1. Number & Algebra

Number Toolkit

Standard Form

Approximation

Upper & Lower Bounds

Percentage Error

Accuracy & Estimation

Solving Equations using a GDC

Exponentials & Logs

Laws of Indices

Introduction to Logarithms

Laws of Logarithms

Sequences & Series

Language of Sequences & Series

Sigma Notation

Arithmetic Sequences & Series

Geometric Sequences & Series

Applications of Sequences & Series

Financial Applications

Compound Interest & Depreciation

Amortisation

Annuities

Complex Numbers

Introduction to Complex Numbers

Operations with Complex Numbers

Complex Roots of Quadratics

Modulus & Argument

Introduction to Argand Diagrams

Further Complex Numbers

Geometry of Complex Numbers

Modulus-Argument (Polar) Form

Exponential (Euler's) Form

Conversion between Forms of Complex Numbers

Frequency & Phase of Trig Functions

Matrices

Introduction to Matrices

Operations with Matrices

Determinants & Inverses

Solving Systems of Linear Equations with Matrices

Eigenvalues & Eigenvectors

The Characteristic Polynomial, Eigenvalues & Eigenvectors

Diagonalisation & Powers of Matrices

2. Functions

Linear Functions & Graphs

Equations of a Straight Line

Parallel & Perpendicular Lines

Further Functions & Graphs

Functions & Mappings

Graphing Functions & Their Key Features

Intersecting Graphs

Quadratic Functions & Graphs

Cubic Functions & Graphs

Exponential Functions & Graphs

Sinusoidal Functions & Graphs

Modelling with Functions

Linear Models

Quadratic Models

Cubic Models

Exponential Models

Direct & Inverse Variation

Sinusoidal Models

Strategy for Modelling Functions

Functions Toolkit

Composite Functions

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 Logarithmic & Logistic Functions & Graphs

Natural Logarithmic Models

Logistic Models

Piecewise Models

3. Geometry & Trigonometry

Geometry Toolkit

Coordinate Geometry

Perpendicular Bisectors

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

Trigonometric Identities & Equations

The Unit Circle

Simple Identities

Graphs of Trigonometric Functions

Solving Equations Using Trigonometric Graphs

Voronoi Diagrams

Drawing Voronoi Diagrams

Interpreting Voronoi Diagrams

Toxic Waste Dump Problem

Matrix Transformations

Matrix Transformations

Matrices of Geometric Transformations

Matrices of Composite Transformations

Determinant of a Transformation Matrix

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

Components of Vectors

Geometric Proof with Vectors

Vector Equations of Lines

Equation of a Line in Vector Form

Equation of a Line in Parametric Form

Angle Between Two Lines

Shortest Distance Between a Point and a Line

Shortest Distance Between Two Lines

Modelling with Vectors

Kinematics with Vectors

Constant & Variable Velocity

Graph Theory

Introduction to Graph Theory

Walks & Adjacency Matrices

Minimum Spanning Trees (Kruskal's Algorithm)

Minimum Spanning Trees (Prim's Algorithm)

Chinese Postman Problem

Travelling Salesman Problem

Nearest Neighbour & Deleted Vertex Algorithms

4. Statistics & Probability

Statistics Toolkit

Sampling

Reliability & Validity of Data Collection Methods

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

Spearman's Rank Correlation Coefficient

Comparison of Correlation Coefficients

Linear Regression

Non-linear Regression

Least Squares Regression Curves & Coefficient of Determination

Logarithmic Scales

Linearising using Logarithms

Probability

Probability & Types of Events

Independent & Mutually Exclusive Events

Conditional Probability

Venn Diagrams

Tree 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

Central Limit Theorem

Confidence Interval for the Mean

Poisson Distribution

Poisson Distribution

Calculating Poisson Probabilities

Hypothesis Testing using the Chi-squared Distribution

Introduction to 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

Powers of Transition Matrices

Steady State & Long-term Probabilities

5. Calculus

Differentiation

Introduction to Derivatives

Differentiating Powers of x

Gradients, Tangents & Normals

Increasing & Decreasing Functions

Local Minimum & Maximum Points

Modelling with Differentiation

Further Differentiation

Differentiating Special Functions

Chain Rule

Product Rule

Quotient Rule

Related Rates of Change

Second Order Derivatives

Stationary Points

Concavity & Points of Inflection

Integration

Numerical Integration using the Trapezoidal Rule

Introduction to Integration

Integrating Powers of x

Finding the Constant of Integration

Finding Areas Using a GDC

Further Integration

Integrating Special Functions

Reverse Chain Rule

Integration by Substitution

Definite Integrals

Negative Integrals

Area Between Curve & y-axis

Area Between a Curve and a Line

Volumes of Revolution

Kinematics

Displacement, Velocity & Acceleration

Calculus for Kinematics

Differential Equations

Separation of Variables

Modelling with Differential Equations

Slope Fields

Approximate Solutions to Differential Equations using Euler's Method

Coupled & Second Order Differential Equations

Coupled Differential Equations

Phase Portraits

Equilibrium Points

Sketching Solution Trajectories

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