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Gradients and areas under graphs: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on A15 Gradients and areas under graphs, 2017–2025, with its mark scheme and examiner’s report.

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1,304 questions

  1. Q21

    November 2024 · Paper 2H

    6 marksR15 Instantaneous and average rates of changeA15 Gradients and areas under graphs
    The whole paper ↗
    November 2024 Paper 2H, question 21: The graph represents the velocity of a ball as it rolls along the ground. 21 (a) Work out an estimate for the acceleration of the ball, in m/s2, after 2 seconds

  2. Q8

    June 2024 · Paper 2H

    3 marksA15 Gradients and areas under graphsR11 Compound units: speed, density and pressure
    The whole paper ↗
    June 2024 Paper 2H, question 8: A lion is sprinting in a straight line away from its den. The graph shows the lion’s distance from the den. Work out the speed of the lion in metres per second.

  3. Q23

    November 2023 · Paper 2H

    5 marksA15 Gradients and areas under graphs
    The whole paper ↗
    November 2023 Paper 2H, question 23: Here is the velocity-time graph of a cyclist for 40 seconds. 23 (a) By dividing the area under the graph into four sections of equal widths, estimate the distan

  4. Q26

    November 2022 · Paper 2H

    4 marksA15 Gradients and areas under graphs
    The whole paper ↗
    November 2022 Paper 2H, question 26: Helena ran an 800-metre race in 140 seconds. The speed-time graph represents the first 100 seconds of her run. Helena ran the last 40 seconds with constant dece

  5. Q25

    June 2022 · Paper 1H

    3 marksA15 Gradients and areas under graphsA14 Graphs in real contexts
    The whole paper ↗
    June 2022 Paper 1H, question 25: Here is the speed-time graph for a 50-second journey. 25 (a) Circle the acceleration, in m/s2, halfway through the journey. 0 2 20 25 25 (b) Work out the total

  6. Q28

    November 2020 · Paper 2H

    3 marksA15 Gradients and areas under graphs
    The whole paper ↗
    November 2020 Paper 2H, question 28: A horse runs in a field. The speed-time graph represents the first 12 seconds of the run. After how many seconds had the horse run a distance of 75 metres? Answ

  7. Q25

    November 2019 · Paper 3H

    4 marksA15 Gradients and areas under graphs
    The whole paper ↗
    November 2019 Paper 3H, question 25: Here is a sketch of a speed-time graph for the first part of a journey. The total distance for the journey is 130 kilometres. How far is left to travel? Answer

  8. Q28

    June 2019 · Paper 3H

    6 marksA15 Gradients and areas under graphsR14 Gradient as a rate of change
    The whole paper ↗
    June 2019 Paper 3H, question 28: Leo runs for 12 seconds. The graph shows his speed. 28 (a) Show that the distance he runs is less than 67.5 metres. 28 (b) Work out his average acceleration for

  9. Q28

    November 2018 · Paper 2H

    6 marksA15 Gradients and areas under graphsR14 Gradient as a rate of change
    The whole paper ↗
    November 2018 Paper 2H, question 28: Izzy runs an 80-metre race in 14 seconds. During the first 6 seconds her speed increases at a constant rate. During the last 8 seconds her speed increases at a

  10. Q24

    June 2018 · Paper 3H

    4 marksA15 Gradients and areas under graphs
    The whole paper ↗
    June 2018 Paper 3H, question 24: The speed-time graph shows 20 seconds of a car journey. Harry wants to estimate the distance the car travels in this time. He uses a triangle and a trapezium, a

  11. Q24

    November 2017 · Paper 2H

    3 marksA15 Gradients and areas under graphs
    The whole paper ↗
    November 2017 Paper 2H, question 24: Beth ran a 200 metre race. Here is a graph of the first 8 seconds of her race. She completed the race at a constant speed of 9 m/s Speed-time graph for Beth Amy

  12. Q23

    June 2017 · Paper 1H

    3 marksA15 Gradients and areas under graphsA14 Graphs in real contexts
    The whole paper ↗
    June 2017 Paper 1H, question 23: Here is a velocity-time graph of a motorbike for 25 seconds. 23 (a) After how many seconds was the acceleration zero? Answer seconds 23 (b) Work out the distanc

  13. Q24

    Specimen · Paper 1H

    4 marksA15 Gradients and areas under graphs
    The whole paper ↗
    Specimen Paper 1H, question 24: Here is the velocity-time graph of a car for 50 seconds. 0 10 20 30 40 50 0 10 20 30 Time (s) Velocity (m/s) 24 (a) Work out the average acceleration during the

  14. Q24

    Specimen · Paper 3H

    4 marksA15 Gradients and areas under graphs
    The whole paper ↗
    Specimen Paper 3H, question 24: Amina and Ben had a cycle race. Here is Amina’s speed-time graph from the start of the race. 0 10 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 8 Speed (metres per secon
All 14 questions on Gradients and areas under graphs, as a list
  1. November 2024, Paper 2H, Q21 (6 marks): The graph represents the velocity of a ball as it rolls along the ground. 21 (a) Work out an estimate for the acceleration of the ball, in m/s2, after 2 seconds
  2. June 2024, Paper 2H, Q8 (3 marks): A lion is sprinting in a straight line away from its den. The graph shows the lion’s distance from the den. Work out the speed of the lion in metres per second.
  3. November 2023, Paper 2H, Q23 (5 marks): Here is the velocity-time graph of a cyclist for 40 seconds. 23 (a) By dividing the area under the graph into four sections of equal widths, estimate the distan
  4. November 2022, Paper 2H, Q26 (4 marks): Helena ran an 800-metre race in 140 seconds. The speed-time graph represents the first 100 seconds of her run. Helena ran the last 40 seconds with constant dece
  5. June 2022, Paper 1H, Q25 (3 marks): Here is the speed-time graph for a 50-second journey. 25 (a) Circle the acceleration, in m/s2, halfway through the journey. 0 2 20 25 25 (b) Work out the total
  6. November 2020, Paper 2H, Q28 (3 marks): A horse runs in a field. The speed-time graph represents the first 12 seconds of the run. After how many seconds had the horse run a distance of 75 metres? Answ
  7. November 2019, Paper 3H, Q25 (4 marks): Here is a sketch of a speed-time graph for the first part of a journey. The total distance for the journey is 130 kilometres. How far is left to travel? Answer
  8. June 2019, Paper 3H, Q28 (6 marks): Leo runs for 12 seconds. The graph shows his speed. 28 (a) Show that the distance he runs is less than 67.5 metres. 28 (b) Work out his average acceleration for
  9. November 2018, Paper 2H, Q28 (6 marks): Izzy runs an 80-metre race in 14 seconds. During the first 6 seconds her speed increases at a constant rate. During the last 8 seconds her speed increases at a
  10. June 2018, Paper 3H, Q24 (4 marks): The speed-time graph shows 20 seconds of a car journey. Harry wants to estimate the distance the car travels in this time. He uses a triangle and a trapezium, a
  11. November 2017, Paper 2H, Q24 (3 marks): Beth ran a 200 metre race. Here is a graph of the first 8 seconds of her race. She completed the race at a constant speed of 9 m/s Speed-time graph for Beth Amy
  12. June 2017, Paper 1H, Q23 (3 marks): Here is a velocity-time graph of a motorbike for 25 seconds. 23 (a) After how many seconds was the acceleration zero? Answer seconds 23 (b) Work out the distanc
  13. Specimen, Paper 1H, Q24 (4 marks): Here is the velocity-time graph of a car for 50 seconds. 0 10 20 30 40 50 0 10 20 30 Time (s) Velocity (m/s) 24 (a) Work out the average acceleration during the
  14. Specimen, Paper 3H, Q24 (4 marks): Amina and Ben had a cycle race. Here is Amina’s speed-time graph from the start of the race. 0 10 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 8 Speed (metres per secon

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