Lesson R15

R15 Average and instantaneous rates of change Quiz: AQA Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson R15, Average and instantaneous rates of change: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 3: Ratio, proportion and rates of change, written with Revision Ninja.

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The 20 questions

  1. (H) Which rate describes the gradient of a curve at a single point?

    • The average rate of change
    • The instantaneous rate of change
    • The total change
    • The constant rate of change

  2. (H) The average rate of change between two points on a curve is the gradient of which line?

    • The chord joining the two points
    • The tangent at the first point
    • The normal at the midpoint
    • The line of symmetry

  3. (H) What is the gradient of the tangent to y = x² at x = 3?

    • 3
    • 12
    • 9
    • 6

  4. (H) For y = x², what is the average rate of change between x = 1 and x = 3?

    • 4
    • 2
    • 8
    • 5

  5. (H) For y = x², what is the gradient of the chord between x = 2 and x = 2.1?

    • 4
    • 4.1
    • 5.2
    • 4.01

  6. (H) Using a chord between x = 2 and x = 2.01 on y = x², estimate the gradient of the tangent at x = 2.

    • 3.99
    • 8
    • 4.01
    • 4.1

  7. (H) A distance-time graph has d = t². What is the instantaneous speed at t = 4 seconds?

    • 2 m/s
    • 16 m/s
    • 8 m/s
    • 4 m/s

  8. (H) For d = t², what is the average speed between t = 0 and t = 4 seconds?

    • 16 m/s
    • 8 m/s
    • 2 m/s
    • 4 m/s

  9. (H) Which method estimates the gradient of a tangent to a curve at a point?

    • Use the midpoint of the x-values of the two points
    • Divide the total change in y by the total change in x
    • Estimate with a chord between points very close together
    • Read the y-intercept of the curve at the given point

  10. (H) On a velocity-time graph, what does the gradient at a point represent?

    • The acceleration at that instant
    • The average speed so far
    • The displacement at that instant
    • The initial velocity

  11. (H) Using the derivative of y = x³, find the gradient at x = 2.

    • 8
    • 24
    • 6
    • 12

  12. (H) What is the average rate of change of y = 2x² + 1 between x = 0 and x = 2?

    • 2
    • 8
    • 4
    • 9

  13. (H) What is the average rate of change of y = 1/x between x = 1 and x = 1.5?

    • −2/3
    • −1/2
    • −3/2
    • 2/3

  14. (H) What is the equation of the tangent to y = x² at the point (1, 1)?

    • y = 2x − 1
    • y = 2x + 1
    • y = x² − 1
    • y = x − 1

  15. (H) The position of an object is s = 5t² metres. What is its velocity at t = 2 seconds?

    • 20 m/s
    • 25 m/s
    • 10 m/s
    • 40 m/s

  16. (H) What does it mean when the gradient of a curve is increasing?

    • The curve is a straight line
    • The curve has no tangent
    • The instantaneous rate of change is increasing
    • The average rate of change is always zero

  17. (H) What is the average rate of change of y = 1/x between x = 2 and x = 4?

    • 0.125
    • −0.125
    • −0.25
    • −0.5

  18. (H) An average rate of change of population is 50 per year over 10 years. What does this mean?

    • The population fell by 50 each year
    • The population grew by 500 in 10 years on average
    • The population was 50 at year 10 exactly
    • The population doubled every 10 years

  19. (H) For y = 3x², what is the gradient at x = −1?

    • 6
    • −3
    • 3
    • −6

  20. (H) Why is the gradient of a chord only an approximation to the gradient of a tangent?

    • The chord always passes through the origin of the axes
    • The chord spans a range of x-values, not just one point
    • The chord has its gradient rounded to the nearest whole number
    • The chord is always parallel to the x-axis at that point

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