1. The Real Number System. Fractions. The Real Numbers. Ordered Pairs and Graphs. Basic Rules of Algebra. Addition of Real Numbers. Subtraction of Real Numbers. Multiplication and Division of Real Numbers. Exponents, Order of Operations, and Mathematical Models. 2. Linear Equations and Inequalities in One Variable. The Addition Property of Equality. The Multiplication Property of Equality. Solving Linear Equations. Formulas and Percents. An Introduction to Problem Solving. Problem Solving in Geometry. Solving Linear Inequalities. 3. Linear Equations in Two Variables. Graphing Linear Equations. Graphing Linear Equations Using Intercepts. Slope. The Slope-Intercept Form of the Equation of a Line. The Point-Slope Form of the Equation of a Line. 4. Systems of Linear Equations. Solving Systems of Linear Equations by Graphing. Solving Systems of Linear Equations by the Substitution Method. Solving Systems of Linear Equations by the Addition Method. Problem Solving Using Systems of Equations. 5. Exponents and Polynomials. Adding and Subtracting Polynomials. Multiplying Polynomials. Special Products. Polynomials in Several Variables. Dividing Polynomials. Dividing Polynomials by Binomials; Synthetic Division. Negative Exponents and Scientific Notation. 6. Factoring Polynomials. The Greatest Common Factor and Factoring by Grouping. Factoring Trinomials Whose Leading Coefficient Is One. Factoring Trinomials Whose Leading Coefficient Is Not One. Factoring Special Forms. A General Factoring Strategy. Solving Quadratic Equations by Factoring. 7. Rational Expressions. Rational Expressions and Their Simplification. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions with the Same Denominator. Adding and Subtracting Rational Expressions with Different Denominators. Complex Rational Expressions. Solving Rational Equations. Applications Using Rational Equations and Proportions. Modeling Using Variation. 8. Functions, More on Systems of Linear Functions. Introduction to Functions. The Algebra of Functions. Systems of Linear Equations in Three Variables. Matrix Solutions to Systems Linear Equations. Determinants and Cramer's Rule. 9. Inequalities and Problem Solving. Interval Notation and Business Applications Using Linear Inequalities. Compound Inequalities. Equations and Inequalities Involving Absolute Value. Linear Inequalities Containing Two Variables. Linear Programming. 10. Radicals, Radical Functions, and Rational Exponents. Radical Expressions and Functions. Rational Exponents. Multiplying and Simplifying Radical Expressions. Adding, Subtracting, and Dividing Radical Expressions. Multiplying with More Than One Term and Rationalizing Denominators. Radical Equations. Complex Numbers. 11. Quadratic Equations and Functions. The Square Root Property and Completing the Square. The Quadratic Formula. Quadratic Functions and Their Graphs. Equations Quadratic in Form. Quadratic and Rational Inequalities. 12. Exponential and Logarithmic Functions. Exponential Functions. Composite and Inverse Functions. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Exponential Growth and Decay; Modeling Data. 13. Conic Sections and Systems of Nonlinear Equations. Distance and Midpoint Formulas; Circles. The Ellipse. The Hyperbola. The Parabola; Identifying Conic Sections. Systems of Nonlinear Equations in Two Variables. 14. Sequences, Induction, and Probability. Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences and Series. The Binomial Theorem. Counting Principles, Permutations, and Combinations. Probability. Appendix A: Are You Prepared for Intermediate Algebra? Appendix B: Where Did That Come From? Selected Proofs.

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