A Level Maths: Surds 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.
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:
- Indices — the index laws underpin all surd manipulation, since sqrt(x) is just x^(1/2)
- GCSE Maths Surds — basic surd arithmetic from GCSE is assumed
A Level Maths surds are exact expressions involving roots — numbers like $\sqrt{2}$, $3\sqrt{5}$, or $\sqrt{2} + \sqrt{3}$. They are the way A Level expects you to leave irrational answers, and confident surd work is a high-leverage skill that pays off across Pure Maths papers, in geometry, trigonometry, and calculus.
You simplify surds by extracting square factors ($\sqrt{50}$ becomes $5\sqrt{2}$), add and subtract like surds ($3\sqrt{2} + 4\sqrt{2} = 7\sqrt{2}$), and multiply and divide them using $\sqrt{a}\sqrt{b} = \sqrt{ab}$ and $\sqrt{a}/\sqrt{b} = \sqrt{a/b}$. The most exam-relevant skill is rationalising the denominator: removing surds from the bottom of a fraction by multiplying top and bottom by the conjugate. For $\frac{1}{2 + \sqrt{3}}$, multiply by $\frac{2 – \sqrt{3}}{2 – \sqrt{3}}$ to get a rational denominator. Once fluent with this, exact-answer questions across Circle Geometry, Trigonometry, and Binomial Expansion become routine.
Surds are essential A Level Maths revision content for AQA, Edexcel, OCR, and OCR MEI students, appearing throughout the Pure Maths strand directly and earning exact-answer marks throughout the rest of the syllabus.
Watch out for…
A few things to be careful with: $\sqrt{a+b}$ is NOT $\sqrt{a} + \sqrt{b}$ — for example $\sqrt{9+16} = 5$, not $7$; when an answer is requested in exact form, always rationalise the denominator; expanding the conjugate gives $(a + \sqrt{b})(a – \sqrt{b}) = a^2 – b$, not $a^2 – \sqrt{b}$; always simplify surds fully ($\sqrt{8}$ should be written as $2\sqrt{2}$); and negative numbers under square roots are not in the real number system at A Level Maths.