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Mathematical Requirements (Appendix C)

Tangents and instantaneous rates of change

  • 3 things to know
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Overview

Recall questions on Tangents and instantaneous rates of change.

What you need to know

Answer each one before you reveal it.

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Key term

What is a tangent to a curve at a point?

Key term

How do you find the instantaneous velocity at a specific time from a displacement-time graph?

Key term

How do you find the instantaneous rate of change at a point on a curved graph?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is a tangent to a curve at a point?

    Model answer

    A straight line that touches the curve at that point and has the same gradient as the curve at that point.

  2. 2

    How do you find the instantaneous velocity at a specific time from a displacement-time graph?

    Model answer

    Draw a tangent to the curve at that time and find the gradient of the tangent.

  3. 3

    How do you find the instantaneous rate of change at a point on a curved graph?

    Model answer

    Draw a tangent to the curve at that point and calculate the gradient of the tangent.

  4. 4

    What is a tangent to a curve?

    Model answer

    A straight line that touches the curve at a point and has the same gradient as the curve there.

  5. 5

    Why should you extend the tangent line when finding the gradient of a tangent to a curve?

    Model answer

    To allow accurate gradient calculation by selecting two well-separated points on the tangent.

  6. 6

    After drawing a tangent to a curve, how do you determine the instantaneous rate of change?

    Model answer

    Calculate the gradient of the tangent line using two points on it.

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