GCE Further Mathematics 2020
Past Questions

In a class of 40 students, 25 study Mathematics, 20 study Physics, and 10 study both subjects. How many students study neither Mathematics nor Physics?

A binary operation ⊕ is defined on the set of integers by $p \oplus q = p^2 + q^2 - pq$. Find $2 \oplus 3$.

If $\log_x 64 = 3$, find x.

Simplify $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$

If the 2nd term of a geometric progression is 6 and the 5th term is 162, find the common ratio.

Find the sum of the first 8 terms of the geometric progression (G.P.): 2, 6, 18, ...

Evaluate the determinant $\begin{vmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{vmatrix}$.

Given that A = [[2, 3], [1, 4]], find the determinant of A.

Simplify $\frac{\sin 2\theta}{1 + \cos 2\theta}$.

Find $\int \frac{1}{5x+3}\, dx$

How many ways can a committee of 3 be chosen from 8 people?

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

A bag contains 5 red balls and 4 blue balls. In how many ways can 3 balls be selected so that at least 2 are red?

Two fair dice are thrown together. What is the probability that the sum of the outcomes is at least 10?

The variance of a set of numbers is 9. What is the standard deviation?

A particle of mass 5 kg is placed on a smooth inclined plane making an angle of 30° with the horizontal. The magnitude of the normal reaction of the plane on the particle is [Take g = 10 ms⁻²]

Two forces F1 and F2 act on a particle, where F1 = (5i + 2j) N and F2 = (-3i + 4j) N. (a) Find the resultant force R = F1 + F2. (b) Find the magnitude of R and the angle it makes with the positive x-a…