OBJECTIVE TEST

Expand (x - 2)(x + 4).

x² + 2x - 8

x² + 2x + 8

x² - 4x - 8

x² - x - 8

If 15% of the length of a rope is 75 cm, find half of the length of the rope.

500 cm

250 cm

150 cm

100 cm

In the diagram below, ACD is an isosceles triangle in which |AD| = |AC| and DC is parallel to BE, find the value of the angle marked x.

55°

62.5°

110°

117.5°

125°

Correct 48,947.2547 to the nearest hundred.

490

48,900

48,950

49,000

Arrangle the following fractions in ascending order: $\frac{7}{12}$ , $\frac{3}{5}$ , $\frac{7}{15}$ , $\frac{3}{4}$

$\frac{3}{5}$ , $\frac{7}{15}$ , $\frac{7}{12}$ , $\frac{3}{4}$

$\frac{7}{12}$ , $\frac{7}{15}$ , $\frac{3}{5}$ , $\frac{3}{4}$

$\frac{7}{15}$ , $\frac{7}{12}$ , $\frac{3}{5}$ , $\frac{3}{4}$

$\frac{3}{5}$ , $\frac{3}{4}$ , $\frac{7}{12}$ , $\frac{7}{15}$

The diagram below shows a circle with centre O, S and T are points on the circle.

Use it to answer the question below

What name is given to the shaded region?

sector

segment

radii

arc

cone

The perimeter of a rectangle is 48 cm. if the length is 14 cm, find its width.

24 cm

20 cm

10 cm

3.4 cm

The ratio 8 : 12 is equivalent to y : 9. What is the value of y.

Find the value of x in the diagram.

28^o

30^o

34^o

60^o

10.

A bag contains 5 red and 7 black balls of the same size. What is the probability of picking a black ball?

11.

Given that r =

and t =

find r + t

12.

If P = {2,3,4,6,8} and Q = {1,2,3,4}, find P∩Q.

{2,3,4}

{7,9,10}

{2,3,4,6,8}

{1,2,3,4,6,8}

13.

The marks obtained by 9 students in a test are 3, 3, 4, 5, 6, 7, 7, 7, 8.

Use this information to answer the question below.

What is the mode?

14.

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

Ruler

A pair of compasses

A set square

A protractor

15.

P = {0, 2, 4, 6} and Q = {1, 2, 4, 5}. Find P ∩ Q.

{0, 6}

{2, 4}

{0, 4}

{0, 2, 6}

{0, 1, 2, 4, 5}

16.

If r = $(\begin{matrix} 2 \\ 5 \end{matrix})$ and t = $(\begin{matrix} -2 \\ -3 \end{matrix})$ , evaluate r + t.

$(\begin{matrix} 0 \\ -2 \end{matrix})$

$(\begin{matrix} 0 \\ 2 \end{matrix})$

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

$(\begin{matrix} 4 \\ 8 \end{matrix})$

17.

Simplify 200 x 0.01 x 372 leaving your answer in standard form.

74.4 x 10¹

7.44 x 10¹

7.44 x 10²

7.44 x 10⁴

18.

Simplify (5m + 3n)-(2m-n).

5m - 4n

3m + 4n

3m - 2n

7m + 4n

19.

If u = $(\begin{matrix} 3 \\ -1 \end{matrix})$ and v = $(\begin{matrix} 6 \\ 1 \end{matrix})$ , find 2u + v.

$(\begin{matrix} 12 \\ 0 \end{matrix})$

$(\begin{matrix} 12 \\ -1 \end{matrix})$

$(\begin{matrix} 6 \\ 1 \end{matrix})$

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

$(\begin{matrix} 6 \\ -1 \end{matrix})$

20.

Kofi deposited ₵500,000.00 with a bank for 2 years at a rate of 10% per annum. Find the simple interest

₵10,000.00

₵20,000.00

₵50,000.00

₵100,000.00

21.

The stem and leaf plot shows the marks scored by students in a French test. Use the information to answer the question below.

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

What is the modal mark?

22.

Which of the following inequalities is represented on the number line?

-2>y>2

-2≤ y < 2

-2 ≥ y > 2

-2 < y ≤ 2

23.

If a = -4 and b = 3, evaluate $\frac{3a + 2b}{ab}$ .

$\frac{3}{2}$

$\frac{1}{2}$

- $\frac{3}{2}$

24.

An angle which is greater than 180^o but less than 360^o is

a right angle.

an acute angle.

an obtuse angle.

a reflex angle.

25.

Simplify $\frac{30}{5(-2)}$

-10

-6

-3

26.

Factorize completely the expression 2xy – 8x + 5y - 20.

(2x + 5)(y – 4)

(2x – 5)(y + 4)

(2x – 5)(y – 4)

(2x + 5)(y + 4)

(x + 5)(y – 4)

27.

Find the angle through which the minute hand of a clock moves from 5.15 p.m. to 5.25 p.m.

30°

45°

60°

120°

28.

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)

29.

Change 17_ten to a base two numeral.

101

1001

1000

10001

30.

If 2y = 5 - 3x, find x when y = 1.

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

-1

31.

Expand (a + 2b)(a - 2b)

a² - 4ab - 4b²

a² + 4ab - 4b²

a² - 4b²

a² + 4b²

32.

In the diagram above, PQSR is a trapezium. PQ is parallel to RS. ∠PQR = ∠QRS. What type of triangle is triangle RQS?

Isosceles

Scalene

Equilateral

Right–angled

Obtuse-angled

33.

The bearing of Atoru from Busase is 275°. What is the bearing of Busase from Atoru?

180°

175°

095°

075°

34.

What is the rule for the following mapping?

x	0	1	2	3	4
↓	↓	↓	↓	↓	↓
y	5	9	13	17	21

y = x + 5

y = 4x + 5

y = 5x + 4

y = 6x + 1

35.

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?

6 hours

3 hours

2 hours

72 hours

36.

Simplify $\frac{1}{3}$ (2 $\frac{2}{3}$ + $\frac{5}{6}$ )

$\frac{13}{4}$

$\frac{7}{6}$

$\frac{13}{18}$

$\frac{31}{18}$

37.

The sum of 5 and x divided by 4 is equal to 3.25. Find the value of x.

2 $\frac{1}{4}$

-3 $\frac{4}{13}$

38.

Make d the subject of the relation n = 2d + 3

d = $\frac{3n}{2}$

d = $\frac{n + 3}{2}$

d = $\frac{n - 3}{2}$

d = $\frac{3 - n}{2}$

39.

If Q = {2, 4, 6, 7, 8, 10} and R = {3, 5, 7, 9, 10, 11}, find Q ∩ R.

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

{7, 10}

{10}

{7}

40.

If 2n - 5 = $\frac{1}{2}$ n, find the value of n.

$\frac{1}{3}$

$\frac{1}{2}$

2 $\frac{1}{2}$

3 $\frac{1}{3}$

THEORY QUESTIONS

(a)

Kofi is n years old now

(i)

How old was he 5 years ago?

(ii)

How old will he be 10 years from now?

(iii)

If his age in 10 years time will be four times his age 5 years ago, how old is he now?

(b)

Convert 2342_five to a base ten numeral

(c)

Given that f = $\frac{vu}{v + u}$ , find v, if f = 20 and u = 5

(a)

The marks obtained by 20 pupils in a test were as follows:

4	8	7	6	2
1	7	4	3	7
6	4	7	5	2
7	5	4	8	3

(i)

Construct a frequency distribution table for this data.

(ii)

What is the mode of the distribution?

(iii)

Calculate the mean mark.

(iv)

What percentage of the pupils passed, if the pass mark is 6?

(v)

What is the probability that a pupil selected at random scored not more than 5 marks?

(b)

Simplify 7 $\frac{2}{3}$ - 4 $\frac{5}{6}$ + 2 $\frac{3}{8}$

(a)

Multiply (a – b) by (2b – a)

(b)

Find the truth set of 2x – 6 ≤ 5 (3 – x).

Illustrate your answer on a number line.

(c)

Given that u = $(\begin{matrix} -2 \\ 3 \end{matrix})$ and v = $(\begin{matrix} 2 \\ 6 \end{matrix})$ , find $\frac{1}{3}$ (u + $\frac{1}{2}$ v).

(a)

A box has length 8.0 cm, width 5.0 cm and height 10.0 cm. Find the

(i)

total surface area of the box

(ii)

the volume of the box

(b)

(i)

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

(ii)

On the same graph sheet mark the x-axis from -5 to 5 and the y-axis from -6 to 6.

(iii)

Plot and join the points A(0,3), B(2,3) and C(4,5) to form triangle ABC.

(iv)

Draw the image A₁B₁C₁ of triangle ABC under a translation by the vector $(\begin{matrix} -1 \\ -1 \end{matrix})$ .

(v)

Draw the image A₂B₂C₂ of triangle ABC under a reflection in the x-axis.

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)

(i)

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

(ii)

On the same graph sheet, mark the x-axis from –5 to 5 and the y-axis from –6 to 6.

(b)

Plot the points,

(i)

P(1, -2) and Q(4, 5)

(ii)

P′ the image of P under a translation by the vector $(\begin{matrix} -5 \\ 0 \end{matrix})$ and Q′, the image of Q by the same vector.

(c)

(i)

Join PQQ′P′.

(ii)

Measure angles PQQ′ and PP′Q′.

(d)

(i)

Find the vectors PQ→ and P′Q'→

(ii)

What is the shape of PQQ′P′?