Free HSC Maths Solver

HSC Mathematics is the Year 12 mathematics qualification in New South Wales, Australia, set by the NSW Education Standards Authority (NESA). It's split into four separate courses of increasing rigour: Mathematics Standard (Standard 1 and Standard 2), Mathematics Advanced, Mathematics Extension 1, and Mathematics Extension 2. Students are placed based on Year 10 performance; Advanced is the 'default' for academic pathways, Ext 1 and Ext 2 are additional courses on top for maths-inclined students.

Mathematics Standard 2 covers: algebra (basic functions, linear models), measurement (Pythagoras, trigonometry, non-right-angled trig, angles of elevation/depression), financial mathematics (simple and compound interest, annuities, loans — heavily tested), statistics (summary statistics, correlation, bivariate data, normal distribution), networks (graphs, minimum spanning trees, critical path analysis). Standard is assessment-focused on real-world applications.

Mathematics Advanced covers: functions (polynomial, exponential, logarithmic, trigonometric), trigonometric functions (sin/cos/tan, radians, identities, general solutions), calculus (differentiation from first principles, product/quotient/chain rule, applications like related rates and optimisation, integration, definite integrals, area and volume), statistical analysis (discrete and continuous distributions, normal). This is the benchmark for university-level maths.

Extension 1 adds: further calculus (inverse functions, inverse trig, anti-differentiation), combinatorics (permutations, combinations, binomial theorem), vectors (2D), proof (mathematical induction, proof by contrapositive), further statistics (binomial distribution applications). Extension 2 adds: complex numbers, further proof, mechanics (projectile motion with air resistance, SHM), further vectors (3D), more integration techniques.

The HSC exam is graded from Band 1 (lowest) to Band 6 (highest). Band 6 requires roughly 90+ marks. NESA's mark schemes reward SHOWING WORKING — a 3-mark question typically awards 1 mark for the right method, 1 for correct substitution, 1 for the final answer with correct units/notation. Students who jump straight to the final answer consistently lose method marks even when correct.

The solver above identifies which course your question belongs to (Standard vs Advanced vs Extension) based on content difficulty, and applies the method NESA marks reward. For Extension 1 proof questions it structures induction correctly (base case → hypothesis → inductive step → conclusion). For Standard financial maths it shows the standard formulae and flags unit conventions (annuities in monthly vs annual).