HSC Year 11-12 Mathematics Practice

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Use this page for HSC Maths practice questions, senior secondary revision, and topic-based exam preparation. Skill Align practice includes student-readable questions, explanations, exercise mode, and test mode for parents comparing Australian senior subject coverage.

Try practice questions:

Year 11 HSC Maths practice questions Year 12 HSC Maths practice questions

HSC Mathematics is structured as a Year 11 Preliminary course followed by the Year 12 HSC course, where final external assessments are completed.

This structure is aligned with publicly available NESA Mathematics 11–12 syllabus information (2024), implemented from 2026 for Year 11 and first examined from the 2027 HSC.

Mathematics Extension 1 builds on Advanced content, while Mathematics Extension 2 is a Year 12 HSC course.

This page focuses on NSW senior mathematics pathways so Preliminary and HSC topic progression can be compared without mixing Standard, Advanced, and Extension difficulty.

For the ACARA v9 Years 11–12 mathematics curriculum, see the Year 11–12 Maths Practice page. The HSC pathways below are structured as Year 11 (Preliminary) and Year 12 (HSC).

Curriculum attribution

Skill Align independently prepares practice pathways aligned to publicly available curriculum and syllabus information.
Skill Align is not affiliated with, endorsed by, or sponsored by ACARA, VCAA, NESA, QCAA, SCSA, SACE, or any state curriculum authority.
Official curriculum, syllabus, study design, and assessment requirements should always be checked on the relevant authority website.
Skill Align modifies and reorganises referenced material for practice and study-planning purposes.

Maths Topics and Subtopics

Year 11 = Preliminary · Year 12 = HSC

Pathway	Year 11 (Preliminary)	Year 12 (HSC)
Mathematics Standard	1. Formulas and Equations text calculation graph diagram analysis • Use formulas, substitution, equations, and practical algebraic reasoning. 2. Linear Relationships text calculation graph diagram analysis • Use linear models, tables, equations, graphs, and interpretation in context. 3. Earning Money text calculation graph diagram analysis • Use wages, salary, allowances, deductions, and earning calculations. 4. Managing Money text calculation graph diagram analysis • Use budgets, bills, discounts, percentages, and personal finance decisions. 5. Applications of Measurement text calculation graph diagram analysis • Use area, volume, scale, units, and practical measurement contexts. 6. Time and Location text calculation graph diagram analysis • Use time, duration, distance, location, and travel contexts. 7. Networks, Paths and Trees text calculation graph diagram analysis • Use vertices, edges, paths, trees, routes, and network interpretation. 8. Data Analysis text calculation graph diagram analysis • Use summary statistics, displays, and interpretation of real-world data.	1. Algebraic Relationships text calculation graph diagram analysis • Use algebraic relationships, formulas, and practical equations. 2. Investment text calculation graph diagram analysis • Use simple and compound investment models in practical contexts. 3. Depreciation and Loans text calculation graph diagram analysis • Use depreciation, loan repayments, and financial decision-making. 4. Right-Angled Triangles text calculation graph diagram analysis • Use right-triangle geometry and trigonometric reasoning. 5. Ratios and Rates text calculation graph diagram analysis • Use ratios, rates, unit pricing, speed, and comparisons. 6. Bivariate Data Analysis text calculation graph diagram analysis • Use paired data, association, scatterplots, and interpretation. 7. Relative Frequency and Probability text calculation graph diagram analysis • Use relative frequency, simple probability, and interpretation. 8. Algebraic Relationships text calculation graph diagram analysis • Use algebraic relationships, formulas, and equation modelling. 9. Investment and Loans text calculation graph diagram analysis • Use investments, loans, repayments, and financial models. 10. Annuities text calculation graph diagram analysis • Use annuity structures, recurrence, payments, and balances. 11. Trigonometry text calculation graph diagram analysis • Use trigonometric models, angles, lengths, and practical measurement. 12. Ratios and Rates text calculation graph diagram analysis • Use rates, ratios, proportional reasoning, and applications. 13. Network Flow text calculation graph diagram analysis • Use network flow, capacity, paths, and optimisation contexts. 14. Critical Path Analysis text calculation graph diagram analysis • Use project networks, scheduling, and critical-path reasoning. 15. Bivariate Data Analysis text calculation graph diagram analysis • Use paired data, association, scatterplots, and interpretation. 16. Relative Frequency and Probability text calculation graph diagram analysis • Use relative frequency, probability models, and interpretation. 17. The Normal Distribution text calculation graph diagram analysis • Use normal-distribution shape, standardisation, and probability interpretation.
Mathematics Advanced	1. Working with Functions text calculation graph diagram analysis • Use function notation, domain, range, composition, and evaluation. 2. Graph Transformations text calculation graph diagram analysis • Use translations, reflections, dilations, and graph interpretation. 3. Trigonometry and Measure of Angles text calculation graph diagram analysis • Use radians, exact values, angle measure, and trigonometric relationships. 4. Trigonometric Identities and Equations text calculation graph diagram analysis • Use identities, equations, and exact trigonometric reasoning. 5. Exponential and Logarithmic Functions text calculation graph diagram analysis • Use exponential and logarithmic relationships, graphs, and modelling. 6. Introduction to Differentiation text calculation graph diagram analysis • Use limits, gradients, derivatives, and rates of change. 7. Probability and Data text calculation graph diagram analysis • Use probability, data displays, summary measures, and interpretation.	1. Further Graph Transformations and Modelling text calculation graph diagram analysis • Use transformations, modelling, curve behaviour, and graphical problem solving. 2. Differential Calculus text calculation graph diagram analysis • Use derivative rules, curve behaviour, rates of change, and tangents. 3. Integral Calculus text calculation graph diagram analysis • Use anti-differentiation, definite integrals, area, and accumulation. 4. Applications of Calculus text calculation graph diagram analysis • Use calculus in motion, optimisation, area, and modelling contexts. 5. Sequences and Series text calculation graph diagram analysis • Use arithmetic, geometric, recursive, and sigma-notation structures. 6. Random Variables text calculation graph diagram analysis • Use probability models, distributions, expected value, and interpretation. 7. Financial Mathematics text calculation graph diagram analysis • Use recurrence, growth, decay, and financial modelling in Advanced contexts.
Mathematics Extension 1	1. Further Work with Functions text calculation graph diagram analysis • Use function structure, transformations, domain, range, and harder graph reasoning. 2. Polynomials text calculation graph diagram analysis • Use polynomial roots, factorisation, identities, and graph behaviour. 3. Further Trigonometry text calculation graph diagram analysis • Use identities, equations, exact relationships, and harder trigonometric manipulation. 4. Introduction to Calculus text calculation graph diagram analysis • Use extended derivative ideas, related rates, and harder applications. 5. Permutations and Combinations text calculation graph diagram analysis • Use arrangements, selections, counting cases, and structured reasoning. 6. The Binomial Theorem text calculation graph diagram analysis • Use binomial expansions, coefficients, and exact algebraic reasoning.	1. Proof by Mathematical Induction text calculation analysis • Use base case, inductive step, and clear proof structure. 2. Introduction to Vectors text calculation graph diagram analysis • Use vector notation, magnitude, direction, and simple vector operations. 3. Inverse Trigonometric Functions text calculation graph diagram analysis • Use inverse trigonometric graphs, domains, ranges, and equations. 4. Further Calculus Skills text calculation graph diagram analysis • Use harder differentiation and integration techniques. 5. Further Applications of Calculus text calculation graph diagram analysis • Use harder applications, rates, optimisation, and modelling. 6. Binomial Distribution and Sampling Distribution of the Mean text calculation graph diagram analysis • Use binomial models, sample means, and distribution interpretation.
Mathematics Extension 2	Year 12 HSC course only	1. The Nature of Proof text calculation analysis • Use rigorous proof, logic, assumptions, and advanced problem solving. 2. Further Work with Vectors text calculation graph diagram analysis • Use vectors, vector equations, geometric interpretation, and applications. 3. Introduction to Complex Numbers text calculation graph diagram analysis • Use complex numbers, the complex plane, modulus-argument form, roots, and loci. 4. Further Integration text calculation graph diagram analysis • Use advanced integration methods and exact calculus techniques. 5. Applications of Calculus to Mechanics text calculation graph diagram analysis • Use calculus, force, acceleration, projectiles, and motion modelling.