**Topical Outline:**

**1. The Language of Algebra**

A. Arithmetic to Algebra

B. Properties of Real Numbers

C. Adding, Subtracting, Multiplying, and Dividing Real Numbers

D. Evaluating Algebraic Expressions

E. Adding, Subtracting, Multiplying, and Dividing Terms

**2. Equations and Inequalities**

A. Solving Equations by the Addition and Multiplication
Properties

B. Formulas and Problem Solving

C. Applications of Linear Equations

D. Solving Percent Applications

E. Inequalities

**3. Polynomials**

A. Exponents and Polynomials

B. Negative Exponents

C. Adding, Subtracting, Multiplying, and Dividing Polynomials

D. Special Products

**4. Factoring**

A. Greatest Common Factor

B. Factoring Trinomials of the Form x^{2} + bx + c

C. Factoring Trinomials of the Form ax^{2} + bx + c

D. Difference of Squares and Perfect Square Trinomials

E. Factoring by Grouping

F. Using the ac Method to Factor

G. Solving Quadratic Equations by Factoring

**5.Rational Expressions**

A. Simplifying Rational Expressions

B. Multiplying and Dividing Rational Expressions

C. Adding and Subtracting Like Rational Expressions

D. Adding and Subtracting Unlike Rational Expressions

E. Equations involving Rational Expressions

F. Applications of Rational Expressions

G. Complex Rational Expressions

**6. An Introduction to Graphing**

A. Solutions of Equations in Two Variables

B. The Rectangular Coordinate System

C. Graphing Linear Equations

D. The Slope of a Line

**7. Graphing and Inequalities**

A. The Slope-Intercept Form

B. Parallel and Perpendicular Lines

C. The Point-Slope Form

D. Graphing Linear Inequalities

**8. Systems of linear equations**

A. Solving by Graphing

B. Solving by Adding

C. Solving by Substitution

**9. Exponents and Radicals**

A. Roots and Radicals

B. Simplifying Radical Expressions

C. Adding, Subtracting, Multiplying, and Dividing Radicals

D. Solving Radical Equations

E. Applications of the Pythagorean Theorem

**10. Quadratic Equations**

A. Quadratic Equations

B. The Quadratic formula

C. Graphing Quadratic Equations