Fiducia TogetherIteration and numerical methods
Solving an equation by repeated approximation when algebra will not do it.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
An iterative formula generates successive approximations to a root, each fed back into the formula, converging on a solution.
Where it applies
Higher tier maths.
How it works
Some equations cannot be solved exactly by algebra, and iteration gets arbitrarily close instead. Trial and improvement is the simpler version of the same idea.
How to use it in your work
Show every iteration to the required accuracy. The marks are for the process, not the final number.
Use the ANS button on the calculator rather than retyping — retyping introduces rounding errors and takes longer.
State the root to the accuracy asked for and no more.
Where to get help
Your teacher and your board's specification and mark scheme.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.