Approximating Values using the Binomial Expansion (AQA A Level Maths) : Revision Note

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Approximating Values

What is the general binomial expansion?

  • The general binomial expansion, as given in the formula booklet, is

Approximating values Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

  • If n ∈ ℕ then the expansion is finite (see Binomial Expansion)

  • Otherwise the expansion is infinitely long

    • It is only valid for |x| < 1 (-1 < x < 1)

    • Only the first few terms of an expansion are usually needed

How do I use a binomial expansion to approximate a value?

Approximating values Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes
  •  Ignoring higher powers of x leads to an approximation

  • The more terms the closer the approximation is to the true value

  • For most purposes, squared or cubed terms are accurate enough

Approximating values Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes

STEP 1  Compare the value you are approximating to (a + bx)n
STEP 2  Solve the appropriate equation to find the value of x
STEP 3  Substitute this value of x into the expansion to find the approximation

Examiner Tips and Tricks

  • You can get a good idea if your approximation is correct by working out the “real” answer using your calculator.

  • Sometimes it helps to factorise out a number before approximating

    • square root of 710 equals 10 square root of 7.1 end root

Worked Example

  

Approximating values Example Diagram 1, A Level & AS Level Pure Maths Revision Notes
Approximating values Example Diagram 2, A Level & AS Level Pure Maths Revision Notes
Approximating values Example Diagram 3, A Level & AS Level Pure Maths Revision Notes
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Paul

Author: Paul

Expertise: Maths Content Creator (Previous)

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.

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