Year 11 - Maths
Logical arguments
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 algebra and algebraic manipulation to construct logical arguments.
Key Notes
- A logical argument is a series of statements that progress in a clear way.
- Each subsequent statement is based on the previous statement being true.
- If a contradiction is reached, it shows that the original assumption was wrong.
Vocabulary To Learn
- Conjecture: A conjecture is a (mathematical) statement that is thought to be true but has not been proved yet.
- Rational number: A rational number is one that can be written in the form a/b where a and b are integers and b is not equal to 0
- Irrational number: An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0
Common Mistakes To Avoid
- Pupils may struggle to write a correct opposing statement.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A logical argument is a series of statements that progress in a clear way. Each subsequent statement is based on the previous statement being true.
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 struggle to write a correct opposing statement. Correction: Encourage pupils to discuss the various proposed opposing statements presented in the first learning cycle. What does each statement actually mean?
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
- 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 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.