In the diagram, O is the center of the circle QRS and ∠SQR = 28°. Find ∠ORS.
Answer
(D)
\(62^0\)
2
Solve \(1 + \sqrt[3]{ x - 3} = 4\)
Answer
(A)
30
3
The angle of a sector of a circle of radius 3.4 cm is 115°. Find the area of the sector.
\((Take \pi = \frac{22}{7})\)
Answer
(A)
\(11.6cm^2\)
4
There are 30 students in a class. 15 study woodwork and 13 study metal work. 6 study neither of the 2 subjects. How many student study woodwork but not metal work?
Answer
(B)
11
5
Mr Manu is 4 times as old as his son, Adu. 7 years ago the sum of their ages was 76. How old is Adu?
Answer
(C)
18years
6
The angle of elevation of the top of a building from a point Z on the ground is 50°. If the height of the building is 124 m, find the distance from Z to the foot of the building.
Answer
(B)
104.05m
7
One-third of the sum of two numbers is 12, twice their difference is 12. Find the numbers.
Answer
(C)
21 and 15
8
In the diagram above, M, N, R are points on the circle centre O. ∠ORN = 48° and ∠RNM = 124°. Find ∠OMN.
For what value of x is \(\frac{ x^2 + 2 }{ 10x^2 - 13x - 3}\) is undefined?.
Answer
(B)
\(\frac{-1}{5}, \frac{3}{2}\)
11
Express \(413_7\) to base 5
Answer
(C)
\(1311_5\)
12
Evaluate, correct to three decimal place \(\frac{4.314 × 0.000056}{0.0067}\)
Answer
(D)
0.036
13
The interior angle of a regular polygon is 6 times its exterior angle find the number of sides of the polygon.
Answer
(D)
14
14
Solve \(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)
Answer
(B)
\(\frac{1}{2}\)
15
If \(log_a 3\) = m and \(log_a 5\) = p, find \(log_a 75\)
Answer
(C)
m + 2p
16
Find the roots of the equations: \(3m^2 - 2m - 65 = 0\)
Answer
(B)
\(( 5, \frac{-13}{3})\)
17
A student measured the height of a pole as 5.98 m which is less than the actual height. If the percentage error is 5%, find correct to two d.p the actual height of the pole.
Answer
(A)
6.29m
18
The radius and height of a solid cylinder is 8 cm and 14 cm respectively. Find, correct to two d.p the total surface area.
(Take \(\pi = \frac{22}{7})\)
Answer
(A)
\(1,106.29cm^2\)
19
Find the value of a in the equation: cos (a + 14)° = sin (4a + 6)°
Answer
(C)
14
20
The radius of a sphere is 3 cm. Find, in terms of π, its volume.
Answer
(D)
\(36\pi cm^3\)
21
m:n = \(2\frac{1}{3} : 1\frac{1}{5}\) and n : q = \(1\frac{1}{2} : 1\frac{1}{3}\), find q : m.
Answer
(B)
16 : 35
22
make x the subject of the relation \(y = \frac{ax^3 - b}{3z}\)
Answer
(C)
x = \(\sqrt[3] \frac{3yz + b}{a}\)
23
An empty cylindrical tank is 140 cm in diameter. If 200 litres of water was poured into the tank. Calculate, correct to the nearest centimeter, the height of the water in the tank. (\(Take \pi = \frac{22}{7})\)
Answer
(C)
13cm
24
Arrange the following in ascending order of magnitude \(110_{two}, 31_{eight}, 42_{five}\)
Answer
(D)
\(110_{two}, 42_{five}, 31_{eight}\)
25
A number is chosen at random from 40 and 50 inclusive. Find the probability that the number is prime.
Answer
(B)
\(\frac{3}{11}\)
26
John was facing S35°E. If he turned 90° in the anticlockwise direction, find his new direction.
Answer
(C)
N55°E.
27
A line L passing through the point (6, -13) is parallel to the line which passes through (7, 4) and (-3, 9). Find the equation of the line L.
Answer
(C)
y = \(\frac{-1}{2}x - 10\)
28
A bag contains 4 white marbles and 3 blue marbles. Another bag contains 5 red and 6 blue marbles. If a marble is picked at random from each bag, find the probability that they are of the same colour.
Answer
(B)
\(\frac{18}{77}\)
29
The truth set of \(8 + 2x - x^2\) = 0 is {p, q}. Evaluate p + q.
Answer
(B)
2
30
The bar chart represents the distribution of marks scored by students in an economics examination. Use the bar chart to answer questions 30 to 32
If the failed mark was 4, what is the probability that a student selected at random passed?
Answer
(D)
0.64
31
What percentage of the students scored at most 5 marks?
Answer
(A)
58.5%
32
How many students scored at least 3 marks?
Answer
(A)
44
33
Factorize completely: \(x^2 - (y + z)^2\)
Answer
(B)
(x + y + z)(x - y - z)
34
An equilateral triangle has a side 2 cm. Calculate the height of the triangle.
Answer
(D)
\(\sqrt{ 3}\)cm
35
Mrs Kebeh stands at a distance of 110 m away from a building of vertical height 58 m. If Kebeh is 2 m tall, find the angle of elevation of the top of the building from her eye.
Answer
(A)
\(27^0\)
36
Consider the statements:
p: Siah is from Foya.
q: Foya is in Lofa.
Write in symbolic for the statement: "If Siah is from Foya, then Foya is in Lofa"
Answer
(C)
p ⇒ q
37
Write the name of a triangle with the vertices (1, -3), (6, 2) and (0,4)?
Answer
(B)
Isosceles triangle
38
The price of a shoe was decreased by 22%. If the new price is $27.3. what is the original price.
Answer
(D)
$35.00
39
In the diagram, NR is a diameter, ∠MNR = x° and, ∠SRN = (5x + 20)°. Find the value of 2x.
Answer
(B)
\(35^0\)
40
Solve: \(log_3 x + log_3 (x - 8) = 2\)
Answer
(C)
9
41
Find the quadratic equation whose roots are \(\frac{2}{3} and \frac{- 3}{4}\)
Answer
(C)
\(12y^2 + y - 6 = 0\)
42
The length of the diagonal of a square is 12 cm. Calculate the area of the square.
Answer
(C)
\(72 cm^2\)
43
In the diagram above, O is the centre of a circle NST. |NT| = |ST| and ∠NTS = 36°. Find the measure of the angle marked t.
Answer
(C)
\(36^0\)
44
Find the value of m in the diagram above.
Answer
(C)
\(130^0\)
45
Find the gradient of the line passing through the points \((\frac{1}{2}, \frac{- 1}{3}) and ( 3 , \frac{2}{3})\)
