4.5 Increasing and decreasing functions Quiz: AQA Further Maths, Unit 4

The 20 questions

1. A function is described as increasing when its gradient dy/dx is what?

   • Negative
   • Zero
   • Undefined
   • Positive

2. A function is described as decreasing when its gradient dy/dx is what?

   • Positive
   • Infinite
   • Negative
   • Zero

3. For y = x^2, on which interval is the function increasing?

   • x = 0 only
   • x > 0
   • x < 0
   • All x

4. Over which set is y = x^3 increasing?

   • All real numbers
   • x = 0 only
   • x > 0 only
   • x < 0 only

5. For y = -x + 3, which describes the function?

   • Constant
   • Increasing for all x
   • Decreasing for all x
   • Increasing only for x > 3

6. For y = x^3 - 3x, where is the function increasing?

   • x > 0
   • -1 < x < 1
   • x < 0
   • x < -1 or x > 1

7. For y = x^2 - 4x, where is the function decreasing?

   • x < 2
   • x > 2
   • x > -2
   • x < -2

8. If dy/dx = -5 at x = 3, what type of function is it at x = 3?

   • Decreasing
   • Increasing
   • Periodic
   • Stationary

9. The temperature T of a cooling cup of tea falls for t > 0. What is the sign of dT/dt?

   • Negative
   • Positive
   • Zero
   • Undefined

10. For y = 2x^3 - 3x^2 - 12x, where is dy/dx positive?

    • -1 < x < 2
    • x > -1 only
    • x < 2 only
    • x < -1 or x > 2

11. For y = 1/x, what is the sign of dy/dx for all valid x?

    • Positive
    • Zero
    • Negative
    • Variable

12. For y = x^2 - 6x + 5, for which x is the function decreasing?

    • x > 3
    • x > 6
    • x < 6
    • x < 3

13. For which values of x is y = x^4 increasing?

    • x < 0
    • x > 0
    • x > 1
    • All x

14. A function increases on (0, 2) and decreases on (2, 5). At what x-value is the local maximum?

    • x = 3.5
    • x = 2
    • x = 0
    • x = 5

15. For y = x^3 - 12x, over which interval is the function decreasing?

    • x > 2
    • x < -2 or x > 2
    • -2 < x < 2
    • x < -2

16. Which gradient condition describes a function that is increasing on an interval?

    • Zero gradient
    • Infinite gradient
    • Positive gradient
    • Negative gradient

17. For y = x^3 - 6x^2 + 9x, where is the function increasing?

    • x < 3 only
    • x < 1 or x > 3
    • x > 1 only
    • 1 < x < 3

18. If dP/dt > 0 for all t, what is happening to the population P?

    • Remaining constant
    • Always increasing
    • Oscillating
    • Always decreasing

19. For y = 2x^2 + 8x + 3, for which x is the function decreasing?

    • x < -2
    • x > -2
    • x < 2
    • x > 2

20. What type of point on a curve occurs where dy/dx = 0?

    • Discontinuity
    • Stationary point
    • Asymptote
    • Inflection only

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