Maths Advanced exam trends & analysis (2020–2025)
Across 2020–2025, Year 12: Calculus is examined most (98 questions), ahead of Year 12: Statistical Analysis (58 questions) and Year 12: Financial Mathematics (34 questions). By topic, Applications of differentiation: stationary points, inflection, optimisation and related rates, Integration techniques: antiderivatives, substitution, definite integrals and the FTC and Bivariate data: scatter plots, Pearson correlation and least-squares regression for HSC Maths Advanced come up most, with Continuous random variables: probability density functions, cumulative distributions, mean and variance and The normal distribution: z-scores, the empirical rule, probabilities and percentiles also recurring.
Based on 250 questions across 6 official NESA exam papers, their marking guidelines and marking feedback.
Work in progress
These exam-trend insights are an early release. The frequencies, mark ranges and figures are still being verified against the official NESA past papers and may change. Treat them as a study guide, not a guarantee of what will be examined.
Most-examined dot points
By module
Every dot point, by exam frequency
Click any dot point for the full verbatim syllabus wording, worked answers and past questions.
Showing 24 of 24 dot points
| Dot point | Times | Marks | Years | Most common mistake |
|---|---|---|---|---|
| Applications of differentiation: stationary points, inflection, optimisation and related ratesyear-12-calculus Determine nature of stationary points; distinguish inflection | 28× | 1–5 | 2020, 2021, 2022, 2023, 2024, 2025 | Determine nature of stationary points; distinguish inflection |
| Integration techniques: antiderivatives, substitution, definite integrals and the FTCyear-12-calculus Use radians for trigonometric calculus | 26× | 1–3 | 2020, 2021, 2022, 2023, 2024, 2025 | Use radians for trigonometric calculus |
| Bivariate data: scatter plots, Pearson correlation and least-squares regression for HSC Maths Advancedyear-12-statistical-analysis Distinguish mean and median; round only at the end | 19× | 1–5 | 2020, 2021, 2022, 2023, 2024, 2025 | Distinguish mean and median; round only at the end |
| Continuous random variables: probability density functions, cumulative distributions, mean and varianceyear-12-statistical-analysis Integral equals 1; antiderivative of sin is -cos; radians | 17× | 1–3 | 2020, 2021, 2022, 2023, 2024, 2025 | Integral equals 1; antiderivative of sin is -cos; radians |
| The normal distribution: z-scores, the empirical rule, probabilities and percentilesyear-12-statistical-analysis Use complementary 'at least one'; empirical percentages | 17× | 1–4 | 2020, 2021, 2022, 2023, 2024, 2025 | Use complementary 'at least one'; empirical percentages |
| Combining functions: sums, differences, products, quotients, squares and reciprocalsyear-12-functions Label asymptotes and intercepts; do not cross asymptotes | 14× | 1–3 | 2021, 2022, 2023, 2024, 2025 | Label asymptotes and intercepts; do not cross asymptotes |
| Reducing-balance loans: repayments, outstanding balance and present value of an annuityyear-12-financial-mathematics Set out recurrence working clearly | 14× | 1–4 | 2020, 2021, 2022, 2023, 2024, 2025 | Set out recurrence working clearly |
| Graph transformations: translations, reflections and dilations for HSC Maths Advanced functionsyear-12-functions Reflect by replacing y with -y; complete the square | 13× | 1–3 | 2020, 2021, 2022, 2023, 2024, 2025 | Reflect by replacing y with -y; complete the square |
| Graphs of sine, cosine and tangent: amplitude, period, phase shift and vertical shiftyear-12-trigonometric-functions Read amplitude and translation from graph | 12× | 1–2 | 2020, 2021, 2022, 2024, 2025 | Read amplitude and translation from graph |
| Geometric sequences and series for HSC Maths Advanced financial modellingyear-12-financial-mathematics Find n from first term, difference and last term | 11× | 1–3 | 2020, 2021, 2022, 2023, 2024, 2025 | Find n from first term, difference and last term |
| Differentiation rules for HSC Maths Advanced: power, chain, product, quotient, exp, log, trigyear-12-calculus Use product rule with brackets; factorise fully | 10× | 1–3 | 2020, 2021, 2022, 2023, 2024, 2025 | Use product rule with brackets; factorise fully |
| Exponential growth and decay: dN/dt = kN, Newton's law of cooling and applicationsyear-12-calculus Differentiate base-other-than-e; instantaneous vs average rate | 10× | 1–4 | 2020, 2021, 2022, 2024 | Differentiate base-other-than-e; instantaneous vs average rate |
| Calculus of trigonometric functions: derivatives, integrals and harmonic motion modellingyear-12-calculus Interpret increasing via derivative/graph; inequalities | 9× | 1–3 | 2020, 2021, 2022, 2023 | Interpret increasing via derivative/graph; inequalities |
| Annuities and future value: deriving the formula and applying it to regular savingsyear-12-financial-mathematics Use future-value table; do not regenerate a series | 8× | 1–3 | 2021, 2022, 2023, 2024, 2025 | Use future-value table; do not regenerate a series |
| Areas between curves and volumes of revolution using definite integralsyear-12-calculus Solve quadratics simultaneously; factorise | 7× | 2–4 | 2020, 2021, 2022, 2023, 2024 | Solve quadratics simultaneously; factorise |
| Exponential and logarithmic graphs: key features, transformations and inverse relationshipyear-12-functions Exponential is a smooth curve with an asymptote | 6× | 1–2 | 2021, 2022, 2023, 2024, 2025 | Exponential is a smooth curve with an asymptote |
| Radians, arc length, sector and segment area for HSC Maths Advancedyear-12-trigonometric-functions Recognise isosceles triangles; perpendicular vs slant height | 6× | 2–4 | 2020, 2022, 2023, 2024, 2025 | Recognise isosceles triangles; perpendicular vs slant height |
| Discrete random variables: probability distribution, expected value, variance and standard deviationyear-12-statistical-analysis Sum probabilities as GP; simplify E(X) series | 5× | 1–3 | 2021, 2023, 2025 | Sum probabilities as GP; simplify E(X) series |
| Solving trigonometric equations: principal values, multiple angles and quadratics in sine and cosineyear-12-trigonometric-functions Solve in radians within the given domain | 5× | 2–4 | 2021, 2022, 2023, 2024, 2025 | Solve in radians within the given domain |
| Logarithmic and exponential calculus: derivatives and integrals of e^x and ln(x)year-12-calculus Adjust numerator to f'(x)/f(x) form; add constant | 4× | 2 | 2020, 2023 | Adjust numerator to f'(x)/f(x) form; add constant |
| Motion along a straight line: displacement, velocity and acceleration via calculusyear-12-calculus Max height when y'(t)=0; t is a step not the answer | 4× | 2–3 | 2021, 2023, 2024 | Max height when y'(t)=0; t is a step not the answer |
| Essential trigonometric identities: Pythagorean, ratio, complementary and double angleyear-12-trigonometric-functions Manipulate fractions; use 1-cos^2=sin^2 | 3× | 1–2 | 2020, 2021, 2025 | Manipulate fractions; use 1-cos^2=sin^2 |
| Composite and inverse functions: existence, formulas, domains and graphsyear-12-functions Sketch the translated hyperbola; correct range notation | 1× | 2 | 2025 | Sketch the translated hyperbola; correct range notation |
| Simple and compound interest, future value and present value for HSC Maths Advancedyear-12-financial-mathematics Convert rate and number of compounding periods | 1× | 2 | 2022 | Convert rate and number of compounding periods |