Algebra and functions
Build reliable manipulation skills and connect equations, graphs, transformations, sequences, and function behaviour across different question styles.
IB Mathematics • SL
IB Math AA SL
Use this IB Math AA SL study guide to browse the syllabus topic structure, study materials, and practice resources.
Structured practice
IB Math AA SL Question Bank
Jump straight into grouped unit practice without losing your place in the syllabus overview.
1. Number and Algebra
2. Functions
2.1 Equations of straight lines, parallel and perpendicular
2.2 Functions, notation domain, range and inverse as reflection
2.3 Graphing
2.4 Key features of graphs, intersections using technology
2.5 Composite functions, identity, finding inverse
2.6 Quadratic function
2.7 Solutions of quadratic equations and inequalities, discriminant and nature of roots
2.8 Reciprocal and simple rational functions, equations of asymptotes
2.9 Exponential and logarithmic functions
2.10 Solving equations graphically and analytically
2.11 Transformation of functions
3. Geometry and Trigonometry
3.1 3d space, volume, angles, distance, midpoints
3.2 2d and 3d trig, sine rule, cosine rule, area
3.3 Angles of elevation and depression, bearings
3.4 Circle, radians, arcs, sectors
3.5 Unit circle definitions of sin, cos, tan. Exact trig ratios, ambiguous case of sine rule
3.6 Pythagorean identity, double angles
3.7 Circular functions, graphs, composites, transformations
3.8 Solving trig equations
4. Statistics and Probability
4.1 Concepts, reliability and sampling techniques
4.2 Histograms, CF graphs, box plots
4.3 Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
4.4 Pearsons, scatter diagrams, eqn of y on x
4.5 Probability concepts, expected numbers
4.6 Combined, mutually exclusive, conditional, independence, prob diagrams
4.7 Discrete random variables
4.8 Binomial distribution
4.9 Normal distribution and calculations
4.10 X on y regression line
4.11 Conditional and independent probabilities, test for independence
4.12 Z values, inverse normal to find mean and standard deviation
5. Calculus
5.1 Introduction of differential calculus
5.2 Increasing and decreasing functions
5.3 Differentiating polynomials, n E Z
5.4 Tangents and normal
5.5 Integration introduction, areas between curve and x axis
5.6 Differentiating polynomials n E Q. Chain, product and quotient rules
5.7 The second derivative
5.8 Testing for max and min, optimisation. Points of inflexion
5.9 Kinematics problems
5.10 Indefinite integration, reverse chain, by substitution
5.11 Definite integrals, areas under curve onto x-axis and areas between curves
Overview
Course overview
How to study IB Math AA SL
IB Math AA SL emphasises algebraic fluency, mathematical structure, and explaining a logical method. Success comes from understanding why a technique works, recognising which method fits a question, and presenting accurate working. Use the topic structure below to connect core skills with targeted revision and exam-style practice.
Calculus and trigonometry
Move beyond memorised procedures by linking derivatives, integrals, rates of change, geometry, identities, and graphical interpretation.
Readable mathematical working
Show a coherent sequence of steps, use correct notation, and make your method visible so partial credit is available even when an arithmetic error occurs.
Assessment at a glance
For the current course assessed before the redesigned first-assessment-2029 syllabus, Paper 1 does not permit technology and Paper 2 requires it. The internal assessment is an individual mathematical exploration. Confirm your examination session with your school and the current IB guide.
| Component | Format | Weighting |
|---|---|---|
| Paper 1 | 1 hour 30 minutes; no technology; short- and extended-response questions | 40% |
| Paper 2 | 1 hour 30 minutes; technology required; short- and extended-response questions | 40% |
| Internal assessment | Individual mathematical exploration | 20% |
Sources: current IB subject guide and IB curriculum update for first assessment 2029.
Revision plan
- 1.Secure algebraic manipulation before attempting harder calculus and function questions.
- 2.Practise the same concept in symbolic, graphical, numerical, and contextual forms.
- 3.Classify mistakes as knowledge, method, notation, calculator, or time-management errors.
- 4.Complete regular timed sets that mix short techniques with longer reasoning questions.
Exam strategy
Write the governing equation or mathematical idea before substituting values. Keep exact forms where appropriate, show intermediate reasoning clearly, and use graphs or technology to check an answer rather than replace the explanation.
Practise IB Math AA SL questionsReview Christos Math AA & AI notes and exercisesFrequently asked questions
What is the focus of IB Math AA SL?
IB Mathematics: Analysis and Approaches SL emphasizes algebraic reasoning, functions, trigonometry, calculus, mathematical structure, and clear working. It suits students who want to understand and apply analytical mathematical methods.
Is a calculator allowed in IB Math AA SL exams?
For the current course assessed before the redesigned first-assessment-2029 syllabus, technology is not permitted in Paper 1 and is required in Paper 2. Students should confirm the current approved-calculator rules with their school.
How is the current IB Math AA SL course assessed?
Paper 1 and Paper 2 each last 1 hour 30 minutes and are each worth 40% of the final grade. Paper 1 does not permit technology, while Paper 2 requires a graphic display calculator. The individual mathematical exploration is worth 20%.
What is the difference between IB Math AA and Math AI?
AA places greater emphasis on analytical methods, algebraic reasoning, and mathematical structure, while AI places greater emphasis on modelling, applications, statistics, and technology. They are separate courses, so students should follow their registered subject and level.