This free Algebra I textbook was written for eighth graders in California to meet the state standards. The chapters were designed to cover specific standards or parts of the standards. The text, unfortunately, does not include any sort of answer key but it does offer students a well-designed textbook that would easily help students in any state. Students who are preparing for college math courses and need a refresher might also find this textbook helpful.

Even without an answer key, this free online mathematics text offers a lot of great sample problems which could prove helpful for homeschool families too.

It was published by CGP Education and included contributions from a number of high school mathematics teachers.

## Table of Contents for Alegra I Textbook

#### Chapter 1 – Working with Real Numbers

##### Section 1.1 — Sets and Expressions

###### Topic 1.1.1 The Basics of Sets

###### Topic 1.1.2 Subsets of the Real Numbers

###### Topic 1.1.3 Unions and Intersections

###### Topic 1.1.4 Algebraic and Numeric Expressions

###### Topic 1.1.5 Coefficients and Evaluating

##### Section 1.2 — The Real Number System

###### Topic 1.2.1 The Number System

###### Topic 1.2.2 Identities and Inverses

###### Topic 1.2.3 The Number Line and Absolute Values

###### Topic 1.2.4 Addition and Multiplication

###### Topic 1.2.5 Subtraction and Division

###### Topic 1.2.6 Order of Operations

###### Topic 1.2.7 Properties of Real Numbers

###### Topic 1.2.8 More on Multiplication

###### Topic 1.2.9 The Real Number Axioms

##### Section 1.3 — Exponents, Roots, and Fractions

###### Topic 1.3.1 Exponent Laws

###### Topic 1.3.2 Square Roots

###### Topic 1.3.3 Properties of Roots

###### Topic 1.3.4 Equivalent Fractions

###### Topic 1.3.5 Multiplying and Dividing Fractions

###### Topic 1.3.6 Adding and Subtracting Fractions

##### Section 1.4 — Mathematical Logic

###### Topic 1.4.1 Mathematical Proofs

###### Topic 1.4.2 Inductive and Deductive Reasoning

###### Topic 1.4.3 Algebraic Statements

##### Chapter 1 — Investigation Counting Collections

#### Chapter 2 — Single Variable Linear Equations

##### Section 2.1 — Algebra Basics

###### Topic 2.1.1 Simplifying Algebraic Expressions

###### Topic 2.1.2 Getting Rid of Grouping Symbols

###### Topic 2.1.3 More Simplifying and Checking Answers

##### Section 2.2 — Manipulating Equations

###### Topic 2.2.1 Properties of Equality

##### Section 2.3 — More Equations Equations

###### Topic 2.3.1 Removing Fractions

###### Topic 2.3.2 Fractional Coefficients in Algebraic Expressions

###### Topic 2.3.3 Eliminating Decimal Coefficients

##### Section 2.4 — Using Equations

###### Topic 2.4.1 Applications of Linear Equations

###### Topic 2.4.2 Coin Tasks

##### Section 2.5 — Consecutive Integer Tasks, Time and Rate Tasks

###### Topic 2.5.1 Consecutive Integer Tasks

###### Topic 2.5.2 Age-Related Tasks

###### Topic 2.5.3 Rate, Time, and Distance Tasks

##### Section 2.6 — Investment and Mixture Mixture Tasks

###### Topic 2.6.1 Investment Tasks

###### Topic 2.6.2 Mixture Tasks

###### Topic 2.6.3 More Mixture Tasks

##### Section 2.7 — Work-Related Tasks

###### Topic 2.7.1 Work Rate

###### Topic 2.7.2 Combined Work Rate

##### Section 2.8 — Absolute Value Equations Equations

###### Topic 2.8.1 Absolute Value Equations

###### Topic 2.8.2 More on Absolute Value

##### Chapter 2 — Investigation Wildlife Park Trains

#### Chapter 3 — Single Variable Linear inequalities

##### Section 3.1 — Inequalities

###### Topic 3.1.1 Inequalities

###### Topic 3.1.2 Addition and Subtraction Properties of Inequalities

###### Topic 3.1.3 Multiplication and Division Properties of Inequalities

##### Section 3.2 — Applications of Inequalities

###### Topic 3.2.1 Multistep Inequalities

###### Topic 3.2.2 Applications of Inequalities

##### Section 3.3 — Compound Inequalities

###### Topic 3.3.1 Compound Inequalities

##### Section 3.4 — Absolute Value Inequalities

###### Topic 3.4.1 Absolute Value Inequalities

##### Chapter 3 — Investigation Mailing Packages

#### Chapter 4 — Linear Equations & Their Graphs

##### Section 4.1 — The Coordinate Plane

###### Topic 4.1.1 The Coordinate Plane

###### Topic 4.1.2 Quadrants of the Plane

###### Topic 4.1.3 Lines

###### Topic 4.1.4 Horizontal and Vertical Lines

##### Section 4.2 — Lines

###### Topic 4.2.1 Points on a Line

###### Topic 4.2.2 Graphing Ax + By = C

###### Topic 4.2.3 Using Line Equations

###### Topic 4.2.4 The x- and y-intercepts

###### Topic 4.2.5 Graphing Lines

##### Section 4.3 — Slope

###### Topic 4.3.1 Slope of a Line

###### Topic 4.3.2 Point-Slope Formula

##### Section 4.4 — More Lines

###### Topic 4.4.1 Parallel Lines

###### Topic 4.4.2 Perpendicular Lines

###### Topic 4.4.3 The Slope-Intercept Form of a Line

###### Topic 4.4.4 More About Slopes

##### Section 4.5 — Inequalities

###### Topic 4.5.1 Regions Defined by Inequalities

###### Topic 4.5.2 Borders of Regions

###### Topic 4.5.3 Regions Defined by Two Inequalities

##### Chapter Chapter 4 — Investigation Tree Growth

#### Chapter 5 — Systems of Equations

##### Section 5.1 — Systems of Equations

###### Topic 5.1.1 The Graphing Method

###### Topic 5.1.2 The Substitution Method

###### Topic 5.1.3 Comparing the Graphing and Substitution Methods

###### Topic 5.1.4 Inconsistent Systems

###### Topic 5.1.5 Dependent Systems

###### Topic 5.1.6 Systems of Equations — Further Examples

##### Section 5.2 — The Elimination Method

##### Topic 5.2.1 Systems of Equations — Elimination

##### Section 5.3 — Applications of Systems of Equations

###### Topic 5.3.1 Systems of Linear Equations — Applications

###### Topic 5.3.2 Systems of Linear Equations — Integer Problems

###### Topic 5.3.3 Systems of Linear Equations — Percent Mix Problems

###### Topic 5.3.4 Systems of Linear Equations — Rate Problems

##### Chapter 5 — Investigation Breaking Even in an Egg Business

#### Chapter 6 – Manipulating Polynomials

###### Section 6.1 — Adding and Subtracting Polynomials

###### Topic 6.1.1 Polynomials

###### Topic 6.1.2 Adding Polynomials

###### Topic 6.1.3 Subtracting Polynomials

###### Topic 6.1.4 Adding and Subtracting Polynomials

##### Section 6.2 — Multiplying Polynomials

###### Topic 6.2.1 Rules of Exponents

###### Topic 6.2.2 Polynomial Multiplication

###### Topic 6.2.3 Polynomial Multiplication – Area and Volume

##### Section 6.3 — Dividing Polynomials

###### Topic 6.3.1 Division by Monomials

###### Topic 6.3.2 Polynomials and Negative Powers

###### Topic 6.3.3 Division by Polynomials — Factoring

###### Topic 6.3.4 Division by Polynomials — Long Division

###### Topic 6.3.5 Division by Polynomials — Applications

##### Section 6.4 — Special Products of Binomials

###### Topic 6.4.1 Special Products of Two Binomials

##### Section 6.5 — Factors

###### Topic 6.5.1 Factors of Monomials

###### Topic 6.5.2 Simple Factors of Polynomials

##### Section 6.6 — Factoring Quadratics

###### Topic 6.6.1 Factoring Quadratics

###### Topic 6.6.2 Factoring Quadratics — ax2 + bx + c

##### Section 6.7 — More on Factoring Factoring Polynomials

###### Topic 6.7.1 Factoring Quadratic Expressions in Two Variables

###### Topic 6.7.2 Factoring Third-Degree Polynomials

##### Section 6.8 — More on Quadratics

###### Topic 6.8.1 The Difference of Two Squares

###### Topic 6.8.2 Perfect Square Trinomials

###### Topic 6.8.3 Factoring by Grouping

##### Chapter 6 — Investigation Pascal’s Triangle

#### Chapter 7 — Quadratic Equations & Their Applications

##### Section 7.1 — Solving Quadratic Equations

###### Topic 7.1.1 Solving Quadratic Equations by Factoring

###### Topic 7.1.2 Quadratic Equations — Taking Square Roots

##### Section 7.2 — Completing the Square

###### Topic 7.2.1 Completing the Square

###### Topic 7.2.2 More on Completing the Square

###### Topic 7.2.3 Solving Equations by Completing the Square

##### Section 7.3 — The Quadratic Formula and Applications

###### Topic 7.3.1 The Quadratic Formula

###### Topic 7.3.2 Applications of Quadratics

##### Section 7.4 — Quadratic Graphs

###### Topic 7.4.1 Graphs of Quadratic Functions

###### Topic 7.4.2 Drawing Graphs of Quadratic Functions

###### Topic 7.4.3 Quadratic Graphs and Completing the Square

##### Section 7.5 — The Discriminant

###### Topic 7.5.1 Quadratic Equations and the Discriminant

##### Section 7.6 — Motion Tasks and Other Applications

###### Topic 7.6.1 Motion Tasks

###### Topic 7.6.2 Economic Tasks

##### Chapter 7 — Investigation The Handshake Problem

#### Chapter 8 — Rational Expressions & Functions

##### Section 8.1 — Rational Expressions

###### Topic 8.1.1 Fractions and Rational Expressions

###### Topic 8.1.2 Equivalent Fractions

##### Section 8.2 — Multiplying and Dividing Rational Expressions

###### Topic 8.2.1 Multiplying Rational Expressions

###### Topic 8.2.2 Dividing Rational Expressions

##### Section 8.3 — Adding and Subtracting Rational Expressions

###### Topic 8.3.1 Fractions with Identical Denominators

###### Topic 8.3.2 Fractions with Different Denominators

##### Section 8.4 — Solving Equations Equations with Fractions

###### Topic 8.4.1 Solving Fractional Equations

###### Topic 8.4.2 Applications of Fractional Equations

##### Section 8.5 — Relations and Functions

###### Topic 8.5.1 Relations

###### Topic 8.5.2 Functions

###### Topic 8.5.3 Function Notation

###### Topic 8.5.4 More on Functions

##### Chapter 8 — Investigation Transforming Functions

#### Appendixes

#### Glossary

#### Formula Sheet

#### Index

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Algebra I