A Level Maths: The Modulus Function Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
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Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Functions — the modulus function is a function with specific properties
- Transformations — needed for sketching modulus graphs as transformations
- Quadratic Equations — needed for solving the equations in each case
A Level Maths the modulus function introduces $|x|$, the absolute value of $x$. This is the function that strips away the sign, so $|3| = 3$ and $|-3| = 3$. Although the function looks simple, working with it requires careful case-splitting that exercises many of the skills you have already built in Functions.
You sketch the graph of $y = |f(x)|$ by reflecting any parts of $y = f(x)$ below the $x$-axis up above it. You sketch the graph of $y = f(|x|)$ by taking the right-hand side of the original graph and reflecting it to the left. You solve equations involving moduli by considering positive and negative cases separately, then checking each solution back in the original equation (some solutions may be spurious). You solve inequalities like $|2x + 1| < 5$ by translating to $-5 < 2x + 1 < 5$ and solving the resulting linear inequality. For more complex modulus inequalities involving two moduli, you split into cases or use sketching.
The modulus function is part of the Pure Maths strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: $|x| = -x$ for negative $x$, NOT for all $x$ — be careful to apply the right case in each region; when solving $|f(x)| = g(x)$, always check solutions in the original equation, as the squaring approach can introduce spurious solutions; the graphs $y = |f(x)|$ and $y = f(|x|)$ are DIFFERENT — make sure you sketch the right one; and for inequalities with two moduli like $|x – 1| < |x + 2|$, split into the three or four regions defined by the moduli rather than guessing.