4.3 Differentiation of kx^n where n is an integer, and the sum of such functions Quiz: AQA Further Maths, Unit 4

The 20 questions

1. What is the derivative of k x^n with respect to x?

   • k x^(n-1)
   • k x^(n+1)
   • n k x^n
   • n k x^(n-1)

2. What is d/dx of 3x^4?

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

3. What is d/dx of 7x?

   • 7x
   • 1
   • 0
   • 7

4. What is d/dx of 9?

   • 0
   • 9
   • 9x
   • 1

5. What is d/dx of x^-2?

   • -2x^-1
   • 2x^-3
   • -2x^-3
   • -x^-3

6. Differentiate 5x^2 + 3x - 4.

   • 5x + 3
   • 10x + 3
   • 10x - 4
   • 10x + 3 - 4

7. Given y = 4/x^3, find dy/dx.

   • -4/x^4
   • -12/x^4
   • -12/x^3
   • 12/x^4

8. Given y = 5/x, find dy/dx.

   • -5/x^2
   • -1/(5x)
   • 5/x^2
   • -5x

9. Given y = (3x + 2)(x - 3), find dy/dx.

   • 6x + 7
   • 6x - 6
   • 6x - 7
   • 3x - 7

10. For y = x^3 - 4x, what is the gradient at x = -1?

    • -7
    • -1
    • 7
    • 1

11. Find dy/dx for y = 2x^2 + 1/x^2.

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

12. Find dy/dx for y = x^4 - 2x^2 + 7.

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

13. For y = 5x^3 - 2x^2 + x - 8, find dy/dx at x = 1.

    • 14
    • 10
    • 16
    • 12

14. Differentiate f(x) = x(x^2 - 1).

    • x^2 - 1
    • 3x^2 - 1
    • 3x^3 - x
    • 3x^2 + 1

15. For y = (2x - 1)^2, what is dy/dx at x = 0?

    • 4
    • -4
    • 1
    • -1

16. Given f(x) = 2x^3 + kx and f'(1) = 10, find k.

    • 10
    • 4
    • -4
    • 6

17. Which expression is the derivative of y = 3x^-2?

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

18. The gradient of y = ax^2 + 3x at x = 2 is 11. Find a.

    • -2
    • 1
    • 2
    • 4

19. Expand (x + 2)^3 and differentiate. What is dy/dx for y = (x + 2)^3?

    • 3x^2 + 6x + 12
    • 3x^2 + 12x + 12
    • x^2 + 4x + 4
    • 3x^2 + 6x + 8

20. For y = x^4 - 3x^2, find dy/dx at x = -2.

    • 20
    • -8
    • -4
    • -20

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