4.6 Understand and use the notation d2y/dx2 Quiz: AQA Further Maths, Unit 4

The 20 questions

1. What rate of change does the second derivative d²y/dx² measure?

   • Rate of gradient
   • Rate of x
   • Value of y
   • Area under curve

2. If y = x^3, what is d^2y/dx^2?

   • x^2
   • 6
   • 6x
   • 3x^2

3. What is d^2y/dx^2 for y = x^4?

   • 12x^2
   • 12x
   • x^2
   • 4x^3

4. What is d^2y/dx^2 for y = 5x^2 + 2x?

   • 10x
   • 5
   • 10
   • 2

5. For y = x^3 - x, what is d^2y/dx^2 at x = 2?

   • 6
   • 10
   • 12
   • 4

6. If d^2y/dx^2 is positive at a point, the curve there is:

   • Concave down
   • Linear
   • Concave up
   • Horizontal

7. For y = 2/x, what is d^2y/dx^2?

   • 2/x^3
   • 4/x^2
   • -4/x^3
   • 4/x^3

8. What mathematical term describes the notation d²y/dx²?

   • Partial derivative
   • Integral
   • Second derivative
   • First derivative

9. For y = x^3 - 3x^2, what is d^2y/dx^2 at x = 1?

   • 0
   • -6
   • 6
   • 3

10. What is d^2y/dx^2 for y = -x^2?

    • -2x
    • -2
    • -x
    • 2

11. For y = x^4 - 4x^3, what is d^2y/dx^2 at x = 3?

    • 36
    • 72
    • 24
    • -36

12. A particle has s = t^3 - 4t^2. What is its acceleration at t = 2?

    • -4
    • 4
    • 8
    • 12

13. Which notation means the second derivative of y with respect to x?

    • y''/x
    • d^2y/dx^2
    • d(x^2)/dy
    • (dy/dx)^2

14. For y = x^3 + ax^2, d^2y/dx^2 = 0 at x = 2. Find a.

    • 6
    • 3
    • -3
    • -6

15. What sign does d^2y/dx^2 have where a curve is concave down?

    • Positive
    • Negative
    • Undefined
    • Zero

16. For y = 3x^4 - 4x^3, what is d^2y/dx^2 at x = 1?

    • -12
    • 36
    • 12
    • 24

17. For y = 1/x^2, what is d^2y/dx^2?

    • 6/x^4
    • -6/x^4
    • 2/x^4
    • 6/x^3

18. For y = x^3 - 3x, is the curve concave up or down when x < 0?

    • Linear
    • Flat
    • Concave up
    • Concave down

19. For y = x^4 - 6x^2, at which x is d^2y/dx^2 = 0?

    • x = 6
    • x = 0 only
    • x = 1 or x = -1
    • x = 2 or x = -2

20. If f'(x) = 3x^2 - 6x, what is f''(x)?

    • 6x - 3
    • 3x - 6
    • 6x
    • 6x - 6

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