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
View this Free Online Material at the source:
Algebra I
