OBJECTIVE TEST

In the diagram, G₁OH₁ is an enlargement of triangle GOH with scale factor k. If |GG₁| = 5cm, |GO| = 2 cm and |G₁H₁| = 1 cm, what is the value of k?

- $\frac{5}{2}$

- $\frac{3}{2}$

- $\frac{2}{5}$

$\frac{2}{3}$

$\frac{3}{2}$

An angle which is more than 90° but less than 180° is

an acute angle

a right angle

an obtuse angle

a reflex angle

Convert 42 to a base two numeral.

1001010_two

1010010_two

1010100_two

101010_two

Solve the equation

-9

-3

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}

A write watch is priced GH₵2,000.00. A shopkeeper allows a discount of 2% on the cost price.

Find the discount on 20 of such wrist watches.

GH₵500.00

GH₵600.00

GH₵800.00

GH₵1,000.00

A typist charges ₵2,000.00 for the first 5 sheets typed and ₵600.00 for any additional sheet. How much will Barbara pay, if she presents 20 sheets for typing?

₵8,000.00

₵11,000.00

₵12,000.00

₵19,000.00

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

$\frac{5}{27}$

$\frac{7}{27}$

$\frac{11}{27}$

$\frac{13}{27}$

A mapping is defined by n → 2n – 3.

What is the image of –2 under the mapping?

–1

–5

–7

10.

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

21a² - 2a - 6c

13a² - 2a - 12c

13a² - 2a

21a² - 2a

11.

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)

12.

Make T the subject of the relation l² = $\frac{4 π^{2} T}{g}$

T = $\frac{gl}{2π}$

T = $\frac{g l^{2}}{2π}$

T = $\frac{l^{2}}{4g π^{2}}$

T = $\frac{g l^{2}}{4 π^{2}}$

13.

What set does the following graph represent?

{x:x < 2}

{x:x ≤ 2}

{x:x > 2}

{x:x ≥ 2}

14.

Use the diagram above to answer the question below.

Angle MON and PMO are

Alternate angles

vertically opposite angles

Corresponding angles

adjacent angles

Complementary angles

15.

An amount of ₵ 5, 400.00 is shared among three sisters in the ratio of their ages. Their ages are 10 years, 6 years and 2 years. Find the share of the youngest sister.

₵ 300.00

₵ 600.00

₵ 1,200.00

₵ 1,800.00

16.

If 13x – 12 = 5x + 60, find x

–9

–6

17.

Express the product of 162.5 x 0.5 in standard form.

81.25 x 10^-1

81.25 x 10

8.125 x 10^-1

8.125 x 10

0.8125 x 10^-2

18.

In the diagram below, triangle QRT is the enlargement of QST.

Which side of triangle QRT corresponds to side QT of triangle QST?

19.

Find the highest(greatest) common factor of 35 and 70.

20.

The length of a rectangular playing field is 5 metres longer than its width. If the perimeter of the field is 150 metres, find its width.

30 metres

35 metres

40 metres

45 metres

21.

If a = 64 and b = 2², find $\frac{a}{b}$ .

$\frac{1}{16}$

$\frac{1}{32}$

22.

Simplify $(3 \frac{1}{2} + 7) \div (4 \frac{1}{3} - 3)$

6 $\frac{7}{8}$

7 $\frac{7}{8}$

10 $\frac{1}{2}$

23.

A car travels 36 kilometres in an hour. Find its speed in metres per second.

10 ms^-1

100 ms^-1

20 ms^-1

200 ms^-1

24.

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

2 $\frac{1}{3}$

4 $\frac{1}{4}$

6 $\frac{2}{3}$

25.

Subtract 125.47 from 203.90

78.57

78.43

-121.57

-122.38

26.

If 2y = 6 – 3x, find y when x = 0

–3

–2

27.

A frog leaps in such a way that its distance, in metres, from its starting position after each leap is given by 4, 7, 10, ...

Find its distance from the starting position after the 10th leap.

28.

The table below shows the ages of children at a birthday party.

Ages(years)	No. of Children
1	3
2	4
3	2
4	5
5	4
6	4
7	6
8	4
9	2
10	1

Use this table to answer the question below.

What is the modal age?

29.

Find the mean of the following set of numbers 10, 12, 14 and 16.

30.

Simplify (2⁶ x 3⁴) ÷ (2⁴ x 3²)

2² x 3²

2² x 3⁶

2¹⁰ x 3²

2¹⁰ x 3⁶

31.

Expand 3a(a – 4b)

3a – 12ab

3a² – 12ab

3a² – 12b

3a² – 12a

32.

Given that A = {2,4,6,8,10} and B = {4,8,12}, find A ∪ B.

{4,8}

{2,8,12}

{4,6,8,12}

{2,4,6,8,10,12}

33.

The following are the scores obtained by girls in a beauty contest: 12, 16, 19, 14, 17, 8, 11, 19.

What is the probability of obtaining a score of 19?

$\frac{1}{9}$

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{19}{53}$

$\frac{19}{108}$

34.

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

$(\begin{matrix} -10 \\ 1 \end{matrix})$

$(\begin{matrix} -10 \\ -1 \end{matrix})$

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

$(\begin{matrix} -6 \\ 2 \end{matrix})$

35.

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?

36.

Ama is 9 years older than Kwame. If Kwame is 18 years old, find the ratio of the age of Kwame to that of Ama.

3 : 2

1 : 3

2 : 3

2 : 1

37.

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

38.

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

39.

What is the missing number in the sequence: -5, -2, 1, ..., 7?

40.

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

THEORY QUESTIONS

(a)

Using a ruler and a pair of compass only:

(i)

construct triangle PQR such that |PR| = 8 cm, |PQ| = 6 cm and |QR| = 5 cm;

(ii)

construct the perpendicular bisector of |PR| and label it l₁;

(iii)

construct the perpendicular bisector of |QR| and label it l₂;

(iv)

Label the point of intersection of l₁ and l₂ as N.

(v)

With N as centre and radius equal to draw a circle.

(b)

(i)

Measure the radius of the circle.

(ii)

Calculate the circumference of the circle, correct to 3 significant figures.

[Take π = 3.14]

Using a scale of 2 cm to 1 unit on both axis, draw two perpendicular lines OX and OY on a graph sheet. Mark the x-axis from –5 to 5 and the y-axis from –6 to 6. Mark the origin O.

(i)

Draw on the same graph sheet, indicating in each case, the co-ordinates of all the vertices the square ABCD where A(1, 2), B(4, 2), C(4, 5) and D(1, 5) are the respective points.

(ii)

Using the y-axis as a mirror line draw the image A₁B₁C₁D₁ of square ABCD where A→A₁,B→B₁, C→C₁ and D→D₁.

(iii)

Draw an enlargement A₂B₂C₂D₂ of the square ABCD with scale factor –1 from O, such that A→A₂, B→B₂, C→C₂ and D→D₂.

(iv)

What single transformation maps A₂B₂C₂D₂ onto the square A₁B₁C₁D₁?

(a)

Copy and complete the table below for the relation: x + y = 180

x	0	30	60	90	120	150	180
y	180			90			0

(b)

(i)

Using a scale of 2 cm to 20 units on both axes, draw two perpendicular axes OX and OY.

(ii)

Mark both axes from 0 to 180.

(iii)

Plot all the seven points. Use a ruler to join all the points.

(c)

Using your graph, find

(i)

y when x = 100;

(ii)

x when y = 70.

(a)

Factorize completely 3a² + 2ab – 12ac – 8bc

(b)

Solve $\frac{x}{4}$ + $\frac{3}{5}$ = $\frac{3x}{2}$ - 2

(c)

Find the solution set of x + 3 > 19 – 3x, where x is a real number.

Illustrate your answer on the number line.

(a)

Using a ruler and a pair of compasses only, construct

(i)

triangle ABC such athat |AB| = 8 cm, angle CBA = 45^o and angle CAB = 60^o.

(ii)

the bisector of angle ACB to meet |AB| at T.

(b)

Measure

(i)

|CT|;

(ii)

angle CTB.

(c)

A boy spent $\frac{3}{8}$ of his money and had GH₵ 15.00 left. How much did he have?

(a)

Antwiwaa bought 25 mangoes, 7 of which were unripe. What percentage of the mangoes were ripe?

(b)

The mapping shows the relationship between x and y. Find the:

(i)

rule for the mapping;

(ii)

values of m and n

(c)

A bus left town X at 6:30 am and arrived at town Y at 1:00 pm. If the bus travelled at an average speed of 100 km per hour, calculate the distance from town X to town Y.