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Instantaneous and average rates of change: Edexcel GCSE Maths questions

Every Edexcel GCSE Maths exam question on R15 Instantaneous and average rates of change, 2017–2025, with its mark scheme and examiner’s report.

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  1. Q12

    June 2025 · Paper 1H

    7 marksR15 Instantaneous and average rates of changeA15 Gradients and areas under graphs
    The whole paper ↗
    June 2025 Paper 1H, question 12: The graph shows the velocity, v m/s, of a particle t seconds after it starts to move. 60 50 40 Velocity (v m/s) 30 20 10 0 0 1 2 3 4 5 6 Time (t seconds) (a) (i

  2. Q14

    June 2024 · Paper 2H

    6 marksA15 Gradients and areas under graphsR15 Instantaneous and average rates of change
    The whole paper ↗
    June 2024 Paper 2H, question 14: The graph shows the velocity of a car, in metres per second, t seconds after it starts to slow down. 30 25 20 Velocity (m/s) 15 10 5 t 0 2 4 6 8 10 Time (t seco

  3. Q15

    November 2023 · Paper 1H

    3 marksR15 Instantaneous and average rates of changeA14 Graphs in real contexts
    The whole paper ↗
    November 2023 Paper 1H, question 15: An object falls from rest. Here is the distance‑time graph for the distance (d metres) fallen by the object t seconds after it starts to fall. d 250 200 150 Dis

  4. Q17

    June 2023 · Paper 3H

    4 marksR15 Instantaneous and average rates of changeA15 Gradients and areas under graphs
    The whole paper ↗
    June 2023 Paper 3H, question 17: Here is a distance-time graph. 100 90 80 70 60 Distance 50 (metres) 40 30 20 10 0 0 1 2 3 4 Time (seconds) (a) Find an estimate of the gradient of the graph at

  5. Q21

    November 2022 · Paper 2H

    4 marksR15 Instantaneous and average rates of changeA15 Gradients and areas under graphs
    The whole paper ↗
    November 2022 Paper 2H, question 21: The graph below gives the volume, in litres, of water in a container t seconds after the water starts to fill the container. 25 20 15 Volume (litres) 10 5 00 5

  6. Q14

    June 2022 · Paper 1H

    4 marksR15 Instantaneous and average rates of changeA15 Gradients and areas under graphs
    The whole paper ↗
    June 2022 Paper 1H, question 14: Here is a speed-time graph. 6 5 4 Speed (m/s) 3 2 1 0 0 2 4 6 8 10 Time (t seconds) (a) Work out an estimate of the gradient of the graph at t = 2 (b) What does

  7. Q15

    November 2021 · Paper 3H

    3 marksR15 Instantaneous and average rates of changeA15 Gradients and areas under graphs
    The whole paper ↗
    November 2021 Paper 3H, question 15: The graph gives the volume of water, in litres, in a container at time t seconds after the water started to flow out of the container. 50 40 30 Volume (litres)

  8. Q19

    November 2019 · Paper 3H

    3 marksR15 Instantaneous and average rates of changeA15 Gradients and areas under graphs
    The whole paper ↗
    November 2019 Paper 3H, question 19: The graph shows information about part of a cyclist’s journey. 20 – 15 – Distance travelled (metres) 10 – 5 – 0 – 0 2 4 6 8 Time (seconds) Work out an estimate

  9. Q14

    June 2019 · Paper 2H

    7 marksA15 Gradients and areas under graphsR15 Instantaneous and average rates of change
    The whole paper ↗
    June 2019 Paper 2H, question 14: A car moves from rest. The graph gives information about the speed, v metres per second, of the car t seconds after it starts to move. v 25 20 15 Speed (m/s) 10

  10. Q14

    June 2018 · Paper 2H

    3 marksR15 Instantaneous and average rates of changeA15 Gradients and areas under graphs
    The whole paper ↗
    June 2018 Paper 2H, question 14: The distance-time graph shows information about part of a car journey. 160 140 120 100 Distance travelled 80 (metres) 60 40 20 0 0 1 2 3 4 5 6 7 8 Time (seconds

  11. Q20

    June 2017 · Paper 2H

    5 marksA18 Quadratic equationsR15 Instantaneous and average rates of change
    The whole paper ↗
    June 2017 Paper 2H, question 20: The diagram shows part of the graph of y = x2 – 2x + 3 y 10 8 6 4 2 –2 O 2 4 x (a) By drawing a suitable straight line, use your graph to find estimates for the
All 11 questions on Instantaneous and average rates of change, as a list
  1. June 2025, Paper 1H, Q12 (7 marks): The graph shows the velocity, v m/s, of a particle t seconds after it starts to move. 60 50 40 Velocity (v m/s) 30 20 10 0 0 1 2 3 4 5 6 Time (t seconds) (a) (i
  2. June 2024, Paper 2H, Q14 (6 marks): The graph shows the velocity of a car, in metres per second, t seconds after it starts to slow down. 30 25 20 Velocity (m/s) 15 10 5 t 0 2 4 6 8 10 Time (t seco
  3. November 2023, Paper 1H, Q15 (3 marks): An object falls from rest. Here is the distance‑time graph for the distance (d metres) fallen by the object t seconds after it starts to fall. d 250 200 150 Dis
  4. June 2023, Paper 3H, Q17 (4 marks): Here is a distance-time graph. 100 90 80 70 60 Distance 50 (metres) 40 30 20 10 0 0 1 2 3 4 Time (seconds) (a) Find an estimate of the gradient of the graph at
  5. November 2022, Paper 2H, Q21 (4 marks): The graph below gives the volume, in litres, of water in a container t seconds after the water starts to fill the container. 25 20 15 Volume (litres) 10 5 00 5
  6. June 2022, Paper 1H, Q14 (4 marks): Here is a speed-time graph. 6 5 4 Speed (m/s) 3 2 1 0 0 2 4 6 8 10 Time (t seconds) (a) Work out an estimate of the gradient of the graph at t = 2 (b) What does
  7. November 2021, Paper 3H, Q15 (3 marks): The graph gives the volume of water, in litres, in a container at time t seconds after the water started to flow out of the container. 50 40 30 Volume (litres)
  8. November 2019, Paper 3H, Q19 (3 marks): The graph shows information about part of a cyclist’s journey. 20 – 15 – Distance travelled (metres) 10 – 5 – 0 – 0 2 4 6 8 Time (seconds) Work out an estimate
  9. June 2019, Paper 2H, Q14 (7 marks): A car moves from rest. The graph gives information about the speed, v metres per second, of the car t seconds after it starts to move. v 25 20 15 Speed (m/s) 10
  10. June 2018, Paper 2H, Q14 (3 marks): The distance-time graph shows information about part of a car journey. 160 140 120 100 Distance travelled 80 (metres) 60 40 20 0 0 1 2 3 4 5 6 7 8 Time (seconds
  11. June 2017, Paper 2H, Q20 (5 marks): The diagram shows part of the graph of y = x2 – 2x + 3 y 10 8 6 4 2 –2 O 2 4 x (a) By drawing a suitable straight line, use your graph to find estimates for the

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