IB Math AA Syllabus & Topics
The following content outlines the syllabus for Mathematics: Analysis and Approaches (AA), a subject within the International Baccalaureate (IB) Diploma Programme.
This course is designed for students who enjoy exploring abstract mathematics, focusing on algebraic methods, calculus, and rigorous problem-solving. It emphasizes mathematical reasoning, formal proofs, and theoretical understanding over practical application.
The syllabus is structured around five main topic groups: Number and Algebra, Functions, Geometry and Trigonometry, Statistics and Probability, and Calculus.
If you're struggling with any topics in the Math AA syllabus, feel free to reach - our team of IB experts has extensive experience helping students from all around the world.
IB Mathematics Analysis and Approaches is offered at both Standard Level (SL) and Higher Level (HL). The syllabus is divided below to reflect the key differences in content and depth between the two levels.
Number and Algebra
SL
| Topic Code | Description |
|---|---|
| 1.1 | - Operations with numbers in the form a × 10k where 1 ≤ a < 10 and k is an integer |
| 1.2 | - Arithmetic sequences and series - Use of the formulae for the nth term and the sum of the first n terms - Sigma notation - Applications and real-life modeling |
| 1.3 | - Geometric sequences and series - Formulae for nth term and sum - Sigma notation - Applications |
| 1.4 | - Financial applications: compound interest and depreciation |
| 1.5 | - Laws of exponents (integer exponents) - Introduction to logarithms (base 10 and e) - Numerical evaluation using technology |
| 1.6 | - Simple deductive proof - LHS to RHS structure - Equality and identity notation |
| 1.7 | - Exponents and logarithms - Rational exponents - Laws of logarithms - Change of base - Solving exponential equations |
| 1.8 | - Sum of infinite convergent geometric sequences |
| 1.9 | - Binomial theorem - Pascal’s triangle - Combinations (nCr) |
HL only
| 1.10 | - Counting principles: permutations and combinations - Binomial theorem for fractional/negative indices |
| 1.11 | - Partial fractions |
| 1.12 | - Complex numbers - Definition of i - Cartesian form z = a + bi - Real/imaginary part, conjugate, modulus, argument - Complex plane |
| 1.13 | - Modulus-argument (polar) form - Euler form - Sums/products/quotients in all forms and geometric interpretation |
| 1.14 | - Complex conjugate roots - De Moivre’s theorem - Powers and roots of complex numbers |
| 1.15 | - Proof by induction and contradiction - Use of counterexamples |
| 1.16 | - Systems of linear equations (up to 3 variables) - Unique, infinite, or no solution |
2. Functions
SL
| Topic Code | Description |
|---|---|
| 2.1 |
- Different forms of the equation of a straight line - Gradient; intercepts - Parallel (m₁ = m₂) and perpendicular lines (m₁ × m₂ = −1) |
| 2.2 |
- Concept of a function: domain, range, graph - Function notation - Modeling with functions - Inverse functions and reflection in y = x |
| 2.3 |
- Graphing functions - Sketches from context - Graphs using technology - Graphing function sums and differences |
| 2.4 |
- Key features of graphs - Intersections using technology - Composite and inverse functions - Identity function |
| 2.6 |
- The quadratic function and graph forms: - Standard form: f(x) = ax² + bx + c - Factor form: f(x) = a(x − p)(x − q) - Vertex form: f(x) = a(x − h)² + k |
| 2.7 |
- Solving quadratic equations and inequalities - Discriminant Δ = b² − 4ac - Reciprocal function and its self-inverse nature - Rational functions: f(x) = (ax+b)/(cx+d) - Asymptotes |
| 2.9 |
- Exponential and logarithmic functions: - f(x) = ax, f(x) = ex - f(x) = logax, f(x) = ln(x) |
| 2.10 |
- Solving equations graphically and analytically - Use of technology - Real-life applications |
| 2.11 |
- Graph transformations: - Translations, reflections - Vertical and horizontal stretches - Composite transformations |
HL only
| 2.12 |
- Polynomial functions: - Graphs, equations, zeros and roots - Factor and remainder theorems - Sum/product of roots |
| 2.13 | - Rational functions |
| 2.14 |
- Odd/even functions - Inverse functions with domain restrictions - Self-inverse functions |
| 2.15 |
- Solving inequalities of the form g(x) ≥ f(x) - Graphical and analytical methods |
| 2.16 | - Modulus equations and inequalities |
3. Geometry and Trigonomentry
SL
| Topic Code | Description |
|---|---|
| 3.1 |
- Distance and midpoint in 3D space - Volume and surface area of 3D solids (pyramids, cones, spheres, hemispheres, combinations) - Angle between lines and between a line and a plane |
| 3.2 |
- Sine, cosine, and tangent ratios - Sine and cosine rules - Area of a triangle |
| 3.3 |
- Applications of trigonometry (right and non-right triangles) - Pythagoras’s theorem - Angles of elevation and depression - Constructing labeled diagrams |
| 3.4 |
- The circle - Radian measure of angles - Arc length and sector area |
| 3.5 |
- Definitions of sinθ and cosθ using the unit circle - Definition of tanθ = sinθ / cosθ - Ambiguous case in sine rule |
| 3.6 |
- Pythagorean identity: cos²θ + sin²θ = 1 - Double angle identities for sine and cosine - Relationships between trigonometric ratios |
| 3.7 |
- Circular functions: sinx, cosx, tanx - Amplitude, periodic nature, graphs - f(x) = a·sin(b(x + c)) + d - Transformations |
| 3.8 |
- Solving trigonometric equations in a finite interval - Graphical and analytical methods - Quadratic forms involving sinx, cosx, or tanx |
HL only
| 3.9 |
- Reciprocal trig ratios: secθ, cosecθ, cotθ - Pythagorean identities - Inverse trig functions: arcsin, arccos, arctan - Graphs, domains, ranges |
| 3.10 |
- Compound angle identities - Double angle identity for tan |
| 3.11 |
- Trig function relationships - Symmetry properties of graphs |
| 3.12 |
- Vectors: position and displacement - Representation with line segments - Base vectors i, j, k - Components, magnitude - Geometric proofs with vectors |
| 3.13 |
- Scalar product (dot product) - Angle between vectors - Perpendicular and parallel vectors |
| 3.14 |
- Vector equation of a line: r = a + λb - Angles between lines - Applications in kinematics |
| 3.15 |
- Coincident, parallel, intersecting, and skew lines - Points of intersection |
| 3.16 |
- Vector product (cross product) - Properties and geometric meaning of |v × w| |
| 3.17 |
- Vector equation of a plane: • r = a + λb + μc • r · n = a · n - Cartesian form: ax + by + cz = d |
| 3.18 |
- Intersections: • line and plane • two planes • three planes - Angles between: • line and plane • two planes |
4. Statistics and Probability
SL
| Topic Code | Description |
|---|---|
| 4.1 |
- Population, sample, random sample - Discrete and continuous data - Bias and reliability - Outliers and sampling techniques |
| 4.2 |
- Data presentation: frequency tables, histograms - Cumulative frequency, graphs - Finding median, quartiles, percentiles, range, IQR - Box and whisker diagrams |
| 4.3 |
- Central tendency: mean, median, mode - Estimation from grouped data - Modal class - Dispersion: IQR, standard deviation, variance - Effects of constant changes - Quartiles of discrete data |
| 4.4 |
- Linear correlation, Pearson’s r - Scatter plots and lines of best fit - Regression line of y on x - Prediction and interpretation of parameters a and b in y = ax + b |
| 4.5 |
- Trial, outcome, relative frequency - Sample space and event - Complementary events - Expected occurrences |
| 4.6 |
- Venn, tree, sample space diagrams - Combined events - Mutually exclusive, conditional, independent events |
| 4.7 |
- Discrete random variables and distributions - Expected value (mean) - Applications |
| 4.8 |
- Binomial distribution - Mean and variance |
| 4.9 |
- Normal distribution curve - Properties and diagrams - Normal and inverse normal calculations |
| 4.10 |
- Regression line of x on y - Use for predictions |
| 4.11 |
- Conditional probabilities - Independent events |
| 4.12 |
- Standardization (z-values) - Inverse normal with unknown mean/standard deviation |
HL only
| 4.13 | - Bayes’ theorem (up to three events) |
| 4.14 |
- Variance of discrete random variables - Continuous random variables and density functions - Mode and median of continuous random variables - Mean, variance, standard deviation (discrete & continuous) - Effects of linear transformations of X |
5. Calculus
SL
| Topic Code | Description |
|---|---|
| 5.1 |
- Concept of a limit - Derivative as gradient function and rate of change |
| 5.2 |
- Increasing/decreasing functions - Interpretation of f′(x) > 0, f′(x) = 0, f′(x) < 0 |
| 5.3 |
- Derivative of f(x) = axⁿ is f′(x) = anxⁿ⁻¹, n ∈ ℤ - Derivatives of polynomial functions with integer exponents |
| 5.4 |
- Tangents and normals at a point - Equations of tangents and normals |
| 5.5 |
- Integration as anti-differentiation - Use of boundary conditions - Definite integrals with technology - Area under curve y = f(x), f(x) > 0 |
| 5.6 |
- Derivatives of xⁿ (n ∈ ℚ), sinx, cosx, eˣ, ln x - Sum, multiple, chain rule, product and quotient rules |
| 5.7 |
- Second derivative - Relationship between f, f′, f′′ and graphical behavior |
| 5.8 |
- Local maxima and minima - Tests for extrema - Optimization - Points of inflection |
| 5.9 |
- Kinematics: displacement, velocity, acceleration - Total distance traveled |
| 5.10 |
- Indefinite integrals - Composite functions - Reverse chain rule |
| 5.11 |
- Definite integrals (analytically) - Area under curves (positive or negative) - Area between curves |
HL only
| 5.12 |
- Continuity and differentiability - Convergence and divergence of limits - Higher-order derivatives |
| 5.13 |
- Evaluation of limits - Repeated use of l’Hôpital’s rule |
| 5.14 |
- Implicit differentiation - Related rates of change - Optimization problems |
| 5.15 |
- Derivatives of tanx, secx, cosecx, cotx, aˣ, logₐx, arcsinx, arccosx, arctanx - Indefinite integrals of above functions - Composites with linear functions - Partial fractions in integrals |
| 5.16 |
- Integration by substitution - Integration by parts (including repeated) |
| 5.17 |
- Area under a curve to the y-axis - Volumes of revolution about x- or y-axis |
| 5.18 |
- First order differential equations - Euler’s method - Separable and homogeneous DEs - Integrating factor method |
| 5.19 |
- Maclaurin series expansions for eˣ, sinx, cosx, ln(1+x), (1+x)^p, p ∈ ℚ - Use of substitution, integration, differentiation to find other series |
