In the diagram, O is the center of the circle QRS and ∠SQR = 28°. Find ∠ORS.
إجابة
(D)
\(62^0\)
2
Solve \(1 + \sqrt[3]{ x - 3} = 4\)
إجابة
(A)
30
3
The angle of a sector of a circle of radius 3.4 cm is 115°. Find the area of the sector.
\((Take \pi = \frac{22}{7})\)
إجابة
(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?
إجابة
(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?
إجابة
(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.
إجابة
(B)
104.05m
7
One-third of the sum of two numbers is 12, twice their difference is 12. Find the numbers.
إجابة
(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?.
إجابة
(B)
\(\frac{-1}{5}, \frac{3}{2}\)
11
Express \(413_7\) to base 5
إجابة
(C)
\(1311_5\)
12
Evaluate, correct to three decimal place \(\frac{4.314 × 0.000056}{0.0067}\)
إجابة
(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.
إجابة
(D)
14
14
Solve \(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)
إجابة
(B)
\(\frac{1}{2}\)
15
If \(log_a 3\) = m and \(log_a 5\) = p, find \(log_a 75\)
إجابة
(C)
m + 2p
16
Find the roots of the equations: \(3m^2 - 2m - 65 = 0\)
إجابة
(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.
إجابة
(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 \(\pi = \frac{22}{7})\)
إجابة
(A)
\(1,106.29cm^2\)
19
Find the value of a in the equation: cos (a + 14)° = sin (4a + 6)°
إجابة
(C)
14
20
The radius of a sphere is 3 cm. Find, in terms of π, its volume.
إجابة
(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.
إجابة
(B)
16 : 35
22
make x the subject of the relation \(y = \frac{ax^3 - b}{3z}\)
إجابة
(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. (\(Take \pi = \frac{22}{7})\)
إجابة
(C)
13cm
24
Arrange the following in ascending order of magnitude \(110_{two}, 31_{eight}, 42_{five}\)
إجابة
(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.
إجابة
(B)
\(\frac{3}{11}\)
26
John was facing S35°E. If he turned 90° in the anticlockwise direction, find his new direction.
إجابة
(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.
إجابة
(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.
إجابة
(B)
\(\frac{18}{77}\)
29
The truth set of \(8 + 2x - x^2\) = 0 is {p, q}. Evaluate p + q.
إجابة
(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?
إجابة
(D)
0.64
31
What percentage of the students scored at most 5 marks?
إجابة
(A)
58.5%
32
How many students scored at least 3 marks?
إجابة
(A)
44
33
Factorize completely: \(x^2 - (y + z)^2\)
إجابة
(B)
(x + y + z)(x - y - z)
34
An equilateral triangle has a side 2 cm. Calculate the height of the triangle.
إجابة
(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.
إجابة
(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"
إجابة
(C)
p ⇒ q
37
Write the name of a triangle with the vertices (1, -3), (6, 2) and (0,4)?
إجابة
(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.
إجابة
(D)
$35.00
39
In the diagram, NR is a diameter, ∠MNR = x° and, ∠SRN = (5x + 20)°. Find the value of 2x.
إجابة
(B)
\(35^0\)
40
Solve: \(log_3 x + log_3 (x - 8) = 2\)
إجابة
(C)
9
41
Find the quadratic equation whose roots are \(\frac{2}{3} and \frac{- 3}{4}\)
إجابة
(C)
\(12y^2 + y - 6 = 0\)
42
The length of the diagonal of a square is 12 cm. Calculate the area of the square.
إجابة
(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.
إجابة
(C)
\(36^0\)
44
Find the value of m in the diagram above.
إجابة
(C)
\(130^0\)
45
Find the gradient of the line passing through the points \((\frac{1}{2}, \frac{- 1}{3}) and ( 3 , \frac{2}{3})\)
