Lesson R15

R15 interpret the gradient at a point on a curve as the instantaneous rate of change Quiz: Pearson Edexcel Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson R15, interpret the gradient at a point on a curve as the instantaneous rate of change: 20 multiple choice questions for the Pearson Edexcel GCSE Maths (1MA1), Unit 3: Ratio, proportion and rates of change, written with Revision Ninja.

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The 20 questions

  1. What does the gradient of a tangent drawn to a curve represent?

    • Total accumulated change
    • Average rate of change
    • Constant rate of change
    • Instantaneous rate of change

  2. What does the gradient of a chord joining two distinct points on a curve give?

    • Minimum rate of change
    • Average rate of change
    • Maximum rate of change
    • Instantaneous rate of change

  3. As the two points defining a chord on a curve move closer together, what does the chord approach?

    • Asymptote
    • Tangent
    • Axis
    • Normal

  4. How do you find the instantaneous speed on a distance-time curve?

    • gradient of tangent
    • area under curve
    • gradient of chord
    • y intercept value

  5. What does the gradient of a tangent at a point on a curve represent?

    • Average rate of change
    • Total change
    • Initial value
    • Instantaneous rate of change

  6. On a velocity-time graph, the gradient of the graph gives:

    • distance travelled
    • displacement
    • acceleration
    • average velocity

  7. The gradient of a chord between (a, f(a)) and (b, f(b)) is:

    • (f(b) − f(a)) ÷ (b − a)
    • f(a) + f(b)
    • f(b) ÷ f(a)
    • (b − a) ÷ (f(b) − f(a))

  8. To estimate the gradient at a point on a curve, what should you draw?

    • a tangent
    • a chord
    • a perpendicular line
    • a line of symmetry

  9. What is the average gradient of y = x² between x = 1 and x = 3?

    • 6
    • 2
    • 4
    • 8

  10. A tangent at (2, 5) to a curve passes through (4, 9). What is its gradient?

    • 4
    • 14
    • 2
    • 0.5

  11. On a distance-time graph, the tangent at t = 10 s passes through (8, 40) and (12, 88). What is the speed?

    • 12 m/s
    • 6 m/s
    • 48 m/s
    • 0.083 m/s

  12. What is the average gradient of y = x³ between x = 0 and x = 2?

    • 2
    • 4
    • 16
    • 8

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

    • 5
    • 45
    • 15
    • 16

  14. A water height h (cm) against time t (min) has h(2) = 6 and h(5) = 24. What is the average rate of change?

    • 18 cm/min
    • 3 cm/min
    • 10 cm/min
    • 6 cm/min

  15. A population-time graph has a tangent gradient of 120 at 3 years. What does this mean?

    • Grew by 120 over 3 years
    • Decreasing by 120 per year
    • Growing by 120 per year
    • Total population is 120

  16. What is the gradient of the chord of y = x² from x = 1 to x = 1.1?

    • 1.1
    • 2
    • 2.1
    • 2.5

  17. Using a chord from x = 2 to x = 2.01 on y = x³, the gradient approximates the rate at x = 2. What is it, to 2 decimal places?

    • 12.6
    • 13.06
    • 12
    • 12.06

  18. What is the equation of the tangent to y = x² at (3, 9), which has gradient 6?

    • y = 3x
    • y = 9x − 18
    • y = 6x + 9
    • y = 6x − 9

  19. What does a tangent gradient of zero on a curve indicate?

    • an asymptote
    • an inflection point
    • the y-intercept
    • a stationary point

  20. For d = t² metres, estimate the speed at t = 5 s using the chord from t = 5 to t = 5.1.

    • 25.5 m/s
    • 10.5 m/s
    • 10 m/s
    • 10.1 m/s

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