Mathematics Advanced · 2021–2025 · 10 min read
Five years of Advanced:
what keeps coming back?
We analysed every atomic question in five recent 100-mark HSC papers to identify the content, skills and response styles students repeatedly encounter.
The short version
Advanced rewards breadth, fluency and sustained working.
Financial mathematics was the largest primary category. Trigonometric modelling, definite integrals and areas, continuous random variables, curve analysis, normal distributions and bivariate data were also substantial recurring sources of marks.
69.8% of all marks were attached to worked solutions or show/prove questions. The course is broad, but most marks still depend on setting up a method correctly and communicating enough working to earn partial credit.
Common question types
The highest-volume categories
Each atomic question is assigned one primary concept category here, so marks are counted once and the complete category distribution totals 500 marks.
Recurring every year
The reliable practice list
Loans, Annuities & Compound Investment
9.6 marks per paper on average · 20 atomic questions
Trigonometric Graphs & Periodic Modelling
7.2 marks per paper on average · 16 atomic questions
Definite Integrals & Areas Under Curves
6.6 marks per paper on average · 15 atomic questions
Continuous Random Variables
5.8 marks per paper on average · 15 atomic questions
Stationary Points & Curve Sketching
5.4 marks per paper on average · 9 atomic questions
Normal Distribution & z-scores
5.4 marks per paper on average · 12 atomic questions
Bivariate Data & Linear Regression
4.8 marks per paper on average · 13 atomic questions
Arithmetic & Geometric Sequences and Series
4.6 marks per paper on average · 10 atomic questions
Graph Transformations
4.6 marks per paper on average · 12 atomic questions
Triangle Trigonometry & Bearings
4.0 marks per paper on average · 9 atomic questions
Radian Measure: Arcs, Sectors & Segments
3.2 marks per paper on average · 6 atomic questions
Exponential & Logarithmic Functions
2.4 marks per paper on average · 8 atomic questions
Conditional Probability & Tree Diagrams
2.4 marks per paper on average · 8 atomic questions
Domain, Range & Composite Functions
1.6 marks per paper on average · 7 atomic questions
Polynomial Graph Recognition & Features
1.4 marks per paper on average · 6 atomic questions
Paper-by-paper pattern
Primary-category marks by year
| Question category | 2021 | 2022 | 2023 | 2024 | 2025 | Average |
|---|---|---|---|---|---|---|
| Loans, Annuities & Compound Investment | 8 | 11 | 11 | 8 | 10 | 9.6 |
| Trigonometric Graphs & Periodic Modelling | 7 | 8 | 5 | 7 | 9 | 7.2 |
| Definite Integrals & Areas Under Curves | 11 | 11 | 4 | 3 | 4 | 6.6 |
| Continuous Random Variables | 8 | 4 | 6 | 6 | 5 | 5.8 |
| Tangents & Gradients of Curves | 9 | — | 7 | 4 | 7 | 5.4 |
| Stationary Points & Curve Sketching | 3 | 9 | 5 | 5 | 5 | 5.4 |
| Normal Distribution & z-scores | 8 | 3 | 4 | 6 | 6 | 5.4 |
| Bivariate Data & Linear Regression | 4 | 4 | 7 | 3 | 6 | 4.8 |
| Arithmetic & Geometric Sequences and Series | 2 | 6 | 5 | 6 | 4 | 4.6 |
| Graph Transformations | 7 | 3 | 7 | 2 | 4 | 4.6 |
| Triangle Trigonometry & Bearings | 5 | 1 | 3 | 4 | 7 | 4.0 |
| Rates of Change & Motion | 10 | 2 | 2 | 5 | — | 3.8 |
| Optimisation & Calculus Modelling | — | 4 | 5 | 3 | 5 | 3.4 |
| Radian Measure: Arcs, Sectors & Segments | 3 | 2 | 4 | 3 | 4 | 3.2 |
| Differentiation Techniques | — | 8 | 1 | 5 | 2 | 3.2 |
| Exponential & Logarithmic Functions | 1 | 2 | 1 | 7 | 1 | 2.4 |
Syllabus outcomes
Average marks associated with each outcome
Where an atomic question is officially mapped to several outcomes, its full marks are associated with each. Outcome figures therefore overlap and should be read individually rather than totalled.
How marks are earned
Most marks require a written method.
Worked solutions
276 marks across five papers
Show/prove questions
73 marks across five papers
Multiple choice
50 marks across five papers
Short answers
44 marks across five papers
Sketching
33 marks across five papers
Written explanations
24 marks across five papers
The 50 multiple-choice marks across five papers matter, but the larger return comes from maintaining method accuracy across Section II and writing enough to preserve partial marks.
Question structure
Do not reduce every paper to isolated drills.
The five papers contain 57 multi-part question structures comprising 142 atomic parts. Some parts share only a topic, while others share a model, graph, diagram or earlier result.
Use isolated category practice to build fluency, but regularly complete whole multi-part questions so you practise interpreting shared information and sustaining notation.
A practical study plan
Turn the pattern into preparation
- 01
Secure the recurring high-mark core
Give regular time to financial mathematics, trigonometric modelling, integration and areas, continuous random variables and curve analysis.
- 02
Rotate the breadth
Keep normal distributions, bivariate data, sequences, graph transformations, triangle trigonometry and rates active rather than cramming them late.
- 03
Mix interpretation with technique
Practise moving between formulas, graphs, tables, probability models and contextual statements—not only executing procedures.
- 04
Mark for method, not just answers
Compare each line with the marking criteria. Learn which substitutions, equations and conclusions earn intermediate marks.
- 05
Use timed full papers
A 100-mark paper tests pacing and switching between strands. Preserve time for longer modelling and reasoning questions near the end.
Methodology and sources
What we counted
We used the official 2021–2025 NSW HSC Mathematics Advanced examination papers and marking materials. Multi-part questions were separated into atomic assessed units for classification, while their original question structure was retained.
- 2021: exam paper · marking guidelines
- 2022: exam paper · marking guidelines
- 2023: exam paper · marking guidelines
- 2024: exam paper · marking guidelines
- 2025: exam paper · marking guidelines
Primary-category marks are mutually exclusive. Outcome marks overlap where official mapping metadata lists multiple outcomes. Multi-part structures are structural counts, not claims that every later part depends on every earlier answer. No Band 1–6 difficulty label has been assigned to individual questions.