GCE Further Mathematics 2023
Past Questions

In a survey of 100 traders in Lagos market, 60 sell rice, 45 sell beans, and some sell both. If 15 traders sell neither rice nor beans, how many traders sell both rice and beans?

Simplify √75 + √48 − √27

Find the value of $x$ if $\log_3(x^2 - 2x) = 1$.

The first term of an arithmetic progression (A.P.) is 3 and the common difference is 4. Find the 10th term.

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

Find the sum to infinity of the geometric series $1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + ...$

If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}$, find $\det(AB)$.

Given that a = 3i + 4j and b = i - 2j, find |a + b|.

Given vectors m = 4i - 3j and n = -4i + 3j, which of the following statements is correct?

Points P, Q and R have position vectors p = i + 2j, q = 4i + 6j and r = 7i + 10j respectively. Which of the following correctly describes the relationship between P, Q and R?

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

The gradient of the curve $y = 2x^3 - 9x^2 + 12x - 4$ at the point where $x = 2$ is

Differentiate $y = (3x + 5)^4$ with respect to $x$.

If $y = \frac{x^2 + 1}{x - 1}$, find $\frac{dy}{dx}$.

Evaluate $\int_{1}^{e} \frac{\ln x}{x}\, dx$

Eight people are to be seated at a round table. In how many distinct ways can they be arranged?

A bag contains 5 red balls, 3 blue balls and 2 green balls. If a ball is drawn at random from the bag, what is the probability that it is NOT red?

A geometric progression (G.P.) has first term a and common ratio r. The third term of the G.P. is 12 and the sixth term is 96. (a) Find the values of a and r. (b) Find the sum of the first 10 terms of…

A curve is defined by the equation y = x³ - 6x² + 9x + 2. (a) Find dy/dx. (b) Determine the coordinates of the stationary points of the curve. (c) Distinguish between the stationary points, stating wh…

(a) Find the integral ∫(3x² + 4x - 5) dx. (b) Evaluate ∫₁³ (2x³ - 6x + 1) dx. (c) A curve passes through the point (2, 7) and its gradient function is given by dy/dx = 3x² - 4x + 1. Find the equatio…