Year 11 - Maths
Multiple approaches to 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 construct a logical argument.
Key Notes
- A logical argument does not have to only be algebraic.
- Geometrical reasoning can be used to argue that something is true.
- Values can be used to demonstrate whether something is true.
Vocabulary To Learn
- Apex: The apex is the point (vertex) which is the greatest perpendicular distance from the base.
- Congruent: If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
- Hypotenuse: The hypotenuse is the side of a right-angle triangle which is opposite the right angle.
Common Mistakes To Avoid
- Proofs have to be solely algebraic and do not involve diagrams.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A logical argument does not have to only be algebraic. Geometrical reasoning can be used to argue that something is true.
2. Use this key word in a maths sentence and explain it clearly. 'Apex'
The apex is the point (vertex) which is the greatest perpendicular distance from the base. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Proofs have to be solely algebraic and do not involve diagrams. Correction: Proofs involve showing that a conjecture holds for multiple cases (general case). A diagram can represent multiple cases.
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
- 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.