AQA Level 2 Certificate Further Maths Paper 1: Non-calculator June 2025 question paper 8365/1

The function f is given by f(x) = 5 x + 3

Work out the domain of the function, giving your answer as an inequality.

The function g is given by g(x) = x³ – 4

Work out the range of the function, giving your answer as an inequality.

A linear sequence starts 2 5 8 11

Work out the position of the term that is the first to have a value greater than 500

AC is a straight line. A is the point (– 3, 2) B is the midpoint of the line AC. B is the point (12, 10)

Work out the coordinates of C.

Work out the distance AB.

Here is a sketch of y = x² + bx + c The graph passes through (– 1, 0) and (5, 0)

Work out the values of b and c.

Here is a sketch of y = tan x for 0° x 360°

You are given that tan 72 ° = k

Work out the two values of x between 0 ° and 360 ° for which tan x = – k

9 3-digit integers are made using three different digits. The digits are chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9

How many more odd integers than even integers can be made?

PQ is perpendicular to QR.

Work out the value of a.

Solve x³ + 10x² + 8x = 0 Where appropriate give your answers in surd form. Simplify your answers where possible.

A, B and C are points on a circle, centre O.

Prove that y = 180 – 5 x

Here are four sketch graphs.

Circle the letter of the sketch graph that represents y = 5^x

(x – 3)(x + 4)(x + p) ≡ x³ + qx² + rx + 24

Work out the values of p, q and r.

Work out the length AC.

The expansions of (4a + x)⁴ and (5 – 2x)³ have the same coefficient of x³

Work out the value of a.

A 60 cm piece of wire is bent to form three sides of a rectangle. It is then attached to a fixed rod as shown in the diagram.

The area of the rectangle is A cm²

Show that A = x (60 – 2 x)

Work out the maximum value of A as x varies.

(x – 1) is a factor of 3x³ + 2x² – 3x – 2

f(x) = (x – 2)(5 x + 4)(3 x + 2) c is a positive integer. The value of f(c) can be written as the product of two prime factors.

Deduce the value of f(c)

A circle has centre (2, 3) and radius 5 A straight line passes through (3, 7) and has a gradient of 2

Work out the coordinates of the two points where the circle and the straight line intersect.

The diagram shows a trapezium. All lengths are in centimetres.

The area of the trapezium is less than 22cm²

Work out the greatest possible range of values of x. Give your answer in the form m x n where m and n are both positive numbers.