Math by First Principles

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Pre-Algebra

1. Foundations of Arithmetic
  1. Place Value and the Number System
  2. Properties of Addition and Multiplication
  3. Order of Operations
  4. The Distributive Property
2. Integers and the Number Line
  1. Negative Numbers and the Number Line
  2. Adding and Subtracting Integers
  3. Multiplying and Dividing Integers
  4. Absolute Value
3. Factors and Multiples
  1. Divisibility Rules
  2. Primes and Composites
  3. Prime Factorization
  4. GCF and LCM
4. Fractions
  1. Understanding Fractions
  2. Equivalent Fractions and Simplifying
  3. Adding and Subtracting Fractions
  4. Multiplying and Dividing Fractions
  5. Mixed Numbers
5. Decimals
  1. Decimal Place Value
  2. Operations with Decimals
  3. Converting Between Fractions and Decimals
  4. Rounding and Estimation
6. Exponents and Roots
  1. Introduction to Exponents
  2. Laws of Exponents
  3. Negative and Zero Exponents
  4. Square Roots
  5. Scientific Notation
7. Ratios, Rates, and Percents
  1. Ratios
  2. Rates and Unit Rates
  3. Proportions
  4. Percent
  5. Percent Increase and Decrease
8. Introduction to Algebra
  1. Variables and Expressions
  2. Evaluating and Simplifying Expressions
  3. Solving One-Step Equations
  4. Solving Two-Step Equations
  5. Inequalities
9. Geometry Basics
  1. Points, Lines, and Angles
  2. Perimeter and Area
  3. Circles
  4. Volume and Surface Area
  5. The Coordinate Plane
10. Data, Counting, and Probability
  1. Mean, Median, Mode, and Range
  2. Reading Data and Graphs
  3. Basic Counting Principles
  4. Introduction to Probability

Algebra I

1. The Language of Algebra
  1. From Arithmetic to Algebra
  2. Fractional Exponents and Radicals
  3. Arithmetic with Expressions
  4. Expanding and Factoring Expressions
  5. Algebraic Fractions
2. Linear Equations
  1. Solving Linear Equations
  2. Linear Equations in Disguise
  3. Word Problems with Linear Equations
  4. Solving for a Variable
3. Systems of Linear Equations
  1. Equations with Two Variables
  2. Solving Systems by Substitution
  3. Solving Systems by Elimination
  4. Word Problems with Systems
  5. Systems with More Variables
4. Ratios, Percents, and Proportion
  1. Ratio Problems
  2. Conversion Factors
  3. Percent Problems
  4. Direct and Inverse Proportion
  5. Rate and Work Problems
5. Graphing Lines
  1. Graphing Linear Equations
  2. Slope
  3. Finding the Equation of a Line
  4. Slope and Intercepts
  5. Parallel and Perpendicular Lines
6. Inequalities
  1. Inequality Basics
  2. Solving Linear Inequalities
  3. Graphing Inequalities
  4. Introduction to Optimization Advanced
7. Quadratic Equations
  1. Introduction to Quadratics
  2. Factoring Quadratics
  3. Factoring Harder Quadratics
  4. Sums and Products of Roots
8. Special Factorizations
  1. Squares of Binomials
  2. Difference of Squares
  3. Sum and Difference of Cubes
  4. Rationalizing Denominators
  5. Factoring by Grouping
9. Complex Numbers and the Quadratic Formula
  1. Imaginary Numbers Advanced
  2. Arithmetic with Complex Numbers Advanced
  3. Completing the Square
  4. The Quadratic Formula
  5. Applications of Quadratics
10. Graphing Quadratics and Inequalities
  1. Parabolas
  2. The Equation of a Circle
  3. Quadratic Inequalities Advanced
  4. Quadratic Optimization
11. Functions
  1. What Is a Function?
  2. Combining and Composing Functions Advanced
  3. Inverse Functions Advanced
  4. Defining New Operations Advanced
12. Graphing Functions
  1. Graphs of Functions
  2. Shifting Graphs
  3. Stretching and Reflecting Graphs
  4. Graphs of Inverse Functions Advanced
13. Polynomials, Exponentials, and Logarithms
  1. Adding and Subtracting Polynomials
  2. Multiplying Polynomials
  3. Exponential Functions
  4. Compound Interest
  5. Introduction to Logarithms Advanced
14. Special Functions
  1. Radical Functions Advanced
  2. Absolute Value Equations and Graphs
  3. Floor and Ceiling Advanced
  4. Rational Functions Advanced
  5. Piecewise Functions
15. Sequences and Series
  1. Arithmetic Sequences
  2. Arithmetic Series
  3. Geometric Sequences
  4. Geometric Series
  5. Telescoping Sums Advanced

Algebra II

1. Equations and Inequalities
  1. Solving Linear Equations
  2. Literal Equations and Formulas
  3. Linear Inequalities
  4. Absolute Value Equations and Inequalities
2. Functions and Their Graphs
  1. Relations and Functions
  2. Function Notation and Evaluation
  3. Graphs of Functions
  4. Transformations of Graphs
  5. Composition of Functions
  6. Inverse Functions
3. Systems of Equations and Inequalities
  1. Systems in Two Variables
  2. Systems in Three Variables
  3. Systems of Inequalities
  4. Matrices and Systems of Equations Advanced
  5. Determinants and Cramer's Rule Advanced
4. Quadratic Functions and Equations
  1. Quadratic Functions and Parabolas
  2. Solving Quadratics by Factoring
  3. Completing the Square
  4. The Quadratic Formula and the Discriminant
  5. Quadratic Inequalities
  6. Sum and Product of Roots
5. Complex Numbers
  1. The Imaginary Unit and Complex Numbers
  2. Arithmetic of Complex Numbers
  3. The Complex Plane and Modulus Advanced
  4. Complex Roots of Quadratics
6. Polynomial Division and Roots
  1. Polynomials and Their Graphs
  2. Polynomial Long Division
  3. Synthetic Division and the Remainder Theorem
  4. The Factor Theorem
  5. The Rational Root Theorem
7. Zeros of Polynomials
  1. The Fundamental Theorem of Algebra
  2. Complex and Irrational Roots
  3. Vieta's Formulas Advanced
  4. Graphing Polynomial Functions
8. Rational Expressions and Functions
  1. Simplifying Rational Expressions
  2. Multiplying and Dividing Rational Expressions
  3. Adding and Subtracting Rational Expressions
  4. Solving Rational Equations
  5. Graphs of Rational Functions
9. Radicals and Rational Exponents
  1. Rational Exponents
  2. Simplifying Radical Expressions
  3. Operations with Radicals
  4. Solving Radical Equations
  5. Rationalizing and Radical Conjugates
10. Exponential and Logarithmic Functions
  1. Exponential Functions and Graphs
  2. Introduction to Logarithms
  3. Properties of Logarithms
  4. Solving Exponential and Logarithmic Equations
  5. Exponential Growth and Decay
  6. The Natural Base e
11. Sequences and Series
  1. Sequences and Notation
  2. Arithmetic Sequences and Series
  3. Geometric Sequences and Series
  4. Infinite Geometric Series
  5. The Binomial Theorem Advanced
12. Conic Sections
  1. Parabolas Advanced
  2. Circles
  3. Ellipses Advanced
  4. Hyperbolas Advanced
13. Probability and Statistics
  1. Counting Principles, Permutations, and Combinations
  2. Introduction to Probability
  3. Data Distributions and Statistics
  4. The Normal Distribution Advanced

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