Solving Quadratic Equations (CIE A Level Maths: Pure 1)

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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 tooSolving 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 workSolving 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 Tip

  • 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

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.