Algebra and Trigonometry

Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, Proofs in Mathematics, and P.S. Problem Solving. P. Prerequisites P.1 Review of Real Numbers and Their Properties P.2 Exponents and Radicals P.3 Polynomials and Special Products P.4 Factoring Polynomials P.5 Rational Expressions P.6 Errors and the Algebra of Calculus P.7 The Rectangular Coordinate System and Graphs 1. Equations, Inequalities, and Mathematical Modeling 1.1 Graphs of Equations 1.2 Linear Equations in One Variable 1.3 Modeling with Linear Equations 1.4 Quadratic Equations and Applications 1.5 Complex Numbers 1.6 Other Types of Equations 1.7 Linear Inequalities in One Variable 1.8 Other Types of Inequalities 2. Functions and Their Graphs 2.1 Linear Equations in Two Variables 2.2 Functions 2.3 Analyzing Graphs of Functions 2.4 A Library of Parent Functions 2.5 Transformations of Functions 2.6 Combinations of Functions: Composite Functions 2.7 Inverse Functions Cumulative Test: Chapters P-2 3. Polynomial Functions 3.1 Quadratic Functions and Models 3.2 Polynomial Functions of Higher Degree 3.3 Polynomial and Synthetic Division 3.4 Zeros of Polynomial Functions 3.5 Mathematical Modeling and Variation 4. Rational Functions and Conics 4.1 Rational Functions and Asymptotes 4.2 Graphs of Rational Functions 4.3 Conics 4.4 Translations of Conics 5. Exponential and Logarithmic Functions 5.1 Exponential Functions and Their Graphs 5.2 Logarithmic Functions and Their Graphs 5.3 Properties of Logarithms 5.4 Exponential and Logarithmic Equations 5.5 Exponential and Logarithmic Models Cumulative Test: Chapters 3-5 6. Trigonometry 6.1 Angles and Their Measure 6.2 Right Triangle Trigonometry 6.3 Trigonometric Functions of Any Angle 6.4 Graphs of Sine and Cosine Functions 6.5 Graphs of Other Trigonometric Functions 6.6 Inverse Trigonometric Functions 6.7 Applications and Models 7. Analytic Trigonometry 7.1 Using Fundamental Identities 7.2 Verifying Trigonometric Identities 7.3 Solving Trigonometric Equations 7.4 Sum and Difference Formulas 7.5 Multiple-Angle and Product-to-Sum Formulas 8. Additional Topics in Trigonometry 8.1 Law of Sines 8.2 Law of Cosines 8.3 Vectors in the Plane 8.4 Vectors and Dot Products 8.5 Trigonometric Form of a Complex Number Cumulative Test: Chapters 6-8 9. Systems of Equations and Inequalities 9.1 Linear and Nonlinear Systems of Equations 9.2 Two-Variable Linear Systems 9.3 Multivariable Linear Systems 9.4 Partial Fractions 9.5 Systems of Inequalities 9.6 Linear Programming 10. Matrices and Determinants 10.1 Matrices and Systems of Equations 10.2 Operations with Matrices 10.3 The Inverse of a Square Matrix 10.4 The Determinant of a Square Matrix 10.5 Applications of Matrices and Determinants 11. Sequences, Series, and Probability 11.1 Sequences and Series 11.2 Arithmetic Sequences and Partial Sums 11.3 Geometric Sequences and Series 11.4 Mathematical Induction 11.5 The Binomial Theorem 11.6 Counting Principles 11.7 Probability Cumulative Test: Chapters 9-11 Appendix A. Concepts in Statistics (web) A.1 Representing Data A.2 Measures of Central Tendency and Dispersion A.3 Least Squares Regression