IB Math AA HL & SL Topic Prediction Guide

#	Topic	Subtopic	M21	M22	M23	M24	Freq	Avg Marks	HL only?	P1 or P2?	May 2027
IB MATH AA — PAPER 1 (NO CALCULATOR) SUBTOPIC FREQUENCY \| May 2021–2024 \| SL & HL
Section A = short response \| Section B = extended response \| All 5 topics examinable \| SL: HL-only subtopics greyed
TOPIC 1: NUMBER & ALGEBRA — free preview
1.1	Num & Alg	Sequences & series — arithmetic/geometric, sigma notation, applications	✔	✔	✔	✔	4	8–12	SL&HL	P1+P2	⭐⭐⭐⭐⭐
1.2	Num & Alg	Logarithms & exponents — laws of logs, solving log/exponential equations	✔	✔	✔	✔	4	6–10	SL&HL	P1	⭐⭐⭐⭐⭐
1.3	Num & Alg	Binomial theorem — expansion, finding specific terms, Pascal's triangle	✔	✔	✔	—	3	5–8	SL&HL	P1	⭐⭐⭐⭐
1.4	Num & Alg	Complex numbers — Cartesian form, modulus, argument, Argand diagram, De Moivre's HL	✔	✔	✔	✔	4	10–15	HL	P1+P2	⭐⭐⭐⭐⭐ HL
1.5	Num & Alg	Proof — induction, contradiction, counterexample, direct proof HL	✔	✔	✔	✔	4	8–12	HL	P1	⭐⭐⭐⭐⭐ HL
1.6	Num & Alg	Systems of linear equations — 3×3, row reduction, unique/no/infinite solutions HL	✔	—	✔	✔	3	6–9	HL	P1	⭐⭐⭐⭐ HL

#	Topic	Subtopic	M21	M22	M23	M24	Freq	Avg Marks	HL only?	P1 or P2?	May 2027
TOPIC 2: FUNCTIONS
2.1	Functions	Function concepts — domain, range, composite, inverse, transformations, sketching	✔	✔	✔	✔	4	8–12	SL&HL	P1+P2	⭐⭐⭐⭐⭐
2.2	Functions	Quadratic functions — completing the square, discriminant, roots, vertex form	✔	✔	✔	✔	4	5–9	SL&HL	P1	⭐⭐⭐⭐⭐
2.3	Functions	Exponential & logarithmic functions — graphs, transformations, solving equations	✔	✔	✔	✔	4	6–10	SL&HL	P1+P2	⭐⭐⭐⭐⭐
2.4	Functions	Rational functions — reciprocal, partial fractions, asymptotes, sketching HL	✔	✔	—	✔	3	6–9	HL	P1	⭐⭐⭐⭐ HL
TOPIC 3: GEOMETRY & TRIGONOMETRY
3.1	Geo & Trig	Circular functions — unit circle, trig ratios, radian measure, arc/sector	✔	✔	✔	✔	4	8–12	SL&HL	P1	⭐⭐⭐⭐⭐
3.2	Geo & Trig	Trig identities & equations — Pythagorean, double angle, compound angle, solving	✔	✔	✔	✔	4	8–12	SL&HL	P1	⭐⭐⭐⭐⭐ CERTAIN
3.3	Geo & Trig	Vectors — 3D, dot product, cross product, lines, planes, angles, intersections HL	✔	✔	✔	✔	4	12–18	HL	P1+P2	⭐⭐⭐⭐⭐ HL
TOPIC 4: STATISTICS & PROBABILITY
4.1	Stats & Prob	Probability — basic rules, tree diagrams, Venn diagrams, conditional probability	✔	✔	✔	✔	4	5–8	SL&HL	P1+P2	⭐⭐⭐⭐⭐
4.2	Stats & Prob	Binomial distribution — P(X=k), mean, variance, applications	✔	✔	✔	—	3	5–8	SL&HL	P1+P2	⭐⭐⭐⭐
4.3	Stats & Prob	Normal distribution — standardising (z-scores), P(a<X<b), inverse normal	✔	✔	✔	✔	4	5–8	SL&HL	P2	⭐⭐⭐⭐⭐
TOPIC 5: CALCULUS — highest mark allocation in AA
5.1	Calculus	Differentiation — chain, product, quotient rules; trig, log, exponential derivatives	✔	✔	✔	✔	4	10–16	SL&HL	P1+P2	⭐⭐⭐⭐⭐ CERTAIN
5.2	Calculus	Applications of differentiation — tangents, normals, optimisation, curve sketching, inflection	✔	✔	✔	✔	4	10–15	SL&HL	P1+P2	⭐⭐⭐⭐⭐ CERTAIN
5.3	Calculus	Integration — anti-differentiation rules, substitution, definite integral, area under curve	✔	✔	✔	✔	4	10–16	SL&HL	P1+P2	⭐⭐⭐⭐⭐ CERTAIN
5.4	Calculus	Differential equations — first order, variables separable, integrating factor, Euler's method HL	✔	✔	✔	✔	4	12–18	HL	P1+P2	⭐⭐⭐⭐⭐ HL
5.5	Calculus	Maclaurin series — Taylor/Maclaurin expansion, convergence, approximation HL	✔	—	✔	✔	3	8–12	HL	P1+P2	⭐⭐⭐⭐ HL
5.6	Calculus	L'Hôpital's rule & limits — indeterminate forms, limits of functions HL	✔	✔	—	✔	3	5–8	HL	P1+P2	⭐⭐⭐⭐ HL

#	Topic	Subtopic	M21	M22	M23	M24	Freq	Avg Marks	HL only?	May 2027
IB MATH AA — PAPER 2 (CALCULATOR) SUBTOPIC FREQUENCY \| May 2021–2024 \| SL & HL
GDC required \| Section A = short response \| Section B = extended response \| All 5 topics examinable \| SL: HL-only rows greyed
CALCULUS (highest marks in Paper 2)
5.1	Calculus	Differentiation applications — optimisation, related rates, kinematics (v=x', a=v')	✔	✔	✔	✔	4	10–18	SL&HL	⭐⭐⭐⭐⭐ CERTAIN
5.2	Calculus	Integration — area between curves, volume of revolution (HL), definite integrals with GDC	✔	✔	✔	✔	4	10–16	SL&HL	⭐⭐⭐⭐⭐ CERTAIN
5.3	Calculus	Differential equations — Euler's method, slope fields; numerical solutions with GDC HL	✔	✔	✔	✔	4	12–18	HL	⭐⭐⭐⭐⭐ HL
STATISTICS & PROBABILITY
4.1	Stats	Normal distribution — P(a<X<b) with GDC, inverse normal, standardisation	✔	✔	✔	✔	4	8–12	SL&HL	⭐⭐⭐⭐⭐
4.2	Stats	Binomial distribution — calculating probabilities, GDC binomcdf/binompdf, applications	✔	✔	✔	✔	4	6–10	SL&HL	⭐⭐⭐⭐⭐
4.3	Stats	Hypothesis testing — z-test, t-test, chi-squared; p-values, significance HL	✔	✔	✔	—	3	8–12	HL	⭐⭐⭐⭐ HL
GEOMETRY & TRIGONOMETRY
3.1	Vectors	Vectors — 3D lines, planes, intersections, angle between planes, distance from point to plane HL	✔	✔	✔	✔	4	14–20	HL	⭐⭐⭐⭐⭐ HL
3.2	Trigonometry	Solving trigonometric equations graphically with GDC; applications in context	✔	—	✔	✔	3	6–10	SL&HL	⭐⭐⭐⭐
FUNCTIONS
2.1	Functions	Modelling with functions — exponential growth/decay, fitting to data, interpreting parameters	✔	✔	✔	✔	4	10–16	SL&HL	⭐⭐⭐⭐⭐
2.2	Functions	Graphical analysis — intersections, zeros, max/min using GDC, sketching complex functions	✔	✔	✔	✔	4	6–10	SL&HL	⭐⭐⭐⭐⭐

Year	Q1 Theme	Primary Topics Q1	Q2 Theme	Primary Topics Q2	HL Focus Areas	May 2027 Signal
IB MATH AA HL — PAPER 3 THEME HISTORY \| May 2021–2024 \| HL ONLY
2 compulsory extended problems per paper \| Topics span multiple syllabus areas \| Unfamiliar contexts tested \| Calculator allowed
M21	Calculus Investigation — functional equations and derivatives	Calculus, Functions	Sequences — proving and extending series patterns	Num & Algebra, Proof	Proof HL	Calculus + proof likely again
M22	Complex number geometry — loci, transformations, Argand diagram proofs	Complex Nos, Geo	Differential equations — modelling with DEs, slope fields, Euler's	Calculus (DEs), Modelling	Complex HL + DEs HL	Complex nos / DEs very likely
M23	Integration investigation — discovering new integration techniques	Calculus, Functions	Proof by induction combined with combinatorics	Proof, Num & Algebra	Proof HL	Induction / combinatorics possible
M24	Vectors investigation — geometric properties in 3D, planes, distance formulae	Vectors, Geo & Trig	Maclaurin series — deriving and applying series expansions	Calculus (Maclaurin), Algebra	Vectors HL + Maclaurin HL	Maclaurin / vectors alternate years

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