This page covers the full IB Math AA HL syllabus. Practise each topic with the AA HL question bank. Download the AA HL formula sheets and use past papers alongside this guide.

1. Number & Algebra

• Partial Fractions, Indices & Standard Form
  • Standard Form
  • Laws of Indices
  • Partial Fractions
• Exponentials & Logs
  • Introduction to Logarithms
  • Laws of Logarithms
  • Solving Exponential Equations
• Sequences & Series
  • Language of Sequences & Series
  • Sigma Notation
  • Arithmetic Sequences & Series
  • Geometric Sequences & Series
  • Applications of Sequences & Series
  • Compound Interest & Depreciation
• Simple Proof & Reasoning
  • Proof by Deduction
  • Disproof by Counter Example
• Proof by Induction & Contradiction
  • Proof by Induction
  • Proof by Contradiction
• Binomial Theorem
  • Binomial Theorem
  • Binomial Coefficients & Pascal’s Triangle
  • Extension of The Binomial Theorem
• Permutations & Combinations
  • Counting Principles
  • Permutations
  • Combinations
• Complex Numbers
  • Introduction to Complex Numbers
  • Operations with Complex Numbers
  • Introduction to Argand Diagrams
  • Modulus & Argument
• Further Complex Numbers
  • Geometry of Complex Numbers
  • Modulus-Argument (Polar) Form
  • Exponential (Euler’s) Form
  • Conversion between Forms of Complex Numbers
  • Complex Roots of Polynomials
  • De Moivre’s Theorem
  • Proof of De Moivre’s Theorem
  • Roots of Complex Numbers
• Systems of Linear Equations
  • Systems of Linear Equations
  • Solving Systems Using Row Reduction
  • Number of Solutions to a System

2. Functions

• Linear Functions & Graphs
  • Equations of a Straight Line
  • Parallel & Perpendicular Lines
• Quadratic Functions & Graphs
  • Quadratic Functions
  • Factorising Quadratics
  • Completing the Square
  • Solving Quadratic Equations
  • Quadratic Inequalities
  • Discriminants
• Functions Toolkit
  • Language of Functions
  • Composite Functions
  • Inverse Functions
  • Odd & Even Functions
  • Periodic Functions
  • Self-Inverse Functions
  • Graphing Functions & Their Key Features
  • Intersecting Graphs
• Other Functions & Graphs
  • Exponential & Logarithmic Functions
  • Solving Equations Analytically
  • Solving Equations Graphically
  • Modelling with Functions
• Reciprocal & Rational Functions
  • Reciprocal & Rational Functions
  • Rational Functions with Quadratics
• Transformations of Graphs
  • Translations of Graphs
  • Reflections of Graphs
  • Stretches of Graphs
  • Composite Transformations of Graphs
• Polynomial Functions
  • Polynomial Division
  • Factor & Remainder Theorem
  • Graphs & Roots of Polynomial Functions
  • Sum & Product of Roots of Polynomials
• Inequalities
  • Solving Inequalities Graphically
  • Polynomial Inequalities
• Modulus Functions & Further Transformations
  • Modulus Functions
  • Modulus Transformations
  • Modulus Equations & Inequalities
  • Reciprocal Transformations
  • Square Transformations

3. Geometry & Trigonometry

• Geometry Toolkit
  • Coordinate Geometry
  • Arcs & Sectors Using Degrees
  • Radian Measure
  • Arcs & Sectors Using Radians
• Geometry of 3D Shapes
  • 3D Coordinate Geometry
  • Volume & Surface Area
• Trigonometry
  • Pythagoras & Right-Angled Trigonometry
  • Sine Rule, Cosine Rule & Area of a Triangle
  • Angles of Elevation & Depression
  • Bearings & Constructions
• The Unit Circle & Exact Values
  • The Unit Circle
  • Exact Values
• Trigonometric Functions & Graphs
  • Graphs of Trigonometric Functions
  • Solving Equations Using Trigonometric Graphs
  • Transformations of Trigonometric Functions
  • Modelling with Trigonometric Functions
• Trigonometric Equations & Identities
  • Simple Identities
  • Compound Angle Formulae
  • Double Angle Formulae
  • Relationship Between Trigonometric Ratios
  • Linear Trigonometric Equations
  • Quadratic Trigonometric Equations
• Inverse & Reciprocal Trigonometric Functions
  • Reciprocal Trigonometric Functions
  • Inverse Trigonometric Functions
• Trigonometric Proof & Equation Strategies
  • Trigonometric Proof
  • Strategy for Trigonometric Equations
• Vector Properties
  • Introduction to Vectors
  • Parallel Vectors
  • Adding & Subtracting Vectors
  • Position & Displacement Vectors
  • Magnitude of a Vector & Unit Vectors
  • The Scalar Product
  • Angle Between Two Vectors & Perpendicular Vectors
  • The Vector Product
  • Areas using the Vector Product
  • Geometric Proof with Vectors
• Vector Equations of Lines
  • Equation of a Line in Vector Form
  • Equation of a Line in Parametric Form
  • Equation of a Line in Cartesian Form
  • Applications to Kinematics
  • Coincident, Parallel, Intersecting & Skew Lines
  • Angle Between Two Lines
  • Shortest Distance Between a Point and a Line
  • Shortest Distance Between Two Lines
• Vector Planes
  • Equation of a Plane in Vector Form
  • Equation of a Plane in Cartesian Form
  • Intersections of a Line & a Plane
  • Intersections of Two Planes
  • Angles Between a Line & a Plane
  • Angles Between Two Planes
  • Shortest Distances with Planes

4. Statistics & Probability

• Statistics Toolkit
  • Sampling & Data Collection
  • Measures of Central Tendency
  • Measures of Dispersion
  • Frequency Tables
  • Linear Transformations of Data
  • Outliers
  • Box & Whisker Diagrams
  • Cumulative Frequency Graphs
  • Histograms
  • Interpreting Data
• Correlation & Regression
  • Scatter Diagrams & Correlation
  • Pearson’s Product-Moment Correlation Coefficient
  • Linear Regression
• Probability
  • Probability & Types of Events
  • Independent & Mutually Exclusive Events
  • Conditional Probability
  • Bayes’ Theorem
  • Venn Diagrams
  • Tree Diagrams
• Discrete Random Variables
  • Discrete Probability Distributions
  • Mean & Variance
  • Transformation of a Single Variable
• Binomial Distribution
  • The Binomial Distribution
  • Calculating Binomial Probabilities
• Normal Distribution
  • The Normal Distribution
  • Calculations with Normal Distribution
  • Standardisation of Normal Variables & z-Values
  • Finding Unknown Parameters
• Continuous Random Variables
  • Probability Density Function
  • Median & Mode of a CRV
  • Mean & Variance of a CRV

5. Calculus

• Limits & Convergence
  • Informal Idea of a Limit
  • Formal Definition of a Limit
  • Infinite Limits & Limits at Infinity
  • Continuity
• Differentiation Toolkit
  • Gradient Function
  • Differentiation from First Principles
  • Rules of Differentiation
  • Higher Derivatives
  • Implicit Differentiation
  • Parametric Differentiation
  • Related Rates of Change
• Applications of Differentiation
  • Tangents & Normals
  • Increasing & Decreasing Functions
  • Stationary Points
  • Optimisation Problems
  • Points of Inflection
  • Sketching Curves
  • Local & Global Extrema
• Integration Toolkit
  • Antiderivatives
  • Definite Integrals
  • Fundamental Theorem of Calculus
  • Substitution
  • Integration by Parts
  • Partial Fractions in Integration
• Applications of Integration
  • Area Between a Curve & the x-Axis
  • Area Between Two Curves
  • Volume of Revolution
  • Kinematics
• Differential Equations
  • Separable Differential Equations
  • First-Order Linear Differential Equations
  • Particular Solutions
  • Modelling with Differential Equations