## Table of Contents

**R. Prealgebra Review**

R.1 Exponents and Order of Operations

R.2 Factors, Primes, and Least Common Multiples

R.3 Fractions

R.4 Decimals

R.5 Percents

**1. Real Numbers and Algebraic Expressions**

1.1 Real Numbers and the Real-Number Line

1.2 Addition of Real Numbers

1.3 Subtraction of Real Numbers

1.4 Multiplication and Division of Real Numbers

1.5 Properties of Real Numbers

1.6 Algebraic Expressions, Translations, and Exponents

1.7 Simplifying Algebraic Expressions

1.8 Translating and Evaluating Algebraic Expressions

**2. Solving Linear Equations and Inequalities**

2.1 Solving Linear Equations: The Addition Property

2.2 Solving Linear Equations: The Multiplication Property

2.3 Solving Linear Equations by Combining Properties

2.4 Solving Literal Equations and Formulas

2.5 Solving Equations Involving Percent

2.6 Solving Linear Inequalities

**3. Graphing Linear Equations and Inequalities; Functions**

3.1 Introduction to Graphing

3.2 Slope of a Line

3.3 Graphing Linear Equations

3.4 More on Linear Equations and Their Graphs

3.5 Graphing Linear Inequalities

3.6 Introduction to Functions

**4. Systems of Equations and Inequalities**

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Elimination

4.4 Solving Systems of Linear Inequalities

**5. Exponents and Polynomials**

5.1 Laws of Exponents

5.2 More Laws of Exponents and Scientific Notation

5.3 Basic Concepts of Polynomials

5.4 Addition and Subtraction of Polynomials

5.5 Multiplication of Polynomials

5.6 Special Products

5.7 Division of Polynomials

**6. Factoring Polynomials**

6.1 Common Factoring and Factoring by Grouping

6.2 Factoring Trinomials Whose Leading Coefficient Is 1

6.3 Factoring Trinomials Whose Leading Coefficient Is Not 1

6.4 Special Factoring

6.5 More Factoring Strategies

6.6 Solving Quadratic Equations by Factoring

**7. Rational Expressions and Equations**

7.1 Rational Expressions and Functions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions

7.4 Complex Rational Expressions

7.5 Solving Rational Equations

7.6 Ratio and Proportion; Variation

**8. Radical Expressions and Equations**

8.1 Radical Expressions and Functions

8.2 Rational Exponents

8.3 Simplifying Radical Expressions

8.4 Addition and Subtraction of Radical Expressions

8.5 Multiplication and Division of Radical Expressions

8.6 Solving Radical Equations

8.7 Complex Numbers

**9. Quadratic Equations, Functions, and Inequalities**

9.1 Solving Quadratic Equations: Square Root Property and Completing the Square

9.2 Solving Quadratic Equations: The Quadratic Formula

9.3 More on Quadratic Equations

9.4 Graphing Quadratic Functions

9.5 Solving Quadratic and Rational Inequalities

**10. Exponential and Logarithmic Functions**

10.1 The Algebra of Functions and Inverse Functions

10.2 Exponential Functions

10.3 Logarithmic Functions

10.4 Properties of Logarithms

10.5 Common Logarithms, Natural Logarithms, and Change of Base

10.6 Exponential and Logarithmic Equations

**11. Conic Sections and Nonlinear Systems**

11.1 Introduction to Conics; The Parabola

11.2 The Circle

11.3 The Ellipse and the Hyperbola

11.4 Solving Nonlinear Systems of Equations

11.5 Solving Nonlinear Inequalities and Nonlinear Systems of Inequalities

**Appendix A. Transition to Intermediate Algebra**

A.1 Review of Introductory Algebra

A.2 Solving Compound Inequalities

A.3 Absolute Value Equations and Inequalities

A.4 Systems of Linear Equations in Three Variables

A.5 Solving Systems of Linear Equations by Using Matrices

**Appendix B. Additional Topics**

B.1 Determinants and Cramer's Rule

B.2 Synthetic Division

**Appendix C. Symbols and Graphing Calculators**

C.1 Table of Symbols

C.2 Introduction to Graphing Calculators