## Table of Contents

**1. Real Numbers**

1.1 Study Skills for Success in Mathematics

1.2 Problem Solving

1.3 Fractions

1.4 The Real Number System

1.5 Inequalities and Absolute Value

1.6 Addition of Real Numbers

1.7 Subtraction of Real Numbers

1.8 Multiplication and Division of Real Numbers

1.9 Exponents, Parentheses, and the Order of Operations

1.10 Properties of the Real Number System

**2. Solving Linear Equations and Inequalities**

2.1 Combining Like Terms

2.2 The Addition Property of Equality

2.3 The Multiplication Property of Equality

2.4 Solving Linear Equations with a Variable on Only One Side of the Equation

2.5 Solving Linear Equations with the Variable on Both Sides of the Equation

2.6 Formulas

2.7 Ratios and Proportions

2.8 Inequalities in One Variable

**3. Applications of Algebra**

3.1 Changing Application Problems into Equations

3.2 Solving Application Problems

3.3 Geometric Problems

3.4 Motion, Money, and Mixture Problems

**4. Exponents and Polynomials**

4.1 Exponents

4.2 Negative Exponents

4.3 Scientific Notation

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials

4.6 Division of Polynomials

**5. Factoring**

5.1 Factoring a Monomial from a Polynomial

5.2 Factoring by Grouping

5.3 Factoring Trinomials of the Form *ax*^{2} + *bx + c*, *a* = 1

5.4 Factoring Trinomials of the Form *ax*^{2} + *bx + c*, *a* ≠ 1

5.5 Special Factoring Formulas and a General Review of Factoring

5.6 Solving Quadratic Equations Using Factoring

5.7 Applications of Quadratic Equations

**6. Rational Expressions and Equations**

6.1 Simplifying Rational Expressions

6.2 Multiplication and Division of Rational Expressions

6.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator

6.4 Addition and Subtraction of Rational Expressions

6.5 Complex Fractions

6.6 Solving Rational Equations

6.7 Rational Equations: Applications and Problem Solving

6.8 Variation

**7. Graphing Linear Equations**

7.1 The Cartesian Coordinate System and Linear Equations in Two Variables

7.2 Graphing Linear Equations

7.3 Slope of a Line

7.4 Slope-Intercept and Point-Slope Forms of a Linear Equation

7.5 Graphing Linear Inequalities

7.6 Functions

**8. Systems of Linear Equations**

8.1 Solving Systems of Equations Graphically

8.2 Solving Systems of Equations by Substitution

8.3 Solving Systems of Equations by the Addition Method

8.4 Systems of Equations: Applications and Problem Solving

8.5 Solving Systems of Linear Inequalities

**9. Roots and Radicals**

9.1 Evaluating Square Roots

9.2 Simplifying Square Roots

9.3 Adding, Subtracting, and Multiplying Square Roots

9.4 Dividing Square Roots

9.5 Solving Radical Equations

9.6 Radicals: Applications and Problem Solving

9.7 Higher Roots and Rational Exponents

**10. Quadratic Equations**

10.1 The Square Root Property

10.2 Solving Quadratic Equations by Completing the Square

10.3 Solving Quadratic Equations by the Quadratic Formula

10.4 Graphing Quadratic Equations

10.5 Complex Numbers

**Appendix A: Review of Decimals and Percent**

**Appendix B: Geometry**