plumiInequalities: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on D.7 Inequalities, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 15 questions on Inequalities, as a list
- June 2025, Paper 2, Q8 (5 marks): The function f is defined by f ( ) = + − 3 2 12 x x x x ( ) x∈ Figure 1 shows the graph of ( ) f y x = Figure 1 x O y 8 (a) The graph of ( ) f y x = is transfo
- June 2025, AS Paper 1, Q9 (4 marks): Solve the inequality 2x + 1 3x – 9 ≥ x – 1 [4 marks]
- June 2024, Paper 2, Q15 (7 marks): The diagram shows the line y = 5 – x O y x 15 (a) On the diagram above, sketch the graph of y = │x2 – 4x│, including all parts of the graph where it intersects
- June 2024, AS Paper 1, Q10 (6 marks): The curve C has equation y = 2x – 10 3x – 5 Figure 1 shows the curve C with its asymptotes. Figure 1 x 5 y O 2 10 (a) Write down the equations of the asymptotes
- June 2023, Paper 1, Q7 (5 marks): The function f is defined by f (x) = sinx + 1 2 (0 × x × 2 ) Find the set of values of x for which f (x) × 1 2 Give your answer in set notation. [5 marks]
- June 2023, Paper 1, Q11 (7 marks): The function f is defined by f (x) = 4x3 − 8x2 − 51x − 45 (x 2 R) 11 (a) (i) Fully factorise f (x) [2 marks] 11 (a) (ii) Hence, solve the inequality f (x) < 0 [
- June 2023, AS Paper 1, Q14 (4 marks): The inequality (x2 – 5x – 24)(x2 + 7x + a) < 0 has the solution set {x : – 9 < x < – 3} ∩ {x : 2 < x < b} Find the values of integers a and b [4 marks]
- June 2022, Paper 1, Q5 (6 marks): It is given that z = − 3 2 + i 11 p 2 is a root of the equation z4 − 3z3 − 5z2 + kz + 40 = 0 where k is a real number. 5 (a) Find the other three roots. [5 mark
- June 2022, Paper 2, Q7 (8 marks): The function f is defined by f (x) = ax − 5 2x + b x 2 R, x 6= 9 2 where a and b are integers. The graph of y = f (x) has asymptotes x = 9 2 and y = 3 7 (a) Fin
- June 2022, AS Paper 1, Q13 (10 marks): A curve C1 has equation y = 2x + 7 3x + 5 13 (a) Write down the equations of the asymptotes of curve C1 [2 marks] 13 (b) On the axes below, sketch the graph of
- November 2021, AS Paper 1, Q16 (8 marks): Curve C has equation y = ax x + b where a and b are constants. The equations of the asymptotes to C are x = −2 and y = 3 x y y = ax x + b O 16 (a) Write down th
- November 2020, Paper 2, Q5 (5 marks): Solve the inequality 2x + 3 x × 1 × x + 5 [5 marks]
- November 2020, AS Paper 1, Q3 (1 mark): Given (x − 1)(x − 2)(x − a) < 0 and a > 2 Find the set of possible values of x. Tick (3) one box. [1 mark] fx : x < 1g ¨ fx : 2 < x < ag fx : 1 < x < 2g ¨ fx :
- November 2020, AS Paper 1, Q14 (7 marks): (a) Given x + 7 x + 1 × x + 1 show that (x + a)(x + b) x + c × 0 where a, b, and c are integers to be found. [4 marks] 14 (b) Briefly explain why this statement
- June 2019, Paper 2, Q3 (1 mark): The set A is defined by A = fx : −p2 < x < 0g ¨ fx : 0 < x < p2g Which of the inequalities given below has A as its solution? Circle your answer. [1 mark] jx2 −
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