CIE A Level Maths: Pure 3

Revision Notes

6.1.2 Change of Sign Failure

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Change of Sign Failure

When can the sign change method fail?

  • There are certain circumstances where a change of sign fails to appropriately reflect the number or existence of roots
  • If the interval is too large there may be more than one root within it
    • An even number of roots mean roots are missed entirely as a sign change is not identified
    • An odd number of roots ( > 1 ) may mean not ALL roots are identified

  • In a discontinuous a sign change may occur which is not caused by a root but by an asymptote
  • If a function touches the x-axis but does not pass through it there would be a root but no sign change

Change of Sign Failure Diagram 1, 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.