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AlgebraIntroduction

Zeroing In

Part of Iteration — GCSE Mathematics

This introduction covers Zeroing In within Iteration for GCSE Mathematics. Revise Iteration in Algebra for GCSE Mathematics with 9 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 1 of 3 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 3

Practice

9 questions

Recall

3 flashcards

Zeroing In

Some equations can't be solved exactly. But we can get closer and closer to the answer by "iterating" - using each answer to calculate a better one. It's like zooming in on a target, getting more accurate each time.
Iteration method diagram

Keep building this topic

Read this section alongside the surrounding pages in Iteration. That gives you the full topic sequence instead of a single isolated revision point.

How Iteration WorksWorked Example

Practice Questions for Iteration

What is the purpose of using an iterative formula in mathematics?

  • A. To find exact algebraic solutions to equations
  • B. To get increasingly accurate numerical approximations to solutions
  • C. To factorise quadratic expressions
  • D. To draw graphs of functions
1 markfoundation

A student uses the iterative formula xₙ₊₁ = xₙ² − 2 with x₀ = 0.5 and obtains the sequence 0.5, −1.75, 1.0625, −0.871, −1.241, ... Explain what is happening.

2 marksstandard

Quick Recall Flashcards

Sum Formula
S_n = a(r^n - 1)/(r - 1) where r is common ratio
Iteration Process
Put xₙ into formula to get xₙ₊₁. Repeat until values converge (settle down).

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