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Go Above and Beyond in Maths
Your progress is not determined simply by how much help you receive. It comes from identifying what you don't yet understand, learning it properly, and then deliberately practising it.
The purpose of this routine is to turn every practice test into a learning opportunity: test yourself, identify your weaknesses, learn the theory, practise those weaknesses, and then test yourself again. Over time, this creates a cycle where each test tells you exactly what you should work on next.
1. Test Yourself
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Complete a practice test — 1 hour
Sit the test under exam conditions. Do not use your notes, stop the timer, or look at the answers. Treat it as a genuine assessment of what you can currently do independently. - Take a break — 15–30 minutes
Complete a 1-hour test for Mathematics Advanced (Math Advanced prelim prep) on even days, and Mathematics Extension 1 (Math Extension 1 prelim prep) on odd days.
2. Diagnose & Learn
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Mark the test and study the theory — 1 hour
Once you have finished, use ChatGPT to quickly obtain the solutions if needed (for example, CTRL+A → CTRL+C → paste into ChatGPT). Spend approximately 15 minutes marking your test.Then spend the remaining 45 minutes identifying the specific topics you got wrong, could not complete, or were unsure about. For each of those topics, read the relevant theory or YouTube videos in their order of difficulty. Go from the easiest to the hardest. here.
Don't just copy the solution. Work out why you got the question wrong and make sure you understand the method well enough to solve a similar question without help.
By the end of this step, you should have a clear list of the specific topics you need to improve.
- Take a break — 15–30 minutes
3. Train Yourself
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Complete targeted practice questions — 1 hour
Now practise the exact topics you identified in your test in their order of difficulty. Go from the easiest to the hardest. Don't simply do another random set of questions. Use your mistakes from the test to determine what you should practise.
For example, if your test shows that you struggle with simultaneous equations, completing the square, or differentiation, find a set of questions specifically targeting those skills. The resources below can help you do this:
You can also create a new practice exam containing questions on the areas you found difficult:
4. Repeat the Cycle
The goal is not to complete one test and move on. Each test should tell you what to work on next.
After completing your targeted practice, take another practice test and repeat the process. You should gradually see the same weaknesses disappear and new weaknesses become visible.
This creates a simple cycle:
Test → Identify weaknesses → Learn the theory → Targeted practice → Test again
Be Consistent
Do this routine five days a week. The aim is not to spend hours doing random maths questions. It is to make every hour of study purposeful by using your performance to decide what you should learn and practise next.
If you consistently follow this process, you will build both your mathematical knowledge and your ability to recognise and solve different types of questions under exam conditions. It should help you make significant progress towards catching up and being prepared for your Year 11 final exams.
Bring the questions you found difficult, the topics you identified as weaknesses, and anything you still don't understand to the tutoring session. This gives us something specific to work on rather than spending the session guessing where you need help.
The Principle
Don't just do more maths. Use maths to find out what you don't know. Then learn it, practise it, and test yourself again.
Physics
NSW HSC Physics — PhET Simulation Links
A searchable table of the PhET simulations supplied in the source list, grouped by the HSC Physics Year 12 modules they most closely support. Select a simulation title or “Open simulation page” to visit PhET.
| Simulation | Suggested learning connection | Link |
|---|---|---|
| Module 5 — Advanced Mechanics | ||
| Projectile Data Lab | Analyse projectile-motion data. | Open simulation page ↗ |
| Projectile Motion | Resolve horizontal and vertical motion; investigate trajectories. | Open simulation page ↗ |
| Vector Addition | Resolve and combine vector quantities. | Open simulation page ↗ |
| Collision Lab | Momentum and collisions; qualitative/quantitative modelling. | Open simulation page ↗ |
| Energy Skate Park | Conservation and transformation of mechanical energy. | Open simulation page ↗ |
| Energy Skate Park: Basics | Introductory energy transformations. | Open simulation page ↗ |
| Gravity Force Lab | Investigate gravitational force and mass/distance relationships. | Open simulation page ↗ |
| Gravity Force Lab: Basics | Introductory gravitational-force relationships. | Open simulation page ↗ |
| Gravity and Orbits | Orbital motion and gravity. | Open simulation page ↗ |
| Kepler's Laws | Orbital relationships and Kepler's laws. | Open simulation page ↗ |
| My Solar System | Gravitational interactions and orbital motion. | Open simulation page ↗ |
| Pendulum Lab | Oscillatory motion and energy changes. | Open simulation page ↗ |
| Masses and Springs | Simple harmonic motion and energy in oscillations. | Open simulation page ↗ |
| Masses and Springs: Basics | Introductory spring oscillations. | Open simulation page ↗ |
| Hooke's Law | Force-extension relationship for springs. | Open simulation page ↗ |
| Friction | Frictional forces and motion. | Open simulation page ↗ |
| Forces and Motion: Basics | Force, mass and acceleration. | Open simulation page ↗ |
| Balancing Act | Torque, balance and rotational equilibrium. | Open simulation page ↗ |
| Module 6 — Electromagnetism | ||
| Generator | Electromagnetic induction and electrical generation. | Open simulation page ↗ |
| Magnets and Electromagnets | Magnetic fields and electromagnets. | Open simulation page ↗ |
| Magnet and Compass | Magnetic fields and compass alignment. | Open simulation page ↗ |
| Faraday's Electromagnetic Lab | Explore induction and changing magnetic fields. | Open simulation page ↗ |
| Faraday's Law | Investigate induced voltage and magnetic-flux change. | Open simulation page ↗ |
| Circuit Construction Kit: AC | AC circuits and circuit behaviour. | Open simulation page ↗ |
| Circuit Construction Kit: AC - Virtual Lab | Virtual AC circuit construction and measurement. | Open simulation page ↗ |
| Circuit Construction Kit: DC | DC circuits, current, voltage and resistance. | Open simulation page ↗ |
| Circuit Construction Kit: DC - Virtual Lab | Virtual DC circuit construction and measurement. | Open simulation page ↗ |
| Ohm's Law | Voltage-current-resistance relationship. | Open simulation page ↗ |
| Resistance in a Wire | Factors affecting electrical resistance. | Open simulation page ↗ |
| Capacitor Lab: Basics | Capacitance, charge and stored electrical energy. | Open simulation page ↗ |
| Coulomb's Law | Electrostatic force between charges. | Open simulation page ↗ |
| Charges and Fields | Electric fields and electric potential patterns. | Open simulation page ↗ |
| Balloons and Static Electricity | Charging by friction and electrostatic interactions. | Open simulation page ↗ |
| John Travoltage | Electron transfer and static electricity. | Open simulation page ↗ |
| Module 7 — The Nature of Light | ||
| Geometric Optics | Ray diagrams, reflection and refraction. | Open simulation page ↗ |
| Geometric Optics: Basics | Introductory reflection and refraction. | Open simulation page ↗ |
| Bending Light | Refraction, reflection and Snell's law. | Open simulation page ↗ |
| Color Vision | Colour perception and additive colour mixing. | Open simulation page ↗ |
| Blackbody Spectrum | Thermal radiation and blackbody spectra. | Open simulation page ↗ |
| Molecules and Light | Interaction of light with matter. | Open simulation page ↗ |
| Quantum Wave Interference | Wave-like behaviour and interference at the quantum scale. | Open simulation page ↗ |
| Wave Interference | Interference and superposition of waves. | Open simulation page ↗ |
| Module 8 — From the Universe to the Atom | ||
| Alpha Decay | Alpha radioactive decay. | Open simulation page ↗ |
| Beta Decay | Beta radioactive decay. | Open simulation page ↗ |
| Build a Nucleus | Nuclear composition, isotopes and stability. | Open simulation page ↗ |
| Build an Atom | Atomic structure and subatomic particles. | Open simulation page ↗ |
| Rutherford Scattering | Evidence for the nuclear model of the atom. | Open simulation page ↗ |
| Models of the Hydrogen Atom | Atomic models and hydrogen energy levels. | Open simulation page ↗ |
| Quantum Measurement | Quantum measurement and probability. | Open simulation page ↗ |
| Quantum Coin Toss | Quantum probability and measurement outcomes. | Open simulation page ↗ |
| Atomic Interactions | Interactions between atoms and charged particles. | Open simulation page ↗ |
| Foundational / cross-module support (often useful for Year 11) | ||
| Buoyancy | Buoyant force and fluid behaviour. | Open simulation page ↗ |
| Buoyancy: Basics | Introductory buoyancy. | Open simulation page ↗ |
| Density | Mass, volume and density. | Open simulation page ↗ |
| Under Pressure | Pressure in fluids. | Open simulation page ↗ |
| Sound Waves | Wave properties and sound. | Open simulation page ↗ |
| Waves Intro | Basic wave properties. | Open simulation page ↗ |
| Wave on a String | Wave speed, frequency, wavelength and amplitude. | Open simulation page ↗ |
| Normal Modes | Standing waves and resonance. | Open simulation page ↗ |
| Fourier: Making Waves | Wave superposition and frequency components. | Open simulation page ↗ |
| Diffusion | Particle motion and diffusion; supporting kinetic-model concepts. | Open simulation page ↗ |
| Gases Intro | Particle model and gas behaviour. | Open simulation page ↗ |
| Gas Properties | Pressure, volume, temperature and particle motion. | Open simulation page ↗ |
| States of Matter | Particle model of solids, liquids and gases. | Open simulation page ↗ |
| States of Matter: Basics | Introductory states of matter. | Open simulation page ↗ |
| Energy Forms and Changes | Energy transfers and transformations. | Open simulation page ↗ |
| Calculus Grapher | Mathematical support for modelling changing quantities. | Open simulation page ↗ |
| Curve Fitting | Data analysis and modelling experimental relationships. | Open simulation page ↗ |
| Plinko Probability | Probability and statistical variation; supporting concept only. | Open simulation page ↗ |
Curriculum note: These are suggested connections, not an official NESA endorsement or a one-to-one syllabus mapping. Some simulations are foundational or cross-module resources rather than direct matches for a Year 12 module. Check the current NESA Physics syllabus and your teacher’s prescribed content when planning study.
| Date | Paper | |||
|---|---|---|---|---|
| 10 Jul | Ascham | |||
| 11 Jul | Barker | |||
| 12 Jul | Baulkham Hills | |||
| 13 Jul | Caringbah | |||
| 14 Jul | Cheltenham Girls | |||
| 15 Jul | Cranbrook | |||
| 16 Jul | Fort St | |||
| 17 Jul | Girraween | |||
| 18 Jul | Hurlstone | |||
| 19 Jul | James Ruse | |||
| 20 Jul | Kincoppal | |||
| 21 Jul | Knox | |||
| 22 Jul | MHS | |||
| 23 Jul | Newcastle Grammar | |||
| 24 Jul | Newington | |||
| 25 Jul | North Sydney Boys | |||
| 26 Jul | North Sydney Girls | |||
| 27 Jul | Penrith | |||
| 28 Jul | Pymble | |||
| 29 Jul | SCEGGS | |||
| 30 Jul | St George Girls | |||
| 31 Jul | Sydney Boys | |||
| 1 Aug | Sydney Girls | |||
| 2 Aug | Sydney Grammar | |||
| 3 Aug | Sydney Tech |
| 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.