The Ultimate HSC Maths Advanced Study Plan (2025)
Your HSC Maths Advanced exam is on 22 October 2025, and the syllabus covers a wide range of topics from algebra to statistics. To help you prepare, here’s a study plan broken into phases, ensuring every syllabus dot point is revised and practised before the big day.
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Phase 1: Core Revision (Weeks 1–3)
(Start 5–6 weeks before the exam)
This phase ensures you systematically review all syllabus topics. Work through each topic in 2-hour blocks, using past examples and textbook questions.
| Syllabus Module | Subtopics | Focus Areas | |
|---|---|---|---|
| 1 | Functions | Functions, Graphs, Polynomials | Domains & ranges, function notation, polynomial factorisation, solving equations graphically |
| 2 | Functions | Further Functions | Rational functions, reciprocal graphs, absolute value functions, inequalities |
| 3 | Trigonometry | Trigonometric Ratios & Applications | Non-right-angled triangles, sine & cosine rules, 3D trig, angles in radians |
| 4 | Trigonometry | Trig Functions & Identities | Trig graphs, Pythagorean identities, solving trig equations including quadratics |
| 5 | Calculus | Differential Calculus | First principles, differentiation rules, tangents/normals, optimisation (max/min problems) |
| 6 | Calculus | Integral Calculus | Indefinite integrals, definite integrals, areas under curves, trapezoidal rule |
| 7 | Calculus | Applications of Calculus | Rates of change, motion problems, growth/decay, exam-style mixed applications |
| 8 | Exponential & Logarithmic Functions | Laws, Equations & Applications | Logarithmic laws, solving exponential equations, exponential growth/decay |
| 9 | Statistical Analysis | Probability | Conditional probability, independence, tree diagrams |
| 10 | Statistical Analysis | Discrete Probability Distributions | Mean & variance, binomial distribution |
| 11 | Statistical Analysis | Data Analysis | Measures of central tendency, standard deviation, least-squares regression line |
| 12 | Statistical Analysis | Random Variables | Expectation, probabilities of intervals, normal distribution introduction |
| 13 | Financial Mathematics | Sequences & Series | Arithmetic & geometric sequences, sigma notation |
| 14 | Financial Mathematics | Financial Applications | Annuities, loans, investments, compound interest |
Phase 2: Practice & Application (Weeks 4–6)
(3–4 weeks before the exam)
Now that you’ve revised the full syllabus, shift into application mode with targeted practice. Each session should involve past paper questions, worked examples, and exam-style problems.
| Focus Topic | Exam Practice Areas | |
|---|---|---|
| 15 | Functions | Composite functions, inequalities, curve sketching |
| 16 | Trigonometry | Complex equations, identities, real-world applications |
| 17 | Calculus I | Differentiation + tangents/normals, optimisation |
| 18 | Calculus II | Integration + areas, rates of change |
| 19 | Exponentials & Logs | Growth/decay problems, solving equations |
| 20 | Probability & Statistics I | Probability distributions, binomial & expectation |
| 21 | Probability & Statistics II | Regression, correlation, interpreting data |
| 22 | Financial Maths | Annuities, loan repayment, long-term investments |
Phase 3: Exam Readiness (Weeks 7–8)
(Final 2 weeks before the exam)
- Week 7: Do at least two timed past papers, mark carefully, and review errors.
- Week 8: Focus on mixed-topic practice, time management, and exam technique. Taper down study intensity in the final days for a confident exam day performance.
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