Intermediate Algebra

1. Real Numbers and Expressions 1.1 Sets and the Structure of Algebra 1.2 Operations with Real Numbers; Properties of Real Numbers 1.3 Exponents, Roots, and Order of Operations 1.4 Evaluating and Rewriting Expressions 2. Linear Equations and Inequalities in One Variable 2.1 Linear Equations and Formulas 2.2 Solving Problems 2.3 Solving Linear Inequalities 2.4 Compound Inequalities 2.5 Equations Involving Absolute Value 2.6 Inequalities Involving Absolute Value 3. Equations and Inequalities in Two Variables; Functions 3.1 Graphing Linear Equations 3.2 The Slope of a Line 3.3 The Equation of a Line 3.4 Graphing Linear Inequalities 3.5 Introduction to Functions and Function Notation 4. Systems of Linear 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 Solving Applications Using Systems of Equations 4.4 Solving Systems of Linear Equations Using Matrices 4.5 Solving Systems of Linear Equations Using Cramer's Rule 4.6 Solving Systems of Linear Inequalities 5. Exponents, Polynomials, and Polynomial Functions 5.1 Exponents and Scientific Notation 5.2 Polynomials and Polynomial Functions 5.3 Multiplying Polynomials 5.4 Dividing Polynomials 5.5 Synthetic Division and the Remainder Theorem 6. Factoring 6.1 Greatest Common Factor and Factoring by Grouping 6.2 Factoring Trinomials 6.3 Factoring Special Products and Factoring Strategies 6.4 Solving Equations by Factoring 7. Rational Expressions and Equations 7.1 Simplifying, Multiplying, and Dividing Rational Expressions 7.2 Adding and Subtracting Rational Expressions 7.3 Simplifying Complex Rational Expressions 7.4 Solving Equations Containing Rational Expressions 7.5 Applications with Rational Expressions; Variation 8. Rational Exponents, Radicals, and Complex Numbers 8.1 Radical Expressions and Functions 8.2 Rational Exponents 8.3 Multiplying, Dividing, and Simplifying Radicals 8.4 Adding, Subtracting, and Multiplying Radical Expressions 8.5 Rationalizing Numerators and Denominators of Radical Expressions 8.6 Radical Equations and Problem Solving 8.7 Complex Numbers 9. Quadratic Equations and Functions 9.1 Completing the Square 9.2 Solving Quadratic Equations Using the Quadratic Formula 9.3 Solving Equations That Are Quadratic in Form 9.4 Graphing Quadratic Functions 9.5 Solving Nonlinear Inequalities 10. Exponential and Logarithmic Functions 10.1 Composite and Inverse Functions 10.2 Exponential Functions 10.3 Logarithmic Functions 10.4 Properties of Logarithms 10.5 Common and Natural Logarithms 10.6 Exponential and Logarithmic Equations with Applications 11. Conic Sections 11.1 Parabolas and the Circles 11.2 Ellipses and Hyperbolas 11.3 Nonlinear Systems of Equations 11.4 Nonlinear Inequalities and Systems of Inequalities Appendices A. Arithmetic Sequences and Series B. Geometric Sequences and Series C. The Binomial Theorem D. Permutations and Combinations (available online via MyMathLab) E. Probability (available online via MyMathLab)