The Ultimate HSC Maths Advanced Study Plan (2025)

Get a complete HSC Maths Advanced study plan for 2025 aligned with the NSW syllabus. Includes a week-by-week guide, revision tips, and practice strategies to help you ace your HSC exam.

10 hours ago • 3 min read

By Manoj Arachige

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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