O LevelAdditional MathsCambridgeRevision NotesCalculusDifferentiationConnected Rates of Change

Connected Rates of Change (Cambridge O Level Additional Maths)

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Connected Rates of Change

What are connected rates of change?

  • In situations involving more than two variables you can use the chain rule to connect multiple rates of change into a single equation
  • Look out for the word "rate"
    • This implies a derivative is involved
    • e.g. The height is increasing at a rate of 4 cm per second means fraction numerator d h over denominator d t end fraction equals 4
  • If the variable is decreasing then the rate will be negative
    • e.g. The height is decreasing at a rate of 4 cm per second means fraction numerator d h over denominator d t end fraction equals negative 4

 Example of a connected rates of change problem

Examiner Tip

  • These problems can involve a lot of letters
    • be sure to keep track of what they all refer to
  • Be especially sure that you are clear about which letters are variables and which are constants
    • these behave very differently when differentiation is involved!

Worked example

Conn Rates of Ch Example, A Level & AS Level Pure Maths Revision Notes

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    Amber

    Author: Amber

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    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.