McIntyre MathsMathematics Extension 2
Extension 2 › Proof

Proof Term 4 · Weeks 1–5 · 10 lessons

The nature of proof

Outcomes MAO-WM-01, ME2-12-01

Lessons

Lesson 1Logic and the language of proofStatements, counterexamples, negation, implication, and the notation used to write proofsReadyLesson 2Quantifiers, converse and contrapositiveQuantifiers, sufficient and necessary conditions, the converse, equivalence and the contrapositiveReadyLesson 3Number proofsDirect proofs about integers: parity, divisibility, cases, counterexamples and inequalitiesReadyLesson 4Proof by contrapositive and contradictionIndirect proof: contrapositive, contradiction, irrationality and infinitely many primesReadyLesson 5Algebraic inequalities IProving inequalities from a − b > 0 and squares being non-negative, and the properties of inequalitiesReadyLesson 6Algebraic inequalities IIAM–GM, the triangle inequality, and building new inequalities from known ones, including in geometryReadyLesson 7Further induction I: series and divisibilityHarder series and divisibility proofs by induction, including cases that start later or step by 2ReadyLesson 8Further induction II: inequalitiesProving inequalities by induction using a chain of inequalitiesReadyLesson 9Further induction III: induction in contextInduction with recursive sequences, derivatives, trigonometry, the binomial theorem, logarithms and geometryReadyLesson 10Calculus and the squeeze theoremProving inequalities with calculus, and using the squeeze theorem to find limitsReady