Google Meet URL for tutoring session.
Whiteboard sessions.
All tutoring resources.
Study Timeline and Resources. Be sure to pick questions relevant to your upcoming exam.
Math Extension 1
Maths Extension 1 Binomial Dist & Functions📄 HSC Mathematics Extension 1 Past Papers
- 2025 HSC Mathematics Extension 1 Exam Paper
- 2025 HSC Mathematics Extension 1 Marking Guidelines
- 2024 HSC Mathematics Extension 1 Exam Paper
- 2024 HSC Mathematics Extension 1 Marking Guidelines
- 2023 HSC Mathematics Extension 1 Exam Paper
- 2023 HSC Mathematics Extension 1 Marking Guidelines
- 2022 HSC Mathematics Extension 1 Exam Paper
- 2022 HSC Mathematics Extension 1 Marking Guidelines
- 2021 HSC Mathematics Extension 1 Exam Paper
- 2021 HSC Mathematics Extension 1 Marking Guidelines
- 2020 HSC Mathematics Extension 1 Exam Paper
- 2020 HSC Mathematics Extension 1 Marking Guidelines
| HSC Paper | Binomial Theorem (Expansions & Coefficients) | Binomial Theorem (Identities & Proofs) | Further Functions (Reciprocal & Trig Graphs) | Further Functions (Inverses & Combinations) |
|---|---|---|---|---|
| 2020 |
Question 14(a)(ii): Combinatorial selection of equal men/women. Question 14(a)(iii): Selection of group with leaders. |
Question 14(a)(i): Proving binomial identity using (1+x)2n. Question 14(a)(iv): Proving identity via reversed selection process. |
Question 11(c): Sketching the reciprocal graph y = 1/f(x) from a given linear/parabolic plot. |
Question 2: Determining domain and range of an inverse function. Question 13(c)(ii): Showing functional equivalence f(x) = g(x) via derivatives. |
| 2021 | Question 11(b): Expanding and simplifying (2a − b)4 using the binomial theorem. | Question 9: Identifying the graph of the composite function y = sin−1(sin x). |
Question 12(d)(ii): Finding the algebraic form and domain of an inverse function. Question 12(d)(iii): Sketching the inverse function graph. |
|
| 2022 | Question 11(c): Determining coefficients of x2 and x3 in the expansion of (1 − x/2)8. |
Question 2: Identifying the transformation y = f(|x|) from a given graph. Question 4: Identifying graphs of f(x) and g(x) from their sum y = f(x) + g(x). Question 13(c): Justifying why a restricted trig function is not a global inverse. |
||
| 2023 | Question 12(d): Applying the Pascal identity nCr = (n−1)Cr−1 + (n−1)Cr to simplify coefficients. | Question 5: Evaluating sin−1(sin α) for a specific quadrant. |
Question 8: Identifying a graph involving absolute value transformations. Question 14(a)(i): Explaining the existence of an inverse function using monotonicity. |
|
| 2024 | Question 12(e): Graphing and solving an inequality for the reciprocal absolute function y = 1/|x−5|. |
Question 14(b): Finding values of k for which a function has an inverse. Question 14(c)(i): Explaining why a sum of inverse tan functions has exactly one solution. |
||
| 2025 |
Question 13(e)(i): Rearranging Pascal’s triangle relation to show a difference of terms. Question 13(e)(ii): Proving a summation identity using the result from 13(e)(i). |
Question 11(a): Finding the algebraic form of the inverse function f−1(x). |
Additional Analysis
Frequency Count
- Binomial Theorem (Expansions & Coefficients): 3 Questions
- Binomial Theorem (Identities & Proofs): 5 Questions
- Further Functions (Reciprocal & Trig Graphs): 4 Questions
- Further Functions (Inverses & Combinations): 11 Questions
Most Commonly Assessed Subtopics
- Inverse Functions: This is the most frequently assessed subtopic, appearing in almost every year. It ranges from algebraic derivation to graphical sketching and formal justifications of existence based on the horizontal line test or monotonicity.
- Binomial Identities: Questions often require students to prove complex identities by either equating coefficients of expansions or using combinatorial arguments (choosing groups and leaders).
- Graphing Relationships: Identifying transformations such as f(|x|) and f(x) + g(x) is a recurring multiple-choice theme.
Noticeable Trends
- Shift to Proof: There is a noticeable shift toward multi-step proofs in Section II, particularly involving Pascal’s triangle identities.
- Conceptual Depth in Functions: Later papers (2023–2025) place a heavier emphasis on the existence and validity of inverse functions rather than simple calculation.
- Reciprocal Graphs: While common in earlier papers, reciprocal graphing (1/f(x)) has evolved into solving more complex inequalities involving these graphs.
Predicted High-Frequency Areas
- Combinatorial Proofs: Given their prominence in 2020 and 2025, proving a binomial identity through a contextual selection argument (for example, committees, groups, or leaders) is highly likely to reappear.
- Domain/Range of Combined Functions: The interaction between absolute values and reciprocal functions remains a core area for testing higher-order graph interpretation and visualization skills.
- Algebraic Inverses: Finding the inverse of rational, exponential, or logarithmic functions is a standard Extension 1 skill likely to persist in Section II.
Math Advanced
Create your own exams based on the topics you want to be assessed on.| HSC Paper | Functions and Relations | Linear | Quadratic | Cubic | Reciprocal |
|---|---|---|---|---|---|
| 2020 | Q1: Domain of a square root function [1]. Q10: Stationary points of a composite function [2]. |
Q11: Modeling water tank volume with linear equations [3]. | Q5: Identifying a parabola graph based on constants [4]. Q30: Intersection and shaded area of two parabolas [5]. |
Q2: Horizontal and vertical translations of a cubic function [1]. Q16: Sketching a cubic curve with stationary points [6]. |
Q25: Perimeter and area relations in a garden bed model [7]. |
| 2021 | Q3: Domain of a logarithmic function [8]. Q21: Sketching a transformed function y = 4f(2x) [9]. |
Q11: Solving a linear algebraic equation [10]. Q17: Interpreting gradient and predicting values in regression lines [11, 12]. |
Q31: Finding equations of tangents to a parabola passing through a point [13]. | Q8: Identifying the equation of a cubic graph from its intercepts [14]. Q16: Finding intervals where a cubic function is increasing [15]. |
Q19: Sketching a hyperbola and showing its asymptotes [16]. Q24: Finding the area bounded by a curve y = 3/(x-1) and a line [17]. |
| 2022 | Q10: Identifying the graph of a composite function g(f(x)) [18]. | Q1: Identifying the graph of y = -2x - 2 [19]. | Q4: Determining the range of a quadratic function [20]. Q19: Finding constants for a translated and dilated parabola [21]. |
Q22: Global maximum and minimum values of a cubic on a closed interval [22]. | Q12: Modeling inverse variation between melting time and temperature [23]. Q28: Solving for constants in a hyperbola equation [24, 25]. |
| 2023 | Q9: Identifying properties of even functions [26]. Q27: Finding values for an absolute value function f(x) = a|x-b| + c [27]. |
Q18: Plotting means and finding the equation of a regression line [28, 29]. | Q10: Comparing lengths of intervals where a line meets y = x² [26]. Q19: Solving an inequality involving a parabola and a line [30]. |
Q4: Determining the equation and constants of a cubic polynomial graph [31]. Q14: Finding the tangent equation for a cubic power function [32]. |
Q3: Determining the domain of a reciprocal function f(x) = 3/(1-x) [33]. |
| 2024 | Q6: Finding the domain of a reciprocal square root function [34]. Q7: Identifying transformations of a given function [34]. |
Q1: Identifying the equation of a linear function from a graph [35]. | Q4: Reflecting a parabola about the x and y axes [34]. Q14: Finding intersection points and area between two parabolas [36, 37]. |
Q19: Sketching a polynomial curve (y = x⁴ - 2x³ + 2) using stationary points [38]. | Q30: Range of values for a limiting sum using a hyperbola graph [39]. Q31: Minimising perimeter for a region defined by A/x [40]. |
| 2025 | Q3: Domain of a square root of a quadratic (semicircle) [41]. Q18: Range of a composite function involving reciprocal components [42]. |
Q14: Describing bivariate data and interpreting regression slopes [43, 44]. | Q11: Finding the turning point of a quadratic graph [45]. Q30: Finding the value of a translation constant for a parabola [46]. |
Q4: Identifying the graph of a cubic polynomial [41]. Q12: Tangent to a function with cubic and reciprocal-square terms [47]. |
Q21: Finding the mode and percentiles of a PDF involving 1/x [48, 49]. |
📄 HSC Mathematics Advanced Past Papers
- 2025 HSC Mathematics Advanced Exam Paper
- 2025 HSC Mathematics Advanced Marking Guidelines
- 2024 HSC Mathematics Advanced Exam Paper
- 2024 HSC Mathematics Advanced Marking Guidelines
- 2023 HSC Mathematics Advanced Exam Paper
- 2023 HSC Mathematics Advanced Marking Guidelines
- 2022 HSC Mathematics Advanced Exam Paper
- 2022 HSC Mathematics Advanced Marking Guidelines
- 2021 HSC Mathematics Advanced Exam Paper
- 2021 HSC Mathematics Advanced Marking Guidelines
- 2020 HSC Mathematics Advanced Exam Paper
- 2020 HSC Mathematics Advanced Marking Guidelines
HELM: Basic Algebra. Date due: 2025-12-09
HELM: Basic Functions. Date due: 2025-12-12
HELM: Equations, Inequalities & Partial Fractions. Date due: 2025-12-15
HELM: Functions and Modelling. Date due: 2025-12-24
HELM: Exponential & Logarithmic Functions. Date due: 2025-12-27
HELM: Trigonometry. Date due: 2025-12-30
HELM: Functions of Several Variables. Date due: 2026-01-02
HELM: Differentiation. Date due: 2026-01-05
HELM: Applications of Differentiation. Date due: 2026-01-08
HELM: Integration. Date due: 2026-01-11
HELM: Applications of Integration – Part 1. Date due: 2026-01-14
HELM: Applications of Integration – Part 2. Date due: 2026-01-17
Physics
November 29
November 30
December 1
December 2
December 3
| HSC Paper | Theory of Special Relativity | Relativistic Calculations | Evidence for Special Relativity | Consequences of Special Relativity |
|---|---|---|---|---|
| 2021 | Question 4: Constant speed of light pulses between frames. |
Question 16: Calculating mass decrease from Sun's energy output using E=mc². Question 28a: Distance calculation based on Earth time and dilated astronaut time. Question 35a,b: Calculating energy release from alpha decay using mass-energy equivalence. |
Question 28b: Limitation on the maximum velocity of a spaceship imposed by special relativity. | |
| 2022 | Question 30a: Qualitative description of how constant speed of light leads to prediction of time dilation. | Question 30b: Calculation of time dilation for light pulses on a moving train at 0.96c. | Question 20: Describing relativistic length contraction at different points on a rolling wheel. | |
| 2023 | Question 22: Time dilation calculation for light pulses from a spacecraft travelling at 0.9c. | |||
| 2024 | Question 27b: Calculating energy released per pion in a proton-antiproton reaction using mass-energy equivalence. | Question 26: Qualitative explanation of muon survival using frames of reference (evidence for time dilation/length contraction). |
Question 12: Relationship between rod speed and measured length contraction. Question 20: Comparing tick rates of atomic clocks in different satellite orbits. Question 27c: Resolving classical predictions of velocities exceeding the speed of light. |
|
| 2025 | Question 34a,b: Foundational theory involving measurements and determination of the speed of light. | Question 19: Calculating mass decrease in a system releasing chemical energy. |
Question 20: Plausibility of particle production based on energy-to-mass conversion in accelerators. Question 32: Comprehensive analysis of the consequences for length, time, and motion with evidence. |
Additional Analysis
1. Frequency Count for Topic Areas
- Theory of Special Relativity: 3 questions
- Relativistic Calculations: 7 questions
- Evidence for Special Relativity: 1 question
- Consequences of Special Relativity: 7 questions
2. Most Commonly Assessed Subtopics
- Time Dilation: Appears consistently across multiple years (2021, 2022, 2023) as the primary calculation task.
- Mass-Energy Equivalence (E=mc²): Frequently assessed through nuclear decay or star energy output calculations (2021, 2024, 2025).
- Length Contraction: Often assessed conceptually or graphically rather than through complex arithmetic (2022, 2024, 2025).
3. Noticeable Trends Across Years
- Shift from Calculation to Analysis: Early papers (2021-2023) focused heavily on direct application of the time dilation formula. Recent papers (2024-2025) include more high-mark extended responses requiring analysis of the consequences and evidence of the theory.
- Integration with Other Topics: Relativity is increasingly integrated with Module 8 (Nuclear/Atomic Physics), specifically using E=mc² to explain particle interactions and stability.
- Graphical Interpretation: The 2024 and 2025 papers show a trend toward interpreting relativistic effects via graphs (e.g., length vs. speed) rather than simple text.
4. Predicted High-Frequency Areas
- Relativistic Momentum: While calculations for time and length are frequent, relativistic momentum is present on the formula sheet but has seen lower frequency in recent extended responses. This is a likely candidate for a future multi-mark calculation.
- Muon Evidence: As one of the few named experimental evidences in the syllabus, the muon decay experiment remains a high-probability topic for mid-range (3-4 mark) explanation questions. 04/06/2026 Particle Physics Meets Nuclear Physics. Merged HSC Trial Papers: CTRL+F to find what questions you want..
- Mass-Energy in Accelerators: Given the focus on the Standard Model in recent papers, questions regarding how energy is converted to mass in particle accelerators (using relativistic principles) are highly likely.
Electromagnetism Video Lessons. Date due: 2026-03-13
Year 12 Physics Sample Assessment Tasks. Date due: 2026-03-14
Electricity and Magnetism Practice Questions. Date due: 2026-03-15
Electromagnetism Exam Practice. Date due: 2026-03-16
Full Practice Test (Exam Conditions). Date due: 2026-03-17
materials relating to the session on the 27th of March 2026
📘 Theory & Complete Notes (Module 7: Nature of Light)
- Complete guide to HSC Physics Module 7 (Nature of Light).
- Comprehensive collection of Nature of Light documents.
- Detailed notes on Light and Quantum Physics.
- Electromagnetic spectrum notes.
📝 Practice Questions & Worksheets
- Module 7 practice questions (Art of Smart).
- Practice questions with worked solutions.
- Large bank of physics questions by topic.
📄 Past Papers & Trial Exams
📚 Exam Guides & Study Resources
- TSFX exam essentials for Module 7.
- Guide to acing HSC Physics exams.
- Matrix Year 12 Physics resource sample.