Edexcel A Level Maths: Pure

Revision Notes

10.1.1 Change of Sign

Change of Sign

What does a change of sign mean?

  • A sign change between f(a) to f(b) means there must be a root between a and b
  • When an equation cannot be solved using the usual analytical methods, we can use change of sign to find approximate solutions
  • We can say a root lies within a particular interval or is correct to a given accuracy
  • Bounds can be used to show a root is correct
  • Using sign change to find a root is only appropriate for continuous functions in a small interval

Change of Sign Diagram 1, AS & A Level Maths revision notes

Exam Tip

  • Remember this will only work if the function is continuous and the interval is small enough.
  • Sign change questions may be part of bigger numerical methods questions.

Worked example

Change of Sign Example Solution, AS & A Level Maths revision notes

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Lucy

Author: Lucy

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels. Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. Lucy has created revision content for a variety of domestic and international Exam Boards including Edexcel, AQA, OCR, CIE and IB.