AQA Level 2 Certificate Further Maths Paper 2: Calculator June 2023 question paper 8365/2

The first four terms of a linear sequence are

15 18.5 22 25.5

Work out an expression for the n th term.

A different linear sequence has n th term 318 – 9 n

Work out the value of the first negative term in the sequence.

A line passes through P (1, k) and Q (r, 6) where k and r are constants. The midpoint of PQ has x-coordinate 5 The gradient of the line is 2

Work out the value of k.

y = 0.5x⁴

Work out the value of x for which the rate of change of y with respect to x is 6.75

The equation of a circle is (x + 7)² + (y – 4)² = 36

Complete these statements.

The coordinates of the centre of the circle are (

Here is a sketch of the curve y = ax² + bx + c where a, b and c are constants. The curve intersects the x-axis at (– 4, 0) and (p, 0) The turning point has x-coordinate 0.5

Work out the value of p.

Solve ax² + bx + c 0

ABC is a triangle with perpendicular height AD.

BD: DC = 2: 3

Work out the size of angle w.

The dimensions of the cuboid are given in centimetres.

The total length of all 12 edges is 300 cm

The volume of the cuboid is V cm³

Use calculus to work out the maximum value of V as x varies.

Line K has equation 4 x – 5 y = 17 Line L passes through the points (3, 6) and (– 5, 16)

Tick (✓) the correct statement about lines K and L.

Show working to support your answer.

Expand and simplify fully (2x³ – 9)(3x² + 4) + x(x – 4)²

VABCD is a pyramid. The square horizontal base, ABCD, has side length 15 cm V is directly above the centre, X, of the base. VA = 28 cm

Work out the size of the angle that VA makes with ABCD.

Work out the least possible values of c and d.

(2x – 3) is a factor of 6x³ – 25x² + 28x – 6

Give all solutions as exact values.

The function h is given by h(x) = ax(3x² – 2) + 5x where a is a positive constant. h is an increasing function for all values of x.

Work out the possible values of a. Give your answer as an inequality.

Here is a sketch of y = cos x for values of x from 0 ° to 360 ° α is an obtuse angle measured in degrees. cos α = – k where k is a positive constant.

Tick (✓) two boxes that show expressions for x where cos x = – k

In these simultaneous equations, k is a positive constant.

3 x + 4 y = k

y = 2 kx

Solve the simultaneous equations. Give the answers in their simplest form in terms of k.

Show that 2 sin³x + 2 sin x cos² x + 5 tan x cos x simplifies to p sin x where p is a constant.

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

Work out the value of x.

Five-digit integers are made using

1 2 7 8 9

For each integer, all the digits are used exactly once. The integers are greater than 40 000 and odd.

How many different integers can be made? You must show your working.