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Edexcel A Level Maths: Pure:復(fù)習(xí)筆記2.8.5 Modulus Functions - Solving Equations

Category: A-level課程, 國(guó)際課程, 教材筆記, 福利干貨 Date: 2022年10月26日 上午11:38

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 ?the two possible equations are

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 - 4 = 2-5 but it is not a solution to |-4| = 2-5?(substitute?x?= 1 into both sides and see why it does not work).

Worked Example

2.8.5-Modulus-functions-Solving-Equations-Example-Diagram-12.8.5-Modulus-functions-Solving-Equations-Example-Diagram-2

 

 

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