GCE Further Mathematics 2021
Past Questions

Evaluate $\frac{3^{n+1} - 3^n}{3^{n-1}}$

Find the remainder when $f(x) = 2x^4 - 3x^3 + x^2 - 5x + 2$ is divided by $(x + 1)$.

How many terms of the arithmetic progression 5, 9, 13, ... must be taken for the sum to equal 165?

If M = [[5, 2], [3, 1]], find M⁻¹, the inverse of M.

Given that $P = \begin{pmatrix} 2 & -1 \\ 4 & 3 \end{pmatrix}$, find the transpose of P, denoted $P^T$.

Find the value of $\cos 300°$.

A sector of a circle has radius 9 cm and an arc length of 6 cm. Find the area of the sector.

Solve for $\theta$ in the range $0° \leq \theta \leq 360°$: $2\cos^2\theta - \cos\theta - 1 = 0$.

Find the derivative of y = 5x³ - 3x² + 7x - 2.

Evaluate ∫(3x² + 2x - 5) dx

Find ∫cos(4x) dx

Find the area enclosed between the curve $y = x^2 - 4$ and the x-axis

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

An arithmetic progression (A.P.) has first term p and common difference d. The 5th term of the A.P. is 21 and the sum of the first 8 terms is 120. (a) Find the values of p and d. (b) Find the 20th ter…

a) A sector of a circle has an area of 75 cm² and a perimeter of 40 cm. Find: i) the radius of the circle, ii) the angle subtended at the centre of the circle in radians, iii) the length of t…

Given that y = (3x + 2)⁴(x² - 1), (a) Find dy/dx, simplifying your answer as far as possible. (b) Hence, find the values of x for which dy/dx = 0. (c) A particle moves along a straight line such that …