Mathematics Extension 2
Mathematics Extension 2 trial papers and questions
Extension 2 is the course where a question is a proof as often as it is a calculation. Writing a trial paper for it means constructing arguments that reward mathematical maturity without stepping outside the syllabus, and then checking every line of a six-question extended-response section. Andrew HSC generates Extension 2 trial papers in HSC format across all five areas of study, with proof and mechanics questions placed where the difficulty shape of the paper calls for them, and exports the paper and its worked solutions as a print-ready PDF.
Proof and mechanics, where the marks are
Two areas give Extension 2 its character, and the bank treats them as first-class topics rather than hard versions of Extension 1 content. Proof spans the two NESA topics MEX-P1 The Nature of Proof and MEX-P2 Further Proof by Mathematical Induction: direct proof, proof by contradiction and by contrapositive, inequality proofs including the arithmetic mean and geometric mean inequality, results in number theory and divisibility, induction extended to inequalities, and geometric proofs by coordinates or vectors. Extension 2 proofs are expected to be more abstract than their Extension 1 counterparts and to require the student to construct the argument, not just complete it.
Mechanics is MEX-M1 Applications of Calculus to Mechanics: simple harmonic motion in both its differential and its velocity-displacement forms, acceleration as a function of position or velocity, motion in a straight line under variable forces, resisted motion with resistance proportional to the speed or to its square, terminal velocity, vertical motion with resistance and projectile motion with resistance. Uniform circular motion, banked tracks and conical pendulums are not in the current course and the generator keeps them out.
A proof in Andrew's bank can carry a Verified · Lean 4 label when it has been formally checked by the Lean 4 proof checker, alongside the Verified · CAS label a computer algebra system gives a calculation. Both labels, and what they do not cover, are explained on how solutions are verified.
The five areas of study
Under the 2017 edition of the syllabus, examined in the HSC today, Mathematics Extension 2 has exactly five areas of study: Proof, Vectors, Complex Numbers, Calculus and Mechanics. The official NESA topics inside them, as listed in Andrew's syllabus registry:
| Code | Topic | Dot points |
|---|---|---|
| MEX-C1 | Further Integration | 7 |
| MEX-M1 | Applications of Calculus to Mechanics | 16 |
| MEX-N1 | Introduction to Complex Numbers | 12 |
| MEX-N2 | Using Complex Numbers | 13 |
| MEX-P1 | The Nature of Proof | 6 |
| MEX-P2 | Further Proof by Mathematical Induction | 4 |
| MEX-V1 | Further Work with Vectors | 14 |
Vectors (MEX-V1) moves into three dimensions: components in i, j and k, magnitude and unit vectors, the dot product and angles between vectors, vector and parametric equations of lines in two and three dimensions, classifying a pair of lines as parallel, intersecting or skew, the vector equation of a sphere, and geometric proofs in three dimensions. The cross product and equations of planes are not in the 2017 course; the 2024 syllabus restores them, which is one reason Andrew keeps the two syllabuses apart (see the new syllabus page).
Complex Numbers (MEX-N1 and MEX-N2) covers Cartesian, polar and exponential form, De Moivre's theorem, the nth roots of unity, loci on the Argand diagram, the conjugate root theorem and factoring over the complex numbers. Calculus (MEX-C1) is the integration toolkit: partial fractions with linear and quadratic factors, integration by parts including the repeated and tabular forms, trigonometric and other substitutions including the half-angle substitution, powers of trigonometric functions, and reduction formulae. Volumes by the shell method and by known cross-sections left the course with the old Volumes topic; the 2024 syllabus restores the shell method.
The paper and its difficulty shape
Andrew's default Extension 2 structure is a 100-mark paper. Section I is multiple choice, Questions 1 to 10 at one mark each. Section II is extended response, Questions 11 to 16, worth 90 marks and answered in writing booklets, with the instruction that responses should include relevant mathematical reasoning and/or calculations. The cover prints reading time, working time, the standard calculator line, the total marks and a per-section summary; each written question opens on its own page with working space scaled to its marks, and a Worked Solutions section follows.
As shipped, the six written questions fall into three zones. The opening, Questions 11 to 13, has nothing below difficulty 5 on the course's own scale, is weighted towards 5 to 7, and may hold a 10 at most once. The challenge, Questions 14 and 15, has nothing below 6 and spreads evenly across 6 to 9. The finale, Question 16, is the paper's final question: its last part is forced to a 10, the hardest thing on the paper, and its other parts sit at 8 or 9. Section I ramps from the preset's floor to a 10 on its last item.
Difficulty is measured against Extension 2 itself. A 10 means as hard as the hardest question an HSC Extension 2 paper has carried, reached through deeper reasoning inside the course, and the generator is told to measure difficulty relative to the course itself, never across courses, and never to reach for techniques outside the course's scope. By default the four presets move the floor: Standard HSC (calibrated to typical HSC exam difficulty) starts Section I at 1, Above Average (a challenging public school trial level) at 2, Selective School (a selective school trial level) at 3 and Elite Selective (a top selective school level) at 5.
Topic selection runs from the whole course down to a single NESA topic, so a department can generate a Complex Numbers assessment task as readily as a full trial. Every paper renders with KaTeX on screen and compiles to PDF with pdflatex, or downloads as a .tex file. Worked solutions are checked by a computer algebra system where available. Teachers remain responsible for reviewing AI-generated content before using it in a formal assessment, and an Extension 2 paper deserves that read more than any other.
Across the department
The same generator and bank serve Mathematics Extension 1, Mathematics Advanced and Mathematics Standard 2. For revision sets rather than examinations, the worksheet generator draws from the same questions, and the question bank can be browsed by topic.
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