7.1.1 Derivative as the gradient of a tangent Quiz: Pearson Edexcel Maths, Unit 7

The 20 questions

1. What does the derivative of a function represent graphically at any given point?

   • Gradient of normal
   • Y-intercept
   • Gradient of tangent
   • Area under curve

2. What is the gradient of the normal line perpendicular to a tangent with gradient 4?

   • 4
   • -1/4
   • 1/4
   • -4

3. Find the gradient of the curve y equals x squared at the point where x equals 3.

   • 3
   • 12
   • 9
   • 6

4. What is the derivative of f of x equals x cubed?

   • x cubed
   • x squared
   • 3x cubed
   • 3x squared

5. At a stationary point on a curve, what is the value of the derivative?

   • Undefined
   • 1
   • Infinity
   • 0

6. What term describes a small change in x used when defining the derivative from first principles?

   • epsilon
   • delta x
   • theta
   • delta y

7. What notation represents the derivative of y with respect to x?

   • f dash x
   • delta y by delta x
   • y squared
   • dy by dx

8. What is another common prime notation for the derivative of function f of x?

   • f inverse x
   • f squared x
   • int f x
   • f dash x

9. Find the gradient of the tangent to y equals 4x minus 3 at any point.

   • 0
   • 4
   • 4x
   • -3

10. What is the gradient of the tangent to the horizontal line y equals 7?

    • 1
    • Infinity
    • 0
    • 7

11. What does the limit as delta x approaches zero of delta y over delta x define?

    • The derivative
    • The integral
    • The mean value
    • The chord gradient

12. Find the y-coordinate when x equals 2 on the curve y equals x cubed minus x.

    • 4
    • 6
    • 2
    • 8

13. What is the gradient of the tangent to y equals 5 root x when x equals 4?

    • 5/4
    • 10
    • 20
    • 5/2

14. Find the gradient of the tangent to y equals 2 over x at x equals 1.

    • 1
    • -2
    • -1/2
    • 2

15. At which x value does the curve y equals x squared minus 4x have a horizontal tangent?

    • 2
    • 0
    • 4
    • -2

16. What is the equation of the tangent line to y equals x squared at the origin?

    • y equals 2x
    • y equals 0
    • y equals x
    • x equals 0

17. What is the rate of change of y equals 3x squared plus 5x when x equals 1?

    • 5
    • 11
    • 3
    • 8

18. What shape has a constant tangent gradient everywhere on its curve?

    • Circle
    • Parabola
    • Straight line
    • Cubic

19. Find the gradient of the tangent to y equals e to the power of 2x at x equals 0.

    • 1
    • 0
    • 2
    • e

20. What is the gradient of the tangent to y equals ln x when x equals 1?

    • e
    • 0
    • 1 over e
    • 1

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