The set of A = {1 ≤  x ≤ 4} and B = {1, 4, 10} are subset of U = {x: 1 ≤ x ≤ 10). Find A ∩ B.

The set of A = {1 ≤  x ≤ 4} and B = {1, 4, 10} are subset of U = {x: 1 ≤ x ≤ 10). Find A′ the complement of A.

Simplify 100110+ 11011 in base two.

Find the sum of 3 +4 + 1 +2 + 3 (mod 5)

Find the base for addition: 35 +43 = 122

In a school, Q = {students who can swim), R = {students over 16 years) and S = {students who are boys). What is Q´ ∩ R´∩ S?

Express 98000 in standard form.

Simplify

The point (5, 1) is reflected in the x-axis. Find the coordinates of the final image.

Which of the following number line represents the solutions of 5 – x > 8?

Simplify (x−1+2√2)(x−1−2√2)

Find the median of the following numbers 40, 30, 32, 39, 39, 34, 35, 35, 37.

Find the coordinates of the image of the point (m, −7) under an anticlockwise rotation through 90° about the origin.

Express log 3 + 3 log 2 − 3 log 4 as a single logarithm.

Evaluate 61.5² – 38.5²

The frequency of vibration, f on a stretched wire is directly proportional to the square root of the length, l and inversely proportional to the square root of the tension, T in the wire. Express T in terms of f, k, and l where k is a constant.

The area S m of a circular path round a circular garden is given by S = π (R² − r2).

If π = 3.14, R = 6m and r = 2m, calculate the value of S.

In the diagram P, Q, R are points on a circle with centre 0. If angle POR = 100°, find angle PQR.

A transformation is given by

Find the image (−2, −3) under this transformation.

Find the mean of 306, 308,304 and 314.

Simplify

If sin x = 0.8192, where 90° < x < 180°, find x.

A box contains 3 black and 5 red balls of the same size. If a ball is picked at random, what is the probability that it is black?

A man spent 58% of his income and the amount of money left was ¢21,000.00. Find his income.

Find the magnitude of u + V.

If 4^x = 2^3x-3, find x.

Kwaku and Attah formed a company and agreed that their profit will be shared in the ratio 4: 5 respectively. At the end of the year, Attah received ¢5000.00 more than Kwaku. How much profit did the company make in the year?

Find the image of the point (0, 1) under T.

Find the equation of the line with gradient 3 which passes through the point (-2, 0).

Solve 6x² − 13x = − 5

In an examination, Otu scored 72% in Mathematics, 68% in Chemistry and x% in Physics. If his mean mark in the three subject was 65%, find x.

Find the length of the arc of a sector of a circle of radius 3.5 cm which subtends an angle of 144° at the centre. [Take π = 22/7]

A company sold 51,644 cars in 1996. In 1997 it sold 54,244 cars. Find the percentage increase in sales, correct to two decimal places.

Solve the inequality 48 < 1/2(1 + x)

Simplify

The diagram above shows the arcs used in the construction of angle PQR. What is the size of this angle?

Find the perimeter of a semi-circular window of radius 30cm. [Take π = 22/7]

Jude travelled a distance of 12 km on a bicycle at an average speed of 8 kmh‾¹. How long did it take him to make the trip?

In a class of 20 students, 16 play soccer,12 play hockey and 2 do not play any of the two games. How many students play only hockey?

Find the coordinates of the image of the point (1/2, 0) under an anti-clockwise rotation through 90° about the origin.

Make r the subject of the relation

v = 1/6πh(3r² +h²)

Find the standard deviation of 5, 6, 7, 8 and 9.

Express (30km, 240°) in the form

The mean of seven numbers is 15. When three numbers are added, the mean of ten numbers become 12. Find the mean of the three numbers.

Find p such that q = 1/2p

Solve the equation 8/(6 − y) = −2

A string 180 cm long is divided in the ratio 2: 3: 4. How long will the longest part of the string be?

A swimming pool with length 30 m and width 12 m is 4 m deep at one end and 1 m deep at the other end. Find the volume of water that will fill it completely.

In the diagram, R, S. T are points on a circle with centre 0, find the relationship between x and y.