Mathematical induction and the binomial theorem, plus the counting techniques that Extension 1 questions assume fluently.
These are the statements the Mathematics Extension 1 syllabus makes about Proof and Combinatorics. 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.
The three-part structure of an induction proof, including extensions to inequalities and divisibility.
Expanding a binomial power, the general term, and using the theorem to find a specified coefficient.
Permutations, combinations, and counting arrangements with restrictions, which underpin the binomial coefficients used elsewhere.
Direct proof, contradiction and counterexample, and choosing the method that suits the claim.
HSC Mathematics Extension 1 - Trial Paper Shape is 70 marks in 120 minutes. Questions on Proof and Combinatorics 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 1 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 and Combinatorics is module 6 of 6 in Mathematics Extension 1. 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 1 dot point by dot point, then writes questions in the shape this course marks. Written answers come back marked against the bands.