AQA Level 2 Certificate Further Maths Paper 2: Calculator June 2025 question paper 8365/2

The 5th term in sequence A is also a term in sequence B.

Work out the position of the term in sequence B.

C and E are points on the circle with equation x² + y² = 144 CD is a straight line. O D: DE = 5: 1

Work out the shaded area. Give your answer as a decimal.

The equation of a straight line is 2 ax + y = 25 where a is a constant. The line passes through the point (3, 1)

Work out the value of the gradient of the line.

4 –5 ≤ n 5

Work out the range of possible values of n²

The equation of a curve is y = x⁵ + px⁴ where p is a constant. When x = – 1 the gradient of the curve is – 3

Work out the value of p.

C is a point on the straight line AB.

AC: CB = 3: 2

Work out the equation of the straight line passing through O and C.

k is a positive integer.

Prove that 4 k (k + 8) – (4 k + 9)(k – 1) is a multiple of 9

The first four terms of a quadratic sequence are

–1 11 31 59

Work out an expression for the n th term. Give your answer in the form an² + b where a and b are constants.

Factorise fully (x – 1)⁹ + (x – 1)⁸(x + 4)

Factorise fully 8y² – 50

Circle the matrix that represents an enlargement, scale factor 3, centre O.

O ABC is the unit square. O (0, 0) A (1, 0) B (1, 1) C (0, 1)

O ABC is mapped to O A ′ B ′ C ′ under a combined transformation of K followed by L.

Work out the coordinates of A ′, B ′ and C ′.

All lengths shown are in centimetres.

Use Pythagoras’ theorem to show that 4w² – 8w – 21 = 0

Work out the size of angle x.

For a curve y = f(x)

Show that the curve has a turning point where x = 3

Use to work out the nature of the turning point. You must show your working.

A, B, C and D are points on a circle. EBF is a tangent.

Work out the value of x.

Solve

Do not use trial and improvement. You must show your working.

ABCDEF is a triangular prism. ABCD is a rectangle and angle BCF is 90 ° AB = 14 cm BC = 8 cm CF = 6 cm M is the midpoint of EF.

Work out the size of angle BMD.

f(x) = 4x³ – 7 g(x) = 6x + 8

Work out the value of x for which f(2 x) = gf(x)

Here is a sketch of the curve with equation y = 4 + 2x – x² The tangent to the curve at the turning point P is shown. The normal to the curve at Q meets this tangent at R.

Work out the x-coordinate of R.

θ is an angle between 270 ° and 360 ° cos θ = and tan θ = –3k where k is a positive constant.

Work out the value of θ.

Work out the values of x between 0 ° and 360 ° for which