OBJECTIVE TEST

Use the graph below to answer the question below.

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

How many minutes did the cyclist spend at town Y?

15 minutes

20 minutes

30 minutes

45 minutes

60 minutes

Simplify: $\frac{1}{2}$ - $\frac{1}{4}$ + $\frac{1}{8}$

$\frac{1}{8}$

$\frac{1}{6}$

$\frac{3}{8}$

$\frac{5}{8}$

$\frac{7}{8}$

The table below gives the distribution of ages of students in a class.

Use it to answer the question below.

Ages (years)	13	14	15	16	17
Number of students	3	10	6	7	4

How many students are in the class?

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

Use the information below to answer the question below

The scores obtained by 8 pupils in a test are 2, 3, 4, 5, 7, 8, 8 and 9

Find the mean score.

4.50

5.75

6.00

8.75

10.00

The point P(5,4) is reflected in the y-axis. Find its image.

(-5,4)

(5,-4)

(-4,5)

(4,-5)

Illustrate 3 < x < 5 on the number line, where x ∈ {rational numbers}.

Evaluate $\frac{20}{a}$ - b, if a = 30 and b = 1.

-1 $\frac{2}{3}$

- $\frac{1}{3}$

$\frac{1}{3}$

1 $\frac{2}{3}$

An iron rod 15 m long is divided into 12 equal parts. How long is each part?

0.80 m

1.25 m

1.50 m

3.00 m

10.

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

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

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

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

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

11.

Write 17_ten in base two numeral.

1001

10001

11001

11011

12.

What is the fifth term of the sequence $\frac{1}{3}$ , $\frac{2}{5}$ , $\frac{7}{15}$ ...?

$\frac{4}{9}$

$\frac{5}{11}$

$\frac{6}{13}$

$\frac{3}{5}$

13.

Express 30% as a fraction in its lowest term.

7⁄10

3⁄20

7⁄20

3⁄10

14.

Jojo and Fiifi shared an amount of money in the ratio 3 : 4 respectively. If Fiifi had ₵ 140, 000 how much was shared?

₵ 200,000.00

₵ 220,000.00

₵ 245,000.00

₵ 280,000.00

15.

The pie chart shows how Kwaku spends his monthly salary.

Use this information to answer the question below.

Kwaku earns GH₵630.00 a month. How much of this does he spend on food?

GH₵140.00

GH₵157.00

GH₵210.00

GH₵350.00

16.

Express 36 as a product of primes.

2 x 3

2² x 3²

2² x 3³

2³ x 3²

17.

Use the diagram below to answer the question below.

Find the value of a°

68°

75°

105°

112°

124°

18.

A car travels at an average speed of 45 km per hour. What distance does it cover in 12 hours?

450 km

480

500 km

540 km

19.

The following marks are the marks obtained by pupils in a test: 2, 3, 5, 2, 3, 4, 2, 3, 5, 3.

Use the information above to answer the question below.

Calculate the mean

3.0

3.2

4.0

4.2

20.

Simplify: $\frac{2a}{3}$ - $\frac{a - b}{2}$ .

a - 3

$\frac{a - 3b}{6}$

$\frac{a + 3b}{6}$

a + 3b

a - b

21.

In the diagram below, line PQ is parallel to RS and UV is a line drawn through PQ and RS.

Use the diagram to answer the question below.

Angle b and angle c are

alternate angles.

vertically opposite angles.

corresponding angles.

interior opposite angles.

22.

Convert 243_five to a base ten numeral.

23.

Simplify 35x⁵y³ ÷ 7xy²

5x⁴y

5x⁴y⁵

5x⁶y

5x⁶y⁵

24.

The difference between two numbers is 168. If the smaller number is 113, find the other number.

223

271

281

291

25.

In an office, $\frac{2}{3}$ of the telephone bill is paid by Tom, $\frac{1}{5}$ by Azuma and the remaining by Tina. What fraction is paid by Tina?

$\frac{2}{15}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{7}{15}$

26.

The ages in years of 10 children at a party are 2,3,3,3,4,4,5,5,5 and 6. If a child is chosen at random, what is the probability that he or she is not less than 5 years old?

$\frac{2}{3}$

$\frac{2}{5}$

$\frac{3}{10}$

$\frac{1}{2}$

27.

If 21 : 2x = 7 : 10, find x.

2 $\frac{1}{4}$

28.

If u = $(\begin{matrix} 6 \\ 9 \end{matrix})$ and v = $(\begin{matrix} 4 \\ -5 \end{matrix})$ , find u + v.

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

$(\begin{matrix} 2 \\ -4 \end{matrix})$

$(\begin{matrix} 10 \\ -14 \end{matrix})$

$(\begin{matrix} 10 \\ 4 \end{matrix})$

29.

How many lines of symmetry does a rectangle have?

30.

In the diagram above, PQ is parallel to RS and |PR| = |QR|.

Use the diagram to answer the question below.

What is a?

134

31.

Simplify 3a²b³ × 4a³b.

12a⁵b⁴

12a⁴b⁵

7a⁵b⁴

7a⁴b⁵

32.

Kwame gets a commission of 20% on bread sold. In one week, Kwame's commission was ₵45,000.00. How much bread did he sell during that week?

₵205,000.00

₵220,000.00

₵225,000.00

₵235,000.00

33.

Arrange the following numbers in ascending order: $\frac{9}{5}$ ,1.88, $\frac{15}{8}$

$\frac{9}{5}$ , $\frac{15}{8}$ ,1.88

$\frac{15}{8}$ ,1.88, $\frac{9}{5}$

1.88, $\frac{9}{5}$ , $\frac{15}{8}$

$\frac{9}{5}$ ,1.88, $\frac{15}{8}$

34.

In the diagram, Q is the set of numbers inside the circle and T is the set of numbers inside the triangle. Find Q U T.

{5}

{6, 7}

{3, 4, 5}

{5, 6, 7}

{3, 4, 5, 6, 7}

35.

Simplify

10y + 3

10y - 3

36.

Write the rule for the mapping:

x	1	2	3	4
↓	↓	↓	↓	↓
y	1	3	5	7

x→2x + 1

x→2x - 1

x→2(x + 1)

x→2(x - 1)

x→x²- 1

37.

Given that vectors u = $(\begin{matrix} -3 \\ 5 \end{matrix})$ and v = $(\begin{matrix} 2 \\ -3 \end{matrix})$ , calculate 2v - u.

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

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

$(\begin{matrix} -7 \\ -11 \end{matrix})$

$(\begin{matrix} 7 \\ -11 \end{matrix})$

38.

Find the rule of the mapping:

1	2	3	4	5	x
↓	↓	↓	↓	↓	↓
5	8	11	14	17	y

x + 2

x + 4

2x + 3

3x + 2

39.

Solve: 3 - (3x+4) ≤ -4

x ≤ 1

x ≥ 1

x ≥ 1⅔

x < 1½

40.

The interior angle of a regular polygon is 135°. How many sides has the polygon?

THEORY QUESTIONS

(a)

In an examination, 50 candiates sat for either Mathematics or English Language.

60% passed in Mathematics and 48% passed in English Language. If each candiate passed in at least one of the subjects, how many candidates passed in:

(i)

Mathematics?

(ii)

English Language?

(b)

Illustrate the information given in (a) on a Venn diagram.

(c)

Using the Venn diagram, find the number of candidates who passed in:

(i)

both subjects;

(ii)

Mathematics only.

(d)

If a = $(\begin{matrix} 4 \\ -5 \end{matrix})$ and b = $(\begin{matrix} 2x \\ 3+y \end{matrix})$ are equal vectors, find the values of x and y.

(a)

M is a set consisting of all positive integers between 1 and 10. P and Q are subsets of M such that P = {factors of 6}, Q = {multiples of 2}

(i)

List the elements of M, P and Q

(ii)

Represent M, P and Q on a Venn diagram

(iii)

Find P ∩ Q

(b)

(i)

Solve the inequality $\frac{2x - 2}{4}$ - $\frac{2x - 1}{3}$ ≤ 1

(ii)

Illustrate your answer on the number line.

(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 $\frac{7}{15}$ - 2 $\frac{2}{3}$ + 1 $\frac{5}{12}$

(ii)

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

(a)

If p = 4, a = 16, b = -5 and c = 3, evaluate p² - $\frac{(a - b)}{c}$

(b)

Solve the inequality 5x – 3(x – 1) ≥ 39. Illustrate your answer on the number line.

(c)

If x = $(\begin{matrix} -3 \\ 2 \end{matrix})$ and y = $(\begin{matrix} 4 \\ -1 \end{matrix})$ , find

(i)

x + 2y

(ii)

3x – y

(a)

Simplify: $\frac{1200 x 1260}{800}$ and write your answer in standard form.

(b)

A plot of land measures 25 m by 12 m. A portion of this plot measuring 8 m by 8 m is used for the cultivation of vegetables.

Find the area of the plot not cultivated.

(c)

The table below shows the performance of Aisha in her final examination.

Subject	Score
English Language	54%
Mathematics	36%
Ga	68%
Science	50%
Social Studies	32%

Draw a pie chart to represent this information.

(a)

Given that P = {multiples of 3} and Q = {positive even numbers} are subsets of µ = {x: 1 ≤ x ≤ 20, where x is a counting number}:

(i)

List the elements in P ∩ Q;

(ii)

List all the subsets in P ∩ Q.

(b)

If $\frac{1}{y}$ = 3k - $\frac{2}{x}$ ,

(i)

make y the subject of the relation.

(ii)

using the result in (b(i), find the value of y when x = -1 and k = 2.