Hand-built revision cheatsheets for IB Mathematics: Analysis & Approaches Higher Level. Every topic from Polynomials through Probability Distributions condensed into one printable page each — formulas, derivative tables, common traps, worked examples, and a per-section exam-attack plan that mirrors the IB mark scheme. Authored by Mr Ejaz Ahmad — IBO-certified, 15+ years teaching IB Math AA HL in Singapore.
The IB Mathematics: Analysis & Approaches HL syllabus is organised into five themes (Number & Algebra, Functions, Geometry & Trigonometry, Statistics & Probability, Calculus). Each theme breaks into 2–9 topics — every topic below has its own dedicated cheatsheet.
Theme 1
Number & Algebra
The biggest theme by topic count, covering everything from polynomial structure through complex numbers, partial fractions, and the AHL extensions of proof, induction, and the binomial theorem. Mostly examined on Paper 1 (no calculator).
Trigonometry from the basic right triangle through compound angle identities and 3D geometry, plus the AHL vectors content (lines, planes, intersections). High-yield for Paper 3 problem-solving.
The largest theme on Paper 3 and the most heavily examined on Papers 1 and 2 combined. From basic derivatives through L'Hôpital's rule, integration techniques, separable differential equations, and Maclaurin series.
Sampling, summary statistics, regression, correlation, conditional probability, Bayes' theorem (HL), and discrete & continuous random variables. Almost entirely examined on Paper 2 (calculator).
Singapore IB students often pick between AA HL, AA SL, AI HL and AI SL. Here is the difference at a glance — choose the row that matches your maths background and university plans.
What makes these IB Math AA HL cheatsheets different
There is plenty of free IB Math content online — much of it written by non-IB teachers, formatted poorly, or wildly inaccurate. These pages are different in three ways.
Written by an IB-certified tutor
Mr Ejaz has been teaching IB Math AA HL for 15+ years to students at SJI International, ACS(I), UWCSEA, GESS, NLCS, OFS, Tanglin, Stamford and Dover Court. Every formula, trap, and worked example is drawn from real student errors he has corrected hundreds of times.
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, forgetting dy/dx in implicit differentiation, or not stating |sin x| ≤ 1 when an equation has no solution. 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 exactly which technique to reach for when you see each question type.
Top 5 marks lost in IB Math AA HL
The most-dropped marks across the AA HL syllabus
Across thousands of marked Photon Academy mock papers, these five errors account for more lost marks than every other mistake combined. Read them once before you start revising — they alone can lift you a grade.
Total distance ≠ net displacement. Integrating velocity gives the signed displacement; for total distance you must split at every t where v(t) = 0 and sum |Δs| on each segment, or compute nInt(abs(v(t)),t,a,b) on the GDC. This is the single biggest dropped mark in HL kinematics.
Dropping lim notation in L'Hôpital's rule. The IB mark scheme requires you to write the lim symbol at every step. Doing the algebra perfectly but omitting the notation costs the final A1 mark — a 100% solve scoring 75%.
f''(a) = 0 claimed as inflexion without sign check. A second derivative being zero is necessary but NOT sufficient for an inflexion. You must verify f'' changes sign across x = a (counter-example: f(x) = x⁴ at x = 0).
Forgetting dy/dx when differentiating a y-term implicitly. d/dx[y²] = 2y · dy/dx, NOT just 2y. Every implicit-differentiation question we have ever seen examined hinges on this rule.
Substituting numerical values BEFORE differentiating in related rates. Differentiate the formula with respect to t first, THEN substitute the numerical values. Substituting first turns variables into constants, so the derivative is zero and the question collapses.
Revision Strategy
How top IB Math AA HL students revise
From Photon Academy's 7-graders, here is the exact revision sequence we coach. Follow it topic by topic for the 4–8 weeks before mock or final exams.
1. Open the formula booklet
Always have the official IB Math formula booklet open while you revise. Cross-reference every formula in each cheatsheet — anything NOT in the booklet must be memorised (reciprocal trig derivatives, key limits, R sin/cos derivation, Bayes' theorem statement).
2. Read the TRAPS first
Skim the red "TRAP" boxes in every section before reading anything else. These are the marks examiners report being lost on year after year. Knowing them up front stops you making the same errors in your next mock.
3. Drill past papers by syllabus reference
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. Repeat until the trigger-to-technique link is automatic.
FAQ
IB Math AA HL frequently asked questions
A few questions IB students and parents in Singapore often ask about the AA HL course and these resources.
How hard is IB Math AA HL compared to A-Level Maths or AP Calculus?
IB Math AA HL is widely considered the hardest pre-university mathematics course taken at scale. It covers more breadth than Singapore A-Level H2 Maths (adding proof, vectors at AHL depth, and full statistics) and more depth than AP Calculus BC. The grade boundary for a 7 typically sits around 75–80% of the total marks, and only about 17% of HL candidates worldwide achieve it. Photon Academy students average 6.4 over the last three cohorts.
How many topics are in the IB Math AA HL syllabus?
There are five syllabus themes — Number & Algebra, Functions, Geometry & Trigonometry, Statistics & Probability, and Calculus — broken into about 20 distinct topics covering both SL and the HL extensions (AHL). Each topic on this hub corresponds to one rigorous sub-area of the syllabus, with its own dedicated cheatsheet.
What is the difference between IB Math AA HL and AA SL?
AA SL covers approximately the first 70% of the AA HL syllabus and is examined on Papers 1 and 2 only. AA HL adds nine extra AHL sub-topics — including L'Hôpital's rule, implicit differentiation, partial fractions, complex numbers, vectors at depth, proof by induction, Bayes' theorem and the generalised binomial series — and adds Paper 3, a 55-minute extended-response paper exclusive to HL students. Within each cheatsheet on this site, sections are tagged either "SL" or "AHL" so SL students can see exactly which sections apply to them.
Which IB Math AA HL topics are examined on Paper 3?
Paper 3 is exclusive to HL students and consists of two extended problem-solving questions worth 55 marks total. It can draw from any HL syllabus area, but the questions historically lean heavily on Calculus (Differentiation, Integration, Differential Equations, Maclaurin Series), Vectors, Proof by Induction, Complex Numbers, and Statistics. Each topic page on this hub flags which Paper 3 techniques are most heavily examined.
Is the IB formula booklet allowed in all three papers?
Yes — the IB Mathematics AA Formula Booklet is available in all three papers (P1, P2, P3). However, several frequently-tested formulas are NOT in the booklet and must be memorised: reciprocal trig derivatives (sec, cosec, cot), the standard limits (sin x / x, eˣ − 1 / x), the R sin/cos formula derivation, Bayes' theorem statement, and a few inverse trig identities. Each cheatsheet on this hub flags these explicitly.
How do top IB Math AA HL students revise these topics?
The most effective revision sequence used by Photon Academy 7-graders: (1) read the cheatsheet end-to-end to refresh formulas; (2) study the TRAPS in red — these are the marks examiners report being lost on year after year; (3) attempt the worked example covered up; (4) attempt 5–10 IB-style past-paper questions on the same syllabus reference; (5) re-read the exam-attack plan. Repeat for each of the 20 topics in the order they're listed above.
Want the full IB Math AA HL library?
The cheatsheets above are free for everyone. Photon Academy students unlock the full library for each topic — the printable PDF cheatsheet, a 40-page Notes booklet, the IB-style Tutorial booklet, full mark-scheme-style Tutorial Solutions with M1/A1/R1 annotations, and Practice Solutions for past-paper-style problems. Enrolled students get free access; non-students can subscribe.
