What you need to know
Check yourself against these “I can” statements.
- I can simplify and expand expressions involving surds
- I can find unknown values by comparing both sides, like √2(3 + a) = b√2 + 4
- I can rationalise denominators, including ones like 2/(3 + √5)
- I can write expressions with roots and powers of x as a single power of x (Further Maths)
- I can solve equations with fractional powers, like x^(-1/2) = 3 (Further Maths)
- I can solve hidden quadratics, like x⁴ − 3x² + 2 = 0 (Further Maths)
Practise this topic
8 resourcesAdvanced Surds
Surds in problems: missing sides from an area, Pythagoras, similar shapes and volumes, linear and simultaneous equations with surd coefficients, substituting, finding unknown integers, surds with letters, indices, quadratic…
⚙️ WorksheetFractional Indices with Algebra
Negative and fractional indices, standard index form, changing the base and combining like terms. Four difficulty levels, timed, click to reveal.
⚙️ WorksheetOperations with Surds
Simplifying, adding, multiplying and squaring surds, expanding brackets, rationalising denominators (a√b and a + b√c), dividing surds, adding and dividing surd fractions, and writing expressions in the form k√n. Fourteen…
⬢ BlockbustersAdvanced Surds Blockbusters
Blockbusters with the questions from the Advanced Surds worksheet: choose its levels for the ordinary hexagons and for the harder ★ ones. Show the answer and the worked solution, or play against the computer with multiple choice.
🔤 Fill the GapsFill the Gaps: Maths Vocabulary
A sentence explaining one of the unit’s key words, with gaps. Pick the right word for each gap from the words scattered round it: the right ones and plenty of wrong ones. A deck for every unit.
⬢ BlockbustersFractional Indices with Algebra Blockbusters
Blockbusters with the questions from the Fractional Indices with Algebra worksheet: choose its levels for the ordinary hexagons and for the harder ★ ones. Show the answer and the worked solution, or play against the computer with…
⬢ BlockbustersOperations with Surds Blockbusters
Blockbusters with the questions from the Operations with Surds worksheet: choose its levels for the ordinary hexagons and for the harder ★ ones. Show the answer and the worked solution, or play against the computer with multiple…
🧩 ConnectionsSurds
Match surds with the same value, from √50 and 5√2 to √2 × √25 and 10/√2. Near-misses like 5√2, 2√5 and √10 from Standard; rationalising on Hard.
These are the pages for Surds & Indices in the GCSE + AQA Further Maths scheme of work, following Pearson Edexcel GCSE (9–1) Higher (1MA1), plus AQA Level 2 Further Mathematics (8365). Open this topic in Mr Wells Maths to see it alongside the rest of the course.