Modulus equations and inequalities
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 3 worked examples, 5 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Distance, never negative
- What modulus means
- Modulus equals a number
Read the transcript of the teaching part
Distance, never negative
How far is the number minus seven from zero? Seven. The modulus of a number is its distance from zero, so the sign disappears. That small idea creates equations with two answers, and inequalities with two regions.
What modulus means
The modulus of x is x itself if x is positive or zero, and minus x if x is negative. So the modulus of an expression is either the expression, or its negative. Its graph is the graph of f with any part below the axis reflected upwards.
Modulus equals a number
If the modulus of f of x equals a, with a positive, then f of x is a, or f of x is minus a. Take modulus of two x minus five equals three. Either two x minus five is three, or it is minus three. So x equals four, or x equals one. If a is negative, there is no solution at all, because a modulus is never negative.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Modulus graphs and inequalities · Modulus inequalities.
The whole chapter: Algebra.
Chapter 3.1: Algebra
- Modulus equations and inequalities 5 min
- The remainder and factor theorems and cubic equations 6 min
- Rational-index binomial expansions, partial fractions and polynomial division 7 min
Also for A Level Maths 9709 Paper 3
Which topics come up most in A Level Maths 9709 Paper 3 past papers, counted from every paper since 2004.