Edexcel A Level Maths: Pure

Revision Notes

8.3.4 Modelling with Differential Equations

A Level Only

What can be modelled with differential equations?

  • Derivative terms like dy/dx are “rates of change”


Notes de_scenes, AS & A Level Maths revision notes


  • There are many situations that involve “change”
    • Temperature
    • Radioactivity
    • Medication
    • Sales

How do I set up a model with differential equations?

  • The first task is to set up a differential equation from a description in words:


Notes de_setup, AS & A Level Maths revision notes

  • Important phrases here are …
    • … “rate of change” – reference to a derivative term like dy/dx
    • directly/inversely proportional to – y = kx, y = k ÷ x
    • formulate – means to write as an equation
      • you may need to choose and define letters for variables
      • V for volume, h for height (of a cylinder, say)


8.3.4 Notes de_setup2, AS & A Level Maths revision notes

  • Some differential equations may involve Connected Rates of Change


Notes de_croc_setup, AS & A Level Maths revision notes

Exam Tip

Use a highlighter (or underline) to pick out important words/phrases.

Read and re-read the question several times.

Jot down bits and pieces as you go; do not expect to go straight from reading to writing down a differential equation.

A Level Only

Worked Example

Example soltn, AS & A Level Maths revision notes


After 24 years teaching A Level Further Maths, Maths whizz Simon focused his attention on tutoring. He’s helped thousands of young people make sense of Maths and now he’s helping you too – aren’t you lucky! He’s even worked as an Edexcel examiner, so knows exactly what they’re looking for.

Join Save My Exams

Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Join Now