Intermediate Algebra with Trigonometry

1 Basic Properties and Definitions 1.1 Basic Definitions 1.2 The Real Numbers, Opposites, Reciprocals, and Absolute Value 1.3 Graphing Simple and Compound Inequalities 1.4 Properties of Real Numbers 1.5 Addition and Subtraction of Real Numbers 1.6 Multiplication, Division, and Order of Operation for Real Numbers Summary and Review Test2 First-Degree Equations and Inequalities 2.1 First-Degree Equations 2.2 First-Degree Inequalities 2.3 Equations with Absolute Value 2.4 Inequalities Involving Absolute Value 2.5 Formulas 2.6 Word Problems Summary and Review Test3 Exponents and Polynomials 3.1 Properties of Exponents I 3.2 Properties of Exponents II 3.3 Polynomials, Sums, and Differences 3.4 Multiplication of Polynomials 3.5 The Greatest Common Factor and Factoring by Grouping 3.6 Factoring Trinomials 3.7 Special Factoring Summary and Review Test4 Rational Expressions 4.1 Basic Properties and Reducing to Lowest Terms 4.2 Division of Polynomials 4.3 Multiplication and Division of Rational Expressions 4.4 Addition and Subtraction of Rational Expressions 4.5 Complex Fractions 4.6 Equations Involving Rational Expressions 4.7 Word Problems Summary and Review Test5 Rational Exponents and Roots 5.1 Rational Exponents 5.2 Simplified Form for Radicals 5.3 Addition and Subtraction of Radical Expressions 5.4 Multiplication and Division of Radical Expressions 5.5 Equations with Radicals 5.6 Addition and Subtraction of Complex Numbers 5.7 Multiplication and Division of Complex Numbers Summary and Review Test6 Quadratic Equations 6.1 Solving Quadratic Equations by Factoring 6.2 Completing the Square 6.3 The Quadratic Formula 6.4 Equations Quadratic in Form 6.5 Word Problems 6.6 More on Inequalities Summary and Review Test7 Linear Equations and Inequalities 7.1 Graphing in Two Dimensions 7.2 The Slope of a Line 7.3 The Equation of a Straight Line 7.4 Linear Inequalities in Two Variables 7.5 Variation Summary and Review Test8 Systems of Linear Equations 8.1 Systems of Linear Equations in Two Variables 8.2 Systems of Linear Equations in Three Variables 8.3 Introduction to Determinants 8.4 Cramer's Rule 8.5 Word Problems Summary and Review Test9 The Conic Sections 9.1 Graphing Parabolas 9.2 The Circle 9.3 Ellipses and Hyperbolas 9.4 Second-Degree Inequalities 9.5 Nonlinear Systems Summary and Review Test10 Relations and Functions 10.1 Relations and Functions 10.2 Function Notation 10.3 Algebra with Functions 10.4 Classification of Functions 10.5 The Inverse of a Function Summary and Review Test11 Logarithms 11.1 Logarithms Are Exponents 11.2 Properties of Logarithms 11.3 Common Logarithms and Computations 11.4 Exponential Equations and Change of Base 11.5 Word Problems Summary and Review Test12 Sequences and Series 12.1 Sequences 12.2 Series and Summation Notation 12.3 Arithmetic Progressions 12.4 Geometric Progressions 12.5 The Binomial Expansion Summary and Review Test13 Introduction to Trigonometry 13.1 Degrees, Radians, and Special Triangles 13.2 Trigonometric Functions 13.3 Tables and Calculators 13.4 Graphing I: Amplitude and Period 13.5 Graphing II: Phase Shift Summary and Review Test14 Trigonometric Identities and Equations 14.1 Proving Identities 14.2 Sum and Difference Formulas 14.3 Double-Angle and Half-Angle Formulas 14.4 Solving Trigonometric Equations Summary and Review Test15 Triangles 15.1 Definition II: Right Triangle Trigonometry 15.2 The Law of Sines 15.3 The Ambiguous Case 15.4 The Law of Cosines Summary and Review TestAppendix A: Synthetic DivisionAppendix B: The DiscriminantAppendix C: Table of Powers, Roots, and Prime FactorsAppendix D: Table of Common LogarithmsAppendix E: Table of Trigonometric FunctionsAnswers to Odd-Numbered Exercises and Chapter TestsIndex