Algebra I
Algebra in full, picking up where Pre-Algebra ends: linear equations and systems, graphing, inequalities, quadratics and complex numbers, functions, exponentials and logarithms, and sequences and series, every step from first principles.
1. The Language of Algebra
- From Arithmetic to Algebra
- Fractional Exponents and Radicals
- Arithmetic with Expressions
- Expanding and Factoring Expressions
- Algebraic Fractions
2. Linear Equations
- Solving Linear Equations
- Linear Equations in Disguise
- Word Problems with Linear Equations
- Solving for a Variable
3. Systems of Linear Equations
- Equations with Two Variables
- Solving Systems by Substitution
- Solving Systems by Elimination
- Word Problems with Systems
- Systems with More Variables
4. Ratios, Percents, and Proportion
- Ratio Problems
- Conversion Factors
- Percent Problems
- Direct and Inverse Proportion
- Rate and Work Problems
5. Graphing Lines
- Graphing Linear Equations
- Slope
- Finding the Equation of a Line
- Slope and Intercepts
- Parallel and Perpendicular Lines
6. Inequalities
- Inequality Basics
- Solving Linear Inequalities
- Graphing Inequalities
- Introduction to Optimization Advanced. This lesson goes beyond core Algebra I. You can skip it.
7. Quadratic Equations
- Introduction to Quadratics
- Factoring Quadratics
- Factoring Harder Quadratics
- Sums and Products of Roots
8. Special Factorizations
- Squares of Binomials
- Difference of Squares
- Sum and Difference of Cubes
- Rationalizing Denominators
- Factoring by Grouping
9. Complex Numbers and the Quadratic Formula
- Imaginary Numbers Advanced. This lesson goes beyond core Algebra I. You can skip it.
- Arithmetic with Complex Numbers Advanced. This lesson goes beyond core Algebra I. You can skip it.
- Completing the Square
- The Quadratic Formula
- Applications of Quadratics
10. Graphing Quadratics and Inequalities
- Parabolas
- The Equation of a Circle
- Quadratic Inequalities Advanced. This lesson goes beyond core Algebra I. You can skip it.
- Quadratic Optimization
11. Functions
- What Is a Function?
- Combining and Composing Functions Advanced. This lesson goes beyond core Algebra I. You can skip it.
- Inverse Functions Advanced. This lesson goes beyond core Algebra I. You can skip it.
- Defining New Operations Advanced. This lesson goes beyond core Algebra I. You can skip it.
12. Graphing Functions
- Graphs of Functions
- Shifting Graphs
- Stretching and Reflecting Graphs
- Graphs of Inverse Functions Advanced. This lesson goes beyond core Algebra I. You can skip it.
13. Polynomials, Exponentials, and Logarithms
- Adding and Subtracting Polynomials
- Multiplying Polynomials
- Exponential Functions
- Compound Interest
- Introduction to Logarithms Advanced. This lesson goes beyond core Algebra I. You can skip it.
14. Special Functions
- Radical Functions Advanced. This lesson goes beyond core Algebra I. You can skip it.
- Absolute Value Equations and Graphs
- Floor and Ceiling Advanced. This lesson goes beyond core Algebra I. You can skip it.
- Rational Functions Advanced. This lesson goes beyond core Algebra I. You can skip it.
- Piecewise Functions
15. Sequences and Series
- Arithmetic Sequences
- Arithmetic Series
- Geometric Sequences
- Geometric Series
- Telescoping Sums Advanced. This lesson goes beyond core Algebra I. You can skip it.