Squared Linear Denominators (CIE A Level Maths: Pure 3)

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Squared Linear Denominators

Partial fractions

Squared Linear Denominators Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

  • In partial fractions the common denominator is split into parts (factors)
  • This is the reverse process to adding (or subtracting) fractions
  • In harder questions there is a repeated factor, this is a squared linear factor

What are squared linear denominators?

Squared Linear Denominators Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

  • A linear factor is of the form (ax + b)
  • It is possible b = 0 so a linear factor could be of the form ax (eg 4x)
  • A squared linear factor is of the form (ax + b)2
  • With b = 0 this would be of the form (ax)2 (x2 would be too!)

Squared Linear Denominators Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes 

How do I find partial fractions with squared linear denominators?

STEP 1        Factorise the denominator (Sometimes the numerator can be factorised too)

STEP 2        Split the fraction into a sum with a squared linear denominator and any other single linear denominators

STEP 3        Multiply by the denominator to get rid of fractions

STEP 4        Substitute values of x to find A, B, etc (or use comparing coefficients)

STEP 5        Write the original as partial fractions  

Squared Linear Denominators Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes

Worked example

Squared Linear Denominators Example Diagram, A Level & AS Level Pure Maths Revision Notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.