4.2 Know that the gradient of a function is the gradient of the tangent at that point. Quiz: AQA Further Maths, Unit 4

The 20 questions

1. The gradient of a curve at a point equals the gradient of its what at that point?

   • Normal
   • Chord
   • Tangent
   • Radius

2. A tangent touches y = x^2 at x = 1. What is its gradient?

   • 1
   • 2
   • -2
   • 0.5

3. Which point lies on the tangent to y = x^2 at x = 1?

   • (3, 2)
   • (2, 3)
   • (2, 4)
   • (0, 1)

4. What is the gradient of y = x^3 at x = 3?

   • 9
   • 18
   • 27
   • 3

5. How does the gradient of a tangent compare to the gradient of the curve at contact?

   • It is identical
   • It is zero
   • It is perpendicular
   • It is doubled

6. For y = 2x^3, what is the gradient at x = -1?

   • -2
   • 2
   • 6
   • -6

7. Which curve has a tangent with gradient 0 at x = 0?

   • y = 1/x
   • y = x^2 + 5
   • y = x^2 + 5x
   • y = 2x + 3

8. The tangent to y = x^2 at (2, 4) has what gradient?

   • 2
   • 4
   • -4
   • 8

9. A ball's height is h = 20t - 5t^2. What is the rate of change of height at t = 2?

   • 20
   • 0
   • 10
   • -10

10. What is the equation of the tangent to y = x^2 - 2x at x = 3?

    • y = 3x - 6
    • y = 2x - 3
    • y = 4x - 9
    • y = 4x + 9

11. What is the gradient of y = x^2 at x = 0.5?

    • 0.5
    • 1
    • 2
    • 0.25

12. At which point on y = x^2 is the tangent parallel to y = 6x + 1?

    • (3, 6)
    • (2, 4)
    • (3, 9)
    • (6, 36)

13. What is the gradient of y = 4x^2 - x at x = 1?

    • 3
    • -7
    • 8
    • 7

14. A curve has a tangent with gradient -3 at x = 2. What does this indicate about the curve there?

    • It is constant
    • It is increasing
    • Its y-value is -3
    • It is decreasing

15. For y = x^3, at x = a the tangent has gradient 12 and a is positive. Find a.

    • 3
    • 2
    • 4
    • 6

16. What is the gradient of y = 5 - 2x at any point?

    • 5
    • -5
    • -2
    • 2

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

    • 2
    • -2
    • -1
    • 1

18. The tangent to y = x^2 at (1, 1) crosses the x-axis at which point?

    • (1, 0)
    • (0.5, 0)
    • (-1, 0)
    • (2, 0)

19. How many tangent lines does a curve have at one point of contact?

    • One
    • Infinitely many
    • Two
    • None

20. For y = x^3 - 2x^2 + x, what is the gradient at x = 2?

    • 9
    • 3
    • 5
    • 7

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