Year 11 - Maths
Making conjectures about patterns and relationships
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 make and test conjectures about the generalisations that underline patterns and relationships.
Key Notes
- A conjecture can be made about underlying patterns.
- The conjecture can be tested to see if it holds.
Vocabulary To Learn
- Prime number: A prime number is an integer greater than one with exactly 2 factors.
- Triangular number: A triangular number is a number that can be represented by a pattern of dots arranged into an equilateral triangle. The term number is the number of dots in a side of the triangle.
- Conjecture: A conjecture is a (mathematical) statement that is thought to be true but has not been proved yet.
Common Mistakes To Avoid
- Conjectures have to be correct so it's really hard to make a conjecture as you don't want to be wrong.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A conjecture can be made about underlying patterns. The conjecture can be tested to see if it holds.
2. Use this key word in a maths sentence and explain it clearly. 'Prime number'
A prime number is an integer greater than one with exactly 2 factors. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Conjectures have to be correct so it's really hard to make a conjecture as you don't want to be wrong. Correction: Conjectures are thought to be true but they may not be. This is why we test and see ways to prove whether a conjecture is true or not. It is perfectly acceptable for a conjecture to be proved wrong.
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
- 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.