Modulus equations and inequalities
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers 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
Last time
Before we start: last time, in Cubic graphs and cubic inequalities, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
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 equations · Modulus inequalities.
The whole chapter: Equations, Inequalities and Graphs, Simultaneous Equations.
Chapter 4: Equations, inequalities and graphs
- Cubic graphs and cubic inequalities 5 min
- Modulus equations and inequalities 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.