OBJECTIVE TEST

Simplify: $(\begin{matrix} -2 \\ 3 \end{matrix})$ - $(\begin{matrix} 1 \\ 5 \end{matrix})$ .

$(\begin{matrix} -1 \\ 2 \end{matrix})$

$(\begin{matrix} -1 \\ 8 \end{matrix})$

$(\begin{matrix} -3 \\ 8 \end{matrix})$

$(\begin{matrix} -1 \\ -2 \end{matrix})$

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

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

Given that r =

and t =

find r + t

The bar chart shows the mark distribution of pupils in a test. Use it to answer the question below

What is the modal mark?

Expand (6 – x)(6 + y)

36 – 6x + 6y – xy

36 – 6x – 6y + xy

36 – 6x – xy

36 + 6y – xy

A man has three children whose ages are 9 years, 12 years and 24 years. Find the ratio of their ages.

1 : 2 : 3

1 : 2 : 4

2 : 3 : 6

3 : 4 : 8

3 : 6 : 8

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

-6

Multiply 247 by 32.

6916

7804

7904

1235

Simplify: -13 – (-3) + (-10).

-26

-20

-10

- 6

10.

Find the difference between the values of (2d)² and 2d², when d = 3.

11.

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

12.

An article which cost GH₵ 600.00 was sold at a discount of 10%. Find the selling price.

GH₵ 60.00

GH₵ 504.00

GH₵ 560.00

GH₵ 540.00

13.

In a school of 940 pupils, the number of girls exceeds the number of boys by 150. How many girls are there in the school?

620

545

470

395

14.

Find the median of the numbers 17,12,15,16,8,18,13 and 14.

14.5

15.5

15.

Use the information below to answer the question below.

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

The Alpha Water Company charges ₵40,000.00 for every 1 m³ of water.

Find how much it will cost to fill the tank completely.

₵180,000.00

₵240,000.00

₵300,000.00

₵360,000.00

16.

Which of the following would you use to measure an angle?

Ruler

A pair of compasses

A set square

A protractor

17.

Make k the subject of the relation, ky - k = y²

18.

Write 39.975 km correct to three significant figures.

39 km

39.975

49 km

40.0 km

40.9 km

19.

Which of the following statements is true?

8+4 < 10

7+4 < 10

6+4 < 10

5+4 < 10

20.

Which of the following best describes the statement: "The locus of points 6 cm from a fixed point O?"

A parallel line 6 cm from O

A vertical line 6 cm from point O

A horizontal line 6 cm from point O

An equilateral triangle of side 6 cm

A circle with centre O and radius 6 cm

21.

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

22.

How many lines of symmetry has a rectangle?

23.

If r = $\frac{m + 1}{m - 2}$ , express m in terms of r.

m = $\frac{2r + 1}{r - 1}$

m = $\frac{2r + 1}{r + 1}$

m = $\frac{2r - 1}{r - 1}$

m = $\frac{2r - 1}{r + 1}$

24.

The circumference of a circular track is 15.4 m. Find the diameter of the track.

[Take π = $\frac{22}{7}$ ]

4.9 m

22 m

24 m

24.5 m

25.

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?

26.

Simplify: -15 - (-20) + (-10).

-45

-5

-25

27.

Evelyn saved GH₵ 35.48 every month for 8 months. How much did she save?

GH₵ 183.60

GH₵ 280.63

GH₵ 283.20

GH₵ 283.84

28.

In an enlargement with scale factor 2, which of the following statements is not true?

Each length is multiplied by 2.

Each angle remains the same.

The shape of the figure does not change.

The size of the figure does not change.

29.

A piece of cloth is 8.4 m long. If 30 cm is needed to sew a napkin, how many napkins can be sewn from this piece of cloth?

30.

Simplify (2⁶ x 3⁴) ÷ (2⁴ x 3²)

2² x 3²

2² x 3⁶

2¹⁰ x 3²

2¹⁰ x 3⁶

31.

A 3.6 m long string is to be cut into pieces, each of length 40 cm. How many pieces can be cut from the string?

32.

Find how many pieces of cloth 5 $\frac{1}{2}$ m long that can be cut from a roll of cloth 121 m long.

665 $\frac{1}{2}$

115 $\frac{1}{2}$

33.

In the diagram, AB is parallel to CD, Angle AGE is 80^o, angle CFG = 5k and angle CFE = r.

Use the information to answer the question below.

Find the value of k

16^o

20^o

80^o

160^o

34.

John's uncle sent him ₵120,000.00 through a bank which charges 5% commission. How much commission was paid?

₵5,000.00

₵6,000.00

₵7,000.00

₵7,200.00

35.

Arrange the following in descending order:

36.

The diagram shows the graph of a linear relation of the form y = mx + c.

Use the graph to answer the question below

Find the slope of the relation.

-2

-1

37.

If r = $(\begin{matrix} 3 \\ 1 \end{matrix})$ and s = $(\begin{matrix} -2 \\ 1 \end{matrix})$ , calculate 6(r + 2s).

$(\begin{matrix} -1 \\ 3 \end{matrix})$

$(\begin{matrix} 1 \\ 3 \end{matrix})$

$(\begin{matrix} 7 \\ 3 \end{matrix})$

$(\begin{matrix} -6 \\ 18 \end{matrix})$

$(\begin{matrix} 6 \\ 18 \end{matrix})$

38.

Add 2.5 to the product of 4.2 and 0.2

13.4

10.9

3.34

1.34

39.

Simplify:5² x 2² x 5² x 2

2² x 5²

2² x 5⁴

2³ x 5²

2³ x 5⁴

40.

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

–1 < x < $\frac{3}{2}$

–1 ≤ x < $\frac{3}{2}$

–1 ≤ x ≤ $\frac{3}{2}$

–1 < x ≤ $\frac{3}{2}$

$\frac{3}{2}$ ≤ x ≤ –1

THEORY QUESTIONS

(a)

There are 20 students in a hostel. 16 of them are fluent in French and 10 of them are fluent in English. Each student is fluent in at least one of the two languages.

(i)

Illustrate this information on a Venn diagram

(ii)

How many students are fluent in both English and French?

(b)

The sum of the ages of two brothers Kofi and Kweku is 35. Kofi's age is two-thirds of Kweku's age. Find their ages.

The following is the result of a survey conducted in a class of a junior secondary school to find the favourite soft drink of each pupil in the class.

Soft Drink	Number of pupils preferring soft drink
Coca-cola	6
Pepsi-cola	5
Pee-cola	8
Fanta	3
Muscatella	5
Mirinda	4
Club-cola	6
Sprite	3

(a)

Draw a bar chart showing this information, using a scale of 2 cm to 1 unit on the vertical axis.

(b)

How many pupils are in the class?

(c)

What is the percentage of pupils who prefer Club-cola?

A landlady rented out her house for ₵240,000.00 for one year. During the year she paid 15% of the rent as income tax. She also paid 25% of the rent as property tax and spent ₵10,000.00 on repairs.

Calculate:

(a)

The landlady's total expenses.

(b)

The remainder of the rent after the landlady's expenses.

(c)

The percentage of the rent she spent on repairs.

(a)

A car runs on the average at 45 km to 5 litres of fuel. Calculate how many litres of fuel are required for a journey of 117 km.

(b)

(i)

Solve for x in the inequality $\frac{2}{3}$ (2x + 5) ≤ 8 $\frac{2}{3}$

(ii)

Illustrate the solution on the number line.

(c)

A factory increased its production by 22 $\frac{1}{2}$ % and produced 49,000 tonnes. How many tonnes was it producing before?

(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)

E and F are subsets of the universal set U such that

U = {natural numbers less than 15}

E = {even numbers between 1 and 15} and

F = {multiples of 4 between 9 and 15}

(i)

List the elements of U, E and F.

(ii)

Draw a Venn diagram to show the sets U, E and F.

(b)

In a school, $\frac{7}{10}$ of the pupils like Mathematics. Half of those pupils who like Mathematics are girls. If there are 240 pupils altogether in the school, how many girls like Mathematics?

(c)

A typist charges 28 Gp for the first five sheets and 8 Gp for each additional sheet she types. How much will she earn, if she types 36 sheets?