OBJECTIVE TEST

How many 15Gp Christmas cards can be bought with GH₵18.00?

120

150

180

270

A bottle of soft drink costs ₵200.00. The commission paid on one bottle is 2% of the cost price. Find the commission paid on 24 bottles of the soft drink.

₵96.00

₵296.00

₵400.00

₵4,704.00

₵4,800.00

If S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, find the probability that a number selected at random from S is odd.

$\frac{3}{8}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{5}{8}$

Find the mean of the following set of numbers 10, 12, 14 and 16.

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

At what rate of simple interest will ₵5,000.00 amount to ₵7,500 if saved for 5 years?

6 $\frac{2}{3}$ %

7 $\frac{1}{2}$ %

10%

12 $\frac{1}{2}$ %

Express 87_ten as a base five numeral.

302_five

322_five

3022_five

3202_five

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

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

10.

The table below shows the ages of children at a birthday party.

Ages(years)	No. of Children
1	3
2	4
3	2
4	5
5	4
6	4
7	6
8	4
9	2
10	1

Use this table to answer the question below.

What is the modal age?

11.

Convert 104_ten to a binary numeral.

1101000

1010100

1101100

1011010

1110100

12.

The mean of three number is 12. If two of the numbers are 14 and 16, find the third number.

13.

The pie chart shows the household budget of a family.

Use the information to answer the question below

If the family's income was GH₵ 40,000.00, how much was spent on clothing?

GH₵ 1,600.00

GH₵ 2,000.00

GH₵ 3,200.00

GH₵ 4,400.00

14.

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

15.

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

16.

Use the information below to answer the question below.

A rectangular tank has length 3 m, width 2 m and height 1.5 m.

If the tank is filled with water to $\frac{2}{3}$ of its capacity, calculate the volume of water in the tank.

4.5 m³

6.0 m³

7.5 m³

13.5 m³

17.

It takes 15 men, 48 days to weed a plot of land. How many men can weed the same plot of land in 16 days, if they work at the same rate?

18.

Simplify: 7(y + 1) – 2(2y + 3)

3y – 5

3y – 2

3y + 1

3y + 4

3y + 13

19.

Find in base ten the value of 4 in 143_five.

20.

From the diagram below, calculate the bearing of point X from Y.

035°

045°

135°

145°

225°

21.

The point P(-2, 3) is translated by a vector $(\begin{matrix} -1 \\ 3 \end{matrix})$ to a point R. Find the coordinates R.

(6, -2)

(-3, 6)

(-3, -6)

(-1, 0)

22.

If p x q x r = 1197, and p = 19, q = 3, find r.

23.

A woman deposited an amount of GH₵ 50,000.00 at a bank for 2 years at a rate of 20% per annum. Find the simple interest.

GH₵ 1,000.00

GH₵ 2,000.00

GH₵ 10,000.00

GH₵ 20,000.00

24.

Mr Adu bought 400 bags of maize for his farm animals. If he used 120 bags to feed the animals, find the percentage of the maize left.

70%

60%

50%

40%

25.

Solve: 3 - (3x+4) ≤ -4

x ≤ 1

x ≥ 1

x ≥ 1⅔

x < 1½

26.

Make a subject of the relation P = 2(a + b)

a = $\frac{P - 2b}{2}$

a = $\frac{P + 2b}{2}$

a = $\frac{2b - P}{2}$

a = $\frac{P - b}{2}$

a = $\frac{P - 2}{b}$

27.

In the diagram above, KGM is a right-angled triangle and angle GKM = 62°. Find the angle of elevation of K from M.

28°

62°

90°

118°

28.

The perimeter of the figure below is 71 cm. Find the diameter of the semi-circumference portion.

[Take π = $\frac{22}{7}$ ]

1.0 cm

3.5 cm

7.0 cm

14.0 cm

29.

In the following diagram, rectangle OABC is enlarged into rectangle OA₁B₁C₁ from center O. OC = 5 cm, OA = 2 cm and AA₁ = 1 cm.

Use the diagram to answer the question below.

Calculate OC₁.

7.5 cm

8 cm

9 cm

12 cm

30.

The length of a rectangular playing field is 5 metres longer than its width. If the perimeter of the field is 150 metres, find its width.

30 metres

35 metres

40 metres

45 metres

31.

A cylinder has a radius 6 cm and height 7 cm. Find its volume.

[Take π = $\frac{22}{7}$ ]

132 cm³

264 cm³

294 cm³

792 cm³

924 cm³

32.

In the diagram, set Q has 30 members and set T has 25 members. Q ∩ T has 10 members.

Find the number of members of Q U T

33.

Given that a = $(\begin{matrix} -2 \\ 3 \end{matrix})$ and b = $(\begin{matrix} 2 \\ -5 \end{matrix})$ , find a + 2b.

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

$(\begin{matrix} 2 \\ 13 \end{matrix})$

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

$(\begin{matrix} 6 \\ 13 \end{matrix})$

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

34.

A mapping is defined by x → x² – 1. What is the image of 3 under the mapping?

35.

The distance from the centre of a circle to any point on it is called

circumference.

diameter.

radius.

sector.

36.

Anowa scored an average of 53 in Science and Mathematics. If she scored 50 and 60 in English Language and Social Studies respectively, find her mean score in all the four subjects.

37.

If (x-3)² = 16, find the positive value of x

38.

Find the median of the following numbers: 46, 68, 34, 37, 76 and 81.

35.5

39.

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 = $\frac{22}{7}$ ]

What is the volume of the cylinder?

176 cm³

44 cm³

$\frac{176}{7}$ cm³

$\frac{88}{7}$ cm³

$\frac{44}{7}$ cm³

40.

Factorize 22ab – 11ac + 6rb – 3rc.

(2b – c) (11a + 3r)

(2b + c) (11a – 3r)

(2b – c) (11a – 3r)

(2b + c) (11a + 3r)

THEORY QUESTIONS

(a)

A doctor treated 2,000 patients over a period of time. If he worked for 5 hours a day and spend 15 minutes on each patient, how many days did the doctor spend to treat all the patients?

(b)

The pie chart shows the distribution of textbooks to six classes A,B,C,D,E and F in a school.

(i)

If class D was given 720 textbooks, how many textbooks were distributed to each of the remaining classes?

(ii)

What is the average number of textbooks distributed to the classes?

(iii)

How many classes had less than the average number of textbooks distributed?

(a)

Given the vectors p = $(\begin{matrix} m + 3 \\ 2 - n \end{matrix})$ , q = $(\begin{matrix} 3m - 1 \\ n - 8 \end{matrix})$ and p = q, find the values of m and n.

(b)

A man shared an amount of money between his children Baaba and William in the ratio 6 : 5. Baaba received GH₵ 1,200.00

(i)

find the total amount shared.

(ii)

William invested his share in an account at the rate of 20% simple interest per annum for 2 years. Find the total amount in his account at the end of the 2 years.

(a)

Copy and complete the table for the relation F = $\frac{9}{5}$ C + 32.

Where F and C are degrees Fahrenheit and degrees Celsius respectively.

°C	0	5	10	15	20	25	30
°F	32				68

(b)

Using a scale of 2 cm to 10 units on the vertical axis (°F) and 2 cm to 5 units on the horizontal axis (°C), draw a linear graph for the relation.

(c)

Use the graph to find the temperature in degrees celsius when F = 55 degrees.

(d)

Interpret the slope of the relation.

(a)

The perimeter of a rectangular plot of land whose length is (2x + 5) m and width (x -10) m is 80 m. Find the

(i)

value of x;

(ii)

area of the plot;

(iii)

cost of weeding the plot at GH₵ 0.24 per m²

(b)

Find the value of x and w in the diagram below if |AB| = |BC|.

(a)

Using a pair of compasses and a ruler only,

(i)

construct triangle ABC such that |AB| = 10 cm, angle ABC = 30° and |BC| = 8 cm. Measure angle ACB.

(ii)

construct a perpendicular from C to meet line AB at D. Measure |CD|.

(b)

Calculate the area of triangle ABC.

(a)

Using a ruler and a pair of compasses only, construct

(i)

triangle ABC such that AB = 12cm, AC = 8cm and BAC = 30°;

(ii)

a perpendicular from C to meet AB at M.

(b)

Measure

(i)

angle ABC;

(ii)

|CM|.

(c)

Calculate the area of triangle ABC.