GCE Mathematics 2021
Past Questions

Simplify $\frac{5\sqrt{2} + \sqrt{50}}{\sqrt{8}}$.

Given that $\log_3(x^2 - 2x) = 1$, find the possible values of $x$.

If $3(2x - 1) = 2(x + 5)$, find the value of x.

Simplify: $\frac{x^2 - 9}{x^2 - x - 6}$

If $p = \frac{q + r}{q - r}$, make r the subject of the formula.

A quadratic equation has roots α and β such that α + β = 3 and αβ = -10. Which of the following is the equation?

A cylindrical tank has a radius of 7 cm and a height of 10 cm. Calculate the total surface area of the tank. [Take π = 22/7]

A sphere has a volume of $\frac{500\pi}{3}$ cm³. Find the radius of the sphere.

ABCD is a cyclic quadrilateral. If angle DAB = 78° and angle ABC = 105°, find angle BCD.

The angles of a triangle are in the ratio 2:3:5. Find the largest angle.

Two exterior angles of a polygon are 45° and 60°, and each of the remaining exterior angles is 35°. How many sides has the polygon?

Simplify $\frac{\sin^2 \theta + \cos^2 \theta}{\cos \theta}$.

If $\cos(3x - 10)° = \sin(x + 20)°$, find the value of x.

The ages of 5 students are 12, 15, 14, 13 and 16 years. Find the mean age.

The mean of the numbers 3, 2x, 5, 7 and 2 is 6. Find the value of x.

The pie chart shows how a student spends his 24-hour day. If the sector representing sleep subtends an angle of 120° at the centre, how many hours does the student spend sleeping?

The probability that it rains on any given day in Lagos during the rainy season is 0.6. What is the probability that it rains on exactly 2 out of 3 randomly chosen days?

Which of the following statements is the negation of 'All traders in Lagos pay tax'?

Find the equation of the line that passes through the point (1, 2) and is parallel to the line $3x - 2y + 5 = 0$.

a) Convert 11011101₂ to base 10. b) (i) Convert 347₁₀ to base 8. (ii) Hence, or otherwise, convert 347₁₀ to base 2. c) Evaluate 1101₂ × 101₂, giving your answer in base 2. d) A number in base 7 …

(a) Solve the simultaneous equations: 3x + 2y = 21 x - y = 2 (b) Given that p = 2, q = -3 and r = 4, evaluate: (i) p²q + r (ii) (p + r)² - 3q (c) Factorise completely: 6x² - 7x - 3

a) Given that sin θ = 5/13 and θ is acute, find without using tables or calculator, the values of: (i) cos θ (ii) tan θ (iii) sin 2θ b) The angle of elevation of the top of a vertical tower …

A bag contains 5 red balls, 3 blue balls and 2 green balls. Two balls are drawn one after the other without replacement. (a) Draw a tree diagram to illustrate all possible outcomes of the two draws. (…

The table below shows the results of a survey of 200 students on their preference for two subjects, Mathematics (M) and English (E). | | Likes M | Does not like M | Total | |---|---|---|---| | Likes …