plumiInequalities: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on B.5 Inequalities, 2018–2025, 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 9 questions on Inequalities, as a list
- June 2025, Paper 2, Q3 (1 mark): The diagram shows the graph with equation y = (x + 2)(x – 7) x 7 O –2 y Solve the inequality. (x + 2)(x – 7) > 0 Tick (✓) one box. [1 mark] x ∈ (–∞, –2) ∩ (7, ∞
- June 2025, Paper 3, Q5 (2 marks): The diagram shows the graphs of y = 2x and y = (x – 3)(x + 4). x y O 3 – 4 The region R is defined by the inequalities (x – 3)(x + 4) ≤ y ≤ 2x and x ≤ 0 Shade t
- June 2024, Paper 2, Q3 (1 mark): Solve the inequality (1 – x)(x – 4) < 0 [1 mark] Tick (✓) one box. {x : x < 1} ∩ {x : x > 4} {x : x < 1} ∩ {x : x > 4} {x : x < 1} ∩ {x : x ≥ 4} {x : x < 1} ∩ {
- June 2024, Paper 2, Q14 (3 marks): The displacement, r metres, of a particle at time t seconds is r = 6t – 2t 2 14 (a) Find the value of r when t = 4 [1 mark] 14 (b) Determine the range of values
- June 2024, Paper 3, Q7 (5 marks): The graphs with equations y = 2 + 3x – 2x2 and x + y = 1 are shown in the diagram below. The graphs intersect at the points A and B 7 (a) On the diagram above,
- June 2023, Paper 2, Q1 (1 mark): The graph of y = ax2 + bx + c has roots x = 2 and x = 5 , as shown in the diagram below. O 5 2 y x State the set of values of x which satisfy ax2 + bx + c > 0 T
- November 2021, Paper 1, Q1 (1 mark): State the set of values of x which satisfies the inequality (x − 3)(2x + 7) > 0 Tick (3) one box. [1 mark] x : − 7 2 < x < 3 x : x < −3 or x > 7 2 x : x < − 7 2
- June 2019, Paper 3, Q4 (3 marks): Sketch the region defined by the inequalities y × (1 − 2x)(x + 3) and y − x × 3 Clearly indicate your region by shading it in and labelling it R. [3 marks] x y
- June 2018, Paper 2, Q4 (6 marks): A curve, C, has equation y = x2 − 6x + k , where k is a constant. The equation x2 − 6x + k = 0 has two distinct positive roots. 4 (a) Sketch C on the axes below
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