plumiInequalities: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on A22 Inequalities, 2017–2025, with its mark scheme and examiner’s report.
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All 35 questions on Inequalities, as a list
- June 2025, Paper 1H, Q2 (2 marks): 1.07 < 9 x < 1.17 where x is an integer. Work out the value of x. x =
- June 2025, Paper 2H, Q20 (1 mark): David has solved the inequality x2 < 16 and represented his solution on the number line below. Give one reason why David’s solution is wrong.
- June 2025, Paper 3H, Q19 (4 marks): On the grid, identify the region represented by x + y < 5 and y < 2x + 4 and y ⩾ 1 Label the region R.
- June 2025, Paper 3H, Q22 (4 marks): Solve 2x2 > 12 – 5x Answer
- November 2024, Paper 1H, Q15 (4 marks): (a) Solve the inequality 20 – 5x ⩽ 30 Answer 15 (b) Represent x > –1 on the number line.
- June 2024, Paper 1H, Q10 (3 marks): (a) Represent –2 < x < 4 on the number line. 10 (b) Solve 5y + 14 ⩾ 11 Answer
- November 2023, Paper 1H, Q17 (3 marks): x and y are integers. 8 ⩽ 4x ⩽ 20 and y – 3x < 12 Work out the largest possible value of y. Answer
- November 2023, Paper 1H, Q27 (1 mark): Write down the solution of x2 < 16 Answer
- November 2023, Paper 3H, Q23 (4 marks): A chocolate box in the shape of a prism is being designed. All lengths are in centimetres. The cross section is a regular hexagon with side x The length is 5x A
- June 2023, Paper 1H, Q2 (1 mark): Solve 2x < 26 Answer 2
- June 2023, Paper 1H, Q18 (1 mark): 6 < x 3 < 7 Circle the possible value of x. 1.9 20 45 290
- November 2022, Paper 1H, Q9 (2 marks): Work out all the integer values of x for which 12 ⩽ 4x < 25 Answer
- November 2022, Paper 1H, Q25 (3 marks): (a) Solve x2 – 5x – 6 < 0 Answer 25 (b) Show the solution to x2 – 5x – 6 < 0 on the number line.
- June 2022, Paper 1H, Q23 (3 marks): On the grid, identify the region represented by x > 3 and y > 1 and x + y ⩽ 7 Label the region R.
- June 2022, Paper 2H, Q4 (1 mark): Circle the inequality represented by the diagram. –5 < x < 1 –5 < x ⩽ 1 –5 ⩽ x < 1 5 ⩽ x ⩽ 1
- November 2021, Paper 1H, Q8 (5 marks): (a) Solve 5x + 6 > 3x + 15 Answer 8 (b) Write down the inequality represented by the number line. Answer
- November 2021, Paper 2H, Q18 (3 marks): On the grid, identify the region represented by x ⩽ 5 y ⩽ 4 x + y > 6 Label the region R.
- November 2021, Paper 3H, Q17 (1 mark): m2 > 9 Circle the possible value of m. –2 8 7 2.8 3 – 2 7
- November 2020, Paper 3H, Q15 (2 marks): Solve 4 > 11 – 3 x Answer
- November 2020, Paper 3H, Q19 (1 mark): The sketch shows the lines x = 1 and y = –3 Which pair of inequalities describes the shaded region? Tick one box. x < 1 and y < –3 x < 1 and y > –3 x > 1 and y
- November 2019, Paper 2H, Q24 (3 marks): Here are two inequalities. –2 ⩽ x ⩽ 3 9 ⩽ x + y ⩽ 11 x and y are integers. Work out the greatest possible value of y – x Answer
- June 2019, Paper 2H, Q10 (3 marks): x is an integer. –4 < x ⩽ 2 and 2 ⩽ x + 3 < 9 Work out all the possible values of x. Answer
- June 2019, Paper 2H, Q24 (3 marks): Here is a sketch of the curve y = x2 + 4x – 12 Work out the values of x for which x2 + 4x – 12 < 0 Give your answer as an inequality. Answer
- November 2018, Paper 3H, Q10 (2 marks): Solve 8 > 3 – 1 2 x Answer
- June 2018, Paper 1H, Q5 (2 marks): Solve 5(x + 3) < 60 Answer
- June 2018, Paper 3H, Q2 (1 mark): Circle the list of all the integers that satisfy –2 < x ⩽ 4 –2, –1, 0, 1, 2, 3 –1, 0, 1, 2, 3 –2, –1, 0, 1, 2, 3, 4 –1, 0, 1, 2, 3, 4
- November 2017, Paper 1H, Q5 (3 marks): (a) Factorise x2 – 100 Answer 5 (b) Solve 7x + 6 > 1 + 2x Answer
- November 2017, Paper 3H, Q1 (1 mark): Circle the inequality shown by the diagram. –4 ⩽ x < 5 –4 ⩽ x ⩽ 5 –4 < x < 5 –4 < x ⩽ 5
- November 2017, Paper 3H, Q23 (2 marks): Joe draws this graph to identify the region R represented by y ⩽ x + 2 and y > 3 – x and x < 3 Make two criticisms of his graph. Criticism 1 Criticism 2
- November 2017, Paper 3H, Q29 (2 marks): Here is the graph of y = f(x) where f(x) is a quadratic function. Write down all the integer solutions of f(x) ⩾ 0 Answer
- June 2017, Paper 1H, Q14 (1 mark): Solve –3x > 6 Answer
- June 2017, Paper 3H, Q6 (2 marks): How are the whole number solutions to A and B different? A Solve 3 ⩽ 3x < 18 B Solve 3 < 3x ⩽ 18
- June 2017, Paper 3H, Q21 (1 mark): Here is a sketch of y = f(x) where f(x) is a quadratic function. The graph intersects the x-axis where x = –2.5 and x = 1 Not drawn accurately Circle the soluti
- Specimen, Paper 1H, Q8 (2 marks): Solve 5x – 2 > 3x + 11 Answer
- Specimen, Paper 3H, Q19 (4 marks): Here are two function machines, A and B. square add 6 Input Output A subtract 3 square Input Output B Both machines have the same input. Work out the range of i
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