Study Timeline and Resources. Be sure to pick questions relevant to your upcoming exam.

Math

Go above and beyond in Maths

The progress you make is not guaranteed by the help you receive; it depends on the effort you put into improving the areas of maths you are currently struggling with.

The rationale behind this routine is simple: identify what you don’t know, learn the theory, and then practise it.

Test yourself

Complete a practice test — 1 hour
Sit the test under exam conditions without using your notes, without stopping and without looking at the answers.

Complete a 1 hour test for Advanced Maths (Math Advanced prelim prep)

Take a break — 15–30 minutes

Mark yourself

Mark the test and study the theory — 1 hour
CTRL+A, CTRL+C and paste into ChatGPT to get the answers quickly once done. Spend around 15 minutes marking the test. Then, for the remaining 45 minutes, read the relevant theory from your textbook (or from the ones I've sourced here) for every question you got wrong or struggled with. Focus on understanding why you got it wrong.
Take a break — 15–30 minutes

Train yourself

Complete targeted practice questions — 1 hour
Work through practice questions specifically targeting the topics and skills you got wrong in the test.

You can source targeted questions from:

Or create your own exams based on what you found tricky:

Be consistent

Do this routine five days a week. If you consistently put in this effort, identify your weaknesses, and deliberately practise them, you should make significant progress towards catching up and being prepared to complete your Year 11 final exams.

The key is not simply doing more maths. It is using each test to identify exactly what you need to improve, learning the relevant theory, and then practising until you can do it confidently. Bring what you find challenging to the tutoring session.

Math Advanced prelim prep

Date	Paper
Thu 13 Aug	Baulkham Hills
Fri 14 Aug	Caringbah
Mon 17 Aug	Cheltenham Girls
Tue 18 Aug	Cherrybrook Tech
Wed 19 Aug	Cranbrook
Thu 20 Aug	Epping Boys
Fri 21 Aug	Fort St
Mon 24 Aug	Girraween
Tue 25 Aug	Gosford
Wed 26 Aug	Hornsby Girls
Thu 27 Aug	James Ruse
Fri 28 Aug	Kambala
Mon 31 Aug	Knox
Tue 1 Sep	Loreto Kirribilli
Wed 2 Sep	Newington
Thu 3 Sep	North Sydney Boys
Fri 4 Sep	North Sydney Girls
Mon 7 Sep	Roseville
Tue 8 Sep	Ryde Secondary College
Wed 9 Sep	SCEGGS
Thu 10 Sep	Shore
Fri 11 Sep	St Aloysius
Mon 14 Sep	St George Girls
Tue 15 Sep	Sydney Boys
Wed 16 Sep	Sydney Girls
Thu 17 Sep	Sydney Grammar
Fri 18 Sep	Sydney Tech

Trial yr 11 exams from other schools

Trial yr 12 exams from other schools

Date	Paper
10 Jul	Baulkham Hills, Caringbah, Cheltenham Girls
11 Jul	Cherrybrook Tech, Cranbrook, Epping Boys
12 Jul	Fort St, Girraween, Gosford
13 Jul	Hornsby Girls, James Ruse, Kambala
14 Jul	Knox, Loreto Kirribilli, Newington
15 Jul	North Sydney Boys, North Sydney Girls, Roseville
16 Jul	Ryde Secondary College, SCEGGS, Shore
17 Jul	St Aloysius, St George Girls, Sydney Boys
18 Jul	Sydney Girls, Sydney Grammar, Sydney Tech

18/06/2026

Year 12 Further Maths - CHAPTER 4: Graphs _ Relations - ANSWERS
Year 12 Further Maths - CHAPTER 4: Graphs _ Relations - QUESTIONS
HELM Stats
Create your own exams based on the topics you want to be assessed on.

HSC Paper	Sequences & Series	Financial Applications	Trigonometric Graphs & Applications
2020	Question 12: Sum of an arithmetic series [1].	Question 26: Recurrence relations and account withdrawals [2-10].	Question 6: Range of a cosine function [11]. Question 15: Bearings and the cosine rule [12-14]. Question 19: Trigonometric identity proof [15]. Question 31: Modelling populations with sine functions [16-22].
2021	Question 14: Common difference of an arithmetic sequence [23].	Question 25: Future value interest factors for annuities [24-27]. Question 29: Compound interest and birthday deposits/withdrawals [28-32].	Question 1: Trigonometric identities [33]. Question 12: Right-angled triangles in semicircles [34]. Question 18: Sine rule and obtuse angles [35]. Question 20: Intersection of lines and trigonometric graphs [36]. Question 27: Solar power model using sine functions [37-43].
2022	Question 17: Arithmetic progression in a "house of cards" [44, 45]. Question 29: Limiting sum of a geometric series [46].	Question 21: Future value factors and investment options [47, 48]. Question 32: Reducing-balance loans and monthly repayments [49-51].	Question 3: Angle of elevation [52]. Question 14: Identifying values in a sine graph [53]. Question 23: Tides modelled by cosine equations [54-56]. Question 25: Solving trigonometric derivatives/equations [57]. Question 28: Circular sectors and shaded area [58].
2023	Question 11: Finding terms in an arithmetic sequence [59]. Question 21: Geometric sequence common ratios [60].	Question 15: Future value interest factors and contributions [61-63]. Question 25: Recurrence relations for account balances [64-69].	Question 16: Arc length and perimeter of circular shapes [70, 71]. Question 20: Solving trigonometric equations [72]. Question 22: 3D trigonometry in a rectangular prism [73, 74]. Question 26: Rate of change in a swing motion model [75, 76]. Question 30: Sketching trigonometric functions with stationary points [77-81].
2024	Question 12: Sum of terms in an arithmetic series [82]. Question 30: Range of values for a limiting sum [83].	Question 24: Savings accounts and future value factors [84-87]. Question 26: Monthly withdrawals and present value factors [88, 89].	Question 20: 3D trigonometry and tower elevation [90-92]. Question 28: Ferris wheel height model [93-96]. Question 31: Perimeter and area of regions subtended by angles [97-101].
2025	Question 13: Solving for terms in a geometric sequence [102].	Question 17: Balance owing on reducing-balance loans [103-106]. Question 20: Comparing lump sums and annuities [107, 108].	Question 15: Sound wave amplitude and period models [109-112]. Question 22: Proving complex trigonometric identities [113]. Question 28: Segment area and arc length of circular paddocks [114-117]. Question 29: Bearings and mountain height elevation [118-125]. Question 31: Number of solutions for trigonometric equations [126].

📄 HSC Mathematics Advanced Past Papers

Physics

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

Date	Paper
Mon 17 Aug	Abbotsleigh
Tue 18 Aug	Ascham
Wed 19 Aug	Barker
Thu 20 Aug	Baulkham Hills
Fri 21 Aug	Blacktown Boys
Mon 24 Aug	Callaghan Jesmond
Tue 25 Aug	Caringbah
Wed 26 Aug	Cheltenham Girls
Thu 27 Aug	Cherrybrook Tech
Fri 28 Aug	Cranbrook
Mon 31 Aug	Fort St
Tue 1 Sep	Frensham
Wed 2 Sep	Girraween
Thu 3 Sep	Gosford
Fri 4 Sep	Hills Grammar
Mon 7 Sep	Hornsby Girls
Tue 8 Sep	Hunters Hill
Wed 9 Sep	Hurlstone
Thu 10 Sep	International Grammar
Fri 11 Sep	James Ruse
Mon 14 Sep	Kambala
Tue 15 Sep	Killara
Wed 16 Sep	Kincoppal
Thu 17 Sep	Kings
Fri 18 Sep	Kinross Wolaroi
Mon 21 Sep	Knox
Tue 22 Sep	Loreto Kirribilli
Wed 23 Sep	Manly
Thu 24 Sep	MLC
Fri 25 Sep	Newcastle Grammar
Mon 28 Sep	Newington
Tue 29 Sep	Normanhurst Boys
Wed 30 Sep	North Sydney Boys
Thu 1 Oct	North Sydney Girls
Fri 2 Oct	Penrith
Mon 5 Oct	Pittwater House
Tue 6 Oct	Port Hacking
Wed 7 Oct	Presbyterian
Thu 8 Oct	Pymble
Fri 9 Oct	Riverview
Mon 12 Oct	Roseville
Tue 13 Oct	SCEGGS
Wed 14 Oct	Scots
Thu 15 Oct	Shore
Fri 16 Oct	St Catherines
Mon 19 Oct	St George Girls
Tue 20 Oct	Stella Maris
Wed 21 Oct	Sydney Boys
Thu 22 Oct	Sydney Girls
Fri 23 Oct	Sydney Grammar
Mon 26 Oct	Sydney Tech
Tue 27 Oct	Westfield Sports

November 29

2021 HSC Physics Exam Paper (PDF)

November 30

2022 HSC Physics Exam Paper (PDF)

December 1

2023 HSC Physics Exam Paper (PDF)

December 2

2024 HSC Physics Exam Paper (PDF)

December 3

2025 HSC Physics Exam Paper (PDF)

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

Electromagnetism Lecture Playlist

Year 12 Physics Sample Assessment Tasks. Date due: 2026-03-14

Physics ATAR Year 12 Sample Assessment Tasks

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

Electricity and Magnetism Full Practice Test

materials relating to the session on the 27th of March 2026

📘 Theory & Complete Notes (Module 7: Nature of Light)

📝 Practice Questions & Worksheets

📄 Past Papers & Trial Exams

📚 Exam Guides & Study Resources

🔗 Additional Supporting Resources

Supplementary waves and thermodynamics materials.

science-s6-physics-module-5-advanced-mechanics.docx

12Physics_-module-6-guide.docx

Problem set for Year 12 Physics

12Physics_-module-7-guide.docx

Mod8

science-physics-s6-learning-sequence-diffraction-of-light.docx

Nature of Light Checklist

Electromagnetic Waves

All electromagnetic radiation travels at constant speed (c) in a vacuum How electromagnetic waves are produced and propagated Prediction of speed of light using permittivity and permeability Hertz experiment (spark-gap oscillator and loop antenna) Measuring speed of electromagnetic waves experimentally

Wave Model of Light

Diffraction and interference in double-slit experiment Why small slit gaps are used Interpreting intensity graphs Constructive and destructive interference Factors affecting interference patterns Producing interference patterns experimentally Solving interference problems Polarised vs unpolarised light How light becomes polarised Solving polarisation problems Evidence for wave model of light

Quantum Model of Light

Photon model of light Energy-frequency-wavelength relationships Temperature and particle energy distribution Black body radiation concept Black bodies as perfect absorbers/emitters Black-body radiation curves Solving black-body problems Classical vs experimental black-body curves Quantised energy explanation Quantum relationships (frequency, intensity, photons) Photoelectric effect Energy and kinetic energy of photoelectrons Photoelectric and thermionic emission data analysis Solving photoelectric effect problems Graphs of photoelectric experiments Applications (e.g. solar cells) Evidence for quantum model of light

Light and Special Relativity

Inertial vs non-inertial frames Einstein’s postulates Simultaneity thought experiment Time dilation thought experiment Time dilation, length contraction, relativistic momentum Solving relativity problems Why mass objects cannot reach light speed Evidence for relativity (muons, atomic clocks) >

Google Meet URL for tutoring session.

Whiteboard sessions.

All tutoring resources.