AQA Level 2 Certificate Further Maths Paper 1: Non-calculator June 2024 question paper 8365/1

Factorise x² – y²

Circle the limiting value of as n → ∞

1 3 4 7

The equations of two straight lines are

y – 3 x = 4 and 6 y = 18 x – 5

Show that the lines are parallel.

Points A (– 12, 1) and B (12, – 1) lie on a circle. AB is a diameter of the circle.

Work out the equation of the circle.

The image of P is (– 8, 7)

Work out the values of x and y.

Solve by factorising 2x³ – 9x² – 5x = 0

ABCDEFGH is a cuboid.

Work out the length AG.

A function f is given by

A sketch of y = f(x) is shown.

Work out the values of a and b.

(3x – 7) is a factor of 3x³ – 4x² – 13x + 14

Work out the other two linear factors.

(x – 2) is a factor of ax⁴ – 3ax³ + 5x – 22

Work out the value of a.

Work out the length BC.

A garden patio is made from two rectangles. All lengths are in metres.

The area of the patio is less than 51m²

Work out the range of possible values of x. Give your answer in the form a x b where a and b are both integers. You must show your working.

Write 2x² – 16x + 7 in the form k(x + m)² + n where k, m and n are integers.

Solve (x – 1)² – 5 = 0

Matrix M represents a reflection in the line y = – x

Write down matrix M

A, B, C and D are points on a circle, centre O. angle OBC: angle ODC = 5: 3

Work out the size of angle OBC. You must show your working.

Rationalise the denominator and simplify fully

The equation of a curve is y = x³ – 3x² + 5

Work out the stationary points of the curve and determine their nature. You must show your working.

Here is the graph of y = −x² + 3x + 6 for −2 x 5

By drawing a suitable straight line, work out approximate solutions to

You must show your working.

The nth term of a quadratic sequence is an² – 5n + c where a and c are integers. The first four terms of the sequence are

2 x 16 y

Work out the values of x and y.