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Mathematical Requirements (Appendix C)

Graphs: Intercepts, Rate of Change and Slope of a Tangent to a Curve

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Overview

Recall questions on Intercepts, Rate of Change and Slope of a Tangent to a Curve.

What you need to know

Answer each one before you reveal it.

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Key term

Why is a tangent needed to find the rate of change on a curved graph?

Key term

Why is the initial rate of an enzyme-controlled reaction compared, rather than the rate later on?

Key term

Explain why a graph of product formed against time levels off.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is meant by the intercept of a graph?

    Model answer

    It is the value at which the line crosses an axis, most often the value of the dependent variable when the independent variable is zero.

  2. 2

    How is the compensation point read from a graph of net carbon dioxide exchange against light intensity?

    Model answer

    It is the light intensity at which the line crosses the horizontal axis, because at that point photosynthesis and respiration proceed at the same rate and there is no net exchange.

  3. 3

    A graph that should pass through the origin instead crosses the vertical axis above zero. What does this suggest?

    Model answer

    It suggests a systematic error, such as an instrument that was not zeroed, since a fixed amount has been added to every reading.

  4. 4

    What is a tangent to a curve?

    Model answer

    It is a straight line that touches the curve at a single point and has the same gradient as the curve at that point.

  5. 5

    Why is a tangent needed to find the rate of change on a curved graph?

    Model answer

    The gradient of a curve changes continuously, so the rate at any instant can only be found from the gradient of the tangent at that point.

  6. 6

    Why is the initial rate of an enzyme-controlled reaction compared, rather than the rate later on?

    Model answer

    At the start the substrate is at its full concentration and no product has accumulated, so the initial rate reflects the conditions being tested.

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