GCSE Maths (AQA)

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Solving by Iteration

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Algebra Solving Equations and Inequalities

Solving by Iteration

7:18 Approximating Solutions
Spec A20
Previous Iteration Formulae Next Deriving Equations
  • The first input in an iterative process should be close to the solution of the equation
  • The equation x^2 + 2x - 10 = 0 can be rearranged to create an iterative formula
  • The iterative formula provides increasingly accurate approximations to the exact solution
  • The iterative process can be visualized graphically by finding where the graph crosses the x-axis
  • The change of sign method can also be used to find a value close to the solution if a graph is not available
  • The starting value for the iterative process is given in an exam, so there is no need to worry about finding it
  • The output from each iteration is used as the input for the next iteration
  • The answer button on a calculator can be used to preserve accuracy and simplify the iterative process
  • Computers can iterate the formula thousands of times to find a very accurate approximation
  • An example is given to demonstrate how to use the iterative process to approximate a solution to an equation
  • The final answer should be rounded to one decimal place

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