HSC
Mathematics

HSC Year 11 Mathematics Standard is the entry-level Year 11 course aligned to the NESA Mathematics Standard Stage 6 syllabus and covers four topics — Algebra, Measurement, Financial Mathematics, and Statistical Analysis — developing practical mathematical skills in real-world contexts. Algebra covers algebraic manipulation and the use of formulae. Measurement covers units, rates, and applications of area, surface area, and volume. Financial Mathematics covers earning and spending money, taxation, and budgeting. Statistical Analysis introduces data collection and display, measures of centre and spread, and the use of technology. Year 11 Standard provides the foundation for Year 12 Standard 1 and Standard 2, and is assessed through school-based assessment tasks throughout the year.

HSC Year 11 Mathematics Advanced is the standard-rigour Year 11 course aligned to the NESA Mathematics Advanced Stage 6 syllabus and covers five topics — Functions, Exponential and Logarithmic Functions, Calculus, Statistical Analysis, and Trigonometric Functions — developing the formal algebraic and calculus foundations required for Year 12 Advanced. Functions introduces function notation, domain and range, and the study of polynomial, exponential, logarithmic, and trigonometric function families. Calculus introduces differentiation and its applications. Statistical Analysis covers probability and data analysis. Trigonometric Functions covers the unit circle, radian measure, and the graphs and transformations of trigonometric functions. Year 11 Advanced is assessed through school-based assessment tasks and is the prerequisite for Year 12 Mathematics Advanced.

HSC Year 11 Mathematics Extension 1 is studied concurrently with Year 11 Advanced and covers the additional Extension 1 topics from the NESA Mathematics Extension 1 Stage 6 syllabus — Functions, Trigonometric Functions, Calculus, and Combinatorics. Functions extends the Advanced content to include inverse functions, polynomial division, and the remainder and factor theorems. Trigonometric Functions extends to inverse trigonometric functions and more complex trigonometric identities and equations. Calculus develops the chain rule, product rule, and quotient rule more rigorously, and introduces rates of change. Combinatorics introduces permutations, combinations, and the binomial theorem. Year 11 Extension 1 is the prerequisite for Year 12 Mathematics Extension 1 and is assessed through school-based assessment tasks throughout the year.

HSC Year 12 Mathematics Standard 1 is the Year 12 course for students following the Standard pathway who are not sitting the external HSC examination in Mathematics, and covers five topics from the NESA Mathematics Standard Stage 6 syllabus — Algebra, Measurement, Financial Mathematics, Statistical Analysis, and Networks — all assessed exclusively through school-based assessment tasks. Standard 1 develops and extends the Year 11 Standard content, with Algebra covering linear and non-linear modelling, Measurement extending to more complex applications, Financial Mathematics covering interest, depreciation, and loans, Statistical Analysis extending to further data analysis and the normal distribution, and Networks introducing graph theory and network diagrams in practical contexts. Standard 1 is a Category B course in the HSC and does not count towards the ATAR, but provides a recognised HSC credential in Mathematics.

HSC Year 12 Mathematics Standard 2 is the Year 12 course for students following the Standard pathway who are sitting the external HSC examination in Mathematics, and covers five topics from the NESA Mathematics Standard Stage 6 syllabus — Algebra, Measurement, Financial Mathematics, Statistical Analysis, and Networks. Standard 2 covers the same five topic areas as Standard 1 but at a greater depth and with the additional requirement of preparation for the external HSC examination, which consists of one exam paper. Statistical Analysis extends to bivariate data analysis, correlation, and the normal distribution including z-scores. Financial Mathematics covers compound interest, annuities, and reducing balance loans. Standard 2 is assessed through school-based assessment tasks and the HSC external examination and contributes to the ATAR. It is the most accessible ATAR-eligible Mathematics course in the NSW HSC.

HSC Year 12 Mathematics Advanced is the core ATAR Mathematics course aligned to the NESA Mathematics Advanced Stage 6 syllabus and covers five topics — Functions, Trigonometric Functions, Calculus, Financial Mathematics, and Statistical Analysis — all directly assessed in the external HSC examination. Calculus is the most heavily weighted topic and covers differentiation and integration of polynomial, trigonometric, exponential, and logarithmic functions, the applications of calculus to curve sketching, optimisation, rates of change, and areas under curves. Statistical Analysis covers probability, discrete and continuous random variables, the binomial distribution, and the normal distribution. Trigonometric Functions extends to inverse trigonometric functions, further identities, and more complex equations. Year 12 Advanced is assessed through school-based assessment tasks and the HSC external examination, and is the standard entry-level ATAR Mathematics course required for most science and engineering university degree programmes.

HSC Year 12 Mathematics Extension 1 is studied concurrently with Year 12 Advanced and covers additional Extension 1 topics from the NESA Mathematics Extension 1 Stage 6 syllabus — Proof, Trigonometric Functions, Calculus, Statistical Analysis, and Vectors. Proof introduces proof by mathematical induction. Trigonometric Functions develops the sum and product formulae, the t-formulae, and further inverse trigonometric function work. Calculus extends the Advanced content to include integration by substitution, the trapezoidal rule, and differential equations. Statistical Analysis introduces the binomial distribution at a greater depth including normal approximations. Vectors introduces two-dimensional vectors, vector equations of lines, and geometric applications. Year 12 Extension 1 is assessed in the HSC through both the Extension 1 examination and, as a prerequisite, the Year 12 Advanced examination, and is required for most mathematically intensive university degree programmes.

HSC Year 12 Mathematics Extension 2 is the most demanding Mathematics course in the NSW HSC curriculum, studied concurrently with both Year 12 Advanced and Year 12 Extension 1, and covers five topics from the NESA Mathematics Extension 2 Stage 6 syllabus — Proof, Vectors, Calculus, Complex Numbers, and Mechanics. Proof develops formal proof techniques including proof by contradiction and extended mathematical induction. Vectors extends to three-dimensional vectors and their applications to lines and planes in three-dimensional space. Calculus covers advanced integration techniques including integration by parts, partial fractions, and trigonometric substitution, as well as volumes of solids of revolution. Complex Numbers introduces the algebra and geometry of complex numbers in Cartesian, polar, and exponential form, De Moivre’s theorem, and complex roots. Mechanics covers simple harmonic motion, projectile motion, and resisted motion. Extension 2 is the highest HSC Mathematics qualification and provides the strongest preparation for university study in mathematics, physics, and engineering.