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Solving Equations with Modulus Functions (OCR A Level Maths A): Revision Note

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OCR Maths A: PureCambridge (CIE) Maths: Pure 3AQA Maths: PureEdexcel Maths: Pure

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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

Examiner Tips and Tricks

  • 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 Notes
Modulus functions - Solving Equations Example Diagram 2
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Paul

Author: Paul

Expertise: Maths Content Creator

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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