IB Math Analysis and Approaches Higher Level (AA HL)

00
Pre Course
  • Straight lines
  • Surds
  • Basic Quadratics
  • Completing the Square
  • Quadratic Discriminat

01

Algebra and Number
  • Inequalities
  • Quadratic and Polynomial Roots
  • Partial Fractions
  • Expansions
  • Sequences and Series
  • Exponents
  • Logarithms
  • Counting
  • Row (Gaussian Reduction)

02

Functions
  • Notation
  • Odd and Even Functions
  • Algebra of Functions
  • Graphing and Functions
  • Factor and Remainder Theorems
03
Trigonometry
  • Non right angled trig.
  • Radian and basic ratios
  • Trig. graphs and transformations
  • Trig formulae - Pythagorean
  • Trig formulae - Double and Compound
  • Reciprocal and inverse trig.

04

Proof
  • Direct proof
  • Proof by contrapositive
  • Proof by contradiction
  • Induction - series
  • Induction - division
  • Induction - other

05

Complex Numbers
  • The number i
  • Complex number algebra
  • The Argand plane and polar form
  • De Moivre's Theorem and roots.
06
Differentiation
  • First principles
  • Simple differentiation
  • Tangents and normals
  • The chain rule
  • Product and Quotient rules
  • Functions and differentiation rules
  • Turning porints
  • Implicit differentiation

07

Integration
  • Anti differentiation
  • Definite integrals
  • Integration by substitution
  • Integration by parts
  • Integration by partial fractions
  • Volumes of revolution
  • Kinetics

08

Statistics and Probability
  • Cumulative frequency and box-plots
  • Basic probability and formulae
  • Discrete tables
  • Binomial distribution
  • Normal distribution
  • Continuos distributions
  • Bayes Theorem
09
Vectors
  • Vector geometry and basics
  • 2d and 3d Vectors line equations
  • The Cross product
  • Vector planes
  • Shortest distance problems

10

Further Calculus
  • Maclaurin's Series
  • L'Hopitals
  • Differential equations
  • Euler's Method
  • Homogeneous equations
  • Integrating factor
  • Maclaurin's Series and differential equations