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The modulus function |x| gives the size of a number regardless of sign. This topic covers sketching y = |f(x)| and y = f(|x|), and solving modulus equations and inequalities. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
The modulus gives the size, ignoring sign, so the graph of the modulus of a function reflects any negative part above the axis. To solve a modulus equation, split it into the positive and negative cases, solve both, then check each against the original — some will not fit.
Before you start
The groundwork here is graph transformations and inequalities. It belongs to the Pure 3 specification. This is the foundation for solving modulus equations.
What you learn
The modulus (or absolute value) |x| is the size of x, ignoring sign. |x| equals x when x is zero or positive, and -x when x is negative. The graph of y=|ax+b| is a V whose vertex sits on the x-axis, where ax+b=0. To draw y=|f(x)|, keep every part of y=f(x) that is on or above the x -axis, and reflect the parts below the axis up in the x -axis. To solve |f(x)|=c (with c≥ 0), solve both f(x)=c and f(x)=-c. The course works through the modulus function, sketching y = |f(x)|, sketching y = f(|x|), and the difference, solving modulus equations and modulus graphs and lines. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Modulus Function is part of the Algebra strand of our free A-level maths courses, studied in the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Related topics students usually take next include Partial Fractions, Quadratic Functions & Discriminant and Solving Quadratics. Endless extra practice on this strand is available on the Algebra revision engine, which generates a fresh question each time.
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