OBJECTIVE TEST

A student spends $\frac{17}{35}$ of his pocket money on transport and fruits. He spends $\frac{5}{6}$ of the remainder on sweets. What fraction of his pocket money does he spend on sweets?

$\frac{4}{7}$

$\frac{3}{7}$

$\frac{17}{35}$

$\frac{18}{35}$

$\frac{17}{42}$

If a = $(\begin{matrix} 2 \\ 1 \end{matrix})$ and b = $(\begin{matrix} 3 \\ -4 \end{matrix})$ , find 2a + b.

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

$(\begin{matrix} 5 \\ -3 \end{matrix})$

$(\begin{matrix} 8 \\ -7 \end{matrix})$

$(\begin{matrix} 3 \\ -4 \end{matrix})$

If A = {2,6,8} and B = {4,6,8,10}, which of the following statements is true?

A ⊂ B

A ∩ B = {2,6,8}

A ∪ B = {2,4,6,8,10}

A ⊃ B

Solve the inequality 2x + 10 ≥ $\frac{7x}{2}$ - 5

x ≤ 10

x ≥ 10

x ≤ 40

x ≥ 40

Find the image of -3 under the mapping x → 2(x + 3).

Arrange the following fractions in ascending order of magnitude, $\frac{2}{5}$ , $\frac{5}{12}$ and $\frac{3}{4}$ .

$\frac{2}{5}$ , $\frac{3}{4}$ , $\frac{5}{12}$

$\frac{2}{5}$ , $\frac{5}{12}$ , $\frac{3}{4}$

$\frac{5}{12}$ , $\frac{2}{5}$ , $\frac{3}{4}$

$\frac{3}{4}$ , $\frac{2}{5}$ , $\frac{5}{12}$

The pie chart shows the monthly expenditure of Mr. Awuah whose monthly income is ₵18,000.00.

Use the chart to answer the question below.

What is the size of the angle that represents savings?

40°

60°

130°

230°

320°

Use the diagram below to answer the question below.

Find the angle marked a.

70^o

50^o

40^o

30^o

What is 16% of ₵500,000.00?

₵80

₵8,000

₵80,000

₵420,000

₵492,000

10.

Which of the following is the set of prime factors of 12?

{2, 3}

{1, 2, 3}

{1, 2, 4, 6}

{2, 3, 4, 6}

11.

Expand (7r - 5)(3r+4).

21r² + 13r - 20

21r² - 13r - 20

21r² - 43r - 20

21r² + 43r - 20

12.

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

13.

In the following figure below, triangle M′ON′ is an enlargement of triangle MON, with centre O.

Use this information to answer the question below

Find the scale factor of the enlargement

–2

–3

14.

A point (2, 1) is reflected in the y-axis. Find its image.

(-1, 2)

(1, -2)

(-2, 1)

(2, -1)

15.

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

$\frac{5}{27}$

$\frac{7}{27}$

$\frac{11}{27}$

$\frac{13}{27}$

16.

The pie chart above shows the distribution of 360 pupils to various houses in a school.

Use it to answer the question below

How many more students are in Yellow House than in Blue House?

100

17.

Use the graph below to answer the question below.

The travel graph describes the journey of a cyclist from Town X to Town Y.

State the period within which he travelled to town Y after his first rest?

1:00 – 2:00 pm

1:00 – 4:00 pm

1:15 – 1:30 pm

1:30 – 2:00 pm

2:00 – 4:00 pm

18.

Write 83000 in standard form.

8.3x10^-4

8.3x10^-3

8.3x10³

8.3x10⁴

19.

In the diagram, QP is parallel to ST, angle QPR = 68^o and angle SRT = 40^o.

Use the information to answer the question below:

Find the value of angle PQR.

40^o

68^o

72^o

108^o

20.

Correct 0.024561 to three significant figures.

0.03

0.025

0.0245

0.0246

21.

Simplify $\frac{1}{2}$ (1 $\frac{1}{2}$ + $\frac{3}{4}$ ÷ $\frac{1}{4}$ )

1 $\frac{1}{2}$

2 $\frac{1}{4}$

2 $\frac{3}{4}$

4 $\frac{1}{2}$

22.

Find the set of integers within the interval -2 < x < 2

{-2,-1,2}

{-2,-1,0}

{-1,0,1}

{-1,1,2}

23.

Arrange the following fractions in descending order of magnitude:

$\frac{2}{3}$ , $\frac{5}{7}$ , $\frac{2}{5}$ , $\frac{1}{2}$ .

$\frac{5}{7}$ , $\frac{2}{5}$ , $\frac{2}{3}$ , $\frac{1}{2}$

$\frac{5}{7}$ , $\frac{2}{3}$ , $\frac{1}{2}$ , $\frac{2}{5}$

$\frac{1}{2}$ , $\frac{2}{5}$ , $\frac{5}{7}$ , $\frac{2}{3}$

$\frac{1}{2}$ , $\frac{5}{7}$ , $\frac{2}{3}$ , $\frac{2}{5}$

24.

P = {1, 2, 3, 8, 10}, Q = {8, 1, x, 3, 2}. If P = Q, what is the value of x?

25.

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

How many pupils took the test?

26.

P = {prime numbers less than 20} and Q = {odd numbers less than 10}.

Find P ∩ Q

{2, 3}

{1, 3, 5, 7, 11)

{3, 5, 7, 9}

{3, 5, 7}

{3, 5, 7, 11}

27.

Simplify: 5 - 7 + 2(3 - 8)

-12

-8

-5

-4

28.

A train is travelling at a speed of 60 km/h. What distance will it cover from 10.45 am to 12.15 pm?

75 km

87 km

90 km

150 km

29.

The ratio 9 : x is equivalent to 36 : 20. What is the value of x?

30.

Change 17_ten to a base two numeral.

101

1001

1000

10001

31.

Given the points S(5, -2) and T(3, 2), calculate the gradient of the line ST.

-2

- $\frac{3}{5}$

$\frac{1}{2}$

32.

If r = $(\begin{matrix} -10 \\ -3 \end{matrix})$ and n = $(\begin{matrix} 8 \\ -6 \end{matrix})$ , find n + r.

$(\begin{matrix} -2 \\ -9 \end{matrix})$

$(\begin{matrix} 2 \\ -9 \end{matrix})$

$(\begin{matrix} 18 \\ 9 \end{matrix})$

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

33.

If one-third of a number is added to one-fifth of the same number, the result is 8. Find the number.

34.

How many edges has a triangular prism?

35.

Write the vector $(\begin{matrix} 6 cm W \\ 4 cm S \end{matrix})$ using cartesian components.

$(\begin{matrix} -6 \\ -4 \end{matrix})$

$(\begin{matrix} -4 \\ -6 \end{matrix})$

$(\begin{matrix} -6 \\ 4 \end{matrix})$

$(\begin{matrix} 6 \\ -4 \end{matrix})$

36.

If s = $(\begin{matrix} -1 \\ 4 \end{matrix})$ and r = $(\begin{matrix} 3 \\ 2 \end{matrix})$ , find 3s + r.

$(\begin{matrix} 0 \\ 14 \end{matrix})$

$(\begin{matrix} 0 \\ 6 \end{matrix})$

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

$(\begin{matrix} 6 \\ 14 \end{matrix})$

37.

In a secondary school class, 23 pupils study Economics, 6 pupils study both Government and Economics. 48 pupils study either Government or Economics or both.

Use this information to answer the question below.

How many pupils study only Government?

38.

Find the value of $\sqrt{6 \frac{1}{4}}$

5.0

4.9

2.5

2.4

1.2

39.

In an examination, Abu answered nine questions in 2 hours. He spent 20 minutes on the first question and the same time on each of the remaining questions.

How many minutes did he spend on each of the other question?

8.0 minutes

10.0 minutes

12.0 minutes

12.5 minutes

40.

Given that 0.03 x y = 2.4, find the value of y.

0.08

0.8

8.0

80.0

THEORY QUESTIONS

An English textbook costs GH₵ 25.00. The author of the book agreed to take 20% of the cost of each book sold. If 1,702 copies were sold, calculate the author's share.

Simplify:

In the diagram, MN = 13 cm, MP = 15 cm, MS = 12 cm and MS is perpendicular to NP.

Calculate length NP.

(a)

Using a ruler and a pair of compasses only, construct triangle PST with angle PST = 30^o, |ST| = 9 cm and |PS| = 12 cm.

(b)

With T as center, draw a circle of radius 6 cm.

(c)

Construct the perpendicular bisector (mediator) of line PS.

(d)

Label the intersections of the circle and the mediator Q₁ and Q₂.

(e)

(i)

Measure |Q₁Q₂|.

(ii)

Measure angle Q₁TQ₂.

(a)

Mr. Mensah's farm is 20 km from his house. He uses his car to travel y km of the distance from his house and then walks 1 $\frac{1}{2}$ hours at the rate of 3 km per hour to get to his farm. Find y.

(b)

The perimeter of a square field is the same as that of a rectangular field. If the length of the rectangular field is 8km and the width is 5km, calculate the area of the square field.

(c)

Find the gradient of the line which passes through the points M(2,-1) and K(-3,6).

(a)

Given that a = $(\begin{matrix} 2 \\ 3 \end{matrix})$ , b = $(\begin{matrix} x \\ -3 \end{matrix})$ and c = $(\begin{matrix} 7 \\ 3 \end{matrix})$ , find:

(i)

the value of x, if 2a + b = c;

(ii)

d = c - 3a;

(iii)

|d|

(b)

A polytank contains 4500 litres of water and $\frac{1}{5}$ of the water is used for cleaning.

(i)

Find the volume of water used for cleaning.

(ii)

What percentage of water is left in the tank?

Using a ruler and a pair of compasses only,

(a)

Construct triangle PQR such that the length of PQ = 10 cm, angle QPR = 90° and angle PQR = 30°.

Measure the length of PR.

(b)

Bisect the angle QRP to meet PQ at M.

(c)

With M as centre, and radius MP draw a circle.

(d)

Measure the radius of the circle.

The mapping below has the rule, y = 2x + 3.

x	0	1	2	3	4
↓	↓	↓	↓	↓	↓
y	-	5	7	-	-

(a)

(i)

Copy the mapping and fill in the missing numbers

(ii)

Using a scale of 2 cm to 1 unit on both axes on a graph sheet, choose the origin O and draw the perpendicular axes OX and OY.

(iii)

On the same graph sheet, mark the x-axis from 0 to 5 and the y-axis from 0 to 12.

(iv)

Plot on the graph sheet the ordered pairs (x, y) from the mapping and join all the points using a straight edge.

(b)

From your graph, find:

(i)

y when x = 3.5;

(ii)

x when y = 8;

(iii)

the gradient of the line y = 2x + 3.