## Table of Contents

**1. Basic Concepts**

1.1 Study Skills for Success in Mathematics, and Using a Calculator

1.2 Sets and Other Basic Concepts

1.3 Properties of and Operations with Real Numbers

1.4 Order of Operations

1.5 Exponents

1.6 Scientific Notation

**2. Equations and Inequalities**

2.1 Solving Linear Equations

2.2 Problem Solving and Using Formulas

2.3 Applications of Algebra

2.4 Additional Application Problems

2.5 Solving Linear Inequalities

2.6 Solving Equations and Inequalities Containing Absolute Values

**3. Graphs and Functions**

3.1 Graphs

3.2 Functions

3.3 Linear Functions: Graphs and Applications

3.4 The Slope-Intercept Form of a Linear Equation

3.5 The Point-Slope Form of a Linear Equation

3.6 The Algebra of Functions

3.7 Graphing Linear Inequalities

**4. Systems of Equations and Inequalities**

4.1 Solving Systems of Linear Equations in Two Variables

4.2 Solving Systems of Linear Equations in Three Variables

4.3 Systems of Linear Equations: Applications and Problem Solving

4.4 Solving Systems of Equations Using Matrices

4.5 Solving Systems of Equations Using Determinants and Cramer’s Rule

4.6 Solving Systems of Linear Inequalities

**5. Polynomials and Polynomial Equations**

5.1 Addition and Subtraction of Polynomials

5.2 Multiplication of Polynomials

5.3 Division of Polynomials and Synthetic Division

5.4 Factoring a Monomial from a Polynomial and Factoring by Grouping

5.5 Factoring Trinomials

5.6 Special Factoring Formulas

5.7 A General Review of Factoring

5.8 Polynomial Equations

**6. Rational Expressions and Equations**

6.1 The Domains of Rational Functions and Multiplication and Division of Rational Expressions

6.2 Addition and Subtraction of Rational Expressions

6.3 Complex Fractions

6.4 Solving Rational Equations

6.5 Rational Equations: Applications and Problem Solving

6.6 Variation

**7. Roots, Radicals, and Complex Numbers**

7.1 Roots and Radicals

7.2 Rational Exponents

7.3 Simplifying Radicals

7.4 Adding, Subtracting, and Multiplying Radicals

7.5 Dividing Radicals

7.6 Solving Radical Equations

7.7 Complex Numbers

**8. Quadratic Functions**

8.1 Solving Quadratic Equations by Completing the Square

8.2 Solving Quadratic Equations by the Quadratic Formula

8.3 Quadratic Equations: Applications and Problem Solving

8.4 Writing Equations in Quadratic Form

8.5 Graphing Quadratic Functions

8.6 Quadratic and Other Inequalities in One Variable

**9. Exponential and Logarithmic Functions**

9.1 Composite and Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Common Logarithms

9.6 Exponential and Logarithmic Equations

9.7 Natural Exponential and natural Logarithmic Functions

**10. Conic Sections**

10.1 The Parabola and the Circle

10.2 The Ellipse

10.3 The Hyperbola

10.4 Nonlinear Systems of Equations and Their Applications

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

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

**Appendix: Geometric Formulas**