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

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. What does the gradient of a tangent to a distance-time graph represent?

   • Total distance
   • Instantaneous speed
   • Average speed
   • Acceleration

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. What does the area below the time axis on a velocity-time graph represent?

    • Acceleration
    • Backward displacement
    • Total distance
    • Negative speed

13. What does the gradient of an account balance against time graph represent?

    • Balance growth rate
    • Initial deposit
    • Account duration
    • Total balance

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. What unit represents the area under a speed-time graph?

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