OBJECTIVE TEST

The ratio of the ages of two sisters is 4 : 3. The elder sister is 3 years older than the younger one. How old is the younger sister?

9 years

12 years

15 years

18 years

Which of the following is not quadrilateral?

square

rectangle

rhombus

triangle

parallelogram

Which of the following best describes the construction?

Constructing a perpendicular at P

Constructing the bisector of line PQ

Constructing an angle of 30^o at P

Constructing an angle of 45^o at P

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

$(\begin{matrix} 5 \\ 1 \end{matrix})$

$(\begin{matrix} 11 \\ 5 \end{matrix})$

$(\begin{matrix} 11 \\ 13 \end{matrix})$

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

$(\begin{matrix} 14 \\ 12 \end{matrix})$

Make n the subject of the relation

n = x(y+1)

n = y(x+1)

If (23 × 82) × 79 = 148,994, find the exact value of (2.3 × 82) × 7.9

1.48994

14.8994

148.994

1489.94

14899.4

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

$(\begin{matrix} 8 \\ 9 \end{matrix})$

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

$(\begin{matrix} 4 \\ 0 \end{matrix})$

$(\begin{matrix} 4 \\ 9 \end{matrix})$

$(\begin{matrix} -4 \\ -9 \end{matrix})$

What is the rule for this mapping?

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	1	3	5	7	9

x→2x - 1

x→2(x - 1)

x→2x + 1

x→2(x + 1)

x→2x - 1

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.

What is the weight of the carton when packed with the tins of milk?

2.06 kg

2.94 kg

3.90 kg

8.50 kg

10.

There are 15 white and 25 black identical balls in a box. If a ball is selected at random from the box, find the probability that it is white.

$\frac{1}{25}$

$\frac{1}{15}$

$\frac{3}{8}$

$\frac{5}{8}$

11.

Factorize completely 5xy + 10ny

5y(x + n)

5y(x + 2n)

5xy(1 + 2n)

5(xy + 2ny)

x(5x + 10n)

12.

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?

$\frac{4}{7}$

$\frac{3}{7}$

$\frac{17}{35}$

$\frac{18}{35}$

$\frac{17}{42}$

13.

Use the equation y = (x + 2)(x - 2) to answer the question below

If x = -1, find y.

–4

–3

14.

The pie chart shows the distribution of crops on a farm of area 250 hectares.

Use it to answer the question below.

Find the area of the plot with corn.

48.6

55.3

62.5 ha

83.3 ha

125.0 ha

15.

Find the simple interest on GH₵ 600.00 which was saved for 8 months at 5% per annum.

GH₵ 20.00

GH₵ 40.00

GH₵ 45.00

GH₵ 240.00

16.

How many 15Gp Christmas cards can be bought with GH₵18.00?

120

150

180

270

17.

If y = - $\frac{1}{2}$ x + 6, find y when x = 4.

-2

18.

Find the value of 124.3 + 0.275 + 74.06, correcting your answer to one decimal place.

198.6

198.7

892.0

892.4

19.

In the diagram below, MNO is a triangle. Angle MON = 72° and angle OMN = 68°.

Find angle ONP.

40°

68°

72°

112°

140°

20.

A van travels 154 km in 1 $\frac{3}{4}$ hours. Find its speed in km/h.

77 km/h

88 km/h

100 km/h

269.5 km/h

21.

A bag contains 12 mangoes of which 4 are not ripe. What is the chance of picking at random a ripe mango from the bag?

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

22.

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

35, 36

30,31

40, 41

31, 41

23.

List the members of the set Q = {Prime factors of 30}

{2,3,5}

{2,6,10}

{3,5,15}

{3,6,15}

24.

If Q = {1,3,5,7,9,10,11,13,15} and T = {1,2,3,5,6,7,10,11,12}, find Q ∪ T.

{1,2,3,5,7,10,11}

{1,3,5,7,9,11,13,15}

{1,2,3,4,5,6,7,8,9,10,11,12,13}

{1,2,3,5,6,7,9,10,11,12,13,15}

25.

Find in base ten the value of 4 in 143_five.

26.

What set does the following graph represent?

{x:x < 2}

{x:x ≤ 2}

{x:x > 2}

{x:x ≥ 2}

27.

Calculate the area of figure PQRST

112.5 cm²

135.0 cm²

180.0 cm²

215.0 cm²

315.0 cm²

28.

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}

29.

The table shows the marks of some students in a test. Use the information to answer the question below.

Marks	0	1	2	3	4	5	6	7	8	9	10
Number of students	3	4	5	4	5	4	7	3	4	2	2

How many students failed the test, if the pass mark was 4?

30.

At eight O'clock, which of the following is the angle between the hour and the minute hands of the clock?

150^o

120^o

90^o

60^o

31.

A bottle of soft drink costs ₵200.00. The commission paid on one bottle is 2% of the cost price. Find the commission paid on 24 bottles of the soft drink.

₵96.00

₵296.00

₵400.00

₵4,704.00

₵4,800.00

32.

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.

33.

Write 39.975 km correct to three significant figures.

39 km

39.975

49 km

40.0 km

40.9 km

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.

List all members of the set {x: 2 < x < 8, x is an integer}

{3, 4, 5}

{2, 3, 4, 5, 6, 7, 8}

{2, 2 $\frac{1}{2}$ , 3, 4, 5, 6, 7, 8}

{3, 3 $\frac{1}{2}$ , 3, 4, 5, 6, 7, 8}

{3, 4, 5, 6, 7}

36.

Convert 84 to a base five numeral.

4130_five

3014_five

314_five

114_five

37.

If 8x - 3(2x - 4) = 4, find the value of x.

-8

-4

38.

A fair coin and a fair die are rolled together once. Find the probability of obtaining a tail and an odd number.

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{1}{2}$

39.

A rectangle has a length of 8 cm and a breadth of 6 cm. How long is its diagonal?

40.

A hawker is carrying a basket load of three types of fruits: oranges, mangoes and pears.

If $\frac{2}{5}$ of the fruits are oranges and $\frac{6}{25}$ mangoes, what percentage of the fruits are pears?

9 %

18 %

64 %

36 %

THEORY QUESTIONS

(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)

(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)

Mark on the same graph sheet, the x-axis from -5 to 5 and y-axis from -6 to 6.

(iii)

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

(iv)

Using the y as mirror line, draw the image triangle A₁B₁C₁ of the triangle ABC such that A → A₁, B → B₁ and C → C₁. Write down the coordinates of A₁, B₁ and C₁.

(v)

Draw the image triangle A₂B₂C₂ of triangle ABC under anticlockwise rotation of 180° about the origin where A → A₂, B → B₂ and C → C₂. Write down the coordinates of A₂, B₂ and C₂.

(b)

Given that a = $(\begin{matrix} -3 \\ 2 \end{matrix})$ , b = $(\begin{matrix} -5 \\ -7 \end{matrix})$ and c = $(\begin{matrix} -4 \\ -1 \end{matrix})$ , evaluate 2a - 3c + b.

Madam Esi used $\frac{1}{4}$ and $\frac{2}{3}$ of her x acres of land to cultivate mangoes and oranges respectively.

(a)

Express, in term of x, the number of acres of the land she used to cultivate:

(i)

mangoes;

(ii)

oranges.

(b)

If madam Esi used 20 more acres of land to cultivate oranges than mangoes, find the value of x.

(c)

How many acres of land was used to cultivate mangoes?

(d)

Calculate, correct to the nearest whole number, the percentage of the land that was not used.

An aeroplane left the Kotoka International Airport on Wednesday at 7:26 pm and reached its destination after nine hours thirty minutes. Find the day and the time the aeroplane reached its destination.

Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes 0x and 0y on a graph sheet for -10 ≤ x ≤ 10 and -12 ≤ y ≤ 12.

Draw on this graph indicating the coordinates of all vertices, the quadrilateral ABCD with vertices A(0,10),B(-6,-2),C(-3,-11) and D(4,3).

iii

Draw the line x = -2 to meet AB at P and CD at Q.

Measure angles BPQ and PQD.

State the relationship between:

angles BPQ and PQD;

lines AB and CD.

(a)

Simplify 2 $\frac{3}{4}$ ÷ $(3 \frac{3}{8} - 1 \frac{1}{2})$

(b)

There are 50 pupils in a class. Out of this number, $\frac{1}{10}$ speak French only and $\frac{4}{5}$ of the remainder speak both French and English. If the rest speak English only,

(i)

find the number of students who speak

(α)

both French and English;

(β)

only English.

(ii)

Draw a Venn diagram to illustrate the above information.

(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).