KUULCHAT
MATHEMATICS MOCK

OBJECTIVE TEST

1.

How many diagonals are in a rectangle?

A.

1

B.

2

C.

3

D.

4

2.

Mr. Mensah withdrew some money from the bank. He gave 1 2 of it to his sons and 1 3 to his daughter. If he had ₵500.00 left, how much did he take from the bank?

A.

₵600.00

B.

₵750.00

C.

₵1500.00

D.

₵2000.00

E.

₵3000.00

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?

A.

6 hours

B.

3 hours

C.

2 hours

D.

72 hours

4.

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.

A.

6 years

B.

12 years

C.

18 years

D.

36 years

5.

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

A.

P ⊂ Q

B.

Q ⊂ P

C.

P = Q

D.

P ∩ Q = Φ

6.

The table below shows the average rainfall in a town from March 2003 to August 2003.

Use it to answer the question below.

Month March April May June July August
Rainfall (mm) 96 147 281 452 265 139

What was the mean rainfall in the town over the six months?

A.

230 mm

B.

281 mm

C.

366 mm

D.

452 mm

7.

Arrange the following fractions from the lowest to the highest: 3 4 , 2 3 and 3 5 .

A.

3 5 , 2 3 , 3 4

B.

3 5 , 3 4 , 2 3

C.

3 4 , 2 3 , 3 5

D.

3 4 , 3 5 , 2 3

E.

2 3 , 3 5 , 3 4

8.

What is the value of the digit 8 in the number 78000?

A.

8 ten thousands

B.

8 thousands

C.

8 hundreds

D.

8 tens

9.

Simplify: -13 – (-3) + (-10).

A.

-26

B.

-20

C.

-10

D.

- 6

10.

Solve:

A.

4

B.

C.

D.

0

11.

Find the gradient of the straight line which passes through the points (-3,4) and (3,-2).

A.

2

B.

1

C.

-2

D.

-1

12.

How many edges has a cube?

A.

4

B.

6

C.

8

D.

12

E.

18

13.

A graph of a straight line AB is shown below.

Use it to answer the question below

Find the gradient of the line AB

A.

1

B.

2

C.

3

D.

4

E.

5

14.

A bus departed from Elmina at 9:15 pm and arrived in Accra at 2:45 am the next day.

How long did the journey take?

A.

4 hours 20 minutes

B.

4 hours 30 minutes

C.

5 hours 30 minutes

D.

5 hours 20 minutes

15.

Solve the equation 2 3 (x - 3) = 5 6 (x + 6).

A.

-42

B.

-12

C.

18

D.

42

16.

Simplify 1 2 (1 1 2 + 3 4 ÷ 1 4 )

A.

1 1 2

B.

2 1 4

C.

2 3 4

D.

4 1 2

E.

6

17.

Expand – x(3 – 2x).

A.

-2x2 - 3x

B.

2x2 - 3x

C.

-2x2 + 3x

D.

2x2 + 3x

18.

Not drawn to scale

In the diagram, PQR is a right-angled triangle with |PR| = 15 cm and |QR| = 12 cm. Find the length PQ.

A.

3.0 cm

B.

8.0 cm

C.

9.0 cm

D.

19.2 cm

19.

A shop increased all its prices by 10%. Calculate the new price for an article which previously sold for ₵7,500.00

A.

₵6,750.00

B.

₵7,575.00

C.

₵7,800.00

D.

₵8,250.00

E.

₵8,350.00

20.

Write 0.55 as a fraction in its lowest term.

A.

11 200

B.

11 20

C.

11 2

D.

11 5

21.

Study the triangle of odd numbers and use it to answer the question below.

13 b c 19
7 9 a
3 5
1

Evaluate: a + b + c

A.

24

B.

29

C.

36

D.

43

22.

In the diagram, P→P1, Q→Q1, R→R1, where P1Q1R1 is an enlargement.

What is the scale factor of this enlargement?

A.

–2

B.

1 3

C.

1 2

D.

2

E.

3

23.

Find the Greatest Common Factor (GCF) of 90, 126 and 72.

A.

6

B.

9

C.

18

D.

24

24.

Find the image of the point (-2,3) under a reflection in the y-axis.

A.

(2,-3)

B.

(-3,2)

C.

(2,3)

D.

(3,2)

25.

The following addition is in base ten. Find the missing addend.

2 3 4 5
+ 1 0 4 5
* * * *
5 1 1 0
A.

1300

B.

1720

C.

2765

D.

4065

E.

9500

26.

What set does the following graph represent?

A.

{x:x < 2}

B.

{x:x ≤ 2}

C.

{x:x > 2}

D.

{x:x ≥ 2}

27.

Which of the following is illustrated on the number line above?

A.

–1 < x < 3 2

B.

–1 ≤ x < 3 2

C.

–1 ≤ x ≤ 3 2

D.

–1 < x ≤ 3 2

E.

3 2 ≤ x ≤ –1

28.

The total numbers of goals scored each month by a football team are:
3, 4, 8, 2, 4, 6, 4, 8, 7 and 6.
What is the mode?

A.

2

B.

4

C.

5

D.

6

E.

8

29.

The population of a town in 1990 was 88,000. The population increased by 20% in 1998. Find the population in 1998.

A.

70,400

B.

94,600

C.

96,800

D.

105,600

30.

It takes 6 students 1 hour to sweep their school compound. How long will it take 15 students to sweep the same compound?

A.

24 minutes

B.

12 minutes

C.

3 hours

D.

2 hours

31.

Solve the inequality 2x + 10 ≥ 7 2 x - 5.

A.

x ≥ 10

B.

x ≤ 10

C.

x ≤ 40

D.

x ≥ 40

32.

Factorize completely the expression 4xy - 16x + 10y – 40.

A.

(y + 4) (4x – 10)

B.

(y – 4) (4x + 10)

C.

(4 – y) (10 – 4x)

D.

(y + 4) (4x + 10)

33.

The numbers 32, 33, 34, ..., ..., 42 form a sequence in base 5. Find the missing numbers.

A.

35, 36

B.

30,31

C.

40, 41

D.

31, 41

34.

The stem and leaf plot shows the weights (kg) of cocoa bags weighed in a week.

Use the information to answer the question below:

Stem Leaf
4 0,5,7,9
5 1,3,4,5,7,8
6 0,2,3,4,4,4,4,5,6,8
7 1,2,3,4,5,8,8,9
8 2,3,5,6,9
9 4,5

How many bags of cocoa were weighed in the week?

A.

35

B.

29

C.

6

D.

41

35.

A rectangular tank has dimensions 2.5 m by 4 m by 5 m. It is filled with water to the brim. If 35 m3 of the water is used, how much water is left in the tank?

A.

50 m3

B.

35 m3

C.

25 m3

D.

15 m3

36.

find the value of n.

A.

0.0105

B.

0.105

C.

105

D.

1050

37.

In an examination 40% of the students failed. The number of students that passed was 180. How many students failed?

A.

120

B.

270

C.

300

D.

450

38.

A trader received a commission of 12 1 2 % on sales made in a month. His commission was ₵35,000.00. Find his total sales for the month.

A.

₵36,250.00

B.

₵59,750.00

C.

₵245,000.00

D.

₵280,000.00

E.

₵315,000.00

39.

Solve: 4x = 32.

A.

2½

B.

3½

C.

5

D.

7

40.

Simplify:

A.

B.

C.

D.

THEORY QUESTIONS

1.

(a)

Using a scale of 2 cm to 2 units on both axes, draw on a graph sheet two perpendicular axes, 0x and 0y, for the interval -10 ≤ x ≤ 10 and -10 ≤ y ≤ 10.

(b)

On the same graph sheet, draw:

(i)

a quadrilateral ABCD with vertices A(2,4),B(2,8),C(8,8) and D(8,4);

(ii)

the image A1B1C1D1 of ABCD under a translation by vector ( -5 -2 ) , where A → A1, B → B1, C → C1 and D → D1;

(iii)

the image A2B2C2D2 of ABCD under a reflection in the y-axis, where A → A2, B → B2, C → C2 and D → D2.

(c)

(i)

What type of quadrilateral is ABCD?

(ii)

Find the gradient of A2B1.

2.

Using a ruler and a pair of compasses only,

(a)

construct a triangle ABC such that |BA| = 10 cm, angle ABC = 90° and angle BAC = 30°. Measure the length BC.

(b)

(i)

Bisect the angle ACB to meet BA at D.

(ii)

What type of triangle is CDA?

(c)

Calculate the area of triangle ABC

3.

(a)

If 4m - 2(3 + 2m) + m(2m + 4) = 0, find the values of m.

(b)

At a political rally, there were 240 women, 200 men, 160 boys and 120 girls.

(i)

Draw a pie chart to illustrate the information.

(ii)

What percentage of the people at the rally were females?

4.

a

If m = ( 2x + 1 2 - 3y ) , n = ( 6 -8 ) and (m + n) = ( 9 -12 ) , find the:

i

values of x and y;

ii

components of m.

b

i

Solve the inequality:

3 4 (x + 1) + 1 ≤ 1 2 (x -2) + 5.

ii

Illustrate the answer in b(i) on a number line.

c

In the diagram, AB is parallel to CD.

Find the value of:

i

x;

ii

y.

5.

a

Express 250 % as a fraction in its lowest term.

b

Use the diagram to find the value of x.

c

Simplify:

d

If q =

and r =

find (q + r).

6.

(a)

The following table shows the distribution of grades obtained by 120 students in an examination.

Grade A B C D
No. of students 14 30 52 24

Draw a pie chart for the distribution.

(b)

(i)

Evaluate: 5 7 15 - 2 2 3 + 1 5 12

(ii)

Factorize: xy -xz +5y -5z.