OBJECTIVE TEST

Find the area of a circle whose diameter is 28 cm.

[Take π = $\frac{22}{7}$ ]

44 cm²

88 cm²

352 cm²

616 cm²

Find one-hundredth of 1.0756

107.56

10.756

0.01756

0.010756

0.001756

In how many years will ₵5,000.00 yield a simple interest of ₵1,000.00 at a rate of 5% per annum.

4 years

5 years

10 years

25 years

30 years

A man divided his 360 cattle among his three sons in the ratio 7 : 6 : 5. How many cattle did the one who had the smallest share receive?

100

120

140

160

The longest chord of a circle is the

segment.

sector.

circumference.

diameter.

Kofi's age in the next ten years will be four times his age five years ago. How old is Kofi now?

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?

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

If $\frac{1}{k}$ = $\frac{1}{k_{1}}$ + $\frac{1}{k_{2}}$ , find k when k₁ = 1 and k₂ = 2.

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{3}{2}$

How many lines of symmetry does a rhombus have?

10.

OPQR is a trapezium whose height is 20 cm. What is the area?

460 cm²

600 cm²

920 cm²

960 cm²

1000 cm²

11.

Simplify 35x⁵y³ ÷ 7xy²

5x⁴y

5x⁴y⁵

5x⁶y

5x⁶y⁵

12.

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

1 $\frac{1}{2}$

2 $\frac{1}{4}$

2 $\frac{3}{4}$

4 $\frac{1}{2}$

13.

Ama is three times as old as Kofi. The sum of their ages is 40. How old is Ama?

10 years

30 years

37 years

43 years

14.

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.

15.

The length of a field, 1.2 km long is represented on a map by a line 40 mm long. What is the scale of the map?

1 : 100

1 : 300

1 : 1000

1 : 3000

1 : 30000

16.

If a = $(\begin{matrix} 3 \\ 3 \end{matrix})$ and b = $(\begin{matrix} 5 \\ -5 \end{matrix})$ , find a + b.

$(\begin{matrix} 2 \\ 8 \end{matrix})$

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

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

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

$(\begin{matrix} 8 \\ -2 \end{matrix})$

17.

The diagram is a square of side 2 cm in which is inscribed a circle with center O.

Use the information to answer the question below.

Find the area of the shaded portion.

[Take π = $\frac{22}{7}$ ]

0.86 cm²

3.00 cm²

6.28 cm²

12.56 cm²

18.

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?

$\frac{1}{6}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{2}{5}$

$\frac{1}{2}$

19.

Convert 42 to a base two numeral.

1001010_two

1010010_two

1010100_two

101010_two

20.

Find the next two terms in the sequence 11,7,3,-1,...,...

5,9

3,7

-4,-9

-5,-9

21.

Express 12/25 in decimal fraction.

0.0408

0.048

0.408

0.48

22.

If a : 27 = 6 : 18, find a.

23.

A refrigerator was sold for GH₵ 200.00 at a loss of 10%. Find the cost price.

GH₵ 180.00

GH₵ 190.48

GH₵ 220.00

GH₵ 222.22

24.

The volume of a cylinder is 40Π cm³. If the height of the cylinder is 10 cm, find the base radius

1 cm

4 cm

2 cm

3 cm

25.

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

26.

Factorize 2pq + 6p -6q - 18.

2(p - 3)(q - 3)

2(p + 3)(q + 3)

2(p - 3)(q + 3)

2(p + 3)(q - 3)

27.

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}

28.

P = {2, 4, 6, 8} and Q = {even counting numbers less than 12}.

What is the relationship between P and Q?

P = Q

P ⊂ Q

P < Q

Q ⊂ P

P ∈ Q

29.

In the triangle XYZ, angle XZY = 90°, |XY| = 13 cm and |YZ| = 5cm.

What is the length of XZ?

4 cm

8 cm

12 cm

65 cm

30.

If 180 oranges were shared among Kwame and Ama in the ratio 7:5, respectively, how many oranges did Ama receive?

31.

Which of the following inequalities is shown on the number line above, where p ∈ {real numbers}?

-2 < p < 3

-2 ≥ p > 3

-2 < p ≤ 3

-2 > p ≥ 3

32.

The diagram is a square of side 2 cm in which is inscribed a circle with center O.

Use the information to answer the question below.

Find the area of the circle.

[Take π = $\frac{22}{7}$ ]

3.14 cm²

6.28 cm²

4.00 cm²

12.56 cm²

33.

What percentage of 5 is 0.25?

20%

25%

34.

Find the simple interest on ₵15,000.00 at rate of 20% per annum for 5 years.

₵10,000.00

₵15,000.00

₵30,000.00

₵50,000.00

₵90,000.00

35.

If the bearing of A from B is 240^o, find the bearing of B from A

040^o

060^o

120^o

300^o

36.

If P¹(4,-5) is the image of P(x,y) translated by r = ( ^-2 ₃), find the values of x and y.

(-6,8)

(-6,-8)

(6,-8)

(6,8)

37.

Arrange the following fractions from the lowest to the highest: $\frac{3}{4}$ , $\frac{2}{3}$ and $\frac{3}{5}$ .

$\frac{3}{5}$ , $\frac{2}{3}$ , $\frac{3}{4}$

$\frac{3}{5}$ , $\frac{3}{4}$ , $\frac{2}{3}$

$\frac{3}{4}$ , $\frac{2}{3}$ , $\frac{3}{5}$

$\frac{3}{4}$ , $\frac{3}{5}$ , $\frac{2}{3}$

$\frac{2}{3}$ , $\frac{3}{5}$ , $\frac{3}{4}$

38.

Make h the subject of the relation V = πr²h.

39.

In the diagram, XYZ is a triangle. YW is a straight line. Angle XYZ = 52° and angle XZW = 125°.

Find angle YXZ.

35°

55°

73°

107°

40.

Simplify: $($ 1 $\frac{1}{2}$ - $\frac{5}{6}$ $)$ x $\frac{9}{10}$ .

$\frac{1}{10}$

$\frac{3}{20}$

$\frac{1}{5}$

$\frac{3}{5}$

THEORY QUESTIONS

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|.

(a)

Factorize (m + n)(2x - y)-x(m + n)

(b)

A and B are subsets of a universal set

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18} such that A = {even numbers} and B = {multiples of 3}.

(i)

List the elements of the sets A, B, (A ∩ B), (A ∪ B) and (A ∪ B)^'.

(ii)

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

(c)

Find the values of x and y in the vector equation:

$(\begin{matrix} 5 \\ 3 \end{matrix})$ + 2 $(\begin{matrix} x \\ y \end{matrix})$ - $(\begin{matrix} 1 \\ -7 \end{matrix})$ = 0

(a)

Evaluate $\frac{0.035 x 1.02}{0.0015}$ , leaving the answer in standard form.

(b)

An amount of GH₵4,200.00 was shared betwen Aba and Kwame. If Aba had $\frac{5}{7}$ of the amount,

(i)

how much did Kwame receive?

(ii)

what percentage of Aba's share did Kwame receive?

(c)

Find the value of x in the diagram below.

Simplify: 5(6 - ab) + 2(-7 + 3ab)

The equation of a straight line is given by 3x - 2y - 6 = 0. Find the:
(i) gradient of the line;
(ii) y-intercept

Adwoa received a commission of 20% on bread she sold. In one week, Adwoa's commission was GH₵ 540.00.
(i) How much bread did she sell during that week?
(ii) Find her average daily commission.

(a)

The diagram AEBCD shows the shape of Mr. Awuah's garden, which is made up of a rectangular portion ABCD and a triangular portion AEB.

|AB| = |DC| = 90 m, |AD| = |BC| = 70 m, |AE| = 48.5 m and |EB| = 50 m. The height of the triangle is 20 m.

Find

(i)

area of ABCD;

(ii)

area of AEB;

(iii)

total area of the garden;

(iv)

perimeter of the garden.

(b)

Find the value of x if $\frac{3x - 2}{5}$ is greater than $\frac{1 - 4x}{10}$ by 5

(a)

(i)

Using a pair of compasses and ruler only, construct triangle XYZ with XZ = 12cm, XY = 10cm and angle XYZ = 90°.

(ii)

Measure YZ.

(iii)

Calculate the area of triangle XYZ

(iv)

Measure angle ZXY.

(b)

An isosceles triangle has a perimeter of (9y – 15) cm.

What is the length of each of the two equal sides, if its third side is (3y – 7) cm?