The nature of proof, including induction extended to stronger forms, and the standards a proof must meet.
These are the statements the Mathematics Extension 2 syllabus makes about Proof. Dux records each one against the questions you answer, so you can see which of them you have actually been tested on and which have never been asked.
What distinguishes a proof from a demonstration, the role of definitions and axioms, and the difference between proof by contradiction, contrapositive and counterexample.
Induction applied to inequalities, divisibility and recurrence relationships, where the inductive step requires a bounding argument.
Induction where the step relies on more than the immediately preceding case, and recognising when strong induction is required.
Proving inequalities by induction, where the inductive step requires a bounding or monotonicity argument.
HSC Mathematics Extension 2 - Trial Paper Shape is 100 marks in 180 minutes. Questions on Proof are not one shape repeated: the command word decides what the marker is looking for, and the mark value decides how much of it. These are the ones Mathematics Extension 2 uses.
Dux writes practice for this module in exactly these shapes, so the drill is the same task the paper sets — not a general knowledge quiz with the module name on it.
Proof opens the Mathematics Extension 2 course. Students routinely lose marks because a question spans two modules, so the neighbouring modules are worth reading next to this one.
Dux diagnoses Mathematics Extension 2 dot point by dot point, then writes questions in the shape this course marks. Written answers come back marked against the bands.