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Direct and inverse proportion: OCR GCSE Maths questions

Every OCR GCSE Maths exam question on R10 Direct and inverse proportion, 2017–2025, with its mark scheme and examiner’s report.

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921 questions

  1. Q8

    June 2024 · Paper 5

    2 marksR10 Direct and inverse proportion
    The whole paper ↗
    June 2024 Paper 5, question 8: (a) y is directly proportional to x. Write down the percentage increase in y when x is increased by 100%. (a) % (b) z is inversely proportional to x. Write down

  2. Q1

    June 2024 · Paper 6

    3 marksA12 Recognising and sketching graphsR10 Direct and inverse proportion
    The whole paper ↗
    June 2024 Paper 6, question 1: Below are six graphs, numbered 1 to 6, that show different relationships between x and y. Graph 1 Graph 2 Graph 3 y y y O x O x O x Graph 4 Graph 5 Graph 6 y y

  3. 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

  4. 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

  5. Q7

    June 2023 · Paper 5

    5 marksR10 Direct and inverse proportion
    The whole paper ↗
    June 2023 Paper 5, question 7: A volunteer packs boxes for a charity. They can pack 5 boxes in 45 seconds. (a) Use this information to show that they can pack 55 boxes in less than 9 minutes.

  6. Q4

    June 2023 · Paper 6

    4 marksR10 Direct and inverse proportionR14 Gradient as a rate of change
    The whole paper ↗
    June 2023 Paper 6, question 4: (a) The time taken to complete a journey halves as the speed doubles. On the axes below, sketch a graph to show this relationship. Time taken O Speed (b) It tak

  7. 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

  8. Q6

    November 2021 · Paper 5

    2 marksR10 Direct and inverse proportionR14 Gradient as a rate of change
    The whole paper ↗
    November 2021 Paper 5, question 6: Here are sketches of five graphs. y y y x x x O O O Graph A Graph B Graph C y y x x O O Graph D Graph E Write the letter of the graph that represents the follow

  9. Q3

    November 2020 · Paper 4

    4 marksR10 Direct and inverse proportion
    The whole paper ↗
    November 2020 Paper 4, question 3: Three people take 2 2 Assuming all people deliver leaflets at the same rate, how long will it take five people to deliver leaflets to 405 houses? Give your answ

  10. 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.

  11. Q1

    November 2019 · Paper 4

    5 marksR10 Direct and inverse proportionN13 Units of measure
    The whole paper ↗
    November 2019 Paper 4, question 1: Carol makes birthday cards. Each card takes the same amount of time to make. She makes 3 cards in 48 minutes. She has an order for 80 cards. Can she complete th

  12. 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 =

  13. 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

  14. Q9

    November 2018 · Paper 6

    2 marksR10 Direct and inverse proportionR14 Gradient as a rate of change
    The whole paper ↗
    November 2018 Paper 6, question 9: These graphs show different relationships between the variables x and y. Graph A Graph B y y x x O O Graph C Graph D y y x x O O Identify the graph which shows

  15. Q10

    November 2018 · Paper 6

    2 marksR14 Gradient as a rate of changeR10 Direct and inverse proportion
    The whole paper ↗
    November 2018 Paper 6, question 10: Sketch a graph which shows that y is directly proportional to x2. y O x

  16. Q10

    June 2018 · Paper 5

    4 marksR10 Direct and inverse proportion
    The whole paper ↗
    June 2018 Paper 5, question 10: Ifsaw noticed this information on her car’s dashboard at the end of her journey. She started her journey with a full tank of fuel and her miles travelled set to

  17. Q6

    June 2018 · Paper 6

    3 marksR13 Proportion equationsR10 Direct and inverse proportion
    The whole paper ↗
    June 2018 Paper 6, question 6: y is inversely proportional to x. y = 0.04 when x = 80. Find the value of y when x = 32. y =

  18. Q1

    November 2017 · Paper 4

    6 marksR10 Direct and inverse proportionR1 Converting units
    The whole paper ↗
    November 2017 Paper 4, question 1: Donald swims 3 lengths of a swimming pool in 93 seconds. (a) Use this information to show that he could swim 100 lengths in under 55 minutes. (b) What assumptio

  19. Q12

    June 2017 · Paper 6

    4 marksR13 Proportion equationsR10 Direct and inverse proportion
    The whole paper ↗
    June 2017 Paper 6, question 12: y is inversely proportional to the square of x. Complete the table. x 10 6 9 4 y
All 19 questions on Direct and inverse proportion, as a list
  1. June 2024, Paper 5, Q8 (2 marks): (a) y is directly proportional to x. Write down the percentage increase in y when x is increased by 100%. (a) % (b) z is inversely proportional to x. Write down
  2. June 2024, Paper 6, Q1 (3 marks): Below are six graphs, numbered 1 to 6, that show different relationships between x and y. Graph 1 Graph 2 Graph 3 y y y O x O x O x Graph 4 Graph 5 Graph 6 y y
  3. 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
  4. 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
  5. June 2023, Paper 5, Q7 (5 marks): A volunteer packs boxes for a charity. They can pack 5 boxes in 45 seconds. (a) Use this information to show that they can pack 55 boxes in less than 9 minutes.
  6. June 2023, Paper 6, Q4 (4 marks): (a) The time taken to complete a journey halves as the speed doubles. On the axes below, sketch a graph to show this relationship. Time taken O Speed (b) It tak
  7. 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
  8. November 2021, Paper 5, Q6 (2 marks): Here are sketches of five graphs. y y y x x x O O O Graph A Graph B Graph C y y x x O O Graph D Graph E Write the letter of the graph that represents the follow
  9. November 2020, Paper 4, Q3 (4 marks): Three people take 2 2 Assuming all people deliver leaflets at the same rate, how long will it take five people to deliver leaflets to 405 houses? Give your answ
  10. 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.
  11. November 2019, Paper 4, Q1 (5 marks): Carol makes birthday cards. Each card takes the same amount of time to make. She makes 3 cards in 48 minutes. She has an order for 80 cards. Can she complete th
  12. 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 =
  13. 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
  14. November 2018, Paper 6, Q9 (2 marks): These graphs show different relationships between the variables x and y. Graph A Graph B y y x x O O Graph C Graph D y y x x O O Identify the graph which shows
  15. November 2018, Paper 6, Q10 (2 marks): Sketch a graph which shows that y is directly proportional to x2. y O x
  16. June 2018, Paper 5, Q10 (4 marks): Ifsaw noticed this information on her car’s dashboard at the end of her journey. She started her journey with a full tank of fuel and her miles travelled set to
  17. 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 =
  18. November 2017, Paper 4, Q1 (6 marks): Donald swims 3 lengths of a swimming pool in 93 seconds. (a) Use this information to show that he could swim 100 lengths in under 55 minutes. (b) What assumptio
  19. 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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