New HSC Maths Extension 2 syllabus from 2027: what's changed

Mathematics Extension 2 has a new syllabus too. The Mathematics Extension 2 11-12 Syllabus (2024) is a Year 12 course that starts in Term 4 2026, and the 2027 HSC is the first exam on it. It replaces the 2017 Extension 2 syllabus, which is examined for the last time in the 2026 HSC.

The five topics you would expect are all still there, and most of the course is the same mathematics. The changes are at the edges: a few topics moved in from Extension 1, one well-known topic (exponential form of complex numbers) left, and mechanics gained forces, inclined planes and pulleys. Everything below comes from reading NESA's 2017 and 2024 documents side by side.

The new course structure

NESA's sample scope and sequence for the course is 60 hours. Extension 2 assumes the whole of Mathematics Advanced and Mathematics Extension 1, so the Extension 1 changes (for example, 3D vectors now starting in Extension 1) matter here too.

What's new or moved in

• Mechanics: forces, inclined planes and pulleys. The focus area now starts with Newton's three laws, $F = m\ddot{x}$, and resolving concurrent forces into components in 2D and 3D. It adds motion on a smooth inclined plane and problems with a single smooth pulley and a smooth plane. None of this was in the 2017 course.
• The squeeze theorem as a proof tool for limits, alongside the existing inequality work (AM-GM, the triangle inequality, calculus and graphical methods).
• Formal logic notation: $P \wedge Q$, $P \vee Q$, negation $\neg P$, and the rules for negating "and", "or" and implications, on top of the 2017 language of implication, converse, contrapositive and quantifiers.
• Vectors and geometry: skew lines in three dimensions, the Cauchy-Schwarz inequality $|\mathbf{a} \cdot \mathbf{b}| \leq |\mathbf{a}||\mathbf{b}|$, properties of the scalar product, and medians, altitudes and bisectors of a triangle in vector form.
• Trigonometric products as sums and differences and the t-formulae moved in from Extension 1. They now sit in Further integration, where they are used for integrals such as $\int \sin mx \cos nx \, dx$ and for solving trigonometric equations.

What's gone or moved out

• Exponential form of a complex number ($z = re^{i\theta}$) and Euler's formula are not in the new syllabus. Complex numbers now use Cartesian and polar (modulus-argument) form, with de Moivre's theorem proved by induction.
• Introductory 3D vectors (coordinates in space, $\mathbf{i}, \mathbf{j}, \mathbf{k}$ components, magnitude, the scalar product in 3D) moved to Extension 1. Extension 2 starts from vector equations of lines and curves.

Unchanged in substance

Proof by contradiction and counterexample, inequalities including AM-GM, further induction (including recursive formulas, calculus and geometric results); vector equations of lines in 2D and 3D, circles and spheres, and vector proofs; complex arithmetic, the Argand plane, modulus and argument, square roots, the conjugate root theorem, de Moivre's theorem, $n$th roots and regions in the complex plane; integration by substitution, partial fractions, integration by parts and recurrence (reduction) formulas; simple harmonic motion, motion with and without resistance, vertical resisted motion, terminal velocity and projectiles with resistance.

School-based assessment

• Components are "Knowledge and understanding of course content" (50%) and "Skills in Working mathematically" (50%).
• NESA's sample Year 12 program is 4 tasks, including a formal written examination, each weighted 10% to 40%. The 2017 sample also listed an assignment or investigation-style task; the new sample does not.
• From Term 4 2026 the updated ACE Rules allow at most one take-home task per HSC course, worth no more than 15%. Mathematics Extension 2 is not exempt (English Extension 2 is, because it has a major work).

The HSC exam

The specification matches the 2017 course: one paper of 100 marks, 3 hours plus 10 minutes reading time, Section I 10 marks of objective-response questions, Section II 90 marks across 37 to 42 items, with at least two items worth 4 or 5 marks. Mathematics Advanced and Extension 1 are assumed knowledge, and you also sit the Extension 1 paper. NESA has published a new Extension 2 reference sheet and an annotated sample exam for the new course, which reuses past HSC questions where they are still relevant.

What this means if you are starting Year 12 now

1. Past papers still work, with two filters: skip questions that need exponential form or Euler's formula, and note that 3D vector basics now belong to Extension 1.
2. Learn the new mechanics early. Inclined planes and pulleys have no past HSC Extension 2 questions yet; resolving forces carefully (components parallel and perpendicular to the plane) is the core skill.
3. Make sure the Extension 1 t-formulae and products-to-sums skills are solid, because they are now tested as Extension 2 integration and equation techniques.
4. Read what's changed in Extension 1, since the Extension 2 exam assumes it.

Our existing Extension 2 pages, such as simple harmonic motion and de Moivre's theorem and roots of unity, were written to the 2017 syllabus and cover content that carries over unchanged.