Cambridge IGCSE Additional Mathematics · Syllabus 0606 · Equations, Inequalities and Graphs
Modulus
What is Modulus?
The modulus of a real number, written with vertical bars, is its distance from zero on the number line, so it is never negative: it equals the number itself when the number is positive or zero, and the negative of the number when the number is negative. Because two different values can sit the same distance from zero, an equation containing a modulus normally produces two branches, both of which must be solved and then tested against any conditions the original equation imposes.
This definition is part of the Equations, Inequalities and Graphs chapter in Cambridge IGCSE Additional Mathematics.
Modulus in context
A modulus measures distance from zero, so it never returns a negative value and it always offers two ways in. A substitution exposes a quadratic hiding inside a quartic, a logarithm or an exponential. A cubic drawn from its three factors turns an awkward inequality into interval reading. In every case the original equation or graph — not the convenient rewritten one — is the final authority.