⅓^x+14

21.

Adwoa and Ama share an amount of ₵6,000.00 in the ratio 3 : 2. Find Adwoa's share.

₵2,000.00

₵2,400.00

₵3,000.00

₵3,600.00

₵4,000.00

22.

Three children share an amount of ₵910,800.00 in the ratio 2 : 3 : 4. What will be the highest share?

₵202,400.00

₵303,600.00

₵404,800.00

₵455,400.00

23.

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

24.

Use the diagram below to answer the question below.

Find the angle marked b.

150^o

140^o

110^o

100^o

25.

Make m the subject of the relation:

q = $\frac{1}{3}$ (m + n)h

m = $\frac{3q}{h}$ - n

m = 3q - hn

m = 3q + hn

m = $\frac{3q}{h}$ + n

26.

A car uses 150 litres of petrol in 45 mins. How many litres of petrol will it use in 1 hour?

375 litres

230 litres

225 litres

200 litres

27.

Simplify $\frac{1}{3}$ + $\frac{1}{9}$ + $\frac{1}{27}$

$\frac{5}{27}$

$\frac{7}{27}$

$\frac{11}{27}$

$\frac{13}{27}$

28.

Express the product of 162.5 x 0.5 in standard form.

81.25 x 10^-1

81.25 x 10

8.125 x 10^-1

8.125 x 10

0.8125 x 10^-2

29.

What is the place value of 7 in 24.376?

Unit

Ten

Tenth

Hundredth

30.

Solve for y, if 3 + 3y = 1 - 13y

- $\frac{1}{8}$

- $\frac{1}{4}$

$\frac{1}{8}$

$\frac{1}{4}$

31.

Find the angle through which the minute hand of a clock moves from 5.15 p.m. to 5.25 p.m.

30°

45°

60°

120°

32.

Find the rule of the mapping:

x	0	3	6	9	12
↓	↓	↓	↓	↓	↓
y	-2	4	10	16	22

y → $\frac{x}{2}$ - 2

y → x - 2

y → x² - 2

y → 2x - 2

33.

Given that 1 kilometre = $\frac{5}{8}$ mile, what is 240 miles in kilometres?

150 km

190 km

384 km

390 km

34.

Simplify: -27 + 18 - (10 - 14) - (-2)

-3

-7

-11

-35

35.

Simplify $\frac{0.24 x 14.3}{5.2}$

6.60

0.70

0.66

0.60

36.

Which of the following inequalities is shown on the number line above, where p ∈ {real numbers}?

-2 < p < 3

-2 ≥ p > 3

-2 < p ≤ 3

-2 > p ≥ 3

37.

Express 34 m 5 cm 6 mm in millimetres.

3,456 mm

34,056 mm

34,506 mm

340,506 mm

38.

Make q the subject of the relation w = $\frac{n - q}{q}$ .

q = $\frac{n - 1}{w}$

q = $\frac{n + 1}{w}$

q = $\frac{n + 2}{1 + w}$

q = $\frac{n}{w + 1}$

q = $\frac{n}{w - 1}$

39.

If x = {1, 2, 3, 4, 5}, find the truth set of 2x + 1 < 7

{1, 2}

{2, 3}

{1, 2, 3}

{3}

{2}

40.

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

THEORY QUESTIONS

The following table shows the frequency distribution of the number of letters in the surnames of some students in a school.

No. of letters	4	5	6	7	8	9	10
No. of students	7	3	2	8	5	3	1

(a)

From the distribution, determine

(i)

the mode;

(ii)

the mean.

(b)

If a student is selected at random, find the probability that his/her name will contain more than 7 letters.

(c)

Draw a bar chart for the distribution.

(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.

(a)

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

(i)

triangle PQR such that |PQ| = 8cm, angle QPR = 60° and angle PQR = 45°.

(ii)

Measure |QR|.

(b)

A rectangular water tank has length 60cm, width 45cm and height 50cm.

Find

(i)

the total surface area of the tank when closed

(ii)

the volume of the tank

(iii)

the height of the water in the tank, if the tank contains 81,000 cm³ of water.

(a)

Using a ruler and a pair of compasses only, construct ∆PQR such that angle PQR = 90°, |PQ| = 5.5 cm and |QR| = 8 cm.

(b)

Construct a perpendicular of PR from Q.

(c)

Locate M, the intersection of the perpendicular and PR.

(d)

Measure:

(i)

|MR|;

(ii)

|QM|.

(e)

Calculate, correct to the nearest whole number, the area of triangle QMR.

(a)

Mansah earns a salary of ₵10,000.00 per month as a sales girl. In addition to the salary, she is given a commission of 1.5% of whatever sales she makes in a month. In January this year, she made sales of ₵7,500,000.00. What was the total amount Mansah earned at the end of January?

(b)

The diagram below shows a circle with centre O and radius 14 cm. The shaded region AOB is a sector with angle AOB = 72°.

Find:

(i)

The length of the minor arc AB

(ii)

The area of the shaded sector AOB

[Take π = $\frac{22}{7}$ ]

(a)

Convert 444_five to a base two numeral.

(b)

A man had three GH₵50.00, seven GH₵20.00 and five GH₵10.00 notes in his pocket. If he bought a bicycle for GH₵150.00 and two mobile phones at GH₵80.00 each, how many GH₵20.00 and GH₵10.00 notes did he have left?