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Proportion equations: OCR GCSE Maths questions

Every OCR GCSE Maths exam question on R13 Proportion equations, 2017–2025, with its mark scheme and examiner’s report.

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921 questions

  1. Q15

    June 2025 · Paper 4

    3 marksR13 Proportion equations
    The whole paper ↗
    June 2025 Paper 4, question 15: y is inversely proportional to the square of x. y 5 when x 6 . = = Find a formula linking x and y.

  2. Q13

    June 2025 · Paper 5

    3 marksR13 Proportion equations
    The whole paper ↗
    June 2025 Paper 5, question 13: p is directly proportional to the square root of m. p = 15 when m = 25. Find the value of p when m = 81. p =

  3. Q12

    November 2024 · Paper 4

    6 marksR13 Proportion equations
    The whole paper ↗
    November 2024 Paper 4, question 12: y is directly proportional to the square of t. y 14 when t 2 . = = t is directly proportional to x. t 12 when x 3 . = = Find a formula for y in terms of x. Give

  4. Q18

    November 2024 · Paper 6

    4 marksR13 Proportion equationsR9 Percentages
    The whole paper ↗
    November 2024 Paper 6, question 18: y is inversely proportional to x Find the percentage decrease in y when x is increased by 25%. %

  5. Q10

    June 2024 · Paper 4

    3 marksR13 Proportion equations
    The whole paper ↗
    June 2024 Paper 4, question 10: Here is a question and an incorrect solution. Question: You are given y \ x and y = 9 when x = 2 . Find a formula linking x and y. Solution: y \ x so y = x + c

  6. Q15

    June 2024 · Paper 6

    3 marksR13 Proportion equations
    The whole paper ↗
    June 2024 Paper 6, question 15: y is inversely proportional to x y 4 when x 12 . = = Find a formula linking x and y.

  7. Q17

    November 2023 · Paper 5

    4 marksR13 Proportion equationsR10 Direct and inverse proportion
    The whole paper ↗
    November 2023 Paper 5, question 17: y is directly proportional to the cube of x. Complete the table. x 1 2 y 7 875

  8. Q10

    November 2023 · Paper 6

    4 marksR13 Proportion equationsR10 Direct and inverse proportion
    The whole paper ↗
    November 2023 Paper 6, question 10: (a) x and y are related by the equation xy 36 . = Tick the correct statement. y is directly proportional to x y is inversely proportional to x y is not proporti

  9. Q15

    June 2023 · Paper 4

    3 marksR13 Proportion equations
    The whole paper ↗
    June 2023 Paper 4, question 15: y is inversely proportional to the square root of x. y = 7 when x = 144. Find the value of y when x = 16. y =

  10. Q11

    June 2023 · Paper 5

    4 marksR13 Proportion equationsR9 Percentages
    The whole paper ↗
    June 2023 Paper 5, question 11: y is directly proportional to the square of x. Find the percentage decrease in y when x is decreased by 30%. %

  11. Q13

    November 2022 · Paper 4

    3 marksR13 Proportion equations
    The whole paper ↗
    November 2022 Paper 4, question 13: y is directly proportional to x . y = 1 when x = 16. Find a formula for y in terms of x.

  12. Q14

    November 2022 · Paper 6

    6 marksR10 Direct and inverse proportionR13 Proportion equations
    The whole paper ↗
    November 2022 Paper 6, question 14: (a) The time taken to paint a wall is inversely proportional to the number of people painting. It takes 40 minutes for 3 people to paint the wall if nobody stop

  13. Q11

    June 2022 · Paper 5

    3 marksR13 Proportion equations
    The whole paper ↗
    June 2022 Paper 5, question 11: y is inversely proportional to x2. y = 9 when x = 2. Find the value of y when x = 10. y =

  14. Q14

    November 2021 · Paper 6

    6 marksR13 Proportion equations
    The whole paper ↗
    November 2021 Paper 6, question 14: y is inversely proportional to the square root of x. y 5 when x 36 . = = (a) Find a formula linking x and y. (a) (b) Find the value of x when y 20 . = (b) x =

  15. Q16

    November 2020 · Paper 4

    3 marksR13 Proportion equations
    The whole paper ↗
    November 2020 Paper 4, question 16: y is inversely proportional to the square of x. y 2 when x 5 . = = Find a formula linking x and y.

  16. Q9

    November 2020 · Paper 6

    4 marksR13 Proportion equationsR10 Direct and inverse proportion
    The whole paper ↗
    November 2020 Paper 6, question 9: x is directly proportional to y. y is directly proportional to z. When x = 10, y = 60. When y = 8, z = 1.6. Find a formula for z in terms of x.

  17. Q14

    November 2019 · Paper 5

    3 marksR13 Proportion equationsR10 Direct and inverse proportion
    The whole paper ↗
    November 2019 Paper 5, question 14: y is inversely proportional to the square root of x. y 7 when x 25 . = = Find the value of y when x 100 . = y =

  18. Q16

    June 2019 · Paper 4

    5 marksR10 Direct and inverse proportionR13 Proportion equations
    The whole paper ↗
    June 2019 Paper 4, question 16: (a) The table shows values of x and y. x 4 16 36 6 3 2 y Show that these values fit the relationship that y is inversely proportional to x . (b) a is inversely

  19. Q14

    November 2018 · Paper 4

    3 marksR13 Proportion equations
    The whole paper ↗
    November 2018 Paper 4, question 14: y is inversely proportional to the square root of x. y is 40 when x is 9. Find a formula linking x and y.

  20. Q11

    June 2018 · Paper 4

    4 marksR13 Proportion equationsR9 Percentages
    The whole paper ↗
    June 2018 Paper 4, question 11: y is directly proportional to the square of x. Find the percentage increase in y when x is increased by 15%. %
All 23 questions on Proportion equations, as a list
  1. June 2025, Paper 4, Q15 (3 marks): y is inversely proportional to the square of x. y 5 when x 6 . = = Find a formula linking x and y.
  2. June 2025, Paper 5, Q13 (3 marks): p is directly proportional to the square root of m. p = 15 when m = 25. Find the value of p when m = 81. p =
  3. November 2024, Paper 4, Q12 (6 marks): y is directly proportional to the square of t. y 14 when t 2 . = = t is directly proportional to x. t 12 when x 3 . = = Find a formula for y in terms of x. Give
  4. November 2024, Paper 6, Q18 (4 marks): y is inversely proportional to x Find the percentage decrease in y when x is increased by 25%. %
  5. June 2024, Paper 4, Q10 (3 marks): Here is a question and an incorrect solution. Question: You are given y \ x and y = 9 when x = 2 . Find a formula linking x and y. Solution: y \ x so y = x + c
  6. June 2024, Paper 6, Q15 (3 marks): y is inversely proportional to x y 4 when x 12 . = = Find a formula linking x and y.
  7. November 2023, Paper 5, Q17 (4 marks): y is directly proportional to the cube of x. Complete the table. x 1 2 y 7 875
  8. November 2023, Paper 6, Q10 (4 marks): (a) x and y are related by the equation xy 36 . = Tick the correct statement. y is directly proportional to x y is inversely proportional to x y is not proporti
  9. June 2023, Paper 4, Q15 (3 marks): y is inversely proportional to the square root of x. y = 7 when x = 144. Find the value of y when x = 16. y =
  10. June 2023, Paper 5, Q11 (4 marks): y is directly proportional to the square of x. Find the percentage decrease in y when x is decreased by 30%. %
  11. November 2022, Paper 4, Q13 (3 marks): y is directly proportional to x . y = 1 when x = 16. Find a formula for y in terms of x.
  12. November 2022, Paper 6, Q14 (6 marks): (a) The time taken to paint a wall is inversely proportional to the number of people painting. It takes 40 minutes for 3 people to paint the wall if nobody stop
  13. June 2022, Paper 5, Q11 (3 marks): y is inversely proportional to x2. y = 9 when x = 2. Find the value of y when x = 10. y =
  14. November 2021, Paper 6, Q14 (6 marks): y is inversely proportional to the square root of x. y 5 when x 36 . = = (a) Find a formula linking x and y. (a) (b) Find the value of x when y 20 . = (b) x =
  15. November 2020, Paper 4, Q16 (3 marks): y is inversely proportional to the square of x. y 2 when x 5 . = = Find a formula linking x and y.
  16. November 2020, Paper 6, Q9 (4 marks): x is directly proportional to y. y is directly proportional to z. When x = 10, y = 60. When y = 8, z = 1.6. Find a formula for z in terms of x.
  17. November 2019, Paper 5, Q14 (3 marks): y is inversely proportional to the square root of x. y 7 when x 25 . = = Find the value of y when x 100 . = y =
  18. June 2019, Paper 4, Q16 (5 marks): (a) The table shows values of x and y. x 4 16 36 6 3 2 y Show that these values fit the relationship that y is inversely proportional to x . (b) a is inversely
  19. November 2018, Paper 4, Q14 (3 marks): y is inversely proportional to the square root of x. y is 40 when x is 9. Find a formula linking x and y.
  20. June 2018, Paper 4, Q11 (4 marks): y is directly proportional to the square of x. Find the percentage increase in y when x is increased by 15%. %
  21. June 2018, Paper 6, Q6 (3 marks): y is inversely proportional to x. y = 0.04 when x = 80. Find the value of y when x = 32. y =
  22. November 2017, Paper 4, Q11 (3 marks): y is inversely proportional to x2 and y = 5 when x = 4. Find a formula linking x and y.
  23. June 2017, Paper 6, Q12 (4 marks): y is inversely proportional to the square of x. Complete the table. x 10 6 9 4 y

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