## Table of Contents

1. Introduction to Algebra

1.1 Numbers, Variables, and Expressions

1.2 Fractions

1.3 Exponents and Order of Operations

1.4 Real Numbers and the Number Line

1.5 Addition and Subtraction of Real Numbers

1.6 Multiplication and Division of Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying and Writing Algebraic Expressions

2. Linear Equations and Inequalities

2.1 Introduction to Equations

2.2 Linear Equations

2.3 Introduction to Problem Solving

2.4 Formulas

2.5 Unit Analysis

2.6 Linear Inequalities

3. Graphing Equations

3.1 Introduction to Graphing

3.2 Equations in Two Variables

3.3 Intercepts; Horizontal and Vertical Lines

3.4 Slope and Rates of Change

3.5 Slope-Intercept Form

3.6 Point-Slope Form

3.7 Introduction to Modeling

4. Systems of Linear Equations in Two Variables

4.1 Solving Systems of Linear Equations Graphically and Numerically

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Elimination

4.4 Systems of Linear Inequalities

5. Polynomials and Exponents

5.1 Rules for Exponents

5.2 Addition and Subtraction of Polynomials

5.3 Multiplication of Polynomials

5.4 Special Products

5.5 Integer Exponents and the Quotient Rule

5.6 Division of Polynomials

6. Factoring Polynomials and Solving Equations

6.1 Introduction to Factoring

6.2 Factoring Trinomials I (x2 + bx + c)

6.3 Factoring Trinomials II (ax2 + bx + c)

6.4 Special Types of Factoring

6.5 Summary of Factoring

6.6 Solving Equations by Factoring I (Quadratics)

6.7 Solving Equations by Factoring II (Higher Degree)

7. Rational Expressions

7.1 Introduction to Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction with Like Denominators

7.4 Addition and Subtraction with Unlike Denominators

7.5 Complex Fractions

7.6 Rational Equations and Formulas

7.7 Proportions and Variation

8. Introduction to Functions

8.1 Functions and Their Representations

8.2 Linear Functions

8.3 Compound Inequalities and Piecewise-Defined Functions

8.4 Other Functions and Their Properties

8.5 Absolute Value Equations and Inequalities

9. Systems of Linear Equations

9.1 Systems of Linear Equations in Three Variables

9.2 Matrix Solutions of Linear Systems

9.3 Determinants

10. Radical Expressions and Functions

10.1 Radical Expressions and Functions

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Operations on Radical Expressions

10.5 More Radical Functions

10.6 Equations Involving Radical Expressions

10.7 Complex Numbers

11. Quadratic Functions and Equations

11.1 Quadratic Functions and Their Graphs

11.2 Transformations and Translations of Parabolas

11.3 Quadratic Equations

11.4 The Quadratic Formula

11.5 Quadratic Inequalities

11.6 Equations in Quadratic Form

12. Exponential and Logarithmic Functions

12.1 Composite and Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithms

12.5 Exponential and Logarithmic Equations

13. Conic Sections

13.1 Parabolas and Circles

13.2 Ellipses and Hyperbolas

13.3 Nonlinear Systems of Equations and Inequalities

14. Sequences and Series

14.1 Sequences

14.2 Arithmetic and Geometric Sequences

14.3 Series

14.4 The Binomial Theorem

Appendix A. Using the Graphing Calculator

Appendix B. Sets

Appendix C. Linear Programming

Appendix D. Synthetic Division