7.3.1 Applying differentiation to gradients, tangents and normals Quiz: Pearson Edexcel Maths, Unit 7

The 20 questions

1. What does the first derivative dy/dx represent at any point on a curve?

   • Gradient of curve
   • Y-intercept
   • Area under curve
   • Second derivative

2. What is the relationship between the gradients of two perpendicular lines like a tangent and normal?

   • Equal
   • Additive inverses
   • Reciprocals
   • Negative reciprocals

3. What is the gradient of the normal to a curve if the tangent gradient is 4?

   • -4
   • 1/4
   • -1/4
   • 4

4. Which formula is used to find the equation of a straight line given a point and gradient?

   • y = mx + c
   • ax + by = c
   • y - y1 = m(x - x1)
   • y2 - y1 = m(x2 - x1)

5. What is the gradient of the tangent to y = x^2 at the point where x = 3?

   • 12
   • 9
   • 6
   • 3

6. At what point on y = x^2 is the gradient equal to 8?

   • x = 4
   • x = 2
   • x = 8
   • x = 16

7. What is the gradient of the normal to y = 3x at any point?

   • 3
   • -3
   • -1/3
   • 1/3

8. What is the gradient of the tangent to y = x^3 - 5x when x = 2?

   • -2
   • 7
   • 12
   • 3

9. What is the y-intercept of the tangent to y = x^2 at the point (2, 4)?

   • -4
   • 4
   • 2
   • 0

10. What is the gradient of a horizontal tangent line on a curve?

    • -1
    • Undefined
    • 0
    • 1

11. What is the gradient of a vertical tangent line on a curve?

    • 1
    • 0
    • Undefined
    • Infinity

12. If the normal to a curve has gradient 2, what is the gradient of the tangent?

    • 1/2
    • 2
    • -2
    • -1/2

13. What is the equation of the tangent to y = x^2 at x = 0?

    • y = x
    • y = 2x
    • y = 0
    • x = 0

14. Find the x-coordinate where the tangent to y = 4x - x^2 has a gradient of zero.

    • x = 1
    • x = 0
    • x = 4
    • x = 2

15. What is the gradient of the tangent to y = 1/x at x = 1?

    • -1
    • 0
    • 1
    • 2

16. What is the gradient of the normal to y = 2x^2 at the point where x = 1?

    • 4
    • -4
    • -1/4
    • 1/4

17. If two curves touch, what must be true of their tangents at the point of contact?

    • Reciprocal gradients
    • Perpendicular gradients
    • Zero gradients
    • Equal gradients

18. What is the gradient of the tangent to y = e^(2x) when x = 0?

    • 0
    • e
    • 1
    • 2

19. What is the exact gradient of the tangent to y = ln(x) at x = e?

    • 0
    • e
    • 1/e
    • 1

20. What is the gradient of the tangent to y = sin(x) at the point where x = 0?

    • 1
    • 0
    • undefined
    • -1

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