Year 11 - Maths
Approximating solutions to equations
Iteration
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils continue to explore composite functions and develop understanding of iteration, building on their work on functions and proof.
Lesson Summary
You will learn to use iteration to find approximate solutions to equations.
Key Notes
- You can rearrange an equation in order to carry out iteration
- This process finds an approximate solution to the equation
- This process is carried out until the outputs are the same to a given degree of accuracy
- Efficient use of the calculator makes this process much faster
Vocabulary To Learn
- Iteration: Iteration is the repeated application of a function or process in which the output of each iteration is used as the input for the next iteration.
Common Mistakes To Avoid
- To find a solution to a given degree of accuracy an iteration can just be rounded.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
You can rearrange an equation in order to carry out iteration. This process finds an approximate solution to the equation.
2. Use this key word in a maths sentence and explain it clearly. 'Iteration'
Iteration is the repeated application of a function or process in which the output of each iteration is used as the input for the next iteration. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: To find a solution to a given degree of accuracy an iteration can just be rounded. Correction: Several successive iterations need to round to the same value to a given degree of accuracy. If in doubt efficient calculator use means many iterations can be generated easily until confident that a digit is fixed.
More Lessons In This Unit
Browse all guides in the Year 11 Maths guide library.