Algebra II
A full second course in algebra: functions and their graphs, systems, quadratics and complex numbers, polynomial and rational functions, radicals, exponential and logarithmic functions, sequences and series, conic sections, and a first look at probability, all from first principles.
1. Equations and Inequalities
- Solving Linear Equations
- Literal Equations and Formulas
- Linear Inequalities
- Absolute Value Equations and Inequalities
2. Functions and Their Graphs
- Relations and Functions
- Function Notation and Evaluation
- Graphs of Functions
- Transformations of Graphs
- Composition of Functions
- Inverse Functions
3. Systems of Equations and Inequalities
- Systems in Two Variables
- Systems in Three Variables
- Systems of Inequalities
- Matrices and Systems of Equations Advanced. This lesson goes beyond core Algebra II. You can skip it.
- Determinants and Cramer's Rule Advanced. This lesson goes beyond core Algebra II. You can skip it.
4. Quadratic Functions and Equations
- Quadratic Functions and Parabolas
- Solving Quadratics by Factoring
- Completing the Square
- The Quadratic Formula and the Discriminant
- Quadratic Inequalities
- Sum and Product of Roots
5. Complex Numbers
- The Imaginary Unit and Complex Numbers
- Arithmetic of Complex Numbers
- The Complex Plane and Modulus Advanced. This lesson goes beyond core Algebra II. You can skip it.
- Complex Roots of Quadratics
6. Polynomial Division and Roots
- Polynomials and Their Graphs
- Polynomial Long Division
- Synthetic Division and the Remainder Theorem
- The Factor Theorem
- The Rational Root Theorem
7. Zeros of Polynomials
- The Fundamental Theorem of Algebra
- Complex and Irrational Roots
- Vieta's Formulas Advanced. This lesson goes beyond core Algebra II. You can skip it.
- Graphing Polynomial Functions
8. Rational Expressions and Functions
- Simplifying Rational Expressions
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Solving Rational Equations
- Graphs of Rational Functions
9. Radicals and Rational Exponents
- Rational Exponents
- Simplifying Radical Expressions
- Operations with Radicals
- Solving Radical Equations
- Rationalizing and Radical Conjugates
10. Exponential and Logarithmic Functions
- Exponential Functions and Graphs
- Introduction to Logarithms
- Properties of Logarithms
- Solving Exponential and Logarithmic Equations
- Exponential Growth and Decay
- The Natural Base e
11. Sequences and Series
- Sequences and Notation
- Arithmetic Sequences and Series
- Geometric Sequences and Series
- Infinite Geometric Series
- The Binomial Theorem Advanced. This lesson goes beyond core Algebra II. You can skip it.
12. Conic Sections
- Parabolas Advanced. This lesson goes beyond core Algebra II. You can skip it.
- Circles
- Ellipses Advanced. This lesson goes beyond core Algebra II. You can skip it.
- Hyperbolas Advanced. This lesson goes beyond core Algebra II. You can skip it.
13. Probability and Statistics
- Counting Principles, Permutations, and Combinations
- Introduction to Probability
- Data Distributions and Statistics
- The Normal Distribution Advanced. This lesson goes beyond core Algebra II. You can skip it.