IB Mathematics: AA
Your modern toolkit for mastering IB Math Analysis & Approaches — clear study guides, interactive tools, and topic-by-topic resources for SL and HL.
Topic 1 · Number & Algebra
Core algebra, sequences, logs, counting, complex numbers, proofs, and systems.
Sequences & Series
Arithmetic/Geometric, Sigma Notation, Applications, Compound Interest…
Exponents & Logs
Exponent & Log Laws, Solving Exponential & Logarithmic Equations…
Binomial Theorem
Binomial Expansion & Theorem, Pascal’s Triangle, Binomial Coefficient nCr…
Counting Principles
Permutations & Combinations, Factorial Notation, Product/Sum Principles…
Complex Numbers
Forms, Roots, De Moivre’s Theorem, Argand Diagram, Geometric Applications…
Proofs
Induction, Contradiction, Counterexample, Simple Deduction…
Systems of Equations
Solving 3×3 Systems, Row Operations, Unique/No/Infinite Solutions…
Topic 2 · Functions
Function properties, transformations, families, and modeling.
Properties of Functions
Domain & Range, Composite, Inverse, Max–Min, Intercepts, Intersections, Sketching…
Quadratics
Quadratic Functions & Equations, Completing the Square, Discriminant, Vertex…
Rational Functions
Asymptotes, Intercepts, Sketching, Reciprocal Functions, GDC…
Exponential & Log Functions
Exponential & Logarithmic Functions & Graphs, Asymptotes, Intercepts…
Transformations
Translations, Reflections, Stretches, Graphs, Composite Transformations…
Polynomials
Factor & Remainder Theorems, Sum & Product of Roots, Zeros, Roots, Factors…
Modulus & Inequalities
Absolute-Value/Modulus Functions, Solving Equations & Inequalities…
Topic 3 · Geometry & Trigonometry
2D/3D geometry, circular functions, and vectors.
Geometry & Shapes
Geometry of 2D & 3D Shapes, Circles, Sectors, Arcs, Triangle Trig, Sine & Cosine Rule, Areas, Bearings…
Trigonometric Functions
Circular Functions, Unit Circle, Trig Ratios & Identities, Solving Trig Equations, Trig Graphs…
Vectors
Basics, Lines, Planes, Space, Angles, Intersections, Scalar/Vector Product, Applications…
Topic 4 · Statistics & Probability
Data analysis, regression, probability, and distributions.
Statistics
Mean–Median–Mode, Variance, Standard Dev., IQR, Stem/Box Plot, Cumulative Frequency…
Bivariate Statistics
Regression Line y=ax+b, Correlation Coefficient r, Strength, Applications…
Probability
Basics, Venn & Tree Diagrams, Combined Events, Independent/Mutually Exclusive, Conditional…
Distributions
Probability Distributions, Binomial & Normal, Random Variables, Applications…
Topic 5 · Calculus
Differentiation, integration, motion, DEs, and series.
Differential Calculus
Differentiation Rules, Curve Properties, Optimization, Related Rates, Limits, L’Hôpital’s Rule…
Integral Calculus
Integration Techniques, Areas Under/Between Curves, Volumes of Solids, Applications…
Kinematics
Displacement, Velocity, Acceleration, Total Distance Traveled, Graphs, GDC Applications…
Differential Equations
First-Order DEs, Euler’s Method, Separable, Homogeneous, Integrating Factor, Applications…
Maclaurin Series
Common Expansions, Substitution, Products, Integration/Differentiation, Differential Equations…
About this Course:
IB Mathematics: Analysis & Approaches (AA) is a rigorous course focused on deep analytical problem-solving. It emphasizes strong algebraic reasoning, mathematical modeling, and formal proof. Both Standard Level (SL) and Higher Level (HL) build a strong foundation in core topics, with HL extending the depth and complexity to prepare for advanced STEM studies.
This toolkit is designed for efficient study and revision. Navigate through the topics to find clear notes on key skills like calculus and the use of technology. Each card links directly to a focused study guide, helping you to master concepts and practice effectively for your exams.
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