An IB Math AA HL revision guide that takes you from the basics to full IB exam questions. Every chapter shows how the IB asks the topic, teaches it step by step, then drills each question type until you can score on it under exam conditions. Written by Mr Ejaz Ahmad, IB Math tutor at Photon Academy, Singapore.
2 volumes, 19 chapters — every AA HL topic, plus Paper 3 and exam strategy
S$100 per volume — an e-book you read in the browser, 2-year access
Free sample chapter — read Chapter 1 (Sequences and series) now, no sign-up
Free worked solutions online — all 501 questions with full mark schemes
One-page topic summaries with formulas, traps and a worked example. IB data booklets.
Full notes booklets, printable cheatsheets, tutorials, and mastery questions with mark-scheme solutions. Maths AA buyers also get the November 2026 predicted paper sets.
A two-volume AA HL course: how the IB asks each topic, every question type, practice in three steps. Free worked solutions online and a free sample chapter.
Best for
Quick revision and exam week
Studying a whole subject end to end
Learning AA HL in order, with a book to work through
Free IB cheatsheets — every formula and exam trap, on one page per topic
IB Maths AA HL cheatsheets: 20 topics
IB Mathematics: Analysis & Approaches HL
All 20 syllabus topics, organised by syllabus area. Each cheatsheet condenses ~12 sub-topics into one revision-ready page with formulas, worked examples, and a "what's NOT in here" list pointing to the gated full library.
IB Math AA HL is the most demanding mainstream IB Mathematics course — five hours a week of pure mathematics covering algebra, functions, trigonometry, vectors, calculus, statistics and probability. The cheatsheets below are the same study sheets Mr Ejaz prints for Photon Academy students before mock exams. Each one targets the exact formula recall, technique selection, and trap avoidance examined on Papers 1, 2 and 3.
All 26 syllabus topics, organised by syllabus area. Each cheatsheet condenses the sub-topics into one revision-ready page with formulas, the exact GDC steps, worked examples, and a "what's NOT in here" list pointing to the gated full library.
IB Math AI HL — All 26 Topics
Applications & Interpretation Higher Level · SL + AHL coverage · GDC-allowed on every paper
IB Math AI HL is the modelling-and-technology mathematics course — statistics, matrices, graph theory, financial maths and applied calculus, with a graphical calculator allowed on all three papers. The cheatsheets below are the same study sheets Mr Ejaz prints for Photon Academy students before mock exams, targeting the exact model choice, GDC steps and traps examined on Papers 1, 2 and 3.
All 24 syllabus topics across the new IB Physics syllabus (first examined May 2025). Organised into the five themes — Space, Time & Motion · Particulate Matter · Wave Behaviour · Fields · Nuclear & Quantum.
IB Physics HL covers everything from Newton's laws and projectile motion through relativity, thermodynamics, electromagnetic induction, and quantum & nuclear physics. The 24 cheatsheets below give you the formula sheets, definitions, derivations, common errors, and exam-attack plans for every topic — written from the perspective of an examiner who has seen the same mistakes thousands of times.
Standard Level cheatsheets: AA SL, AI SL and Physics SL
Studying at SL? Start here
SL and HL share the same cheatsheets — every section is tagged SL or AHL. These SL hubs curate just the SL-relevant topics for each course, so you read only what your exam covers.
There are plenty of free IB notes online — many are inaccurate, formatted poorly, or written by non-IB teachers. These pages are different in three ways.
Written by an IB-certified tutor
Mr Ejaz has been teaching IB Math & Physics for 15+ years. Every formula, every trap, every worked example is drawn from teaching real IB students at SJI International, ACS(I), GESS, NLCS, OFS and UWCSEA. No non-IB content sneaks in.
Mark-scheme aware
Each cheatsheet flags the specific places students lose marks on Papers 1, 2 and 3 — like dropping lim notation in L'Hôpital, or not stating |sin x| ≤ 1. The "TRAPS" boxes mirror IB examiner reports verbatim.
Built for fast revision
Each page is a single scrollable cheatsheet — no clicking through endless sub-pages. Every section has its IB syllabus reference, a "TRICK" tip for shortcut methods, and an exam-attack plan listing what to reach for when you see each question type.
How to revise with these
A 4-step revision flow that actually works
Don't just read the cheatsheet front-to-back. The students who get a 7 use them like this.
Open the data booklet
Keep the official IB data booklet open on a second tab while you revise. Cross-reference every formula on the cheatsheet against where it appears in the booklet — if it's NOT in the booklet, you have to memorise it.
Read the TRAPS first
Skim the red "TRAP" boxes in every section before you read anything else. These are the marks examiners report being lost on year after year. Knowing them up front stops you making the same errors.
Do the worked example
Cover the solution and try the worked example yourself first. Compare your steps to the M1/A1/R1 mark-scheme breakdown — that's how IB awards marks, and it's the difference between 5s and 7s.
Test on past papers
Find one past-paper question per topic on the same syllabus reference (e.g. SL 5.8 for kinematics). The cheatsheet's exam-attack plan tells you which technique to reach for the moment you read the question.
Past paper analysis
See what the IB actually asks: 2021 to 2025
Marks-weighted breakdowns of recent IB papers by topic, with year-by-year trends, grade boundaries and the common errors that cost marks. Free for every course below. For exam-style practice, see the IB predicted papers.
A few things students and parents often ask about the resource library.
Are these IB resources really free?
Yes — every cheatsheet on this site is fully free to view and print. The free cheatsheets cover formulas, key tricks, common traps, and a per-section exam-attack plan. The full library (40-page Notes per topic, IB-style tutorial questions, and mark-scheme-style worked solutions) is gated for enrolled Photon Academy students or via a one-time lifetime library purchase (S$250 per subject).
Who built these IB cheatsheets?
They are written by Mr Ejaz Ahmad, an IBO-certified IB Math and IB Physics tutor with 15+ years of teaching experience in Singapore. Every page is drawn from material he uses daily with Photon Academy students, including those at SJI International, ACS(I), UWCSEA, GESS, NLCS and OFS.
Are the cheatsheets aligned to the new IB syllabus?
Yes. The IB Math AA HL pages cover the syllabus first examined in May 2021, and the IB Physics HL pages cover the new physics syllabus first examined in May 2025. Each section is tagged with the IB syllabus reference (e.g. SL 5.1, AHL 5.12, A.1, D.4) so you can cross-reference the IB subject guide and the official data booklet quickly.
What is the official IB data booklet?
The data booklet is the formula reference document the IB lets you take into Papers 1, 2 and 3. The IB Math AA HL one is called the formula booklet; the IB Physics HL one is called the data booklet. Both are linked at the top of each subject hub here so you can keep them open while you revise from the cheatsheets.
Do you cover SL as well as HL?
Yes — within each HL cheatsheet, every section is tagged "SL" or "AHL" so SL students can see exactly which sections they need to know and which ones are HL-only. SL content is a strict subset of HL content, so reading the HL cheatsheet and skipping the AHL-tagged sections covers the SL syllabus completely — and the Math AA SL, Math AI SL and Physics SL hubs list just the SL topics for you.
Can I download the cheatsheets as PDF?
PDF downloads of the brand-formatted print version are gated for signed-in users (free for enrolled Photon Academy students; available with the one-time lifetime library otherwise). The HTML versions on this site are 100% free, printer-friendly via your browser's "Print to PDF" option, and contain identical content.
What is the difference between the free cheatsheets, the premium library and the e-books?
The free cheatsheets are one-page topic summaries with formulas, traps and a worked example, plus the IB data booklets. The premium library is a one-time payment of S$250 per subject for lifetime access to full notes booklets, printable cheatsheets, tutorials and mastery questions with mark-scheme solutions. The e-books are a structured two-volume course for IB Maths AA HL at S$100 per volume with two years of access, and each comes with free worked solutions online.
Does Photon Academy have IB predicted papers?
Yes. Photon Academy publishes predicted paper sets for IB Maths and Physics, and Set 1 is free. The predicted papers have their own page with the full list of sets and subjects.
Which subjects and levels do the IB resources cover?
Free cheatsheets cover IB Maths AA HL, AI HL and Physics HL by topic, with SL hubs for AA SL, AI SL and Physics SL. Past paper analysis covers Maths AA and AI, Physics, Chemistry and Biology at HL and SL.
Premium IB materials
The full library — lifetime access, per subject
The cheatsheets above stay free forever. Behind them sits the full Photon library: 40-page Notes booklets, printable Cheatsheets, Tutorials built for conceptual understanding, and IB mastery questions — asked the way IB asks, connected across topics, with full mark-scheme solutions. Pay once per subject, keep it for life.
What’s inside every subject — the full depth behind the free cheatsheets
40-page Notes
Every topic explained in full — derivations, methods and the “why”, not just the formula.
Printable Cheatsheets
The brand-formatted PDF of every cheatsheet — print the whole subject for revision.
Tutorials
Worked, marked-up walkthroughs that build real conceptual understanding.
IB Mastery Questions
Asked the way IB asks — connected across topics — with full mark-scheme solutions.
Enrolled Photon Academy students get the full library free, plus the Full Past Papers viewer, Topical Question Bank and Worksheet Builder — see admissions.
Ready for the full library?
The cheatsheets are free for everyone. The full library — printable PDF cheatsheets, 40-page Notes per topic, marked-up Tutorial Solutions, and extra Practice Solutions with detailed walk-throughs — is free for enrolled Photon Academy students, or yours for life with a one-time S$250 purchase per subject.
