Mathematics AI HL

Applications and Interpretations Higher Level

Number and Algebra
Basics
  • Straight lines
  • Surds
  • Simultaneous equations
Number
  • Rounding
  • Scientific Noatation
  • Percentage Error
Quadratics
  • Factorizing
  • Completing the Square
  • Quadratic Formula
  • 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
Functions
Notation
  • Subbing and Solving
  • Domain and Range
  • Functions and Relations
  • Inverse Functions

Graphing Functions

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

Financial Maths

  • Compound Interest
  • Loans
  • Annunities
Geometry and Trigonometry
Basic Trigonometry
  • Right angled triangles
  • Basic trig graphs
  • Area formula
  • Sine rule
  • Cosine rule
Basic Shape
  • Area and Surface Area
  • Volume
Radian and Unit Circle
  • Radian measure
  • 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 and Probability
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
Calculus
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

  • About the x-axis
  • About the y-axis
  • Bounded volume

Kinetics

  • Kinetics

Differential Equations

  • Seperating variables
  • Rates of Change
  • Eulers method
  • Coupled differential equations