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Question 1 of 50
Evaluate, correct to three decimals, \( \frac{4.314\: \times \: 0.000056}{0.067}\)
Question 2 of 50
There are 30 students in a class. 15 study woodwork and 13 study metalwork. 6 study neither of the two subjects. How many students study woodwork but not metalwork?
Question 3 of 50
Solve: \( \scriptsize 2^{5x} \: \div\: 2^x = \sqrt[5]2^{10} \)
Question 4 of 50
Solve \( \scriptsize 1 \:+\: \sqrt[3]{x\:-\:3} = 4 \)
Question 5 of 50
Express 4137 in base 5.
Question 6 of 50
Solve \( \scriptsize \log_3x \: + \: \log_3(x\:-\:8) = 2 \)
Question 7 of 50
Mr. Manu is 4 times as old as his son, Adu. 7 years ago the sum of their ages was 76 years. How old is Adu?
Question 8 of 50
Factorize completely: \( \scriptsize x^2 \: -\: (y\:+\:z)^2 \)
Question 9 of 50
Find the roots of the quadratic equation:
\( \scriptsize 3m^2 \: – \: 2m \: -\: 65 = 0\)
Question 10 of 50
M varies jointly as the square of n and square root of q. If m = 24 when n = 2 and q = 4, find M when n = 5 and q = 9.
Question 11 of 50
If:
\(\scriptsize m:n = 2\frac{1}{3}: 1\frac{1}{5} \)
and \(\scriptsize n:q = 1\frac{1}{2}: 1\frac{1}{3} \)
find q : m
Question 12 of 50
One-third the sum of two numbers is 12. Twice their difference is 12. Find the numbers.
Question 13 of 50
Find the quadratic equation whose roots are:
\( \normalsize \frac{2}{3} \scriptsize \: and \: – \normalsize \frac{3}{4} \)
Question 14 of 50
Make x the subject of the relation:
y = \( \frac{ax^3 \: -\: b}{3z} \)
Question 15 of 50
The price of a shoe was decreased by 22%. if the new price was $27.30, what was the original price?
Question 16 of 50
The radius and height of a solid cylinder are 8 cm and 14 cm respectively. Find, correct to two decimal places, the total surface area.
\( \left[\scriptsize Take \: \pi = \normalsize \frac{22}{7}\right]\)
Question 17 of 50
In the diagram, O is the centre of the circle NST.
\( \scriptsize \overline{NT} = \overline{ST} \: and \: \angle NTS = 36^o.\)
Find the measure of the angle marked t.
Question 18 of 50
A sphere has a radius 3 cm. Find, in terms of π, its volume.
Question 19 of 50
Arrange the following numbers in ascending order of magnitude:
110two , 31eight , 42five
Question 20 of 50
A notebook of length 15 cm was measured by a student as 16.8 cm. Calculate, correct to two decimal places, the percentage error in the measurement.
Question 21 of 50
NOT DRAWN TO SCALE
Find the value of m in the diagram.
Question 22 of 50
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.
Question 23 of 50
An empty cylindrical tank is 140 cm in diameter. If 200 litres of water is poured into the tank, calculate, correct to the nearest centimetre, the height of water in the tank.
\( \left[\scriptsize Take \: \pi = \normalsize \frac{22}{7}\right]\)
Question 24 of 50
Mrs. Kebeh stands at a distance of 110 m away from a building of vertical hight 58 m. if Kebeh is 2 m tall, find the angle of elevation of the top of the building from her eye.
Question 25 of 50
Find the mean deviation of the set of numbers:
14, 15, 16, 17, 18, and 19
Question 26 of 50
The interior angle of a regular polygon is 6 times its exterior angle. Find the number of sides of the polygon.
Question 27 of 50
The length of the diagonal of a square is 12 cm. Calculate the area of the square.
Question 28 of 50
Consider the statements:
p: Siah is from Foya
Write in symbolic form the statement:
“If Siah is from Foya, then Foya is in Lofa”
Question 29 of 50
What is the name of a triangle with vertices (1, -3), (6, 2) and (0, 4)?
Question 30 of 50
NOT DRAWN TO SCALE
In the diagram, \( \scriptsize\overline{NR}\)is a diameter, ∠MNR = xº and ∠SRN = (5x + 20)º.
Find the value of 2x.
Question 31 of 50
Find the value of α in the equation:
cos (α + 14)º = sin(4α + 6)º
Question 32 of 50
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.
Question 33 of 50
The angle of a sector of a circle of radius 3.4 cm is 115º. Find the area of the sector.
\( \left[\scriptsize Take \: \pi = \normalsize \frac{22}{7}\right]\)
Question 34 of 50
The diagonals of a rhombus are 16 cm and 12 cm. Find the length of the side.
Question 35 of 50
The angle of elevation of the top of a vertical building from a point Z on the ground is 50º. If the height of the building is 124 m, find the distance from Z to the foot of the building.
Question 36 of 50
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 decimal places, the actual height of the pole.
Question 37 of 50
NOT DRAWN SCALE
In the diagram, O is the centre of the circle QRS and ∠SQR = 28º. Find ∠ORS.
Question 38 of 50
John was facing S35ºE. If he turned 90º in the anticlockwise direction, find his new direction.
Question 39 of 50
If 2x – 3y = -11 and 3x + 2y = 3, evaluate (y – x)2 .
Question 40 of 50
An equilateral triangle has side 2 cm. Calculate the height of the triangle.
Question 41 of 50
A number is selected at random from 40 to 50 inclusive . Find the probability that the number is prime.
Question 42 of 50
The bar chart represents the distribution of marks scored by students in an Economics examination.
Use the bar chart to answer the question.
If the failed mark was 4, what is the probability that a student selected at random passed?
Question 43 of 50
The bar chart represents the distribution of marks scored by students in an Economics examination.
Use the bar chart to answer the question.
What percentage of the students scored at most 5 marks
Question 44 of 50
The bar chart represents the distribution of marks scored by students in an Economics examination.
Use the bar chart to answer the question.
How many students scored at least 3 marks?
Question 45 of 50
If loga 3 = m and loga 5 = p, find loga 75
Question 46 of 50
NOT DRAWN TO SCALE
In the diagram, M, N, R are points on the circle O. ∠ORN = 48º and ∠RNM = 124º. Find ∠OMN.
Question 47 of 50
Simplify \( \scriptsize 3 \sqrt{2} \: + \: 10 \sqrt{3} \: -\: \normalsize \frac{6}{\sqrt{3}} \)
Question 48 of 50
The truth set of 8 + 2x – x² = 0 is {p, q}. Evaluate p + q.
Question 49 of 50
Find the gradient of the line passing through the points:
\( \left(\normalsize \frac{1}{2}, \: -\frac{1}{3} \right) \scriptsize \: and \: \left(\scriptsize 3,\: \normalsize \frac{2}{3} \right)\)
Question 50 of 50
For what values of x is \( \frac{x^2 \: +\:2}{10x^2 \: – \: 13x \: -\: 3} \) undefined?
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