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##### 1 HL AI
###### Basics
• Straight lines
• Surds
• Simultaneous equations
###### Number
• Rounding
• Scientific Noatation
• Percentage Error
• Factorizing
• Completing the Square
• The Vertex
• The Discriminant
###### Index Rules
• Indices rules
• Indices questions
###### Series
• Arithmetic Series
• Geomrtric Series
• The Sigma Sign

Complex Number

• The Imaginary Number
• Complex Number
• Argand Planes
• Polar and Euler
• Periodic Models

Matrices

• Matrix Basics
• Matrix Algebra
• Eigenvalues and Eigenvectors
• Markov Chains
• Transformations
##### 2 HL AI
###### Notation
• Subbing and Solving
• Domain and Range
• Functions and Relations
• Inverse Functions

Graphing Functions

• Transformations
• Exponents
• Logarithms
• ln and e
###### Modelling
• Power Functions
• Exponential Functions
• Sinusoidal Functions

Financial Maths

• Compound Interest
• Loans
• Annunities
##### 3 HL AI
###### Basic Trigonometry
• Right angled triangles
• Basic trig graphs
• Area formula
• Sine rule
• Cosine rule
###### Basic Shape
• Area and Surface Area
• Volume
• Unit circle and exact trigonometry
###### Trigonometric Graphs
• Transformations
• Modelling

Vector Geometry

• Key terms
• Geometry
• Displacement

Vector Lines

• 3d vectors
• Angle between vectors
• Line equations
• Intersecting vector lines

Cross Product

• Definition
• Area applications

Graph Theory 1

• Informal definaitions
• Formal definitions
• Routes
• Weighteed graphs
• Trees and spanning
• Chinese Postman Problem

Graph Theory 2

• Eulerian graphs
• Hamilton graphs
• Travelling Salesman Problem
###### Statistics
• Data and Central Tendency
• Quartiles and Boxplots
• Correlation and Regression
• Mean and Variance
###### Probability
• Probability
• Venn diagrams
• Formulae
• Tree diagrams and condiontal probability
###### Distributions
• Binomial distributions
• Normal distributions
• Poisson distributons
###### Hypotheses testing
• Spearmans Rank
• Chi Squared Independence
• Chi Squared Goodness of Fit
• t-tests
###### Differentiation Introduction
• Simple differentiation
• Tangents and normals

Differentation Techniques

• Chain rule
• Product rule
• Quotient rule
###### Stationary Points
• Local maximum and minimum
• Optimization
• Inflextion and concavity
###### Integration and Area
• Anti-differentiation
• Definite integration
• Bounded area
• Trapeziodal rule

Integration Substitution

• Substitution

Volumes