AQA Level 2 Certificate Further Maths Paper 2: Calculator June 2022 question paper 8365/2

Factorise fully 12w + 18w²

M is the midpoint of PQ.

Work out the value of a.

Give your answer as a single matrix.

Line A has equation y + 4 x = 6 Line B is parallel to line A and passes through the point (2, 1) The point (d, 2 d) lies on line B.

Work out the value of d.

Work out all the negative integer values of x for which 3x² 48

Prove algebraically that when n is an integer

How many integers between 200 000 and 400 000 can be formed using only the digits

1 2 3 5 8 9

with no repetition of any digit?

A curve has equation y = x³ – 5x² At two points on the curve, the rate of change of y with respect to x is 4

Work out an equation, in terms of x, to represent this information. Give your answer in the form ax² + bx + c = 0 where a, b and c are integers.

Hence, work out the two possible values of x. Give your answers to 3 significant figures.

Work out an expression, in terms of k, for the 4th term. Give your answer in its simplest form.

The 100th term of the sequence is 525

Work out the value of k.

Here is a right-angled triangle.

You are given that a 5

Use trigonometry to work out the range of values of x.

at the point where x = – 1 You must show your working.

A (– 2, 5) and B (4, 13) are points on a circle. AB is a diameter.

Work out the equation of the circle. Give your answer in the form (x – a)² + (y – b)² = c where a, b and c are integers.

PQRS is a cyclic quadrilateral.

Angle PSR = 4(x + 15 °) Angle PQR is 40 ° smaller than angle PSR.

Work out the value of x.

Here is an isosceles triangle. All the angles are acute.

Work out the size of angle y.

ABCDEFGH is a cuboid.

AB = 40 cm BC = 9 cm CG = 20 cm P is a point on HG such that HP: PG = 3: 7 AP = 25 cm

Work out the size of angle APC.

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

f(x) = 2x³ + 11x² + 12x – 9

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

Show that f(x) = 0 has exactly two solutions.

Work out the values of x between 0° and 360° for which

Give your answers to 1 decimal place. You must show your working.

Using powers of 2 or otherwise, work out the non-zero value of x for which

You must show your working.