AQA Level 2 Certificate Further Maths Paper 2: Calculator June 2024 question paper 8365/2

A straight line passes through the point (– 1, – 1) and

Draw the line for values of x from – 3 to 3

2 5n² + 2 38

Work out all the possible integer values of n.

The equation of a curve is y = x⁴ – 3kx² where k is a constant. When x = 2 the rate of change of y with respect to x is 23

Work out the value of k.

Here is some information about three linear sequences, A, B and C.

n th term of C = n th term of A + n th term of B

The n th term of C is 42 – 3 n The first four terms of B are 14 22 30 38

Work out the 20th term of A.

Write down matrix M

The function f is given by f(x) = 3x² + 2 with domain –1 x 4

Work out the range of the function.

Circle the coordinates of the point where the curve crosses the y-axis.

(– 5, 0)
(0, – 5)
(– 13, 0)
(0, – 13)

Write down the coordinates of the maximum point of the curve.

Give your answer in the form a + bxⁿ where a, b and n are integers.

A set of 4-digit integers each have a first digit greater than 6 and a second digit less than 8

What is the greatest possible number of integers in the set that are multiples of 5 ?

f is a cubic function. The curve y = f(x) has a minimum point at (a, 0) and a maximum point at (1, b)

Tick one box for each statement.

ABC and ACD are triangles.

Work out the area of triangle ACD.

The equation of a circle is (x – 2)² + (y + 3)² = 16 The equation of a line is y = 4 – x The circle and line intersect at two points, A and B.

Show that the x-coordinates of A and B satisfy the equation 2x² – 18x + 37 = 0

For A, the x-coordinate and y-coordinate are both positive.

Work out the coordinates of A. Give each coordinate to 2 decimal places.

Expand and simplify fully (3 x – 1)(4 – x)(2 x + 5)

P is the point on the graph y = 3 – x that has x-coordinate – 2

Work out the x-coordinate of Q.

Give your answer in the form + x^c where a, b and c are integers.

A solid cone has base radius 7 cm, perpendicular height h cm and slant height l cm

Work out the size of the angle between the slant height and the base.

ABCDEFGH is a cuboid. ABCD is horizontal. MN is vertical. The acute angle between the planes MNB and HDCG is 36°

Work out the length CN.

In the expansion of (3 + ax)⁵ where a is a non-zero constant

Work out the possible values of a.

AB is the tangent to the circle (x – 3)² + (y – 4)² = 29 at the point (5, 9)

Work out the area of triangle A O B.

g(x) = 18x² + 15x

Work out the values of a, b and c.

A, B and C are points on a circle. PAC is a straight line. PB is a tangent to the circle.