plumiLinear and quadratic equations: AQA Level 2 Further Maths questions
Every AQA Level 2 Further Maths exam question on 2.14 Linear and quadratic equations, 2021–2025, with its mark scheme and examiner’s report.
Paper
All papers
Exam
All years
Calculator
All 32 questions on Linear and quadratic equations, as a list
- June 2025, Paper 1, Q11 (4 marks): Solve x3 + 10x2 + 8x = 0 Where appropriate give your answers in surd form. Simplify your answers where possible. Answer
- June 2025, Paper 2, Q9 (2 marks): f(x) = x2 + px x ⩽ 1 = 2p – 2 1 x x > 1 A sketch of y = f(x) is shown. Work out the value of p. p =
- June 2025, Paper 2, Q14 (5 marks): All lengths shown are in centimetres. 14 (a) Use Pythagoras’ theorem to show that 4w2 – 8w – 21 = 0 14 (b) Work out the size of angle x. x = °
- June 2025, Paper 2, Q19 (4 marks): f(x) = 4x3 – 7 g(x) = 6x + 8 Work out the value of x for which f(2x) = gf(x) x =
- June 2024, Paper 1, Q8 (3 marks): Solve by factorising 2x3 – 9x2 – 5x = 0 Answer
- June 2024, Paper 1, Q14 (4 marks): (a) Write 2x2 – 16x + 7 in the form k(x + m)2 + n where k, m and n are integers. Answer 14 (b) Solve (x – 1)2 – 5 = 0 Answer
- June 2024, Paper 1, Q20 (4 marks): Here is the graph of y = −x2 + 3x + 6 for −2 ⩽ x ⩽ 5 By drawing a suitable straight line, work out approximate solutions to x2 − x 7 2 − 3 = 0 Answer
- June 2024, Paper 1, Q21 (5 marks): ( ) + + = x x x− 4 1 3 1 2 8 Work out the possible values of x. Answer
- June 2024, Paper 2, Q12 (6 marks): 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. 12 (a) Show that
- June 2024, Paper 2, Q19 (4 marks): In the expansion of (3 + ax)5 where a is a non-zero constant 8 × coefficient of x2 = coefficient of x4 Work out the possible values of a. Answer
- June 2023, Paper 1, Q15 (4 marks): Solve – x x 2 1 3 2 2 = x2 + x Answer
- June 2023, Paper 2, Q1 (3 marks): Solve 8 3 3 7 d d − − = 5 2 d =
- June 2023, Paper 2, Q16 (4 marks): (2x – 3) is a factor of 6x3 – 25x2 + 28x – 6 Solve 6x3 – 25x2 + 28x – 6 = 0 Give all solutions as exact values. Answer
- June 2023, Paper 2, Q21 (4 marks): A, B, C, D and E are points on a circle, centre O. Work out the value of x. x =
- June 2022, Paper 1, Q1 (3 marks): (x + 1) is increased by 20% Its value is now the same as (x + 6) Work out the value of x. Answer
- June 2022, Paper 2, Q8 (4 marks): 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 8 (a) Work out an equation, in terms of x, to repre
- June 2022, Paper 2, Q14 (3 marks): PQRS is a cyclic quadrilateral. Angle PSR = 4(x + 15°) Angle PQR is 40° smaller than angle PSR. Work out the value of x. Answer degrees
- June 2022, Paper 2, Q20 (6 marks): f(x) = 2x3 + 11x2 + 12x – 9 20 (a) Use the factor theorem to show that (2x – 1) is a factor of f(x). 20 (b) Show that f(x) = 0 has exactly two solutions.
- November 2021, Paper 1, Q16 (5 marks): f(x) = 200x3 + 100x2 – 18x – 9 16 (a) Use the factor theorem to show that (2x + 1) is a factor of f(x). 16 (b) Hence solve f(x) = 0 Answer
- November 2021, Paper 1, Q17 (3 marks): 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 x2 − 7x +
- November 2021, Paper 1, Q18 (4 marks): Here is a triangle. Use the cosine rule to work out the value of x. Answer
- November 2021, Paper 1, Q23 (6 marks): 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. 23 (a) Angle FHJ = 2x Give reason
- November 2021, Paper 2, Q2 (4 marks): (a) 5m is decreased by 40% The answer is (m + 1) Work out the value of m. Answer 2 (b) Solve – w 3 2 10 = 18 w =
- November 2021, Paper 2, Q8 (4 marks): A function f is given by f(x) = 4x x < 0 = x2 – 8x 0 ⩽ x ⩽ 8 = 16 – 2x x > 8 A sketch of y = f(x) is shown. Work out all the values of x for which f(x) = –12 An
- November 2021, Paper 2, Q10 (3 marks): The radius of a sphere, in cm, is k 3 2 The volume of the sphere, in cm3, is 972π Work out the value of k. Volume of a sphere = 4 3 πr3 where r is the radius An
- November 2021, Paper 2, Q16 (3 marks): The coefficient of x4 in the expansion of (a + 2x)6 is 1500 Work out the two possible values of a. Answer and
- November 2021, Paper 2, Q21 (6 marks): 3x2 + 2bx + 8a can be written in the form 3(x + a)2 + b + 2 Work out the two possible pairs of values of a and b. a = b = a = b =
- Specimen, Paper 1, Q2 (2 marks): Solve 3 7 13 x − = 2 x =
- Specimen, Paper 1, Q3 (4 marks): 3a(2x – 1) + 4(ax + 5) ≡ 60x + b Work out the values of a and b.
- Specimen, Paper 1, Q10 (5 marks): f(x) = x − 1 9 2 g(x) = 3 1 px − where p is a constant. Given that 1 f 3 = 1 g 3 work out the value of p. Answer
- Specimen, Paper 2, Q11 (4 marks): For sequence A, nth term = 30 14 + n n For sequence B, nth term = n 2 The kth term of sequence A equals the kth term of sequence B. Work out the value of k. You
- Specimen, Paper 2, Q17 (4 marks): By multiplying both sides of the equation by x 1 2 Solve x x x − − = 3 1 1 2 2 2 2 3 7 for x > 0 Give your answer to 3 significant figures. You must show your w
Questions, mark schemes and examiner’s reports are © AQA, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every AQA Level 2 Further Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.