Lesson A15

A15 Gradients and areas under graphs Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson A15, Gradients and areas under graphs: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 2: Algebra, written with Revision Ninja.

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The 20 questions

  1. (H) What is the gradient of y = 2x^3 at x = 1?

    • 6
    • 2
    • 3
    • 1

  2. (H) What is the gradient of the tangent to y = x^2 at x = 3?

    • 12
    • 9
    • 6
    • 3

  3. (H) What is the gradient of the chord of y = x^2 between x = 1 and x = 3?

    • 2
    • 4
    • 8
    • 6

  4. (H) A speed-time graph shows a constant 10 m/s for 5 s. What is the distance travelled?

    • 15 metres
    • 5 metres
    • 50 metres
    • 10 metres

  5. (H) What is the area under v = 2t from t = 0 to t = 3 seconds?

    • 9 metres
    • 3 metres
    • 6 metres
    • 18 metres

  6. (H) What does the gradient of a velocity-time graph represent?

    • Distance
    • Displacement
    • Speed
    • Acceleration

  7. (H) What does the gradient of a tangent on a distance-time graph represent?

    • The total distance travelled
    • The average acceleration over the journey
    • The instantaneous speed at that point
    • The time taken to reach that point

  8. (H) Which method estimates an area under a curve by splitting it into trapezia?

    • The sine rule
    • The trapezium rule
    • Completing the square
    • The quadratic formula

  9. (H) Using 3 trapezia of width 1, estimate the area under y = x^2 from x = 0 to x = 3.

    • 4.5 square units
    • 9 square units
    • 9.5 square units
    • 14 square units

  10. (H) What is the gradient of y = 3x^2 at x = 2?

    • 6
    • 2
    • 3
    • 12

  11. (H) A velocity-time graph rises in a straight line from 0 to 12 m/s over 4 s. How far is travelled?

    • 16 metres
    • 12 metres
    • 24 metres
    • 48 metres

  12. (H) What does an area below the x-axis on a velocity-time graph represent?

    • Greater acceleration in the reverse direction
    • A higher speed than the object had before
    • Zero distance travelled over that interval
    • Displacement in the opposite direction

  13. (H) What does the gradient of a graph of account balance against time represent?

    • The starting balance in the account
    • The rate of growth of the balance
    • The number of years the money was saved
    • The total interest paid over the period

  14. (H) What is the gradient of y = 1/x at x = 1?

    • 0
    • -1
    • -2
    • 1

  15. (H) What is the gradient of y = x^3 at x = 1?

    • 2
    • 6
    • 1
    • 3

  16. (H) Using 2 rectangles of width 1 under the left ends, what lower estimate do you get for the area under y = x^2 from 0 to 2?

    • 2 square units
    • 0.5 square units
    • 1 square unit
    • 4 square units

  17. (H) In a speed-time graph, what are the units of the area under the graph?

    • Metres per second squared
    • Metres per second
    • Metres
    • Seconds

  18. (H) What are the units of the gradient of a graph of money in pounds against time in days?

    • Pounds
    • Pounds per day
    • Pounds squared
    • Days per pound

  19. (H) A graph of speed against time is constant at 2 m/s from t = 1 to t = 4. What is the area under it?

    • 6 metres
    • 3 metres
    • 2 metres
    • 8 metres

  20. (H) What is the gradient of y = x^2 at x = -2?

    • -2
    • 4
    • 2
    • -4

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