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DfE statement A20 · Algebra

Iteration

Higher onlyCalculator

Iteration is content statement A20 of the DfE GCSE mathematics subject content, in the algebra area. It is Higher tier only, and it is normally a calculator-paper question. 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: "Find approximate solutions to equations numerically using iteration." (statement A20). 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 A20

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 calculator work, which places it on Papers 2 and 3. Know your own calculator before the exam, keep full accuracy through the working and round only at the end.

Common mistakes

  • Not feeding each output back in as the next input, so the same starting value is used every time.
  • Rounding between iterations, which stops the sequence converging to the accuracy the question asks for.
  • Not using the calculator's answer key, and so retyping a truncated value at each step.

Sample questions (10 of 30)

A20 · IterationQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Algebra

A20

Advanced

A rectangular vegetable plot has an area of 30 m² and its length is 4 m greater than its width, x metres. This gives x² + 4x − 30 = 0, which can be solved using the iterative formula xₙ₊₁ = √(30 − 4xₙ). The starting value is x₀ = 3, so x₁ is the value after the formula has been used once. Work out x₃, and use it to find an estimate for the length of the plot, giving your answer correct to 1 decimal place.

💡 Hints:
Higher worksheetHigher algebra practice

Nearby statements

A1Algebraic notationA2Substitution into formulaeA3Expressions, equations, formulae, identities and inequalitiesA4Simplifying, expanding and factorisingpart Higher

Questions people ask

Is iteration on Foundation or Higher?

Higher only. Foundation papers do not ask for it.

Can I use a calculator for iteration?

Yes, on Papers 2 and 3, which are the calculator papers and where questions on this usually sit. Paper 1 is non-calculator.

What is the single most common mistake here?

Not feeding each output back in as the next input, so the same starting value is used every time.

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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