DfE statement A13 · Algebra

Translations and reflections of graphs

Higher onlyNon-calculator

Translations and reflections of graphs is content statement A13 of the DfE GCSE mathematics subject content, in the algebra area. It is Higher tier only, 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: "Sketch translations and reflections of a given function." (statement A13). 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 A13

Tier

Higher tier only. A Foundation entry is never asked for this, so if you are sitting Foundation you can leave it out of your revision entirely.

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

Translating y = f(x + 3) to the right. Changes inside the bracket move the graph the opposite way — this one goes 3 to the left.
Swapping y = −f(x) and y = f(−x). The first reflects in the x-axis, the second in the y-axis.
Applying y = f(x) + a to the x values rather than shifting the whole curve up by a.

Sample questions (10 of 30)

A13 · Translations and reflections of graphsQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Algebra

A13

Expert

The graph of y = f(x) has a minimum turning point at (2, −3). The graph of y = −f(x) + a has a maximum turning point at (2, 9). Work out the value of a.

💡 Hints:

Higher worksheet Higher algebra practice

Nearby statements

A1Algebraic notation A2Substitution into formulae A3Expressions, equations, formulae, identities and inequalities

Questions people ask

Is translations and reflections of graphs on Foundation or Higher?

Higher only. Foundation papers do not ask for it.

Can I use a calculator for translations and reflections of graphs?

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?

Translating y = f(x + 3) to the right. Changes inside the bracket move the graph the opposite way — this one goes 3 to the left.

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 Algebra at Foundation or at Higher.