## Table of Contents

**1. Real Numbers and Algebraic Expressions**

1.1 Tips for Success in Mathematics

1.2 Algebraic Expressions and Sets of Numbers

1.3 Operations on Real Numbers, and Order of Operation

1.4 Properties of Real Numbers and Algebraic Expressions

**2. Equations, Inequalities, and Problem Solving**

2.1 Linear Equation in One Variable

2.2 An Introduction to Problem Solving

2.3 Formulas and Problem Solving

2.4 Linear Inequalities and Problem Solving

2.5 Compound Inequalities

2.6 Absolute Value Equations

2.7 Absolute Value Inequalities

**3. Graphs and Functions**

3.1 Graphing Equations

3.2 Introduction to Functions

3.3 Graphing Linear Functions

3.4 The Slope of a Line

3.5 Equations of Lines

3.6 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions

3.7 Graphing Linear Inequalities

**4. Systems of Equations**

4.1 Solving Systems of Equations in Two Variables

4.2 Solving Systems of Equations in Three Variables

4.3 Systems of Linear Equations and Problem Solving

4.4 Solving Systems of Equations by Matrices

4.5 Systems of Linear Inequalities

**5. Exponents, Polynomials, and Polynomial Functions**

5.1 Exponents and Scientific Notation

5.2 More Work with Exponents and Scientific Notation

5.3 Polynomials and Polynomial Functions

5.4 Multiplying Polynomials

5.5 The Greatest Common Factor and Factoring by Grouping

5.6 Factoring Trinomials

5.7 Factoring by Special Products

5.8 Solving Equations by Factoring and Problem Solving

**6. Rational Expressions**

6.1 Rational Functions and Multiplying and Dividing Rational Expressions

6.2 Adding and Subtracting Rational Expressions

6.3 Simplifying Complex Fractions

6.4 Dividing Polynomials: Long Division and Synthetic Division

6.5 Solving Equations Containing Rational Expressions

6.6 Rational Equations and Problems Solving

6.7 Variation and Problem Solving

**7. Rational Exponents, Radicals, and Complex Numbers**

7.1 Radicals and Radical Functions

7.2 Rational Exponents

7.3 Simplifying Radical Expressions

7.4 Adding, Subtracting, and Multiplying Radical Expressions

7.5 Rationalizing Denominators and Numerators of Radical Expressions

7.6 Radical Equations and Problem Solving

7.7 Complex Numbers

**8. Quadratic Equations and Functions**

8.1 Solving Quadratic Equations by Completing the Square

8.2 Solving Quadratic Equations by the Quadratic Formula

8.3 Solving Equations by Using Quadratic Methods

8.4 Nonlinear Inequalities on One Variable

8.5 Quadratic Functions and Their Graphs

8.6 Further Graphing of Quadratic Functions

**9. Exponential and Logarithmic Functions**

9.1 The Algebra of Functions; Composite Functions

9.2 Inverse Functions

9.3 Exponential Functions

9.4 Exponential Growth and Decay Functions

9.5 Logarithmic Functions

9.6 Properties of Logarithms

9.7 Common Logarithms, Natural Logarithms, and Change of Base

9.8 Exponential and Logarithmic Equations and Problem Solving

**10. Conic Sections**

10.1 The Parabola and the Circle

10.2 The Ellipse and the Hyperbola

10.3 Solving Nonlinear Systems of Equations

10.4 Nonlinear Inequalities and Systems of Inequalities

**11. Sequences, Series, and the Binomial Theorem**

11.1 Sequences

11.2 Arithmetic and Geometric Sequences

11.3 Series

11.4 Partial Sums of Arithmetic and Geometric Sequences

11.5 The Binomial Theorem

** **

**Appendix A. Geometry**

**Appendix B. Stretching and Compressing Graphs of Absolute Value Functions**

**Appendix C. Solving Systems of Equations Using Determinants**

**Appendix D. An Introduction to Using a Graphing Utility**

**Appendix E. Contents of Student Resources**