CIE AS Maths: Pure 2

Revision Notes

1.1.2 Modulus Functions - Solving Equations

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Modulus Functions - Solving Equations

Modulus graphs and equations

  • Two non-parallel straight-line graphs would intersect once
  • If modulus involved there could be more than one intersection
  • Deducing where these intersections are is crucial to solving equations

2-8-5-modulus-functions---solving-equations-notes-diagram-2_1

 

How do I solve modulus equations?

  • STEP 1        Sketch the graphs including any modulus (reflected) parts
        • (see Modulus Functions – Sketching Graphs)
  • STEP 2        Locate the graph intersections
  • STEP 3       Solve the appropriate equation(s) or inequality
        • For vertical line straight f left parenthesis x right parenthesis vertical line equals vertical line straight g left parenthesis x right parenthesis vertical line the two possible equations are straight f left parenthesis x right parenthesis equals straight g left parenthesis x right parenthesis and straight f left parenthesis x right parenthesis equals negative straight g left parenthesis x right parenthesis

2-8-5-modulus-functions---solving-equations-notes-diagram-32-8-5-modulus-functions---solving-equations-notes-diagram-3_1

Exam Tip

  • Sketching the graphs is important as solving algebraically can lead to invalid solutions.
  • For example, x = 1 is a solution to x minus 4 equals 2 x minus 5 but it is not a solution to vertical line x minus 4 vertical line equals 2 x minus 5 (substitute x = 1 into both sides and see why it does not work).

Worked example

Modulus functions - Solving Equations Example Diagram 1, A Level & AS Level Pure Maths Revision NotesModulus functions - Solving Equations Example Diagram 2

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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.