HSC Maths Syllabus Explained: What's Actually on the Exam
Last updated: 20 July 2026
The NESA syllabus documents are long, dense, and written in language that seems designed to confuse students. This guide translates the syllabus into plain English so you know exactly what you need to learn and what's likely to show up on the exam.
The four HSC Maths courses
NSW offers four HSC Mathematics courses, from easiest to hardest:
- Standard 2 (2 units) - no calculus, focuses on practical maths
- Advanced (2 units) - calculus-based, for university-bound STEM students
- Extension 1 (1 unit, taken with Advanced) - extends Advanced with harder content
- Extension 2 (1 unit, taken with Ext 1) - the hardest maths course in the HSC
The syllabus changed in 2020 (for the 2020 HSC exam onwards). If you're sitting the HSC in 2026, you're on the current syllabus. Any past paper from 2020 onwards is relevant.
Standard 2 syllabus
Five topics, no calculus. The focus is on practical, real-world mathematics.
Algebra
Linear equations, simultaneous equations, quadratics. Rearranging formulas. This is foundational and shows up throughout the exam. Most of the algebra in Standard 2 is Year 10 level with some harder applications.
Measurement
Area and volume of standard and composite shapes. Unit conversion. Rates and ratios. Similar figures and scale factor. Straightforward content but easy to lose marks on units.
Financial mathematics
The biggest topic in Standard 2. Interest (flat-rate and reducible), depreciation, GST, tax, wages, overtime, investments, loans, annuities. The formula sheet has the annuity formulas. You need to know when to use each one.
This is where most Standard 2 students win or lose the exam. If your financial maths is strong, you're in good shape.
Statistical analysis
Mean, median, mode, range, standard deviation, interquartile range. Box plots, histograms, scatter plots. Normal distribution and z-scores. Correlation.
The normal distribution questions are where Standard 2 gets tricky. You need to understand z-scores and the empirical rule, not just memorise formulas.
Networks
Network diagrams, trees, minimum spanning tree (Prim's algorithm), shortest path (Dijkstra's algorithm), critical path analysis. New content for most students. Visual and logical rather than computational.
Advanced syllabus
Six topics, calculus-based. Builds on Year 11 Advanced.
Functions
Polynomial, exponential, logarithmic, and trigonometric functions. Graphing, transformations, composite and inverse functions. Domain and range.
Trigonometric functions
Radian measure, unit circle, identities (Pythagorean, compound angle), solving trig equations, applications.
Calculus: Differentiation
The derivative concept (limits, first principles). Power, product, quotient, and chain rules. Derivatives of exponentials, logs, and trig functions. Applications: tangent lines, optimisation, stationary points, rates of change. Implicit differentiation.
This is the heart of Advanced. If your differentiation is weak, the whole course falls apart.
Calculus: Integration
Anti-differentiation, definite and indefinite integrals. Area under and between curves. Trapezoidal rule. Applications (displacement from velocity, total change).
Financial mathematics
Sequences and series (arithmetic and geometric). Compound interest. Annuities and loans. Uses the same formulas as Standard 2 but with a calculus-informed perspective.
Statistical analysis
Discrete probability distributions (expected value, variance). Continuous random variables. Normal distribution (deeper than Standard 2). Sampling and estimates.
Extension 1 syllabus
Extends Advanced with additional content and harder questions.
Everything in Advanced, plus:
- Harder functions and trigonometry
- Integration by substitution and differential equations
- Combinatorics (permutations, combinations, binomial theorem, Pascal's triangle)
- Vectors (operations, dot product, geometric applications)
- Mathematical induction (proof)
- Binomial distribution
- Harder calculus applications
Extension 2 syllabus
Four major new topics on top of everything in Extension 1:
- Complex numbers (the biggest new concept)
- Further calculus (integration by parts, partial fractions, volumes)
- Mechanics (projectile motion, SHM, resisted motion)
- Proof (contradiction, contrapositive, harder induction, inequalities)
What actually shows up on the exam
Based on HSC papers from 2020-2025, here's what tends to appear:
In Advanced
- A differentiation question involving the chain rule (almost guaranteed)
- An integration question involving area between curves (almost guaranteed)
- An optimisation question (very common)
- A normal distribution question with z-scores (very common)
- A financial maths question involving annuities (common)
- A graphing question requiring transformations (common)
- A question testing multiple topics combined (usually the hardest question)
In Extension 1
- Integration by substitution (almost guaranteed)
- A combinatorics question (almost guaranteed)
- A vectors question (almost guaranteed)
- Mathematical induction (almost guaranteed, usually 4-5 marks)
- A differential equations question (common)
- Binomial distribution (common)
In Extension 2
- Complex numbers in polar form (almost guaranteed)
- Integration by parts (almost guaranteed)
- A mechanics question (almost guaranteed)
- A proof question, often involving contradiction (almost guaranteed)
- Volumes of revolution (very common)
- A question combining complex numbers with polynomials (common)
In Standard 2
- An annuity or loan repayment question (almost guaranteed)
- A normal distribution question (almost guaranteed)
- A network question involving Prim's or Dijkstra's (almost guaranteed)
- A measurement question involving composite shapes (very common)
- A statistics question involving box plots or standard deviation (very common)
- A question involving tax or wages (common)
How to use the syllabus
Don't read the syllabus document cover to cover. Use it as a checklist:
- Print the topic list for your course
- Next to each sub-topic, rate yourself: green (confident), yellow (shaky), red (no idea)
- Spend 70% of your study time on the red and yellow topics
- Re-rate yourself every two weeks
- Aim to have everything green 2 weeks before the exam
The syllabus tells you what to learn. Your practice tells you what you've learned. The gap between the two is where you should be studying.
Want to practise?
PracticePapers.io covers all four HSC Maths courses with auto-marking, worked solutions, and weak-areas tracking. Free during beta.
Based on the current NESA HSC Mathematics syllabuses. Always check the official NESA website for the most up-to-date syllabus documents. PracticePapers.io is not affiliated with NESA.