Solving Quadratic Equations (AQA AS Maths) : Revision Note

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Solving Quadratic Equations

Solving quadratic equations

  • We can solve quadratic equations when they are written in the form a x squared plus b x plus c equals 0

  • If given an unusual looking equation, try to rearrange it into this form first

  • The three ways to solve a quadratic you must know are

    • Factorising

    • Completing the square

    • Quadratic formula

Solving a quadratic equation by factorising

  • Factorising is a great way to solve a quadratic quickly but won't work for all quadratics

  • If the numbers are simple, try factorising first

  • Once factorised, set each bracket to = 0 and solve

Solving Quadratic Equations Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

Solving a quadratic equation by completing the square

  • Completing the square will work for any quadratic

  • Make sure you know how to complete the square

  • Remember this will help with questions involving turning points too

    Solving Quadratic Equations Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

     

Solving a quadratic equation by the quadratic formula

  • The quadratic formula might look complicated but it just uses the coefficients a, b and c from the quadratic equation 

  • The quadratic formula will work for any quadratic

Solving Quadratic Equations Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes

 

Solving a quadratic equation by using a calculator

  • Most calculators now have the ability to solve quadratics

  • Get used to how your calculator functions work

    Solving Quadratic Equations Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes
  • So the solution to the quadratic equation 2 x squared plus 5 x space minus space 12 space equals space 0 are x = 1.5 and x = -4

Examiner Tips and Tricks

  • A calculator can be super-efficient but be aware some marks are for method

  • There will never be many marks for solving a quadratic at AS/A level

  • Use your judgement:

    • is it a “show that” or “prove” question?

    • how many marks?

    • how long is the question?

  • Remember the quadratic formula with a song... there are loads of fun ones on YouTube

Worked Example

Solving Quadratic Equations Example Diagram, 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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