OBJECTIVE TEST

The area of a sector of a circle is 40 cm². If the sector subtends an angle of 140° at the centre, find the area of the circle.

102.86 cm²

111.56 cm²

120.38 cm²

132.06 cm²

1.639 X 10^-2

1.639 X 10^-1

1.639 X 10¹

1.639 X 10²

Given that 6log(x + 4) = log64, find the value of x.

-2

-4

Dina and Rose were given GH₵ 875.08 to be shared in the ratio 3:2 respectively. If Rose shared her part of the money between Efua and Ama in the ratio 1:2 respectively, how much was Ama's share?

GH₵ 116.68

GH₵ 175.02

GH₵ 233.35

GH₵ 340.32

Simplify $\frac{9 - x^{2}}{3x - x^{2}}$ , where x ≠ 3

$\frac{3-x}{x}$

$\frac{3+x}{x}$

$\frac{3}{x}$

$\frac{x-3}{x}$

Make x the subject of the relation:

-1

1⁄3

- 1⁄3

The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?

, find the value of x.

10.

Express, correct to three significant figures, 0.003597.

0.00359

0.00360

0.004

0.359

11.

If 6 and 14 are consective terms in arithmetic progression (A.P), find the value of p.

12.

Solve the equation: t - ⁹⁄₅ = -1¹⁄₁₅ .

t = 3⁄5

t = 11⁄15

t = 4⁄5

t = 13⁄15

13.

The length of a rectangular lawn is 3 cm longer than the width. If the perimeter is 42 cm, find the width.

6 cm

9 cm

12 cm

15 cm

14.

Given that p = x - $\frac{1}{x}$ and q = x² + $\frac{1}{x^{2}}$ , express q in terms of p.

q = (p² + 2)

q = (p - 2)²

q = (p + 2)²

q = (p² - 2)

15.

Find the 11^th term of $\frac{1}{4}$ , $\frac{5}{8}$ ,1, 1 $\frac{3}{8}$ , ... .

16.

If 2^a = √64 and b⁄a = 3, evaluate a² + b²

160

250

17.

If 23_x = 1111_two, find the value of x.

18.

Evaluate $\frac{53,000,000 x 0.002}{0.0004}$

6.65 x 10⁸

6.65 x 10⁷

6.65 x 10^-7

6.65 x 10^-8

19.

-1⁄2

1⁄3

1⁄2

-1⁄3

20.

A bag contains 32 blue, 28 black and 20 red identical balls of same size. If a ball is picked at random, what is the probability that it is not red?

$\frac{1}{4}$

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{3}{4}$

21.

In the diagram P,Q,R,S are points on the circle. If ∠PQS = 32^o and ∠PRQ = 61^o, find ∠QPS.

32^o

61^o

87^o

93^o

22.

The area of a trapezium is 49 cm². If the parallel sides are 6 cm and 7 cm long, find, correct to one decimal place, the distance between the parallel sides.

6.5 cm

6.8 cm

7.4 cm

7.5 cm

23.

The shadow of a vertical pole is 50 cm. If the height of the pole is 2 m, find, correct to the nearest degree, the angle of elevation of the sun from the ground level.

45°

56°

60°

76°

24.

Mary and charity entered into a business partnership and ageed to share their porfit in the ratio 4 : 5 respectively. If Mary received Gh ¢ 5,000.00 less than Charity, how much profit did they make?

GH¢30,000.00

GH¢35,000.00

GH¢40,000.00

GH¢45,000.00

25.

A die is rolled once. Find the probability of obtaining a number less than 3.

$\frac{1}{6}$

$\frac{5}{6}$

$\frac{2}{3}$

$\frac{1}{3}$

26.

y=29

y=-29

y=-19

y=19

27.

An arc subtends an angle of 72° at the center of the circle. Find the length if the radius of the circle is 3.5 cm [Take Π = 22⁄7]

2.2 cm

4.4 cm

8.8 cm

6.6cm

28.

Find the equation whose roots are

and

2x² -4x + 6 = 0

4x² -4x - 3 = 0

2x² +3x + 4 = 0

4x² -4x + 3 = 0

29.

y varies inversely as the square of x. When x = 3, y = 100. Find the value of x when y = 25.

x = 30

x = 12

x = 6

x = 5

30.

A car moves at an average speed of 30 kmh^-1. How long does it take to cover 200 metres?

2.4 seconds

24 seconds

144 seconds

240 seconds

31.

Bala sold an article for N6,900.00 and made a profit of 15%. calculate his percentage profit if he had sold it for N6,600.00.

13%

12%

10%

32.

In a class of 39 student, 25 offer Fante and 19 offer Twi. Five student do not offer any of the two languages. How many student offer only Twi?

33.

find the equation of a straight line passing through the point (1,-5) and having gradient of 3⁄4

3x-4y-23 = 0

3x-4y+23 =0

3x+4+23 =0

3x+4y-23= 0

34.

The arc of a circle 50 cm long subtends an angle 75^o at the centre of the circle.

Find, correct to three significant figures, the radius of the circle.

[Take π = $\frac{22}{7}$ ]

76.4 cm

61.2 cm

38.2 cm

8.74 cm

35.

A rectangular board has length 15 cm and width xcm.If the side are doubled,find its new area

15x cm²

30x cm²

45x cm²

60x cm²

36.

Consider the following statements:

M: Helena studies hard;
N: Helena passes her examination.

If M ⇒ N

If Helena does not study hard, then she will pass her examination.

If Helena does not study hard, then she will not pass her examination.

If Helena passes her examination, then she had not studied hard.

If Helena does not pass her examination, then she had not studied hard.

37.

There are 8 boys and 4 girls in a lift.what is the probability that the first person who steps out of the lift will be a boy

1⁄4

2⁄3

1⁄3

3⁄4

38.

39.

If (0.25)^y find the value of y.

-5⁄2

-3⁄2

3⁄2

5⁄2

40.

Correct 9453 x 10^-6 to 3 significant figures.

0.009

0.00945

0.00950

0.010

41.

Evaluate (0.064)^-1/3.

-5/2

-2/5

2/5

5/2

42.

Find the number of even integers between 11 and 97.

43.

Find the equation of the line passing through P(4,1) and parallel to 2x + 5y = -10.

5x + 2y = 13

5x - 2y = 10

2x - 5y = 10

2x + 5y = 13

44.

Calculate the value x.

48°

55°

58°

70°

45.

Simplify: $\frac{1}{2}$ (x-1)- $\frac{1}{3}$ ( $\frac{1}{2}$ x-1).

$\frac{1}{6}$ (x-1)

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

$\frac{1}{6}$ (2x-1)

$\frac{1}{6}$ (1-2x)

46.

Simplify:

5⁄8

5⁄32

5⁄64

5⁄72

47.

A woman buys 3 exercise books at GH₵ 0.4 each and 9 exercise books at GH₵ 0.2 each. What is the average cost of an exercise book?

GH₵ 0.35

GH₵ 0.30

GH₵ 0.22

GH₵ 0.25

48.

Metuh is nine times as old as his cousin, Fafa. In six years time, he will be five times as old as Fafa. Find Fafa's present age.

5 years

6 years

7 hears

8 years

49.

A ladder, 10 m long, touches a side of a building at a height of 8 m. At what height would a ladder with length 12 m touch the building, if it makes the same angle with the ground?

(Assume that the ladder and building are on the same horizontal ground)

10.6 m

10.4 m

10.0 m

9.6 m

50.

Factorize completely

(2x2y)(x-y) + (2x -2y)(x + Y).

2(x - y)

2(x - y)(x + Y)

4(x-y

4(x - y)(x + y)

THEORY QUESTIONS

The first three terms of an Arithmetic Progression (A.P:) are (x + 1),(4x - 2) and (6x - 3)

respectively.If the last term is 18, find the:

(a)

vale of x;

(b)

Sum of the terms of the progression.

The angle of a sector of a circle with radius 22cm is 60^o. If the sector is folded such that the straight edges coincide, forming a cone,calculate correct to one decimal place, the:

(a)

radius;

(b)

height;

(c)

volume;

of the cone;

[Take π = ²²⁄₇]

Z varies directly as x and inversely as twice the cube root of y. If Z = 8, when x = 4 and y = 1/8 find the relation for y in terms of x and Z.

(a)

Solve, correct to one decimal place, tan (θ + 25^o) = 5.145, where 0^o ≤ θ ≤ 90^o.

(b)

In the relation t = m √(n² + 4r):

(i)

make n the subject of the relation;

(ii)

find the positive value of n when t = 25, m = 5 and r = 4.

find, correct to two decimal places, the value of x

Without using mathematical tables or calculators, evaluate

leaving the answer in standard form.