Inequalities: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 2.8 Inequalities, 2019–2025, with its mark scheme and examiner’s report.

All 77 questions on Inequalities, as a list

June 2025 (R), Paper 1 Foundation, Q21 (4 marks): x −3 −2 0 1 2 3 −1 (a) Write down the inequality shown on the number line.  (b) Solve the inequality 7 a 5 3 a 28 Show clear algebraic working.
June 2025 (R), Paper 1 Higher, Q6 (4 marks): x −3 −2 0 1 2 3 −1 (a) Write down the inequality shown on the number line.  (b) Solve the inequality 7 a 5 3 a 28 Show clear algebraic working.
June 2025 (R), Paper 2 Higher, Q21 (3 marks): Solve the inequality 2 x x 2 7 15 0 Show clear algebraic working.
June 2025, Paper 1 Higher, Q16 (4 marks): f (x) = 9 – x where x  0 2 g (x) = 4x (a) Find f (b) Solve fg (x) < 0 Show clear algebraic working.
June 2025, Paper 2 Foundation, Q26 (5 marks): (a) Solve the inequality 7 – 3t < 2t + 15 The region R, shown shaded in the diagram, is bounded by three straight lines. y 10 9 8 7 6 5 R 4 3 2 1 x O 1 2 3 4 5
June 2025, Paper 2 Higher, Q9 (5 marks): (a) Solve the inequality 7 – 3t < 2t + 15 The region R, shown shaded in the diagram, is bounded by three straight lines. y 10 9 8 7 6 5 R 4 3 2 1 O x 1 2 3 4 5
June 2025, Paper 2 Higher, Q19 (3 marks): Solve the inequality 4 x 2 x 4 15 0 Show clear algebraic working.
November 2024, Paper 1 Foundation, Q25 (6 marks): (a) (i) Factorise x x 2 5 24 (ii) Hence, solve x 5 x 24 0 2 (b) Solve the inequality 3 y y 5 7 10 Show clear algebraic working.
November 2024, Paper 1 Higher, Q8 (6 marks): (a) (i) Factorise x x 2 5 24 (ii) Hence, solve x 2 5 x 24 0 (b) Solve the inequality 3 y y 5 7 10 Show clear algebraic working.
November 2024, Paper 2 Foundation, Q23 (4 marks): (a) On the grid, draw the straight line with equation (i) x = 3 (ii) y = 1 (iii) x y 7 Label each line with its equation. y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 8
November 2024, Paper 2 Higher, Q7 (4 marks): (a) On the grid, draw the straight line with equation (i) x = 3 (ii) y = 1 (iii) x y 7 Label each line with its equation. y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 8
November 2024, Paper 2 Higher, Q20 (3 marks): Solve the inequality 10 x x 2 11 21 0 Show clear algebraic working.
June 2024 (R), Paper 2 Higher, Q20 (4 marks): Solve 6 x x 2 7 20 0 Show clear algebraic working.
June 2024, Paper 2 Foundation, Q18 (4 marks): (a) On the grid, draw the straight line with equation (i) y = 2 (ii) x = 6 (iii) y = x + 1 Label each line with its equation. y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6
June 2024, Paper 2 Higher, Q2 (4 marks): (a) On the grid, draw the straight line with equation (i) y = 2 (ii) x = 6 (iii) y = x + 1 Label each line with its equation. y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6
June 2024, Paper 2 Higher, Q15 (7 marks): (a) Make g the subject of e = g 11 + 2 (b) Solve the inequality 3y 2 + 4y – 32 > 0 Show your working clearly.
November 2023, Paper 1 Foundation, Q22 (5 marks): (a) Solve the inequality 8 x − x − 4 3 10 The region R, shown shaded in the diagram, is bounded by three straight lines. y 9 8 7 6 5 4 R 3 2 1 O x 1 2 3 4 5 6 7
November 2023, Paper 1 Higher, Q8 (5 marks): (a) Solve the inequality 8 x − x − 4 3 10 The region R, shown shaded in the diagram, is bounded by three straight lines. y 9 8 7 6 5 4 R 3 2 1 O x 1 2 3 4 5 6 7
November 2023, Paper 2 Foundation, Q12 (6 marks): (a) Expand x(x + 3) (b) Factorise 8p + 10 (c) Make e the subject of y = eh ‒ f Janya thinks of a whole number. She calls her whole number w Janya writes down th
June 2023 (R), Paper 2 Foundation, Q23 (5 marks): (a) Solve 9 – 4x > 17 y 8 7 6 5 4 R 3 2 1 O 1 2 3 4 5 6 7 8 9 10 x (b) Write down the three inequalities that represent the shaded region R
June 2023 (R), Paper 2 Higher, Q8 (5 marks): (a) Solve 9 – 4x > 17 y 8 7 6 5 4 R 3 2 1 O 1 2 3 4 5 6 7 8 9 10 x (b) Write down the three inequalities that represent the shaded region R
June 2023, Paper 1 Foundation, Q22 (4 marks): y 9 8 7 6 5 4 3 2 1 R –4 –3 –2 –1 O 1 2 3 4 5 x –1 –2 –3 The region R, shown shaded in the diagram, is bounded by three straight lines. Find the inequalities th
June 2023, Paper 1 Higher, Q7 (4 marks): y 9 8 7 6 5 4 3 2 1 R –4 –3 –2 –1 O 1 2 3 4 5 x –1 –2 –3 The region R, shown shaded in the diagram, is bounded by three straight lines. Find the inequalities th
January 2023 (R), Paper 2 Foundation, Q17 (3 marks): –8 < 2y  2 y is an integer. (a) Find all the possible values of y (b) Write down the inequality shown on the number line. x –5 –4 –3 –2 –1 0 1 2 3 4 5
January 2023 (R), Paper 2 Higher, Q3 (3 marks): –8 < 2y  2 y is an integer. (a) Find all the possible values of y (b) Write down the inequality shown on the number line. x –5 –4 –3 –2 –1 0 1 2 3 4 5
January 2023, Paper 1 Foundation, Q25 (6 marks): (a) Factorise y2 – 2y – 48 (b) Write down the inequality shown on the number line x –2 –1 0 1 2 3 4 5 (c) Solve the inequality 7w + 6 > 12w + 14
January 2023, Paper 1 Higher, Q10 (6 marks): (a) Factorise y2 – 2y – 48 (b) Write down the inequality shown on the number line x –2 –1 0 1 2 3 4 5 (c) Solve the inequality 7w + 6 > 12w + 14
January 2023, Paper 1 Higher, Q11 (3 marks): y 8 7 6 5 4 3 2 R 1 x – 3 – 2 – 1 1 2 3 4 5 6 O – 1 – 2 – 3 – 4 The region R, shown shaded in the diagram, is bounded by the straight lines with equations 2x +
January 2023, Paper 2 Higher, Q22 (3 marks): Solve the inequality 6x2 + 37x  35 Show clear algebraic working. for Question 23
June 2022 (R), Paper 1 Foundation, Q25 (2 marks): Solve the inequality 3 – 4x  11
June 2022 (R), Paper 1 Higher, Q9 (2 marks): Solve the inequality 3 – 4x  11
June 2022 (R), Paper 2 Higher, Q19 (4 marks): f(x) = x 2 – 4 g(x) = 2x + 1 Solve fg(x) > 0 Show clear algebraic working.
June 2022, Paper 2 Foundation, Q18 (4 marks): (a) On the grid, draw and label with its equation the straight line with equation (i) y = 1 (ii) x = 2 (iii) x + y = 7 y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 8 (b)
June 2022, Paper 2 Higher, Q2 (4 marks): (a) On the grid, draw and label with its equation the straight line with equation (i) y = 1 (ii) x = 2 (iii) x + y = 7 y 8 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 8 (b)
June 2022, Paper 2 Higher, Q15 (7 marks): (a) Solve 4 5 3 2 − = 13 3 2 Show clear algebraic working. x = (b) Solve the inequality 2y2 − 7y − 30  0 Show your working clearly.
January 2022 (R), Paper 1 Foundation, Q15 (3 marks): n is an integer. (a) Write down all the values of n such that –2  n < 3 (b) On the number line, represent the inequality y  1 y –3 –2 –1 0 1 2 3
January 2022 (R), Paper 1 Higher, Q1 (3 marks): n is an integer. (a) Write down all the values of n such that –2  n < 3 (b) On the number line, represent the inequality y  1 y –3 –2 –1 0 1 2 3
January 2022 (R), Paper 2 Foundation, Q20 (5 marks): (a) Solve 4y + 5 > 12 x 4 7 (b) Solve 6 x 5 2 Show clear algebraic working. x =
January 2022 (R), Paper 2 Foundation, Q24 (5 marks): (a) Write down an equation of the straight line with gradient –3 and which passes through the point with coordinates (0, 5) (b) Show, by shading on the grid, th
January 2022 (R), Paper 2 Higher, Q3 (5 marks): (a) Solve 4y + 5 > 12 x 4 7 (b) Solve 6 x 5 2 Show clear algebraic working. x =
January 2022 (R), Paper 2 Higher, Q7 (5 marks): (a) Write down an equation of the straight line with gradient –3 and which passes through the point with coordinates (0, 5) (b) Show, by shading on the grid, th
January 2022, Paper 1 Foundation, Q21 (5 marks): (a) Solve the inequality 5x – 7  2 (b) (i) Factorise y2 – 2y – 35 (ii) Hence, solve y2 – 2y – 35 = 0
January 2022, Paper 1 Higher, Q6 (5 marks): (a) Solve the inequality 5x – 7  2 (b) (i) Factorise y2 – 2y – 35 (ii) Hence, solve y2 – 2y – 35 = 0
January 2022, Paper 2 Higher, Q13 (3 marks): The shaded region in the diagram is bounded by three lines. The equation of one of the lines is given. y 6 4 2 x + 2y = 8 x −2 2 4 6 8 10 O −2 Write down three
January 2022, Paper 2 Higher, Q22 (5 marks): Here is a rectangle. (2x + 3) cm Diagram NOT accurately drawn (x − 1) cm Given that the area of the rectangle is less than 75 cm2 find the range of possible val
November 2021, Paper 1 Foundation, Q21 (5 marks): (i) Solve the inequalities –7  2x – 3 < 5 (ii) On the number line, represent the solution set to part (i) x – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6
November 2021, Paper 1 Higher, Q9 (5 marks): (i) Solve the inequalities –7  2x – 3 < 5 (ii) On the number line, represent the solution set to part (i) x – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6
November 2021, Paper 2 Higher, Q13 (3 marks): y 4 y = 2x + 2 2 O –4 –2 2 4 x R –2 –4 The region R, shown shaded in the diagram, is bounded by three straight lines. Write down the three inequalities that def
June 2021, Paper 1 Foundation, Q22 (5 marks): (a) x –3 –2 –1 0 1 2 3 Write down the inequality shown on the number line. −4  2y < 6 y is an integer. (b) Write down all the possible values of y. (c) Solve t
June 2021, Paper 1 Higher, Q7 (4 marks): −4  2y < 6 y is an integer. (a) Write down all the possible values of y. (b) Solve the inequality 7t – 3  2t + 31 Show your working clearly.
January 2021 (R), Paper 1 Foundation, Q18 (4 marks): (a) On the number line, show the inequality –2  y < 1 y –3 –2 –1 0 1 2 3 n is an integer. (b) Write down all the values of n that satisfy –3.4 < n  2
January 2021 (R), Paper 1 Higher, Q3 (4 marks): (a) On the number line, show the inequality –2  y < 1 y –3 –2 –1 0 1 2 3 n is an integer. (b) Write down all the values of n that satisfy –3.4 < n  2
January 2021 (R), Paper 2 Foundation, Q18 (3 marks): The shaded region R, shown in the diagram below, is bounded by the straight line with equation y = 3x – 2 and by two other straight lines. Write down the three
January 2021 (R), Paper 2 Higher, Q7 (3 marks): The shaded region R, shown in the diagram below, is bounded by the straight line with equation y = 3x – 2 and by two other straight lines. Write down the three
January 2021, Paper 2 Foundation, Q18 (4 marks): y 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 (a) On the grid, draw and label the straight line with equation (i) x = 1.5 (ii) y = x (iii) x + y = 6 (b) Show, by shading on
January 2021, Paper 2 Foundation, Q19 (7 marks): (a) Expand and simplify 4x(2x + 5) – 3x(2x – 3) 5 n Given that y × y = y 13 6 y (b) work out the value of n. n = (c) (i) Solve the inequality 7t – 8 < 2t + 7 (i
January 2021, Paper 2 Higher, Q4 (4 marks): y 7 6 5 4 3 2 1 O x 1 2 3 4 5 6 7 (a) On the grid, draw and label the straight line with equation (i) x = 1.5 (ii) y = x (iii) x + y = 6 (b) Show, by shading on
January 2021, Paper 2 Higher, Q5 (7 marks): (a) Expand and simplify 4x(2x + 5) – 3x(2x – 3) 5 n Given that y × y = y13 6 y (b) work out the value of n. n = (c) (i) Solve the inequality 7t – 8 < 2t + 7 (ii
November 2020 (R), Paper 2 Foundation, Q22 (5 marks): (a) Factorise x2 – x – 42 (b) Solve the inequality 3x + 15 < 8x + 3 Show clear algebraic working.
November 2020 (R), Paper 2 Foundation, Q24 (3 marks): Show, by shading on the grid, the region that satisfies all three of the inequalities x  4 and y  –2 and y  x Label the region R. y 7 6 5 4 3 2 1 O x –5 –4 –
November 2020 (R), Paper 2 Higher, Q9 (5 marks): (a) Factorise x2 – x – 42 (b) Solve the inequality 3x + 15 < 8x + 3 Show clear algebraic working.
November 2020 (R), Paper 2 Higher, Q11 (3 marks): Show, by shading on the grid, the region that satisfies all three of the inequalities x  4 and y  –2 and y  x Label the region R. y 7 6 5 4 3 2 1 O x –5 –4 –
November 2020, Paper 2 Foundation, Q14 (5 marks): (a) Factorise 25f – 10 (b) Make y the subject of the formula c = 5y – h (c) Solve the inequality 4x + 7 > 2
November 2020, Paper 2 Higher, Q1 (6 marks): (a) Simplify g6 × g4 (b) Simplify k10 ÷ k3 (c) Simplify (3cd4)2 (d) Solve the inequality 4x + 7 > 2
November 2020, Paper 2 Higher, Q17 (5 marks): The diagram shows a rectangle. (2x – 4) cm Diagram NOT accurately drawn (3x + 2) cm The area of the rectangle is A cm2 Given that A < 3x + 27 find the range of
January 2020 (R), Paper 2 Foundation, Q25 (4 marks): (a) Write down the integer values of x that satisfy the inequality −2 < x  4 The region R, shown shaded in the diagram, is bounded by three straight lines. Dia
January 2020 (R), Paper 2 Higher, Q11 (4 marks): (a) Write down the integer values of x that satisfy the inequality –2 < x  4 The region R, shown shaded in the diagram, is bounded by three straight lines. y D
January 2020 (R), Paper 2 Higher, Q19 (6 marks): (a) Solve 4 − 3 x 3 x − 5 − = − 3 5 2 Show clear algebraic working. x = (b) Solve the inequality 5y2 – 17y  40
January 2020, Paper 1 Higher, Q10 (3 marks): The shaded region in the diagram is bounded by three lines. The equation of one of the lines is given. y 6 4 2 −6 −4 −2 O 2 4 6 x −2 y = 1 3 x − 2 −4 −6 Write d
January 2020, Paper 2 Foundation, Q11 (6 marks): Here are five mathematical signs + > = ∈ < (a) Write one of these five signs in each box so that each of these statements is true. (i) 4 °C 9 °C (ii) –3 °C –8 °
January 2020, Paper 2 Foundation, Q23 (5 marks): (a) Solve the inequality 2x + 7 > 4 (b) Solve x2 – 3x – 40 = 0 Show clear algebraic working.
January 2020, Paper 2 Higher, Q7 (5 marks): (a) Solve the inequality 2x + 7 > 4 (b) Solve x2 – 3x – 40 = 0 Show clear algebraic working.
June 2019 (R), Paper 2 Foundation, Q17 (3 marks): (a) -1 Write down the inequality shown on the number line. (b) Solve the inequality 4y - 13 ≤ y + 8
June 2019 (R), Paper 2 Higher, Q1 (3 marks): (a) x í í í 0 1 2 3 4 5 Write down the inequality shown on the number line. (b) Solve the inequality 4yí- y + 8
June 2019, Paper 2 Foundation, Q22 (4 marks): The straight line L has gradient 5 and passes through the point with coordinates (0, -3) (a) Write down an equation for L. (b) 5 4 3 R 2 1 -1 -2 1 2 3 --1 --2-
June 2019, Paper 2 Higher, Q10 (4 marks): The straight line LKDVJUDGLHQWDQGSDVVHVWKURXJKWKHSRLQWZLWKFRRUGLQDWHV í (a) Write down an equation for L. (b) y 5 4 3 R 2 1 O x –2 –1 1 2 3 4 –1
January 2019 (R), Paper 2 Higher, Q8 (5 marks): (a) Simplify fully 15 k m 4 3 5 km 2 (b) Solve the inequality 7 < 4x − 1  17

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