Hand-built revision cheatsheets for IB Mathematics: Applications & Interpretation Higher Level. Every topic — from Sequences and Matrices through Graph Theory, Regression and Differential Equations — condensed into one printable page each: formulas, the exact GDC steps, common traps, a worked Paper-2-style example, and a per-section exam-attack plan. The same sheets Mr Ejaz prints for Photon Academy students before mocks. By Mr Ejaz Ahmad — IBO-certified, 15+ years teaching IB Math in Singapore.
The IB Mathematics: Applications & Interpretation HL syllabus is organised into five themes. Every topic below has its own dedicated free cheatsheet with a downloadable PDF.
The largest AI HL theme — sequences and financial maths through matrices, Markov chains and complex numbers. The AHL matrix and eigenvalue work is Paper 3 gold.
Arithmetic & geometric sequences and series, sum to infinity, sigma notation, and growth problems on the GDC.
FreeIndex laws, fractional & negative indices, exponential equations, logarithms, change of base and log scales.
FreeCompound interest, depreciation, annuities, loan repayments and amortisation with the GDC finance solver.
FreeRounding, significant figures, standard form, percentage error, and upper & lower bounds.
FreeMatrix arithmetic, products, determinants, inverses and solving AX=B — all on the GDC.
FreeEigenvalues & eigenvectors, transition matrices, n-step states and long-run steady states.
FreeCartesian, polar & Euler forms, modulus-argument, De Moivre, roots, AC phasors and complex eigenvalues.
Function notation, domain and range, and the modelling toolkit: fitting and using linear, exponential and power models.
Trigonometry and its graphs, Voronoi diagrams, vectors, graph theory and matrix transformations — the most application-heavy, 'AI-flavoured' theme.
SOHCAHTOA, the sine & cosine rules, area, sectors, bearings and 3-D trigonometry.
FreeAmplitude, period and phase of sinusoidal models — tides, Ferris wheels — and solving in a range.
FreePerpendicular bisectors, nearest-site regions, Voronoi vertices and the toxic-waste-dump problem.
FreeMagnitude, unit vectors, the dot product & angle, vector lines and particles that meet.
FreeAdjacency matrices, walks via matrix powers, spanning trees, Dijkstra and the travelling-salesman problem.
Free2×2 matrix transformations, enlargements, rotations, reflections, area factor |det| and compositions.
The heart of AI — summarising data, correlation and regression, probability, distributions, confidence intervals and hypothesis testing, all on the GDC.
Central tendency & spread from the GDC, grouped data, outlier fences, box plots and ogives.
FreeScatter diagrams, correlation r, R², the least-squares regression line and prediction.
FreeSample spaces, complements, unions, independence, two-way tables, tree diagrams and Bayes.
FreeExpected value, the binomial and normal distributions, inverse normal and Poisson.
FreeStandard error, margin of error, confidence-interval limits, width and required sample size.
Freeχ² tests, expected frequencies, degrees of freedom, t-tests and the decision rule.
Differentiation and integration for real-world optimisation and kinematics, plus differential equations and coupled systems on Paper 3.
The power rule, tangents & normals, stationary points and applied optimisation on the GDC.
FreeReverse power rule, definite integrals, area under a curve, the trapezoidal rule and kinematics.
FreeDisplacement, velocity & acceleration by calculus, at-rest points and projectile motion.
FreeExponential & Newton-cooling models, separable DEs and Euler's method.
FreeTrace–determinant phase behaviour, eigenvalue portraits, Euler on systems and second-order reduction.
The pages above are free forever. When you're ready to drill to a 7, these are the same resources Photon Academy students use — one-time purchases, no subscription.
Every AI HL topic's full Notes PDF, an IB-style Tutorial booklet (25+ questions), mark-scheme Tutorial Solutions with M1/A1 annotations, and the predicted question types for the next session. Lifetime access.
Unlock the LibraryFull Paper 1, 2 and 3 predicted sets with mark schemes, matched to the current AI HL syllabus and recent examiner trends. Start with two free sets, then unlock the rest.
See Predicted PapersThe Studio drills each AI HL topic to mastery with adaptive question ladders; the Diagnostic marks your handwritten working and pinpoints exactly which sub-skills to fix.
Try Photon LearnThe official IB Mathematics: Applications & Interpretation formula booklet is provided in Papers 1, 2 and 3. Every cheatsheet here cross-references it — anything not listed in the booklet must be memorised, and we flag those explicitly. Download it from the official IB subject page.
There is plenty of free IB Math content online — much of it written for AA, not AI, or wildly inaccurate. These pages are built specifically for Applications & Interpretation HL.
Mr Ejaz has taught IB Math for 15+ years across Singapore's top international schools. Every formula, trap and worked example is drawn from real student errors corrected hundreds of times.
AI is an applications course. These sheets show the exact GDC steps — regression, 1-variable stats, matrices, inverse normal, the finance solver — and the modelling judgement examiners actually reward.
One scrollable page per topic: formulas, TRICK shortcuts, red TRAP boxes drawn from examiner reports, a worked Paper-2-style example and an exam-attack plan mapping question cues to methods.
A few questions IB students and parents in Singapore often ask about the AI HL course and these resources.
The cheatsheets above are free for everyone. Photon Academy students unlock the full library for each topic — the printable PDF, a full Notes booklet, the IB-style Tutorial booklet, mark-scheme-style Tutorial Solutions with M1/A1 annotations, and predicted-paper questions. Enrolled students get free access; others can buy the Lifetime Library.
Prefer live coaching? Join a small-group IB Math tuition class with Mr Ejaz — full library access is included free for enrolled students.