AQA Level 2 Certificate Further Maths Paper 1: Non-calculator June 2023 question paper 8365/1

The function f is given by f(x) = 2 x + 1

Work out x when f(x) = – 5

The function g is given by g(x) = x²

Work out fg(3)

Factorise fully 6x²y + 21xy

Circle the transformation matrix that represents a reflection in the line y = – x

S (7, 2) and T (5, – 4) are points on a straight line.

Work out the gradient of the line.

Work out the distance between S and T. Give your answer in the form a where a and b are both integers greater than 1

X_n and Y_n are the nth terms of two sequences.

Prove that every term of the sequence with nth term Y_n – X_n is a multiple of 3

The equation of a curve is y = x⁶ + 4x² – 7

Work out the equation of the tangent to the curve at the point (1, – 2) Give your answer in the form y = mx + c

The diagram below shows a cone and a prism. All measurements are in cm The cone has base radius r and perpendicular height x. The prism has a triangular cross section with base y and perpendicular height y. The length of the prism is x.

The volume of the cone is four times the volume of the prism.

Express r in terms of y.

A circle has centre (0, 0) and radius 5 A straight line has equation 2 y = x + 5

Work out the coordinates of the two points where the circle and straight line intersect. Do not use trial and improvement. You must show your working.

Rationalise the denominator and simplify fully

Work out the positive value of x for which = 55

Write down the value of x for 0° ≤ x ≤ 360° when sin x = –1

Give your answer in its simplest form.

The expansions of (1 + 12x)⁴ and (a + 4x)³ have the same coefficient of x²

Work out the value of a.

The curve y = ax³ + bx² + 7 has a stationary point at (–2, 11)

Work out the values of a and b.

8x² + 20x + n ≡ c(x + d)² + 3 where c, d and n are constants.

Work out the values of c, d and n.

P, Q and R are points on a circle, centre O. Angle POR = 120 ° PQ = 4 cm QR = 5 cm

Work out the radius of the circle. Give your answer in the form where k is an integer.