Mathematics AA HL

Analysis and Approaches Higher Level

Number and Algebra
Basics
  • Straight lines
  • Surds
  • Simultaneous equations
Quadratics
  • Factorizing
  • Completing the Square
  • Quadratic Formula
  • The Vertex
  • The Discriminant
Series
  • Arithmetic Series
  • Geomrtric Series
  • The Sigma Sign

Binomials and Counting

  • Binomial expansions (positive)
  • Binomial expansions (neagtive)
  • Counting

3×3 Equations

  • 3×3 Equations

Partial Fractions

  • Linear factors
  • Quadratic factors
  • Repeated factors
Proof
  • Direct proof
  • Contrapositive
  • Contradiction
  • Induction series
  • Induction division
  • Induction others

Complex Numbers

  • The number i
  • Complex number operations
  • Complex number GDC
  • Complex conjugate
Functions
Notation
  • Subbing and Solving
  • Domain and Range
  • Composite Functions
  • Functions and Relations
  • Inverse Functions
  • Odd and Even Functions
Graphing Functions
  • Transformations
  • Reciprocals
  • Modulus and Inequalities
Logarithms and Exponentials
  • Exponents
  • Logarithms
  • ln and e
  • Modelling

Factor and Remainder Theorem

  • Factor theorem
  • Remainder theorem

Roots of Polynomials

  • Quadratic roots
  • Polynomial roots

Geometry and Trigonometry
Basic Trigonometry
  • Right angled trigonometry
  • Basic trig graphs
  • Area formula
  • Sine rule
  • Cosine rule
Unit Circle and Radians
  • Radian measure
  • Unit circle and exact trigonometry
Trigonometric Formulae
  • Compound angle
  • Double angle
  • Reciprocal angles
  • Inverse angles
  • Pythagorean identities
Trigonometric Graphs
  • Transformations
  • Modelling

Complex Number

  • Modulus and argument
  • De. Moivre and roots

Vector Geometry

  • Key terms
  • Geometry
  • Displacement

Vector Lines

  • 3d vectors
  • Angles between vectors
  • Line equations in 3d
  • Intersecting lines

Cross Product

  • Definition
  • Area applications

Vector Planes

  • Equations of planes
  • Intersecting planes

Shortest Distance

  • Shortest distance problems
Statistics and Probability
Statistics
  • Data and central tendency
  • Quartiles and Boxplots
  • Correlation and regression
  • Mean and Variance
Probability
  • Probability
  • Venn diagrams
  • Formulae
  • Trees and conditional probability
Discrete Distributions
  • Tables and functions
  • Binomials
Continuos Distributions
  • Normal distributions
  • Continuous functions

Bayes Theorem

  • Bayes theorem
Calculus
Differentiation Introduction
  • First principles
  • Simple differentaion
  • Tangents and normals
Differentation Techniques
  • Chain rule
  • Product rule
  • Quotient rule
  • Functions
Stationary Points
  • Local maximum and minimum
  • Optization
  • Inflexion and concavity

Implicit Differentiation

  • Implicit diffeerntiation

L'Hopitals

  • L'Hopitals
Integration and Area
  • Anti differentiation
  • Definite integration
  • Bounded area
Integration Techniques
  • Substitution
  • By Parts
  • Partial Fractions
Volumes
  • The x-axis
  • The y-axis
  • Bounded volume
Kinetics
  • Kinetics
Differential Equations
  • Separating variables
  • Rates of change
  • Eulers Method
  • Homogeneous equations
  • Integrating factor

Maclaurin's Series

  • Expansions
  • Calculus
  • Differential equations