Edexcel A Level Maths: Pure

Revision Notes

2.8.5 Modulus Functions - Solving Equations

A Level Only

Modulus functions

  • The modulus function makes any ‘input’ positive
  • |x| = x   if x ≥ 0   |f(x)| = f(x)   if f(x) ≥ 0
  • |x| = -x if x < 0   |f(x)| = -f(x)   if f(x) < 0
  • Sometimes called absolute value

 

Modulus Functions - Solving Equations Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

Modulus graphs and equations

Modulus Functions - Solving Equations Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

 

  • 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

 

How do I solve modulus equations?

Modulus Functions - Solving Equations Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes

 

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

A Level Only

Worked Example

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

 

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

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