KUULCHAT
S.H.S MATHEMATICS MOCK

#### OBJECTIVE TEST

1.

36. The foot of a ladder is 6 m from the base of an electric pole the top of the ladder rests against the pole at a point 8 m above the ground. How long is the ladder

A.
7m
B.
10m
C.
12m
D.
14

2.

Which of the following describes the set P = {1,2,3,4,5,6}?

A.

P = {Prime numbers < 7}

B.

P = {x:x is a positive integer < 7}

C.

P = {rational numbers < 7}

D.

P = {x:x is a real number < 7}

3.

Simplify:
A.
5⁄8
B.
5⁄32
C.
5⁄64
D.
5⁄72

4.

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

A.
48
B.
90
C.
160
D.
250

5.

solve 4x2 - 16x + 15 = 0

A.

A. x = -1 1⁄2 or -2 1⁄2

B.

B. x = 1 1⁄2 or -2 1⁄2

C.

C. x = 1 1⁄2 or 2 1⁄2

D.

D. x = 1 1⁄2 or -2 1⁄2

6.

An empty rectangular tank is 250 cm long and 120 cm wide. If 180 litres of water is poured into the tank, calculate the height of the water.

A.

4.5 cm

B.

5.0 cm

C.

5.5 cm

D.

6.0 cm

7.

(27.63)2 - (12.37)2

A.
610
B.
611
C.
612
D.
614

8.

Simplify:
A.

B.

C.

D.

9.

If (0.25)y find the value of y.

A.
-5⁄2
B.
-3⁄2
C.
3⁄2
D.
5⁄2

10.

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)

A.

10.6 m

B.

10.4 m

C.

10.0 m

D.

9.6 m

11.

Find the truth set of the equation (x -2)2 + 3 = (x + 1)2 - 6.

A.

{-2}

B.

{-1}

C.

{1}

D.

{2}

12.

Make b the subject of the relation:

Ib = 1⁄2 (a+b)h

A.
al⁄2-h
B.
al⁄2l-h
C.
2l-h⁄al
D.
ah⁄2l-h

13.

If log102 = 0.3010 and log102y = 1.8060, find, correct to the nearest whole number, the value of y.

A.

7

B.

6

C.

5

D.

4

14.

If the sequence x,4,16,y is Geometric Progression (GP), find the ratio of x:y.

A.

64:1

B.

8:1

C.

1:3

D.

1:64

15.

Evaluate (0.064)-1/3.
A.
-5/2
B.
-2/5
C.
2/5
D.
5/2

16.

H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y ?

A.
H = p⁄y2
B.
H = p⁄2y2
C.
H = 2p⁄y2
D.
H = p⁄4y2

17.

A.
0.6
B.
0.9
C.
1.2
D.
2.4

18.

The area of a sector of a circle and the length of its arc are 231 cm2 and 66 cm respectively. Calculate the radius of the circle

[Take Π = 22/7]

A.

3.5 cm

B.

7.0 cm

C.

10.5 cm

D.

14.0 cm

19.

A.
-1
B.
1⁄3
C.
- 1⁄3
D.
1

20.

A.
y=29
B.
y=-29
C.
y=-19
D.
y=19

21.

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.

A.

6.5 cm

B.

6.8 cm

C.

7.4 cm

D.

7.5 cm

22.

Make x the subject of the relation:

A.

B.

C.

D.

23.

In the diagram,POS and ROT are straight lines.QPQP is a parallelogram,

|QS| = |QT| and ∆OST = 50°; Calculate tyhe value of ∆OPQ

A.
160°
B.
140°
C.
120°
D.
100°

24.

A.
7
B.
6
C.
5
D.
4

25.

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

A.

15x cm2

B.

30x cm2

C.

45x cm2

D.

60x cm2

26.

A.
4√7 + √2
B.
4√7 - 9√2
C.
4√7 - 11√2
D.
4√7 - 21√2

27.

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?
A.
GH¢30,000.00
B.
GH¢35,000.00
C.
GH¢40,000.00
D.
GH¢45,000.00

28.

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.

A.
13%
B.
12%
C.
10%
D.
5%

29.

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?
A.
6
B.
7
C.
8
D.
9

30.

Factorize: p2q2 - 6pqr + 9r2

A.

(pq-3r)2

B.

(pq - 3r)(pq + 3r)

C.

(pq+3r)2

D.

(pr+3q)(pr-3q)

31.

Solve the equation: t - 95 = -1115 .

A.

t = 3⁄5

B.

t = 11⁄15

C.

t = 4⁄5

D.

t = 13⁄15

32.

Two friends, Dede and Kofi decided, to buy the same type of car. They found out that the car cost ₦3,000,000.00. The amount of money (f) which Dede had was not enough to buy the car but Kofi had enough money (k) to buy the car. Which of the of the following inequalities is true?

A.

f≤₦3,000,000.00 ≤ k

B.

f> ₦3,000,000.00 > k

C.

f< ₦3,000,000.00 ≤ k

D.

f≥ ₦3,000,000.00 ≥ k

33.

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

A.

3x-4y-23 = 0

B.

3x-4y+23 =0

C.

3x+4+23 =0

D.

3x+4y-23= 0

34.

The total surface area of a solid cylinder is 165cm2.

If the base diameter is 7cm, calculate its height [Take ϖ = 22⁄7]

A.
2.0 cm
B.
4.0 cm
C.
4.5 cm
D.
7.5 cm

35.

Factorize completely

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

A.

2(x - y)

B.

2(x - y)(x + Y)

C.

4(x-y

D.

4(x - y)(x + y)

36.

Arrange the following in ascending order of magnitude: 0.45,¾ and 25%

A.

¾, 0.45, 25%

B.

¾, 25%, 0.45

C.

0.45, 25%, ¾

D.

25%, 0.45, ¾

37.

In the diagram O is the centre of the circle with raduis 18 cm. If the angle ∠ZXY = 70° , calculate the length of arc ZY. [Take π = 22⁄7

A.
80 cm
B.
44 cm
C.
22 cm
D.
11 cm

38.

Express, correct to three significant figures, 0.003597.
A.
0.00359
B.
0.00360
C.
0.004
D.
0.359

39.

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

A.

1⁄4

B.

2⁄3

C.

1⁄3

D.

3⁄4

40.

A.
3⁄5
B.
3⁄4
C.
5⁄3
D.
4⁄3

41.

3p = 4q and 9p = 8q - 12, find the value of pq

A.
-12
B.
-7
C.
7
D.
12

42.

A man bought a car which costs ₦5,000,000.00 from a dealer on hire purchase. He pays a deposit of ₦3,000,000.00 and agrees to pay the balance at 8% compound interest per annum. If he pays ₦1,000,000.00 at the end of each year, how much will be remaining to be paid after two years?
A.
₦92,800.00
B.
₦252,800.00
C.
₦320,000.00
D.
₦332,000.00

43.

If 6 and 14 are consective terms in arithmetic progression (A.P), find the value of p.
A.
8
B.
6
C.
10
D.
9

44.

Not drawn to scale

In ∆XYZ, ∣YZ∣ = 32 cm, ∠YXZ = 52 ° and ∠XZY = 90 °.

Find, the correct to nearest centimetre. ∣XZ∣.

A.
13cm
B.
20 cm
C.
25 cm
D.
31 cm

45.

Evaluate:
A.
√2 - 1
B.
2√2 - 1
C.
√2 + 1
D.
2√2 + 1

46.

Given that 3 x 91 + x=27-x,find the value of x.
A.
-35
B.
-123
C.
-2
D.
-3

47.

A.

1.639 X 10-2

B.

1.639 X 10-1

C.

1.639 X 101

D.

1.639 X 102

48.

Find the equation whose roots are
and
.
A.

2x2 -4x + 6 = 0

B.

4x2 -4x - 3 = 0

C.

2x2 +3x + 4 = 0

D.

4x2 -4x + 3 = 0

49.

Find the angle which arc of the length 22 cm subtends at the centre of a circle of radius 15cm. [Take π = 22⁄7 ]

A.
156°
B.
96°
C.
84°
D.
70°

50.

A.

x+2⁄x-2

B.

x-2⁄x+4

C.

x+7⁄x-7

D.

x-7⁄x-7

#### THEORY QUESTIONS

1.

(a)

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

(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.

2.

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

(a)

(b)

height;

(c)

volume;

of the cone;
[Take π = 227]
3.

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.

4.
Without using mathematical tables or calculators, evaluate
leaving the answer in standard form.
5.
If
find, correct to two decimal places, the value of x
6.
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.