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KS4 / GCSE · Mathematics — Higher

Iteration

What is it

Iteration is a method for finding approximate solutions to equations that can't be solved exactly, by repeatedly substituting a value into a rearranged formula (xₙ₊₁ = ...) until the answer converges.

Why it matters

Iteration introduces the idea of numerical methods — solving problems through repeated approximation rather than an exact formula — a concept that becomes central in university-level mathematics and computer science.

Exam tip

Keep at least 4-5 decimal places at every step of an iteration and don't round early — early rounding is the most common reason a student's iteration fails to converge to the expected answer.

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