Year 11 - Maths
Building on composite functions
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 expand your thinking on composite functions to consider a more efficient way to write composite functions comprised of many functions.
Key Notes
- A composite function could be many iterations of one original function
- To write this in function notation would be cumbersome
- There is more efficient notation that can be used in these circumstances
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
- Pupils are very familiar with exponents but the introduction of 'subscript' notation may confuse them. For example, they may think $$x_2$$ must be a function of $$x$$ because $$x^2$$ is.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A composite function could be many iterations of one original function. To write this in function notation would be cumbersome.
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: Pupils are very familiar with exponents but the introduction of 'subscript' notation may confuse them. For example, they may think $$x_2$$ must be a function of $$x$$ because $$x^2$$ is. Correction: Use of language helps. When talking through an iterative formula like $$x_{t+1}=8x_t +6$$ say, "The next $$x$$ value is equal to eight lots of the current $$x$$ value plus six" whilst pointing at it. Get pupils to do the same back to you.
More Lessons In This Unit
Browse all guides in the Year 11 Maths guide library.