Edexcel GCSE Maths

Revision Notes

3.7.2 Iteration - Applications

How do I solve problems with iteration?

  • To solve equations using iteration two things are required:
  • The equation f(x) = 0 needs to be rewritten into the form x = g(x)
    • Some equations may need rearranging to get to the f(x) = 0 stage too!
    • There may be more than one way to rearrange to get the form x = g(x) but a question will state which one to show
  • An initial value (x0) (or starting value)
    • This is the first estimate of a solution to the equation f(x) = 0

It App Notes fig2, downloadable IGCSE & GCSE Maths revision notes

  • A solution to the equation f(x) = 0 is also called a root
    • On a graph, a root is where the curve crosses the x-axis
    • On one side of the root the value of f(x) will be positive
    • On the other side of the root the value of f(x) will be negative
  • This is called the change of sign rule
    • Two values, a and b, chosen appropriately, lead to f(a) and f(b) having different signs
    • It does not matter which one is positive and which is negative, they just need to have different signs
    • In exam questions a and b are usually given but can be hidden
      Look for phrases such as “… solution between …”, “… root in the interval …”
  • This information can then be used to find an initial estimate (x0) of a solution

It App Notes fig3, downloadable IGCSE & GCSE Maths revision notes

  • Once x = g(x) and x0 are known, the iterative process can begin
  • See Revision Notes Iteration – Using a Calculator

Exam Tip

When writing down an iterative formula, write it down without the n and n+1
Go back and add these in afterwards.

Worked Example

It App Notes Example fig1 sol, downloadable IGCSE & GCSE Maths revision notes

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