GCE Further Mathematics 2024
Past Questions

If P = {1, 2, 3, 4, 5} and Q = {2, 4, 6, 8}, find P ∩ Q.

A binary operation * is defined on the set of real numbers by $a * b = \frac{a+b}{1+ab}$, where $ab \neq -1$. If the operation is commutative, find the identity element $e$ such that $a * e = a$.

Which of the following is a factor of the polynomial $p(x) = x^3 - 6x^2 + 11x - 6$?

Express $\dfrac{3x^2 + x + 2}{(x^2 + 1)(x - 1)}$ in partial fractions.

The 3rd and 7th terms of an arithmetic progression are 10 and 26 respectively. Find the first term.

The sum of the first n terms of a series is given by $S_n = 3n^2 + 2n$. Find the 5th term of the series.

If $\sin\theta = \frac{5}{13}$ and $\theta$ is acute, find the value of $\tan\theta$.

The expression $\sin(A + B) - \sin(A - B)$ simplifies to:

Find the derivative of $y = x^2 \sin x$.

Evaluate $\int x e^{x}\, dx$

In how many ways can the letters of the word LAGOS be arranged?

Find the value of $^{10}P_3$.

How many 4-digit numbers greater than 4000 can be formed using the digits 2, 3, 4, 5, 6 if repetition is not allowed?

In a class of 40 students, 18 study Mathematics, 22 study English and 6 study both subjects. How many students study neither Mathematics nor English?

The probabilities that Ade and Bisi will pass an examination are 2/3 and 3/4 respectively. Find the probability that only one of them passes the examination.

The ages (in years) of seven teachers in a school are: 34, 28, 46, 39, 52, 41 and 30. Find the mean absolute deviation of the distribution.

(a) The universal set U = {x : x is a positive integer, x ≤ 20}. Sets A and B are subsets of U such that A = {x : x is a prime number} and B = {x : x is an odd number}. (i) List the elements of A and…

1. (a) Without using tables or calculator, simplify: (√75 - √48) / √3, leaving your answer in the simplest form. [4 marks] (b) Given that log₂(x + 3) + log₂(x - 1) = 5, find the value(s) of x. [6 mar…

A matrix M is given by M = [[2, 1, -1], [1, 3, 2], [-1, 2, 4]]. (a) Find the determinant of M. [4 marks] (b) Find the matrix of cofactors of M. [6 marks] (c) Hence, find the inverse of M, M⁻¹. [4 mark…

Two matrices P and Q are defined as: P = [[3, k], [2, 5]] and Q = [[1, -2], [0, 4]] where k is a real constant. (a) Find PQ in terms of k. [3 marks] (b) Given that det(PQ) = 46, find the value of k. …

A position vector of point P is 3i + 4j and the position vector of point Q is 7i - 2j. (a) Find the vector PQ. (b) Find |PQ|, the magnitude of PQ. (c) Find the unit vector in the direction of PQ. (d) …

a) Prove the identity: (cos θ)/(1 - sin θ) - (cos θ)/(1 + sin θ) = 2 tan θ. b) i) Express 3 sin x + 4 cos x in the form R sin(x + α), where R > 0 and 0° < α < 90°. State the values of R and α correct…

(a) Using integration by substitution or otherwise, find ∫ x(2x² + 3)⁴ dx. (b) (i) Sketch the curves y = x² and y = 4x - x² on the same axes, indicating clearly their points of intersection. (ii)…

A committee of 5 people is to be chosen from 6 men and 4 women. (a) In how many ways can the committee be selected if there are no restrictions? [3 marks] (b) In how many ways can the committee be sel…