DfE statement N8 · Number
Exact calculation: fractions, surds and π
Exact calculation: fractions, surds and π is content statement N8 of the DfE GCSE mathematics subject content, in the number area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Calculate exactly with fractions, surds and multiples of π; simplify surd expressions involving squares (e.g. √12 = √(4×3) = √4 × √3 = 2√3) and rationalise denominators." (statement N8). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "surds", "simplify surd expressions involving squares and rationalise denominators". Everything else in the statement is Foundation content.
Calculator
This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.
Common mistakes
- Splitting a root over an addition: √(9 + 16) is 5, not √9 + √16 = 7.
- Simplifying √12 as 3√2. Take out the largest square factor: √12 = √4 × √3 = 2√3.
- Rationalising by multiplying only the denominator by the surd, which changes the value of the fraction. Multiply numerator and denominator.
- Leaving √9 unsimplified inside an answer, so 2√3 × 3√3 is written as 6√9 rather than 18.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is exact calculation: fractions, surds and π on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "surds", "simplify surd expressions involving squares and rationalise denominators" — are Higher only; the rest is Foundation content.
Can I use a calculator for exact calculation: fractions, surds and π?
Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.
What is the single most common mistake here?
Splitting a root over an addition: √(9 + 16) is 5, not √9 + √16 = 7.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Number at Foundation or at Higher.