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DfE statement N6 · Number

Powers and roots

part HigherNon-calculator

Powers and roots is content statement N6 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 3 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: "Use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5; estimate powers and roots of any given positive number." (statement N6). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.

— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement N6

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: "estimate powers and roots of any given positive number". 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

  • Reading 5³ as 5 × 3 = 15 rather than 5 × 5 × 5 = 125.
  • Estimating a square root by halving: giving √50 as 25 instead of a little over 7.
  • Assuming the square root of a number between 0 and 1 is smaller than the number — √0.25 is 0.5, which is larger.

Sample questions (10 of 30)

N6 · Powers and rootsQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Number

N6

Intermediate

Work out −(−3)⁴ + (−3)³

💡 Hints:
Foundation worksheetHigher worksheetFoundation number practiceHigher number practice

Nearby statements

N4Factors, multiples, primes, HCF and LCMN5Systematic listing and the product rule for countingpart HigherN7Calculating with roots and indicespart HigherN8Exact calculation: fractions, surds and πpart Higher

Questions people ask

Is powers and roots on Foundation or Higher?

Both, but not all of it. The parts the DfE prints in bold — "estimate powers and roots of any given positive number" — are Higher only; the rest is Foundation content.

Can I use a calculator for powers and roots?

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?

Reading 5³ as 5 × 3 = 15 rather than 5 × 5 × 5 = 125.

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.

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