GCE Mathematics 2023
Past Questions

A trader sells an article for ₦3,600 and makes a profit of 20%. What was the cost price of the article?

The product of the roots of the equation 2x² + 5x - 3 = 0 is:

Using the quadratic formula, solve 2x² - 3x - 2 = 0. The roots are:

Find the range of values of x for which $3x - 5 > x + 7$.

If y varies directly as x and y = 15 when x = 3, find y when x = 7.

A quantity T varies directly as the cube of m and inversely as n. If T = 54 when m = 3 and n = 2, find T when m = 2 and n = 4.

The base of a right-angled triangle is 24 cm and its hypotenuse is 25 cm. Find the area of the triangle.

A circle has a chord of length 16 cm. If the chord is 6 cm from the centre of the circle, find the radius of the circle.

In the diagram, PQ is parallel to RS. If angle QPT = 65° and angle RST = 48°, find angle PTS.

O is the centre of a circle and angle AOB = 140°, where A and B are points on the circle. Find the angle in the alternate segment, that is, the angle subtended by arc AB at any point on the major arc.

In triangle PQR, PQ = 8 cm, QR = 6 cm and angle PQR = 120°. Find PR, correct to the nearest whole number. [Use the cosine rule]

The scores of 8 students in a test are: 5, 8, 7, 6, 9, 5, 7, 5. What is the modal score?

A bag contains 5 red balls, 3 blue balls and 2 green balls. If a ball is picked at random from the bag, what is the probability that it is blue?

If $n(U) = 50$, $n(A) = 30$, $n(B) = 25$, and $n(A \cup B) = 45$, find $n(A \cap B)$.

In a class of 40 students, 25 study French, 20 study Hausa, and 8 study both languages. How many students study neither French nor Hausa?

Find the distance between the points P(3, 4) and Q(-1, 1).

(a) (i) Simplify: (3x² - 12) / (x² + x - 6) (ii) Hence, or otherwise, solve: (3x² - 12) / (x² + x - 6) = 6 (b) The sum of two numbers is 15 and the sum of their squares is 137. Find the two num…

A rectangular garden has a length that is 3 m more than twice its width. If the area of the garden is 44 m², find: (a) Write down a quadratic equation in terms of the width, x, of the garden. [3 marks…

In the diagram, ABCD is a cyclic quadrilateral in which AB = BC. The diagonal BD is produced to E such that angle AEB = 35° and angle ABE = 75°. (a) Find angle BAE. (b) Find angle ADB. (c) If angle B…