OBJECTIVE TEST

Which of the following sets of angles form the interior angles of a right angled triangle?

{20°, 50°, 90°}

{80°, 60°, 90°}

{45°, 45°, 90°}

{65°, 90°, 35°}

A mapping is defined by n → 2n – 3.

What is the image of –2 under the mapping?

–1

–5

–7

Tins of milk each of volume 77 cm³ and weight 170 g were packed into an empty carton of volume 1540 cm³ and weight 500 g.

How many tins of milk can be packed to fill the carton?

In the relation v = u+ at, find v when u = 6, a = 10 and t = 2

120

Write down all the integers within the interval 21 < y ≤ 27.

{21, 22, 23, 24, 25, 26, 27}

{22, 23, 24, 25, 26, 27}

{21, 22, 23, 24, 25, 26}

{22, 23, 24, 25, 26}

In an examination, 154 out of 175 candidates passed. What percentage failed?

12%

13%

18%

The number of pupils who attended hospital from eight classes on a particular day are:

1,5,3,1,7,5,1,1.

Find the median number.

M = {multiples of 3 between 10 and 20}
N = {even numbers between 10 and 20}.

Find M ∩ N.

{12, 18}

{12, 15, 18}

{12, 14, 16, 18}

{12, 14, 15, 16, 18}

{10, 12, 14, 15, 18, 20}

Simplify 3(5a² + 2c) - 2a(1 - 3a) - 6c.

21a² - 2a - 6c

13a² - 2a - 12c

13a² - 2a

21a² - 2a

10.

Find the equation of the straight line passing through the points (-3,5) and (6,8)

y = ⅓^x

y = ⅓^x+6

y = ⅓^x-10

y = ⅓^x+14

11.

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

35, 36

30,31

40, 41

31, 41

12.

Write two hundred and two million, two thousand, two hundred and two in figures.

202,002,202

202,020,202

202,022,202

202,200,202

13.

How many lines of symmetry has a square?

14.

The hypotenuse and a side of a right-angled triangle are 13 cm and 5 cm respectively. Find the length of the third side.

8 cm

9 cm

12 cm

17 cm

15.

Convert 134_five to a base ten numeral

220

16.

Which of the following expressions is illustrated on the number line.

x ≤ -2

x < -2

x ≥ -2

x > -2

17.

Find the tangent of the angle marked y in the diagram below.

$\frac{3}{5}$

$\frac{3}{4}$

$\frac{4}{5}$

$\frac{4}{3}$

$\frac{5}{3}$

18.

Change 10111_two to base ten.

19.

Expand: (2a - b)(a - b)

2a² + 3ab - b

2a² - 3ab - b²

2a² + 3ab + b

2a² - 3ab + b²

20.

Make x the subject of the relation, v² = u² + 2ax.

x = u² + 2av²

x = $\frac{v^{2} - u^{2}}{a^{2}}$

x = $\frac{u^{2} - v^{2}}{2a}$

x = $\frac{v^{2} - u^{2}}{2a}$

21.

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

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

- $\frac{1}{3}$

$\frac{1}{3}$

1 $\frac{2}{3}$

22.

The table below shows the day and night temperatures of a town during a week. Use it to answer the question below.

Week	Temperature (^oC)
Week	Day	Night
Monday	33	24
Tuesday	29	25
Wednesday	32	23
Thursday	34	26
Friday	32	24
Saturday	30	24
Sunday	30	25

On which day was the change in temperature the least?

Monday

Saturday

Sunday

Tuesday

23.

In the diagram, line AB is parallel to line PD. Find the value of x.

20^o

80^o

100^o

120^o

24.

Expand (6 – x)(6 + y)

36 – 6x + 6y – xy

36 – 6x – 6y + xy

36 – 6x – xy

36 + 6y – xy

25.

Write 98 as a product of its prime factors.

2 x 7

2² x 7

2 x 7²

2² x 7²

26.

If q = $(\begin{matrix} -2 \\ 3 \end{matrix})$ and r = $(\begin{matrix} 3 \\ -2 \end{matrix})$ , find q - r.

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

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

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

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

27.

Convert 121_five to a base ten numeral.

28.

Express 4382.93 in standard form.

438293 x 10⁴

43.8293 x 10²

4.38293 x 10⁴

4.38293 x 10³

29.

Express 2700 as a product of prime numbers.

2² × 3² × 5²

2 × 3³ × 5²

2² × 3³ × 5²

2 × 3² × 5³

30.

I gave a storekeeper a GH₵10.00 note for goods I bought. He asked me for another 15 Gp for ease of change. If he then gave me 50 Gp, how much did I pay for the goods?

GH₵9.35

GH₵9.45

GH₵9.65

GH₵10.65

31.

A quadrilateral with one pair of opposite sides parallel is called

kite.

rectangle.

square.

trapezium.

32.

Write 0.01723 in standard form.

0.01723 x 10^-2

0.01723 x 10²

1.723 x 10^-2

1.723 x 10²

33.

Which of the following is true?

{0, 2, 6, 9, 12} is a subset of even numbers.

{-1, 0, 2, 3, 5} is a subset of odd numbers.

{-2, -1, 1, 3, 9} is a subset of integers.

{2, 3, 5, 7, 27} is a subset of prime numbers.

{9, 18, 21, 27, 36} is a subset of multiples of 9.

34.

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

35.

Which of the following is arranged in ascending order?

-25, -64, 4, 17

-64, -25, 4, 17

-64, -25, 17, 4

17, 4, -25, -64

36.

Write 356.07 in standard form.

35.607 x 10

35.607 x 10²

3.5607 x 10²

3.5607 x 10^-2

0.35607 x 10³

37.

The table below gives the number of goals scored by a football team in a league season:

Number of goals scored in a match	0	1	2	3	4	5
Frequency	1	7	6	4	1	1

Use it to answer the question below.

What is the mean number of goals scored by the team?

38.

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

223

271

281

291

39.

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 fraction of Mr. Awuah's income is spent on food?

$\frac{1}{6}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{2}{5}$

$\frac{1}{2}$

40.

Factorize $\frac{1}{4}$ px² + $\frac{1}{8}$ px.

$\frac{1}{4}$ px(x + 2)

$\frac{1}{4}$ px(x + $\frac{1}{2}$ )

$\frac{1}{8}$ px( $\frac{1}{2}$ x + 2)

$\frac{1}{8}$ px(x + 2)

THEORY QUESTIONS

(a)

Simplify $\frac{2a + 4b}{3}$ - $\frac{3(a - b)}{2}$

(b)

Solve 5(a – 5) – $\frac{1}{2}$ (2a + 6) = 4

(c)

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

Using a ruler and a pair of compasses only,

(a)

draw |PQ| = 9 cm

(b)

construct a perpendicular to PQ at Q

(c)

construct angle QPS = 60° at the point P on PQ such that |PS| = 6.5cm

(d)

construct a line parallel to PQ through S. let the perpendicular through Q and the parallel through S, meet at R. Measure |PR|.

Adamu was travelling a distance of 40 km from Kadumgu to Datanu. Sixty minutes after starting the journey, he made a stop at Cooltown, 10 km from Kadumgu to rest for 30 minutes. He then continued the journey from Cooltown and reached Datanu 60 minutes later.

(a)

Using a scale of 2 cm to 20 minutes on the horizontal axis and 2 cm to 5 km on the vertical axis, draw a distance-time graph for Adamu's journey.

(b)

Use the graph to determine the:

(i)

distance from Cooltown to Datanu;

(ii)

total time (in minutes), taken by Adamu to make the whole journey including the rest time;

(iii)

average speed of Adamu from Cooltown to Datanu.

(c)

If Adamu did not rest but travelled to Datanu within the time, what was his average speed?

(a)

Using a ruler and a pair of compasses only,

(i)

construct a triangle XYZ with length XY = 7 cm, length YZ = 5 cm and angle XYZ = 45^o.

(ii)

Measure and write down the length of XZ.

(b)

Given that the circumference of a circle is 44 cm, find

(i)

the radius of the circle;

(ii)

the area of the circle.

[Take π = $\frac{22}{7}$ ]

Using a scale of 2 cm to 1 unit on both axes, draw on a graph sheet two perpendicular axes 0x and 0y for -5 ≤ x ≤ 5 and -5 ≤ y ≤ 5.

Plot, indicating the coordinates of all perpendicular points A(2,3) and B(-3,4). Draw a straight line passing through the points A and B.

Plot on the same graph sheet, indicating the coordinates of the points C(4,2) and D(-2,-3). Draw a straight line passing through the points to meet line AB.

Using the graphs in (a):

find the values of y when x = -2;

measure the angle between the lines AB and CD.

(a)

Copy and complete the table for the relation y = 5 - 2x for -3 ≤ x ≤ 4.

x	-3	-2	-1	0	1	2	3	4
y	11			5		1		-3

(b)

Using a scale of 2 cm to 1 unit on th x-axis and 2 cm to 2 units on the y-axis, draw on a graph sheet two perpendicular axes ox and oy for -5 ≤ x ≤ 5 and -12 ≤ y ≤ 12.

(c)

(i)

Using the table, plot all the points of the relation y = 5 - 2x.

(ii)

Draw a straight line through all the points.

(d)

Using the graph, find the:

(i)

value of y when x = -2.6;

(ii)

value of x when y = -2.8;

(iii)

gradient of the line.