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Algebra 2

Sets

  • Introduction to Sets

Numbers

  • The Evolution of Numbers
  • Prime and Composite Numbers
  • Fundamental Theorem of Arithmetic
  • Whole Numbers and Integers
  • Rational Numbers
  • Irrational Numbers
  • Rational Numbers and Irrational Numbers
  • Real Numbers
  • Imaginary Numbers
  • Complex Numbers
  • Adding and Subtracting Complex Numbers
  • Multiplying and Dividing Complex Numbers
  • Absolute Value of Complex Numbers
  • The Complex Plane
  • Common Number Sets

Inequalities

  • Introduction to Inequalities
  • Properties of Inequalities
  • Solving Inequalities
  • Absolute Value Inequalities
  • Solving Rational Inequalities
  • Solving Inequality Word Questions
  • Intervals

Exponents

  • Exponents
  • Variables with Exponents
  • Using Exponents in Algebra
  • Squares and Square Roots
  • Squares and Square Roots in Algebra
  • nth Root
  • Fractional Exponents
  • Laws of Exponents
  • Exponents of Negative Numbers

Polynomials

  • What is a Polynomial?
  • Types of Polynomials
  • Monomials, Binomials, and Polynomials
  • Adding Polynomials
  • Subtracting Polynomials
  • Dividing Polynomials
  • Multiplying Binomials
  • Polynomials – Long Division
  • Degree (of an Expression)
  • Special Binomial Products
  • Multiplying Binomials
  • Difference of Two Cubes
  • Polynomial Remainder Theorem
  • Factoring in Algebra
  • Factorization of Polynomials Using Factor Theorem
  • How do you use the factor theorem?
  • How to factorise a polynomial by splitting the middle term?
  • Review Factoring Polynomials
  • Zeros of a Polynomial Function
  • Factors and Coefficients of a Polynomial
  • Roots of Polynomials: Sums and Products
  • Rational Expressions
  • Using Rational Expressions
  • Review Factoring Polynomials
  • Solving Polynomial Equations of Higher Degree
  • Examining Graphs of Polynomial Equations of Higher Degree

Graphing Polynomials

  • How Polynomials Behave
  • Polynomials: The Rule of Signs
  • Polynomials: Bounds on Zeros

Equations

  • Equations and Formulas
  • Solving Equations
  • Simplify
  • Solving Word Questions
  • Zero Product Property
  • Implication and Iff
  • Theorems, Corollaries, Lemmas

Graphs

  • Cartesian Coordinates
  • Pythagoras’ Theorem
  • Distance Between 2 Points
  • Graph of an Equation
  • Finding Intercepts From an Equation
  • Symmetry in Equations

Linear Equations

  • Equation of a Straight Line
  • Linear Equations
  • Point-Slope Equation of a Line
  • Equation of a Line from 2 Points
  • Midpoint of a Line Segment
  • Parallel and Perpendicular Lines

Functions

  • What is a Function?
  • Domain, Range and Codomain
  • Evaluating Functions
  • Increasing and Decreasing Functions
  • Maxima and Minima of Functions
  • Even and Odd Functions
  • Set-Builder Notation
  • Common Functions Reference:
    • Square Function
    • Square Root Function
    • Cube Function
    • Reciprocal Function
    • Absolute Value Function
    • Floor and Ceiling Function
  • Function Transformations
  • Operations with Functions
  • Composition of Functions
  • Finding Domains of Composite Functions
  • Inverse Functions

Equations of Second Degree

  • Quadratic Equations
  • Factoring Quadratics
  • Solving A Quadratic Equation By Factoring
  • Completing the Square
  • Solving a Quadratic Equation by Completing the Square
  • Derivation of Quadratic Formula
  • Graphing Quadratic Equations
  • A Summary of the Methods of Solving Quadratic Equations
  • Quadratic Equations in the Real World
  • Circle Equations

Solving

  • Mathematical Models and Mathematical Models 2
  • Approximate Solutions
  • Intermediate Value Theorem
  • Solving Radical Equations
  • Change of Variables
  • Algebra Mistakes

Solving Inequalities

  • Solving Inequalities
  • Graphing Linear Inequalities
  • Inequality Grapher
  • Solving Quadratic Inequalities
  • Solving Rational Inequalities
  • Absolute Value in Algebra
  • Absolute Value Equations

Exponents and Logarithms

  • Introduction to Logarithms
  • Exponents, Roots and Logarithms
  • Working with Exponents and Logarithms
  • Logarithmic Equations
  • Exponential Function
  • Logarithmic Function
  • Exponential Growth and Decay

Systems of Linear Equations

  • Systems of Linear Equations
  • Solving Systems Of Equations By Elimination Method
  • Solving Systems Of Equations By Substitution Method
  • Cross Multiplication Method For Solving Equations
  • Graphical Method Of Solving Linear Equations In Two Variables
  • Matrices
  • Special Types of Matrices
  • Scalar, Vector, Matrix and Vectors
  • Dot Product
  • Cross Product
  • How to Multiply Matrices
  • Determinant of a Matrix
  • Inverse of a Matrix:
    • Using Elementary Row Operations (Gauss-Jordan)
    • Using Minors, Cofactors and Adjugate
  • Solving Systems of Linear Equations Using Matrices
  • Solving Linear Quadratic Systems Algebraically
  • Solving Linear Systems Algebraically Using Substitution
  • Solving a Linear Quadratic System Graphically
  • Solving Linear Systems Graphically

Probability

  • Probability
  • Probability – Types of Events
  • The Basic Counting Principle
  • Probability and Permutations
  • Combinations and Permutations

Sequences, Series and Partial Sums

  • Sequences
  • Sigma Notation
  • Partial Sums
  • Arithmetic Sequences and Sums
  • Geometric Sequences and Sums

Finally
These last few subjects use what you have learned above.

  • Partial Fractions
  • Mathematical Induction
  • Pascal’s Triangle
  • Binomial Theorem
  • Binomial Theorem for any Index

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