15
Topics
IB Group 5 — Mathematics
IB Mathematics: Analysis and Approaches 2026
Math AA focuses on pure mathematics — proof, algebra, functions, trigonometry, calculus, and statistics. HL is one of the most demanding IB subjects and is required or preferred by many top universities for STEM. SL is sufficient for most science and economics applications.
HL · 240hSL · 150h
HL & SL
Levels
20%
IA Weight
240h
HL Hours
Past Papers Archive
Browse IB Mathematics: Analysis and Approaches past papers
View the normalized archive for Mathematics: Analysis and Approaches, organized by session and file type.
Syllabus Topics
Official topic breakdown with approximate teaching hours.
| Topic | SL Hours | HL Hours |
|---|---|---|
| Topic 1: Number and Algebra | 19h | 39h |
| SL: sequences, series, logs, binomial theorem, proof by deduction | 19h | 0h |
| HL adds: complex numbers (Cartesian/polar/Euler), proof by induction, systems of equations, permutations & combinationsHL only | — | 20h |
| Topic 2: Functions | 21h | 32h |
| SL: domain/range, inverse, transformations, quadratic/exponential/log functions | 21h | 0h |
| HL adds: polynomial division (factor/remainder theorem), rational functions, modulus, inequalitiesHL only | — | 11h |
| Topic 3: Geometry and Trigonometry | 25h | 51h |
| SL: trig (unit circle, identities, double angle), 3D geometry, sine/cosine rules | 25h | 0h |
| HL adds: vectors in 3D (dot/cross product, lines, planes), reciprocal trig, compound angle identitiesHL only | — | 26h |
| Topic 4: Statistics and Probability | 27h | 33h |
| SL: descriptive stats, probability, binomial/normal distributions, regression | 27h | 0h |
| HL adds: Bayes' theorem, continuous random variables, PDFs, variance transformationsHL only | — | 6h |
| Topic 5: Calculus | 28h | 55h |
| SL: differentiation (chain/product/quotient), optimisation, integration, area between curves | 28h | 0h |
| HL adds: implicit diff, related rates, integration by parts/substitution, volumes of revolution, differential equations, Maclaurin seriesHL only | — | 27h |
| Total | 150h | 240h |
Assessment Structure
External Assessment
Paper 1 (no calculator, short and extended response, 40% SL / ~33% HL). Paper 2 (GDC allowed, 40% SL / ~33% HL). Paper 3 (HL only — two open-ended problem-solving questions, GDC allowed, ~20%, 60 min). Mathematical Exploration IA (20%).
Internal Assessment — Mathematical Exploration
HL: 20%SL: 20%
A 12–20 page exploration of a mathematical topic of the student's choice, assessed on mathematical communication, mathematical content, personal engagement, reflection, and use of mathematics.
Exam Tips for IB Mathematics: Analysis and Approaches
1
Paper 1 (no GDC): practise all algebraic and calculus techniques by hand — know your log laws and trig identities cold
2
Show all working even when the answer is wrong — method marks follow each step
3
HL Maclaurin series and differential equations are frequently examined in Paper 3 — dedicate specific revision sessions
4
For IA, choose a topic you're genuinely curious about — personal engagement criteria are easy marks if authentic
5
HL vectors (Topic 3) are vast — make a dedicated revision sheet for lines and planes in 3D
Grade Boundaries
View all subjects →| Session | Level | Grade 7 | Grade 6 | Grade 5 | Grade 4 | Grade 3 | Grade 2 | Max |
|---|---|---|---|---|---|---|---|---|
| May 2024 | HL | 76 | 62 | 49 | 35 | 23 | 13 | 100 |
| May 2024 | SL | 76 | 63 | 47 | 33 | 22 | 12 | 100 |
Grade boundaries shown are percentages. Actual boundaries vary by session and are set after grading. Use the score calculator →
Predict your IB Mathematics: Analysis and Approaches grade
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Related IB Subjects
Frequently Asked Questions
What topics are in IB Mathematics: Analysis and Approaches?
IB Mathematics: Analysis and Approaches covers Topic 1: Number and Algebra, SL: sequences, series, logs, binomial theorem, proof by deduction, HL adds: complex numbers (Cartesian/polar/Euler), proof by induction, systems of equations, permutations & combinations, Topic 2: Functions, SL: domain/range, inverse, transformations, quadratic/exponential/log functions, HL adds: polynomial division (factor/remainder theorem), rational functions, modulus, inequalities, Topic 3: Geometry and Trigonometry, SL: trig (unit circle, identities, double angle), 3D geometry, sine/cosine rules, HL adds: vectors in 3D (dot/cross product, lines, planes), reciprocal trig, compound angle identities, Topic 4: Statistics and Probability, SL: descriptive stats, probability, binomial/normal distributions, regression, HL adds: Bayes' theorem, continuous random variables, PDFs, variance transformations, Topic 5: Calculus, SL: differentiation (chain/product/quotient), optimisation, integration, area between curves, HL adds: implicit diff, related rates, integration by parts/substitution, volumes of revolution, differential equations, Maclaurin series. HL students study additional depth and some HL-only extensions. Total teaching hours: HL 240, SL 150.
How is IB Mathematics: Analysis and Approaches assessed?
Paper 1 (no calculator, short and extended response, 40% SL / ~33% HL). Paper 2 (GDC allowed, 40% SL / ~33% HL). Paper 3 (HL only — two open-ended problem-solving questions, GDC allowed, ~20%, 60 min). Mathematical Exploration IA (20%). The Internal Assessment (Mathematical Exploration) counts for 20% of the final grade at SL and 20% at HL.
What is the IB Mathematics: Analysis and Approaches IA?
The IB Mathematics: Analysis and Approaches IA is the Mathematical Exploration. A 12–20 page exploration of a mathematical topic of the student's choice, assessed on mathematical communication, mathematical content, personal engagement, reflection, and use of mathematics. It accounts for 20% of the final grade at SL and 20% at HL.
Should I take IB Mathematics: Analysis and Approaches HL or SL?
Take HL if Mathematics: Analysis and Approaches is relevant to your university course (Mathematics, physics, engineering, and computer science. Required by many top universities for STEM entry.), or if you are genuinely strong in the subject. HL adds 90 extra hours of content and deeper examination requirements. SL is suitable if you need the subject for the diploma but it is not your primary focus.