Year 11 - Maths
Writing a generalised statement about specific number properties
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 describe a situation using algebraic symbols.
Key Notes
- A conjecture about a generalisation can be expressed algebraically.
- The algebraic expression can be used to test the conjecture.
- Substituting values can reveal whether the conjecture is wrong.
- Substituting values cannot prove the conjecture unless all possibilities are exhausted.
Vocabulary To Learn
- Conjecture: A conjecture is a (mathematical) statement that is thought to be true but has not been proved yet.
- Generalise: To generalise is to formulate a statement or rule that applies correctly to all relevant cases.
Common Mistakes To Avoid
- Pupils may think it is acceptable to use the same letter for all expressions.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A conjecture about a generalisation can be expressed algebraically. The algebraic expression can be used to test the conjecture.
2. Use this key word in a maths sentence and explain it clearly. 'Conjecture'
A conjecture is a (mathematical) statement that is thought to be true but has not been proved yet. 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 think it is acceptable to use the same letter for all expressions. Correction: It may be acceptable for the letter to be the same but that depends on what the letter is representing.
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
- Problem solving with functions and proof Study Guide
- Proving or disproving a statement Study Guide
- Solving equations involving composite functions Study Guide
- Solving equations involving functions Study Guide
- Writing a proof Study Guide
- Writing composite functions Study Guide
Browse all guides in the Year 11 Maths guide library.