Mathematics AA HL

Analysis and Approaches Higher Level

##### 1 HL AA
###### Basics
• Straight lines
• Surds
• Simultaneous equations
• Factorizing
• Completing the Square
• 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
• Repeated factors
###### Proof
• Direct proof
• Contrapositive
• Induction series
• Induction division
• Induction others

Complex Numbers

• The number i
• Complex number operations
• Complex number GDC
• Complex conjugate
##### 2 HL AA
###### 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

• Polynomial roots
##### 3 HL AA
###### Basic Trigonometry
• Right angled trigonometry
• Basic trig graphs
• Area formula
• Sine rule
• Cosine rule
• 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
• 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
###### 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
###### Differential Equations
• Separating variables
• Rates of change
• Eulers Method
• Homogeneous equations
• Integrating factor

Maclaurin’s Series

• Expansions
• Calculus
• Differential equations