OBJECTIVE TEST

If 15% of the length of a rope is 75 cm, find half of the length of the rope.

500 cm

250 cm

150 cm

100 cm

Priscila's age i k years while Mary's age is b years. If Mary is 15 years older than Priscila, Which of the following statements is correct?

2k + b = 15

b - k = 15

k - b = 15

2b + k = 15

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

20%

40%

60%

80%

The bar chart shows the distances of 5 villages, P, Q, R, S and T from a market town.

Use it to answer the question below.

Which village is farthest from the market town?

What property of addition is defined by (a + b)+ c = a + (b + c)?

Union

Inverse

Commutative

Distributive

Associative

Prices of items in a shop were reduced by 10% during a reduction sale. If a customer bought an electric fan for ₵81,000.00, what was its original price?

₵72,900.00

₵73,900.00

₵89,100.00

₵90,000.00

For what value of x is 3^x = 81?

Given that r =

and t =

find r + t

Simplify -35 – (-15) + (-30)

–50

10.

Find the median of the following marks: 2, 4, 10, 3, 6, 12.

11.

Subtract 125.47 from 203.90

78.57

78.43

-121.57

-122.38

12.

Write the number 34.1 in standard form.

3.41 x 10^-2

3.41 x 10^-1

3.41 x 10⁰

3.41 x 10

13.

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

14.

If m = 3 and n = -3, evaluate $\frac{1}{2}$ (3m - n)

-6

15.

If 4 - x = 3(4x + 5), find the value of x.

$\frac{11}{13}$

1 $\frac{6}{13}$

-1 $\frac{6}{13}$

$\frac{-11}{13}$

16.

P = {odd numbers between 20 and 30} and Q = {23, 29}. Which of the following is true?

P ⊂ Q

Q ⊂ P

P = Q

P ∩ Q = Φ

17.

A trader buys a dozen pens at GH₵ 4.80 and sells them at 48 Gp each. Find her percentage profit.

10%

15%

20%

18.

If 8.51 ÷ 2.3 = 3.7, find the value of 85.1 ÷ 2.3

0.037

0.37

3.7

370

19.

A boy throws a die once. What is the probability of getting the number 4?

$\frac{1}{6}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{5}{6}$

20.

If 2x = 5(x - 2) + 7, find the value of x.

-5 $\frac{2}{3}$

-1

5 $\frac{2}{3}$

21.

Evaluate $\frac{0.63 x 0.70}{9.00}$

0.0049

0.049

0.49

4.9

22.

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

alternate angles

corresponding angles

vertically opposite angles

co-interior angles

23.

Find the L.C.M of 10, 15 and 25.

120

150

300

24.

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

240

720

25.

Expand – x(3 – 2x).

-2x² - 3x

2x² - 3x

-2x² + 3x

2x² + 3x

26.

Find the difference between 432_five and 143_five

234_five

334_five

1130_five

1310_five

27.

Use the diagram below to answer the question below.

Find the angle marked d.

38^o

40^o

48^o

88^o

28.

Kofi invested GH₵ 150,000 at 2.5% per annum simple interest. How long will it take this amount to yield an interest of GH₵11,250.00?

2 years

3 years

4 years

5 years

29.

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

30.

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

- $\frac{1}{2}$

-2

$\frac{1}{2}$

31.

Convert 37_ten to a base two numeral.

100101

100111

101101

110101

32.

A man was 24 years old when his son was born. Now he is three times as old as his son. Find the age of the son.

6 years

12 years

18 years

36 years

33.

If Y = {house, tree} and V = {cat, house, tree} which of the following is true of Y and V?

Y = V

Y ⊂ V

V ⊂ Y

V ∈ Y

Y ∈ V

34.

Tony shared $\frac{2}{3}$ of his plot of land equally among his three sons. What fraction of the plot did each get?

$\frac{2}{9}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{5}{9}$

35.

What fraction of 3 weeks is 18 days?

⅙

6⁄7

1⁄7

9⁄11

36.

Calculate the area of the figure ABCD above.

72 cm²

90 cm²

108 cm²

126 cm²

37.

How many lines of symmetry has a rhombus?

38.

State the rule of the following mapping:

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	1	4	9	16	25

x→x

x→2x

x→3x

x→x²

x→x³

39.

The angles of a triangle are in the ratio 3 : 2 : 1. Find the value of the smallest angle.

30°

45°

60°

90°

40.

Use the information below to answer the question below

In the diagram above, the cylinder has diameter 4 cm and length 14 cm.

[Take π = $\frac{22}{7}$ ]

The area of the base is

176 cm²

44 cm²

$\frac{176}{7}$ cm²

$\frac{88}{7}$ cm²

$\frac{44}{7}$ cm²

THEORY QUESTIONS

(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 woman borrowed ₵2,000,000.00 from a bank at a rate of 15% per annum simple interest for 2 years.

(a)

Find

(i)

the interest for the 2 years;

(ii)

how much she paid in all to the bank after the 2 years.

(b)

She used the ₵2,000,000.00 to purchase a fridge and sold it at a profit of 45%. Find the selling price of the fridge.

(c)

If she used the amount raised from the sale of the fridge to pay for the bank loan and interest, find how much money is left.

(a)

A fair die and a fair coin are thrown together once.

(i)

Write down the set of all possible outcomes.

(ii)

Find the probability of obtaining a prime number and a tail.

(b)

The map of a field is drawn to a scale of 1 : 100. If the width and area of the field on the map are 8 cm and 88 cm² respectively, find in m², the area of the actual field.

(c)

Copy and complete the 3 x 3 magic square such that the sum of the numbers in each row, column and diagonal is equal to 21.

10	3
	7

(a)

Evaluate $\frac{2^{7} x 3^{4} x 5^{3}}{2^{3} x 3^{2} x 5^{2}}$ , leaving your answer in standard form.

(b)

Kwame rode a bicyble for a distance of x km and walked for another $\frac{1}{2}$ hour at a rate of 6 km per hour. If Kwame covered a total distance of 10 km, find the distance x he covered by bicycle.

(c)

A rectangular tank of length 22 cm, width 9 cm and height 16 cm is filled with water. The water is poured into a cylindrical container of radius 6 cm. Calculate the

(i)

volume of the rectangular tank.

(ii)

depth of water in the cylindrical container.

[Take π = $\frac{22}{7}$ ]

(a)

The pie chart shows angles representing the number of candidates who applied for admission into four programmes at a senior secondary school. The number of pupils who applied were 1080.

Find:

(i)

the angle x° representing the Vocational programme.

(ii)

the number of candidates who applied for Business programme.

(iii)

correct to the nearest whole number the percentage of the number of applicants who applied for General Programme.

(b)

The data below shows the distribution of the masses of pupils in a school. On a graph paper, draw a bar chart for the distribution.

Mass (kilograms)	19	20	21	22	23	24
Frequency	5	9	19	25	18	4

The diagram above is a plane figure made up of a rectangle of sides 50 cm by 28 cm and an equilateral triangle of height 24.25 cm. A circle is cut out of the rectangle as shown. If the circle touches three sides of the triangle,

Calculate

(a)

the perimeter of the figure;

(b)

the area of the remaining portion of the figure.

[Take π = $\frac{22}{7}$ ]