4.1 Know that the gradient function dy/dx gives the gradient of the curve and measures the rate of change of y with respect to x Quiz: AQA Further Maths, Unit 4

The 20 questions

1. What does the gradient function dy/dx measure on a graph of y against x?

   • Maximum value
   • Total area
   • Rate of change
   • Y-intercept

2. If y = x^2, what is dy/dx?

   • x
   • x^2
   • 2
   • 2x

3. For y = x^3, what is dy/dx when x = 2?

   • 3
   • 12
   • 6
   • 8

4. If y = 3x^2, what is dy/dx when x = 1?

   • 1
   • 9
   • 3
   • 6

5. If dy/dx = 4 at a point on a curve, what is the gradient of the curve there?

   • 4
   • 0.25
   • -0.25
   • -4

6. What is dy/dx for the constant function y = 5?

   • 5
   • 0
   • x
   • 1

7. If dh/dt = -3 at t = 2, what is happening to the height h?

   • Remaining constant
   • Decreasing
   • Undefined
   • Increasing

8. Cost C = 2x^2 + 5x. What is dC/dx when x = 3?

   • 17
   • 11
   • 23
   • 6

9. What is the gradient function of y = x^4?

   • 4x^3
   • x^4/4
   • x^3
   • 4x^4

10. For y = x^2 + 3x, at which x is dy/dx equal to 0?

    • x = 3
    • x = 0
    • x = 1.5
    • x = -1.5

11. Displacement s = t^3 - 6t. What is the velocity ds/dt at t = 2?

    • -6
    • 12
    • 2
    • 6

12. Another name for the gradient function dy/dx is:

    • The intercept
    • The derivative
    • The integral
    • The average gradient

13. The gradient function of a curve is 2x - 4. At which x is the gradient zero?

    • x = 4
    • x = 0
    • x = -2
    • x = 2

14. For the curve y = x^3 - 3x, at which x values is the gradient zero?

    • x = 1 only
    • x = 1 or x = -1
    • x = 0 or x = 3
    • x = 3 or x = -3

15. For y = 2x^2 - 8x + 1, the gradient is zero at x = k. Find k.

    • 8
    • -2
    • 2
    • 4

16. For y = 6x^2 - 3x + 2, what is dy/dx when x = 1?

    • 3
    • 15
    • 9
    • -9

17. For a sphere, V = (4/3) pi r^3. What is dV/dr?

    • 4 pi r^2
    • 12 pi r^3
    • 4 pi r
    • (4/3) pi r^2

18. What is the gradient of y = (x + 1)(x - 2) at x = 0?

    • -2
    • 0
    • -1
    • 1

19. Find the x-coordinate where y = x^2 - 4x + 7 has gradient 2.

    • 2
    • 1
    • 3
    • 4

20. For y = x^5, what is dy/dx at x = -1?

    • 1
    • -5
    • -1
    • 5

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