1.
The diagram shows a circle centre O. Use it to answer the question below.
Find the value of y.
43°
47°
54°
86°
2.
The table shows the distribution of the ages of members of a school choir.
Use the table to answer the question below
Age(years) | 15 | 16 | 17 | 18 |
No. of students | 5 | 6 | 3 | 1 |
Find the median age.
15 years
16 years
16 years
17 years
3.
In ∆XYZ, |YZ| = 32 cm, ∠ YXZ = 52° and ∠ XZY = 90°. Find, correct to the nearest centimetre, |XZ|.
13 cm
20 cm
25 cm
31 cm
4.
Find the nth term of the Geometric Progression (G.P): , , , ...
2n - 1
2n
5.
Correct 0.00798516 to three significant figures.
0.0109
0.0800
0.00799
0.008
6.
Given that P ∝ and x ∝ vt express P in terms of v and t.
P ∝
P ∝
P ∝ vt
P ∝
7.
If (0.25)y = 32, find the value of y.
-
-
8.
If and -3 are the roots of px2 + qx + r = 0, find the values of p, q and r.
p = 2, q = -5, r = 3
p = 2, q = 5, r = 3
p = 2, q = 5, r = -3
p = -2, q = 5, r = 3
9.
Find the value of x in the diagram.
41
37
35
31
10.
Express 0.0063075 correct to three significant figures.
0.006
0.0063
0.00631
0.0060
11.
In triangle XYZ, |XY| = 8 cm and Z is equidistant from X and Y.
If Z is 5 cm from X, find the area of the triangle.
24 cm2
18 cm2
12 cm2
10 cm2
12.
If tan x = , 0 < x < 90, evaluate
13.
If the area of the trapezium MNOP is 300 cm2, find the value of x.
15 cm
12 cm
10 cm
20 cm
14.
In the diagram, O is the centre of the circle WXY. |WX| = |XZ| and ∠ ZXY = 26°. Find ∠ XYZ.
62°
42°
52°
32°
15.
From a height of 2 m above the ground and at a horizontal distance of 12 m from a tree, the angle of elevation of the top of the tree is 30°.
How tall is the tree?
8 m
8 m
14 m
18 m
16.
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
17.
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?
18.
If (x + 2) is a factor of x2 + px - 10, find the value of p.
-7
7
-3
3
19.
A woman pours 85 litres of kerosene into a cylindrical container with radius 7 cm.
Calculate, correct to the nearest cm, the depth of the kerosene in the container.
[Take π = ]
240 cm
552 cm
480 cm
595 cm
20.
Given that tan x = , find the value of (sin x cos x)
21.
The fourth term of an Arithmetic Progression (A.P) is 37 and the first term is -20. Find the common difference.
17
19
57
63
22.
Solve: - = .
x = 0
x = 5
x = 4
x = 2
23.
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
24.
Make m the subject of the relation k = .
m =
m =
m =
m =
25.
Given that sin A = , 0° ≤ A ≤ 90°, find the value of (tan A - cos A)
-
-
26.
A box contains 40 identical balls of which 10 are red and 12 are blue. If a ball is selected at random from the box, what is the probability that it is neither red nor blue?
27.
Two buses start from the same station at 9.00 am and travel in opposite directions along the same straight road. The first bus travels at a speed of 72 km/h and the second at 48 km/h.
At what time will they be 240 km apart?
10.00 a.m.
11.00 a.m.
12.00 noon
1.00 p.m.
28.
The first of a Geometric Progression (G.P) is 3 and the 5th term is 48. Find the common ratio.
16
8
4
2
29.
In the diagram, RT is a tangent to the circle at R, ∠ PQR = 70°, ∠ QRT = 52°, ∠ QSR = y and ∠ PRQ = x.
Use the diagram to answer the question below.
Find the value of y.
18°
52°
60°
45°
30.
The graph of y = x2 - 5x + k passes through the point (3, 1). Find the value of k.
2
3
7
5
31.
The diagonal of a rhombus are 12 cm and 5 cm.
Calculate its perimeter.
26 cm
24 cm
17 cm
34 cm
32.
In the first year, Mr. Kwakye's annual salary was $1,560.00. His salary was increased each year by a constant value, y until it was $13,980.00 in the 13th year. Calculate the value of y.
$955.38
$1,230.00
$1,129.09
$1,035.00
33.
A chord of a circle with radius 5 cm subtends an angle of 70° at the centre.
Find, correct to one decimal place, the length of the chord.
8.2 cm
5.7 cm
4.1 cm
2.9 cm
34.
In the diagram, O is the centre of the circle PQR, |PS| = |PQ| and ∠RQS = 23o. Find the value of x.
23o
38o
46o
67o
35.
If 101two + 12y = 23five, find the value of y.
5
6
7
8
36.
Find the value of x for which is not defined.
1
2
-1
37.
An amount of ₦ 550,000.00 was realized when a principal, x was saved at 2% simple interest for 5 years. Find the value of x.
₦ 500,000.00
₦ 490,000.00
₦ 480,000.00
₦ 470,000.00
38.
A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of ₦ 22,800.00 was paid as import duty, calculate the cost of the engine.
₦60,000.00
₦120,000.00
₦24,000.00
₦18,000.00
39.
Eric sold his house through an agent who charged 8% commission on the selling price. If Eric received $117,760.00 after the sale, what was the selling price of the house?
$120,000.00
$125,000.00
$128,000.00
$130,000.00
40.
In the diagram, ∆PQR is similar to ∆PWY. WY||QR, |QR| = 15 cm, |WY| = 6 cm and |WP| = 4 cm.
Find |WQ|.
6 cm
12 cm
10 cm
8 cm
41.
The expresson will be undefined when x equals
{-3, 0}.
{-3, -1}.
{0, -1).
{0, 1}.
42.
Simplify: + .
43.
If 2a = and = 3, evaluate a2 + b2.
48
90
160
250
44.
Number of subjects | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Number of students | 2 | 1 | 4 | 3 | 8 | 5 | 4 | 3 |
The table shows the number of subjects registered by a class of students for an examination.
Use the information to answer the question below
Calculate the mean of the distribution.
2
3
8
5
45.
If 17 = 3 mod x, find the least value of x.
3
5
7
9
46.
Find the equation whose roots are - and 1.
2x2 -4x + 6 = 0
4x2 -4x - 3 = 0
2x2 +3x + 4 = 0
4x2 -4x + 3 = 0
47.
Find the value of x that satisfies the equation: (x + 5) = 1 - .
1
4
3
2
48.
The following are scores obtained by some students in a test:
8 | 18 | 10 | 14 | 18 | 11 | 13 |
14 | 13 | 17 | 15 | 8 | 16 | 13 |
Use this information to answer the question below
How many students scored above the mean score?
7
8
9
10
49.
Evaluate
6.65 x 108
6.65 x 107
6.65 x 10-7
6.65 x 10-8
50.
A man will be (x + 10) years old in 8 years time. If 2 years ago he was 63 years, find the value of x
55
63
57
67
(a)
A company bids for two contracts G and H. The probabilities that it will win contracts G and H are and respectively.
Find the probability that the company wins:
(i)
both contracts;
(ii)
only one contract.
(b)
Amaka drove a car from Samoa to Mepeasem at an average speed of 60 km/h in 135 minutes. On her return journey, she took 3 minutes less to arrive at Samoa.
Find correct to one decimal place the:
(i)
distance between Samoa and Mepeasem;
(ii)
the return speed.
(a)
Using ruler and a pair of compasses only, construct:
(i)
the quadrilateral ABCD such that |AB| = 6.5 cm, |BC| = 9 cm, |AD| = 4 cm, ∠ ABC = 60° and ∠ BAD = 120°;
(ii)
the perpendicular bisectors of BC and CD.
(b)
Locate the point of intersection, T, of the two bisectors in (a(ii).
(c)
With the point T in (b) as centre, draw a circle to pass through the vertices B, C and D.
(d)
Measure:
(i)
|BT|;
(ii)
|CD|.
In the diagram, ABD is a triangle, |AC| = 50 cm and |CD| = d cm.
Find, correct to one decimal place,:
(a)
the value of d;
(b)
|BD|.
(a)
From the top, X of a building 320 m high, the angles of depression of the top, Y and bottom, Z of another building on the same horizontal ground are 29° and 41° respectively.
(i)
Illustrate the information in a diagram.
(ii)
Calculate, correct to the nearest metre, the height of the other building.
(b)
The time taken to travel a distance of 120 km was reduced by 30 minutes when the speed was increased by 20 km/h. Calculate the initial speed.
The mean age of a second year class of a school is 18. At the end of the promotion examination, 3 students aged 20, 19 and 19 years were repeated. The new mean age of the class became 18.
Calculate the number of students who were in the class before the promotion examination.
(a)
Copy and complete the following table for the relation: y = 2(x + 2)2 - 3 for -5 ≤ x ≤ 2.
x | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 |
y | -1 | -3 | 5 |
(b)
Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of the relation y = 2(x + 2)2 - 3 for -5 ≤ x ≤ 2.
(c)
Use the graph to find the solution of:
(i)
2(x + 2)2 = 3;
(ii)
2(x + 2)2 = 5.
(d)
For what values of x, from the graph is y increasing in the interval?