Year 11 - Maths
Problem solving with functions and proof
Functions and proof
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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 will further develop their understanding of algebraic notation and graphs by learning about functions, their inverses and composite functions.
Lesson Summary
You will learn to use your knowledge of functions and proof to solve problems.
Key Notes
- In order to prove something, you may need to use any of your maths skills and knowledge.
- It is important to define any algebraic expressions at the start of a proof.
- This is so it is clear what cases you are proving.
Vocabulary To Learn
- Function: A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
- Expression: An expression contains one or more terms, where each term is separated by an operator.
Common Mistakes To Avoid
- Pupils may struggle with showing why the false proofs are false.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
In order to prove something, you may need to use any of your maths skills and knowledge. It is important to define any algebraic expressions at the start of a proof.
2. Use this key word in a maths sentence and explain it clearly. 'Function'
A function is a mathematical relationship that uniquely maps values of one set to the values of another set. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may struggle with showing why the false proofs are false. Correction: Checking what each variable represents will help pupils see why each of the 'proofs' do not work.
More Lessons In This Unit
- Checking and securing understanding of functions Study Guide
- Defining function notation Study Guide
- Finding the inverse of a function Study Guide
- General algebraic forms for specific number properties Study Guide
- Logical arguments Study Guide
- Making conjectures about patterns and relationships Study Guide
- Multiple approaches to logical arguments Study Guide
- Proving or disproving a statement Study Guide
- Solving equations involving composite functions Study Guide
- Solving equations involving functions Study Guide
- Writing a generalised statement about specific number properties Study Guide
- Writing a proof Study Guide
- Writing composite functions Study Guide
Browse all guides in the Year 11 Maths guide library.