AQA Level 2 Certificate Further Maths Paper 1: Non-calculator June 2022 question paper 8365/1

(x + 1) is increased by 20% Its value is now the same as (x + 6)

Work out the value of x.

The point (–6, –4) lies on a straight line with gradient

Work out the coordinates of the point where the line crosses the y-axis.

g(x) = 6 – 3 x

Circle the value of tan² 30° 4 (a)

On the axes, sketch

(3x a)(5x 4) 15x² 2x b

Work out the values of a and b.

Work out the length of BC.

Use matrix multiplication to show that, in the x - y plane,

• a rotation, 90° anticlockwise about the origin, followed by

• a reflection in the line y = x

is equivalent to a reflection in the x-axis.

A quadratic sequence starts – 2 – 1 4 13

Work out an expression for the n th term.

A different quadratic sequence has nth term n² + 10n

Use an algebraic method to work out how many terms in the sequence are less than 2000 Do not use trial and improvement. You must show your working.

Expand and simplify fully (3 + 2x)⁵

One term in the sequence is

Work out the value of n.

Write down the limiting value of the sequence as n →

Simplify fully (6x³y^–2 + 9x⁵y) ÷ 3x²y^–3

Rearrange ef = to make e the subject.

B, C and D are points on a circle, centre P. AB and AC are tangents to the circle.

Solve the simultaneous equations

xy = – 3

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

The point P lies on the circle x² + y² = 16 The line O P is at an angle of 60 ° to the positive x - axis.

Show that the coordinates of point P are (2, 2

Work out the equation of the tangent to the circle at P. Write your answer in the form x + ay = b where a and b are constants.

In triangle RST RS: ST = 1: 4

Work out the exact value of sin θ.

Write 6x² – 24x + 17 in the form a(x + b)² + c where a, b and c are integers.

The curve y = x⁴ – 18x² has three stationary points.

Work out the coordinates of the three stationary points and determine their nature. You must show your working.