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Inequalities: Edexcel GCSE Maths questions

Every Edexcel GCSE Maths exam question on A22 Inequalities, 2017–2025, with its mark scheme and examiner’s report.

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997 questions

  1. Q7

    June 2025 · Paper 1H

    6 marksA22 InequalitiesA4 Simplifying, expanding and factorising
    The whole paper ↗
    June 2025 Paper 1H, question 7: (a) Simplify 3 2 m 2 m x – 8 (b) Solve 7 + x  5 2 (c) Solve 9 < 2y + 4 < 12

  2. Q15

    June 2025 · Paper 2H

    5 marksA22 Inequalities
    The whole paper ↗
    June 2025 Paper 2H, question 15: (a) On the grid, show by shading, the region that satisfies all of these inequalities. x + y < 5 y > 1 x > 2 y < 3x – 2 Label the region R. y 6 4 2 x O –6 –4 –2

  3. Q21

    June 2025 · Paper 2H

    2 marksA22 Inequalities
    The whole paper ↗
    June 2025 Paper 2H, question 21: Solve (3x – 1)(5x + 2) < 0

  4. Q13

    June 2024 · Paper 2H

    3 marksA22 Inequalities
    The whole paper ↗
    June 2024 Paper 2H, question 13: y 6 5 4 3 2 1 x O –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 On the grid, shade the region R that satisfies all the following inequalities. x  2 y  –3 y

  5. Q16

    June 2024 · Paper 2H

    2 marksA22 Inequalities
    The whole paper ↗
    June 2024 Paper 2H, question 16: Solve (4x – 3) (x + 5) < 0

  6. Q17

    November 2023 · Paper 1H

    4 marksA22 InequalitiesA4 Simplifying, expanding and factorising
    The whole paper ↗
    November 2023 Paper 1H, question 17: (a) Factorise 6x2 – 5x – 4 (b) Hence, or otherwise, solve 6x2 – 5x – 4 < 0

  7. Q4

    November 2023 · Paper 3H

    4 marksA22 Inequalities
    The whole paper ↗
    November 2023 Paper 3H, question 4: Jenna is asked to show the inequality –3 < x  4 on a number line. Here is her answer. x –5 –4 –3 –2 –1 0 1 2 3 4 5 (a) Write down two mistakes Jenna has made.

  8. Q24

    June 2023 · Paper 1H

    5 marksA22 Inequalities
    The whole paper ↗
    June 2023 Paper 1H, question 24: Find the set of possible values of x for which 2 – 25 < 0 and 12 – 5x – 3x 2 > 0 4x You must show all your working.

  9. Q4

    June 2023 · Paper 2H

    6 marksA22 Inequalities
    The whole paper ↗
    June 2023 Paper 2H, question 4: –2  n < 5 n is an integer. (a) Write down the greatest possible value of n. (b) On the number line below, show the inequality –4  m < 1 m –6 –5 –4 –3 –2 –1 0

  10. Q16

    November 2022 · Paper 2H

    4 marksA22 Inequalities
    The whole paper ↗
    November 2022 Paper 2H, question 16: The shaded region shown on the grid is bounded by four straight lines. y 6 4 2 O x −6 −4 −2 2 4 6 −2 −4 −6 Find the four inequalities that define the shaded reg

  11. Q11

    November 2022 · Paper 3H

    2 marksA22 InequalitiesN1 Ordering numbers
    The whole paper ↗
    November 2022 Paper 3H, question 11: x and y are integers such that 3 < x < 8 4 < y < 10 and x + y = 14 Find all the possible values of x.

  12. Q1

    June 2022 · Paper 1H

    2 marksA22 Inequalities
    The whole paper ↗
    June 2022 Paper 1H, question 1: Solve 7x − 27 < 8

  13. Q22

    June 2022 · Paper 2H

    5 marksA22 Inequalities
    The whole paper ↗
    June 2022 Paper 2H, question 22: Find algebraically the set of values of x for which x2 − 49 > 0 and 5x2 − 31x − 72 > 0

  14. Q17

    November 2021 · Paper 1H

    3 marksA22 Inequalities
    The whole paper ↗
    November 2021 Paper 1H, question 17: On the grid show, by shading, the region that satisfies all of these inequalities. 2y + 4 < x x < 3 y < 6 – 3x Label the region R. y 6 5 4 3 2 1 O x –6 –5 –4 –3

  15. Q1

    November 2021 · Paper 2H

    3 marksA22 Inequalities
    The whole paper ↗
    November 2021 Paper 2H, question 1: (a) Write down the inequality shown on this number line. x –5 –4 –3 –2 –1 0 1 2 3 4 5 (b) On the number line below, show the inequality –3  y < 4 y –5 –4 –3 –2

  16. Q1

    November 2020 · Paper 3H

    5 marksN7 Laws of indicesA22 Inequalities
    The whole paper ↗
    November 2020 Paper 3H, question 1: (a) Simplify n3 × n5 . (b) Simplify c d 3 4 c d 2 . x > 7 (c) Solve 5 2

  17. Q13

    November 2020 · Paper 3H

    5 marksA22 Inequalities
    The whole paper ↗
    November 2020 Paper 3H, question 13: (a) On the grid show, by shading, the region that satisfies all these inequalities. x  0 x  2 y  x + 3 2x + 3y  6 Label the region R. y 8 7 6 5 4 3 2 1 −3 −

  18. Q23

    November 2019 · Paper 2H

    6 marksA22 InequalitiesG23 Area of a triangle (½ab sin C)
    The whole paper ↗
    November 2019 Paper 2H, question 23: The diagram shows a parallelogram. (2x 150° x) cm The area of the parallelogram is greater than 15 cm2 (a) Show that 2x2 – 21x + 40 0 (b) Find the range of poss

  19. Q1

    June 2019 · Paper 2H

    5 marksA22 Inequalities
    The whole paper ↗
    June 2019 Paper 2H, question 1: (a) Solve 14n 11n + 6 (b) On the number line below, show the set of values of x for which –2 x + 3 - 4 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

  20. Q18

    June 2019 · Paper 3H

    6 marksA4 Simplifying, expanding and factorisingA22 Inequalities
    The whole paper ↗
    June 2019 Paper 3H, question 18: (a) Show that (2x  1)(x  3)(3x  7) can be written in the form ax3  bx2  cx  d where a, b, c and d are integers. 9 2 ( ) (b) Solve 1 x − 25
All 26 questions on Inequalities, as a list
  1. June 2025, Paper 1H, Q7 (6 marks): (a) Simplify 3 2 m 2 m x – 8 (b) Solve 7 + x  5 2 (c) Solve 9 < 2y + 4 < 12
  2. June 2025, Paper 2H, Q15 (5 marks): (a) On the grid, show by shading, the region that satisfies all of these inequalities. x + y < 5 y > 1 x > 2 y < 3x – 2 Label the region R. y 6 4 2 x O –6 –4 –2
  3. June 2025, Paper 2H, Q21 (2 marks): Solve (3x – 1)(5x + 2) < 0
  4. June 2024, Paper 2H, Q13 (3 marks): y 6 5 4 3 2 1 x O –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 On the grid, shade the region R that satisfies all the following inequalities. x  2 y  –3 y
  5. June 2024, Paper 2H, Q16 (2 marks): Solve (4x – 3) (x + 5) < 0
  6. November 2023, Paper 1H, Q17 (4 marks): (a) Factorise 6x2 – 5x – 4 (b) Hence, or otherwise, solve 6x2 – 5x – 4 < 0
  7. November 2023, Paper 3H, Q4 (4 marks): Jenna is asked to show the inequality –3 < x  4 on a number line. Here is her answer. x –5 –4 –3 –2 –1 0 1 2 3 4 5 (a) Write down two mistakes Jenna has made.
  8. June 2023, Paper 1H, Q24 (5 marks): Find the set of possible values of x for which 2 – 25 < 0 and 12 – 5x – 3x 2 > 0 4x You must show all your working.
  9. June 2023, Paper 2H, Q4 (6 marks): –2  n < 5 n is an integer. (a) Write down the greatest possible value of n. (b) On the number line below, show the inequality –4  m < 1 m –6 –5 –4 –3 –2 –1 0
  10. November 2022, Paper 2H, Q16 (4 marks): The shaded region shown on the grid is bounded by four straight lines. y 6 4 2 O x −6 −4 −2 2 4 6 −2 −4 −6 Find the four inequalities that define the shaded reg
  11. November 2022, Paper 3H, Q11 (2 marks): x and y are integers such that 3 < x < 8 4 < y < 10 and x + y = 14 Find all the possible values of x.
  12. June 2022, Paper 1H, Q1 (2 marks): Solve 7x − 27 < 8
  13. June 2022, Paper 2H, Q22 (5 marks): Find algebraically the set of values of x for which x2 − 49 > 0 and 5x2 − 31x − 72 > 0
  14. November 2021, Paper 1H, Q17 (3 marks): On the grid show, by shading, the region that satisfies all of these inequalities. 2y + 4 < x x < 3 y < 6 – 3x Label the region R. y 6 5 4 3 2 1 O x –6 –5 –4 –3
  15. November 2021, Paper 2H, Q1 (3 marks): (a) Write down the inequality shown on this number line. x –5 –4 –3 –2 –1 0 1 2 3 4 5 (b) On the number line below, show the inequality –3  y < 4 y –5 –4 –3 –2
  16. November 2020, Paper 3H, Q1 (5 marks): (a) Simplify n3 × n5 . (b) Simplify c d 3 4 c d 2 . x > 7 (c) Solve 5 2
  17. November 2020, Paper 3H, Q13 (5 marks): (a) On the grid show, by shading, the region that satisfies all these inequalities. x  0 x  2 y  x + 3 2x + 3y  6 Label the region R. y 8 7 6 5 4 3 2 1 −3 −
  18. November 2019, Paper 2H, Q23 (6 marks): The diagram shows a parallelogram. (2x 150° x) cm The area of the parallelogram is greater than 15 cm2 (a) Show that 2x2 – 21x + 40 0 (b) Find the range of poss
  19. June 2019, Paper 2H, Q1 (5 marks): (a) Solve 14n 11n + 6 (b) On the number line below, show the set of values of x for which –2 x + 3 - 4 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
  20. June 2019, Paper 3H, Q18 (6 marks): (a) Show that (2x  1)(x  3)(3x  7) can be written in the form ax3  bx2  cx  d where a, b, c and d are integers. 9 2 ( ) (b) Solve 1 x − 25
  21. November 2018, Paper 2H, Q19 (5 marks): Solve 22 32 4 Show all your working.
  22. June 2018, Paper 1H, Q20 (5 marks): n is an integer such that 3n + 2 - 14 and > 1 n + 2 5 Find all the possible values of n.
  23. November 2017, Paper 1H, Q23 (5 marks): Here is a rectangle and a right-angled triangle. 3x – 2 2x x – 1 x All measurements are in centimetres. The area of the rectangle is greater than the area of th
  24. November 2017, Paper 2H, Q14 (3 marks): is 3 marks)
  25. June 2017, Paper 3H, Q13 (4 marks): y 4 3 2 1 –6 –4 –2 O 2 4 6 x –1 –2 –3 –4 Write down the three inequalities that define the shaded region.
  26. June 2017, Paper 3H, Q19 (3 marks): Solve 2x2 + 3x – 2 

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