HSC Extension Two Maths Proof Exam

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Important: These tests take time to write, if you’re in a position consider buying me a coffee so I can keep doing this in the long term.

Mathematics proof worksheet with multiple-choice questions about logic, irrational numbers, negation, weather scenarios, and ordering of complex numbers.
A mathematics exam question sheet with problem number six, including subparts about odd numbers, irrationality, prime numbers, and properties of even and odd integers.
Mathematics exam questions with various algebraic and geometric problems, including proofs and inequalities.
A page with detailed solutions and explanations for multiple-choice questions, numbered 1 through 5, in a text document.
Page of handwritten mathematical math problems, equations, and solutions, including algebra and number theory.
A page with mathematical notes, including algebraic inequalities, properties of primes, and trigonometric identities.
Photograph of handwritten mathematical equations and proofs on a sheet of paper.
A mathematical proof involving calculations with exponents, derivatives, limits, and algebraic expressions.


Below is a skills checklist I wrote based on the syllabus, if you can do everything listed below you should be in a good position for both your school’s proof test and the proof questions in the HSC.

  • Understand the formal language and symbols of proof

  • Understand proof by contradiction

  • Use examples and counter examples

  • Prove results involving inequalities

  • Prove equality, inequality, divisibility, calculus, geometric, probability and recursive results by induction