OBJECTIVE TEST

Use the following information to answer the question below.

The pie chart below shows how a man spends his monthly salary.

What percentage of his salary does he save?

16.7%

21.7%

25.0%

29.2%

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

Find angle ONP.

40°

68°

72°

112°

140°

Simplify 0.1 x 0.02 x 0.003 (leaving your answer in standard form)

6x10^-7

6x10^-6

6x10⁵

6x10⁶

A match box contains 40 sticks. If 15 of them are spolit, find the probability that a stick chosen at random is not spoilt?

If 2x = 5(x - 2) + 7, find the value of x.

-5 $\frac{2}{3}$

-1

5 $\frac{2}{3}$

If a⁶ ÷ a⁴ = 64. Find a

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

Multiply (8s - 7) by (8s + 7).

64s² + 49

64s² - 49

16s² + 42

If E = {prime numbers between 10 and 20} and F = {odd numbers between 0 and 16},
find E ∩ F.

{11}

{11, 13}

{3, 11, 13}

{3, 11, 13, 15}

10.

XYZ is a right-angled triangle with length of sides as shown.

Which of the following equations gives the value of z²?

z² = (x² + y²)

z² = (x - y)

z² = (y² - y²)

z² = (x² - y²)

11.

The following addition is in base ten. Find the missing addend.

	2	3	4	5
+	1	0	4	5
	*	*	*	*
	5	1	1	0

1300

1720

2765

4065

9500

12.

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)

13.

The locus of points equidistant from a fixed point is called a

chord.

circle.

mediator.

diameter.

14.

Find the slope of the line 3x - 6y = 33.

-3

15.

A shop is rented at GH₵ 9.00 per month. How much money is paid in 1½ years?

GH₵ 162.00

GH₵ 135.00

GH₵ 6.00

GH₵ 13.00

16.

If y = c + bx², find y when c = $\frac{14}{5}$ , b = $\frac{4}{5}$ and x = 2.

17.

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)

18.

Arrange the following fractions in ascending order: 4 $\frac{1}{4}$ , 4 $\frac{1}{2}$ , 4 $\frac{1}{3}$

4 $\frac{1}{4}$ , 4 $\frac{1}{3}$ , 4 $\frac{1}{2}$

4 $\frac{1}{3}$ , 4 $\frac{1}{2}$ , 4 $\frac{1}{4}$

4 $\frac{1}{2}$ , 4 $\frac{1}{3}$ , 4 $\frac{1}{4}$

4 $\frac{1}{4}$ , 4 $\frac{1}{2}$ , 4 $\frac{1}{3}$

19.

The diagram shows the graph of a linear relation of the form y = mx + c.

Use the graph to answer the question below

Find the equation of the relation.

y = -2x + 3

y = -2x + 2

y = 2x + 3

y = 2x - 3

20.

A trader received a commission of 25% on the sales he made in a month. His commission was ₵180,000.00. Find his total sales for the month.

₵135,000.00

₵150,000.00

₵240,000.00

₵540,000.00

₵720,000.00

21.

Given that 1 : 3 = x : 21, find the value of x.

22.

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

23.

The rule of mapping is x → 2x² - 1. What number does x = 2 map to?

24.

Find the gradient of the line that joins the points A(-3,5) and B(7,-2).

25.

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 = $\frac{g l^{2}}{4 π^{2}}$

26.

Given the vectors m = $(\begin{matrix} 5 \\ -1 \end{matrix})$ and n = $(\begin{matrix} -4 \\ 2 \end{matrix})$ , find 2m + n.

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

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

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

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

27.

Simplify: $\frac{5^{7} x 5^{-4}}{5^{3}}$ .

28.

If P = {2,3,5,7} and Q = {2,4,6,8}, find P∩Q.

{2}

{3}

{4}

{5}

29.

Describe the set of M = {2, 3, 5, 7, 11, 13, 17, 19} in words.

M = {odd numbers less than 20}

M = {factors of 19}

M = {prime numbers less than 20}

M = {whole numbers less than 20}

30.

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

31.

Find the value of $\sqrt{6 \frac{1}{4}}$

5.0

4.9

2.5

2.4

1.2

32.

Simplify: -15 - (-20) + (-10).

-45

-5

-25

33.

13	12	17
E	F	10
11	16	G

Use the magic square above to answer the question below

Find the value of F.

34.

The marks obtained by 5 girls in a test are: 10, 15, 8, 18, 12.

Find the median mark.

35.

Evaluate $\frac{1}{3}$ [(5 – 1) – (2 – 7)]

-3

-1

36.

Two sides of a parallelogram are 5.8 m and 8.2 m long. Find its perimeter

11.0 m

36.6 m

28.0 m

47.6 m

37.

On a map, two towns P and Q are 15.5 cm apart. The scale of the map is 1 cm: 4 km. Calculate the actual distance between P and Q.

15.5 km

31 km

46 km

60 km

62 km

38.

There are 6 girls and 18 boys in a class. What percentage of the class are girls?

14.40%

25.00%

33.33%

66.67%

75.00%

39.

The addition below was carried out in base x. Find x.

	2	4	3
	2	2	1
1	0	1	4	_x

Four

Five

Six

Seven

40.

The height of a flag pole in a scale drawing is 5 cm. If the scale is 1 cm to 3 m, what is the actual height of the pole?

10 m

15 m

8 m

5 m

THEORY QUESTIONS

(a)

The volume of a cylinder is 220 cm³. The radius of the cross-section is 2.5 cm. Find the height of the cylinder.

[Take π = $\frac{22}{7}$ ]

(b)

Each of the interior angles of a regular polygon is 140°. How many sides does it have?

(a)

The table shows the number of students who scored more than 80% in the listed subject.

Subject	Number of students
Biology	26
Physics	30
Chemistry	32
French	38
Geography	24
History	30

(i)

Draw a pie chart for the distribution.

(ii)

What is the probability that a student chosen at random from the distribution, offers Chemistry?

(b)

A woman bought 210 oranges for GH₵7.50. She sold all of them at 3 for 15 Gp. Find the

(i)

total selling price of the oranges;

(ii)

percentage profit.

(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-axes from –5 to 5 and the y-axis from –6 to 6.

(b)

On the same graph sheet, plot the points A(2, 5), B(4, 3) and C(1, 1). Join the points A, B and C to form a triangle.

(c)

Reflect triangle ABC in the y-axis such that A→A₁, B→B₁ and C→C₁. Label the vertices of triangle A₁B₁C₁

(d)

Translate triangle A₁B₁C₁ by the vector $(\begin{matrix} 3 \\ -4 \end{matrix})$ such that A₁→A₂, B₁→B₂, and C₁→C₂. Label the vertices of triangle A₂B₂C₂

(e)

Join the vertices A₁B₁B₂ and C. Name the figure formed.

(f)

Find A₁B₁→

(a)

Fred is (x - 1) years old now. How old:

(i)

was he 4 years ago?

(ii)

will he be 8 years from now?

(iii)

is he now, if his age in 8 years time will be three times his age 4 years ago?

(b)

The perimeter of a rectangular cocoa from is 497 km. The length of the farm is 2¹⁄₂ times the width. Find the:

(i)

width;

(ii)

length of the farm.

(a)

In a class of 70 students, 40 belong to the Red Cross Society, 27 belong to the Girls' Guide Society and 12 belong to both the Red Cross Society and the Girl's Guide Society. The remaining students do not belong to any of the two societies.

(i)

Illustrate the information on a Venn diagram.

(ii)

How many students belong to the Red Cross Society only?

(iii)

How many students do not belong to any of the two societies?

(b)

A farmer uses $\frac{1}{3}$ of his land to plant cassava, $\frac{2}{5}$ of the remaining land to plant maize and the rest vegetables.

If vegetables cover an area of 10 acres, what is the total area of the farmer's land.

(a)

Using a ruler and a pair of compasses only, construct triangle XYZ, such that |XY| = 6cm, |XZ| = 8cm and |YZ| = 10cm.

(b)

(i)

Construct the mediator of line YZ

(ii)

construct the mediator of line XZ

(iii)

Locate O, the point of intersection of the mediators of lines YZ and XZ.

(iv)

With centre O and radius OY, draw a circle.

(c)

Measure the radius of the circle you have drawn in (b) (iv) above and hence calculate the circumference of the circle.

[ Take π = 3.14 ]