DfE statement N3 · Number

Inverse operations and priority of operations

Both tiersNon-calculator

Inverse operations and priority of operations is content statement N3 of the DfE GCSE mathematics subject content, in the number area. It is on both tiers, 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: "Recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions); use conventional notation for priority of operations, including brackets, powers, roots and reciprocals." (statement N3). 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 N3

Tier

Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.

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

Working strictly left to right, so 3 + 4 × 2 is answered as 14 instead of 11.
Reading −3² as 9. The index applies to the 3 only, so it is −9; (−3)² is 9.
Ignoring that a fraction bar brackets the whole numerator, so (6 + 4)/2 is evaluated as 6 + 2.

Sample questions (10 of 30)

N3 · Inverse operations and priority of operationsQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Number

Beginner

Work out 2 × (−3 + 7)

💡 Hints:

Foundation worksheet Higher worksheet Foundation number practice Higher number practice

Nearby statements

N1Ordering numbers and inequality symbols N2The four operations and place value N4Factors, multiples, primes, HCF and LCM N5Systematic listing and the product rule for countingpart Higher

Questions people ask

Is inverse operations and priority of operations on Foundation or Higher?

Both. It is Foundation content, so it can be asked on either tier.

Can I use a calculator for inverse operations and priority of operations?

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?

Working strictly left to right, so 3 + 4 × 2 is answered as 14 instead of 11.

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.