AQA Level 2 Certificate Further Maths Paper 1: Non-calculator November 2021 question paper 8365/1

Work out the distance between the points A (– 3, 7) and B (5, 1)

y = x(2x⁴ – 7x³)

Work out an expression for the rate of change of y with respect to x.

Here are four sketch graphs.

Circle the letter of the sketch graph that represents 3 x + 2 y = 5

The function f is given by f(x) = 3 x – 5

Work out the domain of the function.

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

Work out the range of the function.

A term of the sequence has a value of 5

Work out the value of n.

Write down the limiting value of the sequence as n →

Here is a sketch of y = sin x for 0° x 360°

You are given that sin 220 ° = – k

Work out the two values of x for 0° x 360° for which y = k

Solve 2x² + 4 (2x – 3)(x + 1)

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

The first four terms of a quadratic sequence are

0 1 0 – 3

Work out an expression for the n th term.

Work out the values of a and b.

A circle, centre C (4, – 2), passes through the origin and point A (8, 0) on the x-axis. The tangent at A is shown.

Work out the equation of the circle.

Work out the equation of the tangent to the circle at A.

Here is a sketch of y = k^x where k 0

Work out the value of k.

B is a point on the curve with x-coordinate – 1

Work out the y-coordinate of B.

Work out the value of x where 0° x 90° for which 3 tan² x = 1

f(x) = 200x³ + 100x² – 18x – 9

Use the factor theorem to show that (2 x + 1) is a factor of f(x).

Hence solve f(x) = 0

Here is the graph of y = x² − 6x + 5 for values of x between 0 and 6

By drawing a suitable linear graph on the grid, work out approximate solutions to

Here is a triangle.

Use the cosine rule to work out the value of x.

y = f(x) is the graph of a cubic function.

The function is

Draw a possible sketch of y = f(x) for values of x from – 2 to 6

ABC is a triangle. The perpendicular from A meets BC at D.

Work out the length, in cm, of AD.

F, H, K and J are points on a circle. Chords HJ and KF intersect at L. EFG is a tangent to the circle. FH and JK are parallel.

Angle FHJ = 2 x

Give reasons why angle FKJ and angle HJK are also equal to 2 x.

Work out the values of x and y. You must show your working. Do not use trial and improvement.