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IB Mathematics AA HL - Lecture Notes

The IB Mathematics Analysis & Approaches (AA) Higher Level (HL) Lecture Notes page are clear, comprehensive, and well-organized, making complex concepts easy to understand. With detailed explanations, diagrams, and examples, they are perfect for exam review and enhancing understanding, offering essential support for academic success.

IB Mathematics AA HL

Topic 1: Number & Algebra

Numbers & Rounding

Numbers & Rounding

Sequences & Series

Sequences in General

Arithmetic Sequences

Arithmetic Sequences

Geometric Sequences

Geometric Sequences

Percentage Change

Percentage Change - Finance Application

Binomial Theorem

Binomial Theorem

Deductive & Contradiction

Deductive and Contradiction

Mathematical
Induction

Mathematical Induction

Systems of Linear
Equations

Systems of Linear Equations

Complex Numbers & Plane

Complex Numbers and Complex Plane

Sec 1.11 & 1.13

Polynomials over Complex Numbers

Polynomials Over Fields

De Moivre's Theorem & Root of zⁿ=a

De Moivre's Theorem and Roots of zⁿ=a

Sec 1.14 - 1.15

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IB Mathematics AA HL

Topic 2: Functions

Linear
Functions

Linear Functions

Quadratic Functions

Quadratic Functions

Functions and Basics

Composition
of Functions

Composite Functions

Inverse Functions

Inverse Functions

Function Transformation

Transformations of Functions

Horizontal and Vertical Asymptotes

Exponential Functions

Exponents and Growth

Logarithmic Functions

Logarithms

Exponential Equations

Exponential Equations

Polynomial
Functions

Polynomial Functions

Sum & Product of Roots

Sum and Product of Roots

Rational Functions

Rational Functions

Polynomial & Rational Inequalities

Polynomial and Rational Inequalities

Modulus Equations & Inequalities

Modulus Equations and Inequalities

Symmetries of Functions

More Transformations

IB Mathematics AA HL

Topic 3: Geometry & Trigonometry

3D Coordinate Geometry

Three-Dimensional Geometry

Sine Rule &
Cosine Rule

Triangles and Rules

Bearings and Elevation

The Trigonometric Circle

Unit Circle & Trigonometric Identities

Sin, Cos, Tan Definition

Trigonometric Equations

Solving Equations

Trigonometric Functions

Graphs of Sin, Cos, Tan

Advanced Identities

More Identities and Equations

Inverse Trig
Functions

Arcsin, Arccos, Arctan

Vectors:
Geometric

Geometric Representation

Vectors:
Algebraic

Algebraic Representation

Angle Between Vectors

Vector Lines
(2D)

Vector Equation 2D

Vector Lines
(3D)

Vector Equation 3D

Vector
Kinematics

Kinematics

Vector Cross
Product

Cross Product

Vector Equations
of Planes

Planes

Intersections
in 3D

Intersections Among Lines and Planes

Distances
in 3D Space

Distances

IB Mathematics AA HL

Topic 4: Statistics & Probability

Basic Concepts
of Statistics

Basic Statistical Concepts

Central Tendency & Spread

Measures of Central Tendency

Frequency Tables
& Grouped Data

Grouped Data Analysis

Linear
Regression

Regression and Best Fit Lines

Elementary
Set Theory

Set Theory and Venn Diagrams

Probability
Foundations

Introduction to Probability

Conditional
Probability

Conditional and Independent Events

Probability Tree Diagrams

Discrete Random
Variables

Discrete Probability Distributions

Binomial
Distribution

The Binomial Distribution

Normal
Distribution

The Normal Distribution

Continuous
Distributions

Continuous Random Variables

Permutations &
Combinations

Combinations and Permutations

IB Mathematics AA HL

Topic 5: Calculus

Intro to Limits
& Derivatives

Introduction to Limits and Derivatives

Product &
Quotient Rules

Linearity, Product and Quotient Rules

Chain Rule

Tangents &
Normals

Tangent and Normal Lines

Monotonicity
& Extremum

Monotonicity and Extremum

Concavity &
Inflection

Concavity and Points of Inflection

Graph of the
Derivative

The Graph of the Derivative

Optimization

Indefinite
Integrals

The Indefinite Integral

Integration by
Substitution

Integration by Substitution

Definite Integrals
& Area

Definite Integrals and Area Between Curves

Kinematics

More
Derivatives

More Derivatives

Implicit
Differentiation

Implicit Differentiation

Related Rates

Continuity &
Differentiability

Continuity and Differentiability

L'Hôpital's
Rule

L'Hôpital's Rule

Partial Fractions

Partial Fractions

Further
Substitution

Further Integration by Substitution

Integration
by Parts

Integration by Parts

Volumes of
Revolution

Volumes of Revolution

Differential
Equations

Differential Equations

Maclaurin
Series

Maclaurin Series