IB Maths AA 1.11 Notes

This page contains our IB Maths AA notes for 1.11. By reading each one of these notes, you will fully cover the content for IB Maths AA 'Additional proofs'.

All Topic 1 Sub-topics 1.1: Scientific Notation 1.2: Arithmetic Sequences 1.3: Geometric Sequences 1.4: Interest 1.5: Exponents & Logs 1.6: Deductive Proofs 1.7: Binomial Theorem (HL)1.8: Counting principles (HL)1.9: Partial fractions (HL)1.10: Complex numbers (HL)1.11: Additional proofs (HL)1.12: Systems of equations

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Chapters

1. Choosing a proof method

2. Proof by mathematical induction

3. Proof by contradiction

4. Proof by counterexample

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Choosing a proof method

In this section, proof is extended beyond direct algebraic deduction. The main methods are proof by mathematical induction, proof by contradiction, and proof by counterexample. These are important because they allow us to justify statements about integers, show that certain claims must be true, or show that a statement is not always true.

To choose the right method, ask simple questions:

If a statement is about all positive integers and has a clear pattern in $n$ , induction is often the best method.
If assuming the opposite leads naturally to an impossibility, contradiction is often best.
If the task is to show a statement is not always true, use a counterexample.

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