Advanced algebra and functions
Develop the symbolic control needed for complex functions, sequences, series, equations, and transformations that feed into later topics.
IB Mathematics • HL
IB Math AA HL
Use this IB Math AA HL study guide to browse the syllabus topic structure, study materials, and practice resources.
Structured practice
IB Math AA HL Question Bank
Jump straight into grouped unit practice without losing your place in the syllabus overview.
1. Number and Algebra
1.1 Using standard form
1.2 Arithmetic sequences and series
1.3 Geometric sequences and series
1.4 Financial apps – compound interest, annual depreciation
1.5 Intro to logs
1.6 Simple proof
1.7 Laws of exponents and logs
1.8 Sum of infinite geo sequence
1.9 Binomial theorem where n is an integer
1.10 Perms and combs, binomial with negative and fractional indices
1.11 Partial fractions
1.12 Complex numbers – Cartesian form and Argand diag
1.13 Polar and Euler form
1.14 Complex roots of polynomials, conjugate roots, De Moivre’s, powers & roots of complex numbers
1.15 Proof by induction, contradiction, counterexamples
1.16 Solution of systems of linear equations
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
2.12 Factor and remainder theorems, sum and product of roots
2.13 Rational functions
2.14 Odd and even functions, self-inverse, inverse and domain restriction
2.15 Solutions of inequalities
2.16 Graphing modulus equations and inequalities
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
3.9 Reciprocal trig ratios and their pythagorean identities. Inverse circular functions
3.10 Compound angle identities
3.11 Relationships between trig functions
3.12 Vector definitions
3.13 Scalar (dot) product
3.14 Vector equation of line
3.15 Classification of lines
3.16 Vector product
3.17 Vector equations of a plane
3.18 Intersections of lines & planes
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
4.13 Bayes theorem
4.14 Properties of discrete and continuous random variables
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
5.12 First principles, higher derivatives
5.13 Limits and L’Hopitals
5.14 Implicit functions, related rates, optimisation
5.15 Further derivatives and indefinite integration of these, partial fractions
5.16 Integration by substitution, parts and repeated parts
5.17 Areas under curve onto y-axis, volume of revolution (about x and y axes)
5.18 1st order DE’s – Euler method, variables separable, integrating factor, homogeneous DE using sub y=vx
5.19 Maclaurin series
Overview
Course overview
How to study IB Math AA HL
IB Math AA HL rewards deep understanding, flexible algebra, rigorous reasoning, and the ability to combine ideas in unfamiliar problems. Efficient revision should strengthen prerequisite skills while steadily increasing the complexity and independence of your problem solving. This course hub provides a structured route through the syllabus and into targeted practice.
Calculus and proof
Practise rigorous arguments and multi-stage calculus problems, with attention to conditions, notation, exact values, and the logic connecting each step.
Unfamiliar problem solving
Combine topics under time pressure, test alternative approaches, and learn when to simplify, substitute, transform, sketch, or prove a result.
Assessment at a glance
For the current course assessed before the redesigned first-assessment-2029 syllabus, Paper 1 does not permit technology; Papers 2 and 3 require it. Paper 3 focuses on extended problem solving, and 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 | 2 hours; no technology; short- and extended-response questions | 30% |
| Paper 2 | 2 hours; technology required; short- and extended-response questions | 30% |
| Paper 3 | 1 hour; technology required; extended problem-solving questions | 20% |
| Internal assessment | Individual mathematical exploration | 20% |
Sources: current IB subject guide and IB curriculum update for first assessment 2029.
Revision plan
- 1.Audit prerequisite algebra before spending time on advanced techniques.
- 2.Study worked reasoning, then reproduce the solution without looking at the steps.
- 3.Practise proof and extended-response questions alongside routine exercises every week.
- 4.Use full timed papers to refine question selection, checking, and recovery after getting stuck.
Exam strategy
On unfamiliar questions, write down what is known, identify a related theorem or representation, and make one justified step at a time. Preserve exact values, state necessary conditions, and return later if a single problem begins to consume the paper.
Practise IB Math AA HL questionsReview Christos Math AA & AI notes and exercisesFrequently asked questions
What is the focus of IB Math AA HL?
IB Mathematics: Analysis and Approaches HL develops advanced algebra, functions, trigonometry, calculus, proof, and unfamiliar problem solving. It requires flexible symbolic reasoning and the ability to combine ideas across the syllabus.
Is a calculator allowed in IB Math AA HL exams?
For the current course assessed before the redesigned first-assessment-2029 syllabus, technology is not permitted in Paper 1 and is required in Papers 2 and 3. Students should confirm approved-calculator requirements for their session.
How is the current IB Math AA HL course assessed?
Paper 1 and Paper 2 each last 2 hours and are each worth 30%. Paper 3 lasts 1 hour and is worth 20%, while the individual mathematical exploration is worth 20%. Paper 1 does not permit technology; Papers 2 and 3 require it.
What is the difference between IB Math AA HL and AA SL?
AA HL includes additional higher-level content, studies shared ideas in greater depth, and adds Paper 3. Both levels require strong analytical reasoning, but students should revise from the syllabus and page matching their registered level.