Start from what is given
Translate even, odd, rational and divisibility statements into algebra and move forward logically.
IB MATHEMATICS AA · HIGHER LEVEL · PREMIUM
Methods of Proof
A story-led Higher Level proof chapter that keeps the language simple and mathematical. It develops direct proof, counterexamples and contradiction before moving into irrational roots, irrational logarithms, integer-solution arguments and polynomial questions with no integer zeros.
THE MAIN IDEA
Choose the proof method before doing the algebra.
The chapter is written as a mathematical story rather than a formal-logic sheet. Students learn what they are allowed to assume, what they must show, how a single counterexample destroys a universal claim, and how contradiction works by temporarily assuming the opposite and forcing an impossibility.
One example can be enough
Disprove universal claims efficiently while respecting every condition in the question.
Assume the opposite
Use parity, prime factors and rational forms to force an impossible conclusion.
Irrationality + integer zeros
Work with roots, logarithms and polynomial structures in longer exam-style proofs.
INSIDE THE PACK
Proof explained slowly, then tested seriously.
12 pages
Narrative teaching, many worked examples and three adapted IB-style proof questions at the end.
52 questions · 7 pages
Direct proof, counterexamples, contradiction, irrationality, logarithms and difficult integer-zero arguments.
7 pages
Detailed reasoning for the full worksheet, written in the same natural proof language as the notes.
NEW TOPIC PRICING
Included in Topic 1 HL · Number & Algebra · €35
This chapter is no longer sold individually. One €35 topic purchase unlocks this chapter together with the other currently listed resources in Topic 1 HL · Number & Algebra inside the protected CF Maths My Notes library.
Open the complete topic bundle →NEXT HL PROOF UNIT
Mathematical Induction
Continue with the separate induction chapter after mastering the proof methods in this pack.