1. Number & Algebra

Number Toolkit

Standard Form

Approximation & Estimation

Solving Equations using a GDC

Exponentials & Logs

Exponents

Logarithms

Sequences & Series

Language of Sequences & Series

Arithmetic Sequences & Series

Geometric Sequences & Series

Applications of Sequences & Series

Financial Applications

Compound Interest & Depreciation

Amortisation & Annuities

Complex Numbers

Introduction to Complex Numbers

Modulus & Argument

Introduction to Argand Diagrams

Further Complex Numbers

Geometry of Complex Numbers

Forms of Complex Numbers

Applications of Complex Numbers

Matrices

Introduction to Matrices

Operations with Matrices

Determinants & Inverses

Solving Systems of Linear Equations with Matrices

Eigenvalues & Eigenvectors

Eigenvalues & Eigenvectors

Applications of Matrices

2. Functions

Linear Functions & Graphs

Equations of a Straight Line

Further Functions & Graphs

Functions

Graphing Functions

Properties of Graphs

Modelling with Functions

Linear Models

Quadratic & Cubic Models

Exponential Models

Direct & Inverse Variation

Sinusoidal Models

Strategy for Modelling Functions

Functions Toolkit

Composite & Inverse Functions

Transformations of Graphs

Translations of Graphs

Reflections of Graphs

Stretches of Graphs

Composite Transformations of Graphs

Modelling with Logarithmic, Logistic & Piecewise Functions

Properties of Further Graphs

Natural Logarithmic Models

Logistic Models

Piecewise Models

3. Geometry & Trigonometry

Geometry Toolkit

Coordinate Geometry

Radian Measure

Arcs & Sectors

Geometry of 3D Shapes

3D Coordinate Geometry

Volume & Surface Area

Trigonometry

Pythagoras & Right-Angled Trigonometry

Non Right-Angled Trigonometry

Applications of Trigonometry & Pythagoras

Trigonometric Identities & Equations

The Unit Circle

Simple Identities

Solving Trigonometric Equations

Voronoi Diagrams

Voronoi Diagrams

Toxic Waste Dump Problem

Matrix Transformations

Matrix Transformations

Determinant of a Transformation Matrix

Vector Properties

Introduction to Vectors

Position & Displacement Vectors

Magnitude of a Vector

The Scalar Product

The Vector Product

Components of Vectors

Geometric Proof with Vectors

Vector Equations of Lines

Vector Equations of Lines

Shortest Distances with Lines

Modelling with Vectors

Kinematics with Vectors

Constant & Variable Velocity

Graph Theory

Introduction to Graph Theory

Walks & Adjacency Matrices

Minimum Spanning Trees

Chinese Postman Problem

Travelling Salesman Problem

Bounds for Travelling Salesman Problem

4. Statistics & Probability

Statistics Toolkit

Sampling

Data Collection

Statistical Measures

Frequency Tables

Linear Transformations of Data

Outliers

Univariate Data

Interpreting Data

Correlation & Regression

Bivariate Data

Correlation Coefficients

Linear Regression

Non-linear Regression

Non-linear Regression

Logarithmic Scales

Linearising using Logarithms

Probability

Probability & Types of Events

Conditional Probability

Sample Space Diagrams

Probability Distributions

Discrete Probability Distributions

Expected Values

Random Variables

Linear Combinations of Random Variables

Unbiased Estimates

Binomial Distribution

The Binomial Distribution

Calculating Binomial Probabilities

Normal Distribution

The Normal Distribution

Calculations with Normal Distribution

Combinations of Normal Distributions & Sample Mean Distributions

Sample Mean Distribution

Confidence Interval for the Mean

Poisson Distribution

Poisson Distribution

Calculating Poisson Probabilities

Hypothesis Testing using the Chi-squared Distribution

Hypothesis Testing

Chi-squared Test for Independence

Goodness of Fit Test

Hypothesis Testing for Population Parameters

Hypothesis Testing for Mean (One Sample)

Hypothesis Testing for Mean (Two Sample)

Binomial Hypothesis Testing

Poisson Hypothesis Testing

Hypothesis Testing for Correlation

Type I & Type II Errors

Transition Matrices & Markov Chains

Markov Chains

Transition Matrices

5. Calculus

Differentiation

Introduction to Differentiation

Applications of Differentiation

Modelling with Differentiation

Further Differentiation

Differentiating Special Functions

Techniques of Differentiation

Related Rates of Change

Second Order Derivatives

Stationary Points

Concavity & Points of Inflection

Integration

Numerical Integration using the Trapezoid Rule

Introduction to Integration

Applications of Integration

Further Integration

Integrating Special Functions

Techniques of Integration

Definite Integrals & Areas

Volumes of Revolution

Kinematics

Displacement, Velocity & Acceleration

Calculus for Kinematics

Differential Equations

Modelling with Differential Equations

Separation of Variables

Slope Fields

Approximate Solutions to Differential Equations

Coupled & Second Order Differential Equations

Coupled Differential Equations

Second Order Differential Equations

Exam boards

• DP IB Applications & Interpretation (AI): SL
• DP IB Analysis & Approaches (AA): SL
• DP IB Analysis & Approaches (AA): HL

Study tools

• DP IB Applications & Interpretation (AI) · Exam Questions
• DP IB Applications & Interpretation (AI) · Flashcards
• DP IB Applications & Interpretation (AI) · Past Papers

Related links

• IB Maths · Revision Notes
• IB Maths · Exam Questions
• IB Maths · Flashcards
• IB Maths · Past Papers
• IB Maths · Glossary