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Direct and inverse proportion: AQA GCSE Maths questions

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

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1,304 questions

  1. Q8

    November 2024 · Paper 1H

    3 marksR10 Direct and inverse proportion
    The whole paper ↗
    November 2024 Paper 1H, question 8: (a) In this part, assume that each person works at the same rate. 10 people can complete a job in 9 hours. If 15 people work on the same job, how many hours wil

  2. Q10

    November 2024 · Paper 3H

    3 marksA12 Recognising and sketching graphsR10 Direct and inverse proportion
    The whole paper ↗
    November 2024 Paper 3H, question 10: A car will travel 60 miles. Draw a graph to show the average speed of the car for times taken between 1 hour and 6 hours. You may use the table to help you. Tim

  3. Q3

    June 2024 · Paper 2H

    3 marksR10 Direct and inverse proportionR13 Proportion equations
    The whole paper ↗
    June 2024 Paper 2H, question 3: A chef has a tub of blueberries. She wants to use all the blueberries put the same number of blueberries on each dessert. D is the number of desserts. b is the

  4. Q20

    June 2024 · Paper 3H

    5 marksR10 Direct and inverse proportionR13 Proportion equations
    The whole paper ↗
    June 2024 Paper 3H, question 20: P, Q, and R have positive values. P is directly proportional to Q When P = 8, Q = 2 R is inversely proportional to Q2 When R = 10, Q = 3 Work out the value of R

  5. Q19

    November 2023 · Paper 2H

    1 markR10 Direct and inverse proportion
    The whole paper ↗
    November 2023 Paper 2H, question 19: A is directly proportional to B4 The value of B is doubled. Pete thinks that the value of A will be 8 times bigger because 4 × 2 is 8 Is he correct? Tick a box.

  6. Q14

    June 2022 · Paper 1H

    3 marksR10 Direct and inverse proportion
    The whole paper ↗
    June 2022 Paper 1H, question 14: 15 workers can complete a job in 8 days. How many more workers are needed to complete the job in 6 days? Assume that all of the workers work at the same rate. A

  7. Q7

    June 2022 · Paper 2H

    3 marksR10 Direct and inverse proportion
    The whole paper ↗
    June 2022 Paper 2H, question 7: Sam types a constant number of words per minute. He takes 8 minutes to type a report of 416 words. How long does it take him to type an essay of 1534 words? Giv

  8. Q26

    November 2019 · Paper 2H

    5 marksR13 Proportion equationsR10 Direct and inverse proportion
    The whole paper ↗
    November 2019 Paper 2H, question 26: P, Q and R have positive values. P is directly proportional to the square of Q. When P = 1.25, Q = 0.5 Q is inversely proportional to R. When Q = 0.5, R = 6 Wor

  9. Q10

    June 2019 · Paper 1H

    4 marksA14 Graphs in real contextsR10 Direct and inverse proportion
    The whole paper ↗
    June 2019 Paper 1H, question 10: The number of items, n, made in 1 hour by a machine is given by n = t 60 t is the time in minutes the machine takes to make one item. The value of t changes for

  10. Q18

    November 2018 · Paper 1H

    4 marksR10 Direct and inverse proportion
    The whole paper ↗
    November 2018 Paper 1H, question 18: Beth and Mia translate documents from Spanish into English. A set of documents that would take Beth 8 days would take Mia 10 days. Beth starts to translate the

  11. Q9

    November 2018 · Paper 2H

    4 marksR10 Direct and inverse proportion
    The whole paper ↗
    November 2018 Paper 2H, question 9: The diagrams show the position of a tap when off and fully on. The tap is fully on when the angle of turn is 180° When fully on, water flows out of the tap at 1

  12. Q21

    November 2018 · Paper 2H

    5 marksR13 Proportion equationsR10 Direct and inverse proportion
    The whole paper ↗
    November 2018 Paper 2H, question 21: y is inversely proportional to x y = 4 when x = 9 21 (a) Work out an equation connecting y and x. Answer 21 (b) Work out the value of y when x = 25 Answer

  13. Q10

    June 2018 · Paper 1H

    2 marksR10 Direct and inverse proportion
    The whole paper ↗
    June 2018 Paper 1H, question 10: y is inversely proportional to x. Complete the table. x 12 6 y 4 8

  14. Q4

    November 2017 · Paper 1H

    1 markR10 Direct and inverse proportion
    The whole paper ↗
    November 2017 Paper 1H, question 4: y = x 10 If the value of x doubles, what happens to the value of y? Circle your answer. ÷ 2 × 2 ÷ 5 × 5

  15. Q25

    November 2017 · Paper 1H

    3 marksR10 Direct and inverse proportion
    The whole paper ↗
    November 2017 Paper 1H, question 25: 15 machines work at the same rate. Together, the 15 machines can complete an order in 8 hours. 3 of the machines break down after working for 6 hours. The other

  16. Q6

    November 2017 · Paper 2H

    4 marksR10 Direct and inverse proportionG16 Area of 2D shapes and volume of prisms
    The whole paper ↗
    November 2017 Paper 2H, question 6: The graph shows information about prisms with the same volume. 6 (a) Give one example to show the volume is 24 cm3 6 (b) The diagram shows a prism with volume 2

  17. Q17

    Specimen · Paper 1H

    4 marksR10 Direct and inverse proportion
    The whole paper ↗
    Specimen Paper 1H, question 17: To complete a task in 15 days a company needs 4 people each working for 8 hours per day. The company decides to have 5 people each working for 6 hours per day.

  18. Q20

    Specimen · Paper 2H

    4 marksR10 Direct and inverse proportion
    The whole paper ↗
    Specimen Paper 2H, question 20: y is directly proportional to x x 36 a y 2 5 Work out the value of a. Answer
All 18 questions on Direct and inverse proportion, as a list
  1. November 2024, Paper 1H, Q8 (3 marks): (a) In this part, assume that each person works at the same rate. 10 people can complete a job in 9 hours. If 15 people work on the same job, how many hours wil
  2. November 2024, Paper 3H, Q10 (3 marks): A car will travel 60 miles. Draw a graph to show the average speed of the car for times taken between 1 hour and 6 hours. You may use the table to help you. Tim
  3. June 2024, Paper 2H, Q3 (3 marks): A chef has a tub of blueberries. She wants to use all the blueberries put the same number of blueberries on each dessert. D is the number of desserts. b is the
  4. June 2024, Paper 3H, Q20 (5 marks): P, Q, and R have positive values. P is directly proportional to Q When P = 8, Q = 2 R is inversely proportional to Q2 When R = 10, Q = 3 Work out the value of R
  5. November 2023, Paper 2H, Q19 (1 mark): A is directly proportional to B4 The value of B is doubled. Pete thinks that the value of A will be 8 times bigger because 4 × 2 is 8 Is he correct? Tick a box.
  6. June 2022, Paper 1H, Q14 (3 marks): 15 workers can complete a job in 8 days. How many more workers are needed to complete the job in 6 days? Assume that all of the workers work at the same rate. A
  7. June 2022, Paper 2H, Q7 (3 marks): Sam types a constant number of words per minute. He takes 8 minutes to type a report of 416 words. How long does it take him to type an essay of 1534 words? Giv
  8. November 2019, Paper 2H, Q26 (5 marks): P, Q and R have positive values. P is directly proportional to the square of Q. When P = 1.25, Q = 0.5 Q is inversely proportional to R. When Q = 0.5, R = 6 Wor
  9. June 2019, Paper 1H, Q10 (4 marks): The number of items, n, made in 1 hour by a machine is given by n = t 60 t is the time in minutes the machine takes to make one item. The value of t changes for
  10. November 2018, Paper 1H, Q18 (4 marks): Beth and Mia translate documents from Spanish into English. A set of documents that would take Beth 8 days would take Mia 10 days. Beth starts to translate the
  11. November 2018, Paper 2H, Q9 (4 marks): The diagrams show the position of a tap when off and fully on. The tap is fully on when the angle of turn is 180° When fully on, water flows out of the tap at 1
  12. November 2018, Paper 2H, Q21 (5 marks): y is inversely proportional to x y = 4 when x = 9 21 (a) Work out an equation connecting y and x. Answer 21 (b) Work out the value of y when x = 25 Answer
  13. June 2018, Paper 1H, Q10 (2 marks): y is inversely proportional to x. Complete the table. x 12 6 y 4 8
  14. November 2017, Paper 1H, Q4 (1 mark): y = x 10 If the value of x doubles, what happens to the value of y? Circle your answer. ÷ 2 × 2 ÷ 5 × 5
  15. November 2017, Paper 1H, Q25 (3 marks): 15 machines work at the same rate. Together, the 15 machines can complete an order in 8 hours. 3 of the machines break down after working for 6 hours. The other
  16. November 2017, Paper 2H, Q6 (4 marks): The graph shows information about prisms with the same volume. 6 (a) Give one example to show the volume is 24 cm3 6 (b) The diagram shows a prism with volume 2
  17. Specimen, Paper 1H, Q17 (4 marks): To complete a task in 15 days a company needs 4 people each working for 8 hours per day. The company decides to have 5 people each working for 6 hours per day.
  18. Specimen, Paper 2H, Q20 (4 marks): y is directly proportional to x x 36 a y 2 5 Work out the value of a. Answer

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