| |
| |
| P. Prerequisites | |
| |
| |
| Modeling the Real World | |
| |
| |
| Real Numbers | |
| |
| |
| Integer Exponents | |
| |
| |
| Rational Exponents and Radicals | |
| |
| |
| Algebraic Expressions | |
| |
| |
| Discovery Project: Visualizing a Formula | |
| |
| |
| Factoring Algebraic Expressions | |
| |
| |
| Rational Expressions | |
| |
| |
| Chapter P Review | |
| |
| |
| Chapter P Test | |
| |
| |
| Focus on Problem Solving: General Principles | |
| |
| |
| |
| Equations and Inequalities | |
| |
| |
| Basic Equations | |
| |
| |
| Modeling with Linear Equations | |
| |
| |
| Discovery Project: Equations Through the Ages | |
| |
| |
| Quadratic Equations | |
| |
| |
| Complex Numbers | |
| |
| |
| Other Types of Equations | |
| |
| |
| Inequalities | |
| |
| |
| Absolute Value Equations and Inequalities | |
| |
| |
| Chapter 1 Review | |
| |
| |
| Chapter 1 Test | |
| |
| |
| Focus on Modeling: Making the Best Decisions | |
| |
| |
| |
| Coordinates and Graphs | |
| |
| |
| The Coordinate Plane | |
| |
| |
| Discovery Project: Visualizing Data | |
| |
| |
| Graphs of Equations in Two Variables | |
| |
| |
| Graphing Calculators: Solving Equations and Inequalities Graphically | |
| |
| |
| Lines | |
| |
| |
| Modeling: Variation | |
| |
| |
| Chapter 2 Review | |
| |
| |
| Chapter 2 Test | |
| |
| |
| Focus on Modeling: Fitting Lines to Data | |
| |
| |
| |
| Functions | |
| |
| |
| What is a Function | |
| |
| |
| Graphs of Functions | |
| |
| |
| Discovery Project: Relations and Functions | |
| |
| |
| Increasing and Decreasing Functions: Average Rate of Change | |
| |
| |
| Transformations of Functions | |
| |
| |
| Quadratic Functions: Maxima and Minima | |
| |
| |
| Combining Functions | |
| |
| |
| Discovery Project: Iteration and Chaos | |
| |
| |
| One-to-One Functions and Their Inverses | |
| |
| |
| Chapter 3 Review | |
| |
| |
| Chapter 3 Test | |
| |
| |
| Focus on Modeling: Modeling With Functions | |
| |
| |
| |
| Polynomial and Rational Functions | |
| |
| |
| Polynomial Functions and Their Graphs | |
| |
| |
| Dividing Polynomials | |
| |
| |
| Real Zeros of Polynomials | |
| |
| |
| Discovery Project: Zeroing in on a Zero | |
| |
| |
| Complex Zeros and the Fundamental Theorem of Algebra | |
| |
| |
| Rational Functions | |
| |
| |
| Chapter 4 Review | |
| |
| |
| Chapter 4 Test | |
| |
| |
| Focus on Modeling: Fitting Polynomial Curves to Data | |
| |
| |
| |
| Exponential and Logarithmic Functions | |
| |
| |
| Exponential Functions | |
| |
| |
| Discovery Project: Exponential Explosion | |
| |
| |
| Logarithmic Functions | |
| |
| |
| Laws of Logarithms | |
| |
| |
| Exponential and Logarithmic Equations | |
| |
| |
| Modeling with Exponential and Logarithmic Functions | |
| |
| |
| Chapter 5 Review | |
| |
| |
| Chapter 5 Test | |
| |
| |
| Focus on Modeling: Fitting Exponential and Power Curves to Data | |
| |
| |
| |
| Trigonometric Functions of Angles | |
| |
| |
| Angle Measure | |
| |
| |
| Trigonometry of Right Triangles | |
| |
| |
| Trigonometric Functions of Angles | |
| |
| |
| Discovery Project: Similarity | |
| |
| |
| The Law of Sines | |
| |
| |
| The Law of Cosines | |
| |
| |
| Chapter 6 Review | |
| |
| |
| Chapter 6 Test | |
| |
| |
| Focus on Modeling: Surveying | |
| |
| |
| |
| Trigonometric Functions of Real Numbers | |
| |
| |
| The Unit Circle | |
| |
| |
| Trigonometric Functions of Real Numbers | |
| |
| |
| Trigonometric Graphs | |
| |
| |
| Discovery Project: Predator-Prey Models | |
| |
| |
| More Trigonometric Graphs | |
| |
| |
| Modeling Harmonic Motion | |
| |
| |
| Chapter 7 Review | |
| |
| |
| Chapter 7 Test | |
| |
| |
| Focus on Modeling: Fitting Sinusoidal Curves to Data | |
| |
| |
| |
| Analytic Trigonometry | |
| |
| |
| Trigonometric Identities | |
| |
| |
| Addition and Subtraction Formulas | |
| |
| |
| Double-Angle, Half-Angle, and Sum-Product Identities | |
| |
| |
| Inverse Trigonometric Functions | |
| |
| |
| Discovery Project: Where to Sit at the Movies | |
| |
| |
| Trigonometric Equations | |
| |
| |
| Chapter 8 Review | |
| |
| |
| Chapter 8 Test | |
| |
| |
| Focus on Modeling: Traveling and Standing Waves | |
| |
| |
| |
| Polar Coordinates and Vectors | |
| |
| |
| Polar Coordinates | |
| |
| |
| Graphs of Polar Equations | |
| |
| |
| Polar Form of Complex Numbers | |
| |
| |
| DeMoivre's Theorem | |
| |
| |
| Discovery Project: Fractals | |
| |
| |
| Vectors | |
| |
| |
| The Dot Product | |
| |
| |
| Discovery Project: Sailing Against the Wind | |
| |
| |
| Chapter 9 Review | |
| |
| |
| Chapter 9 Test | |
| |
| |
| Focus on Modeling: Mapping the World | |
| |
| |
| |
| Systems of Equations and Inequalities | |
| |
| |
| Systems of Equations | |
| |
| |
| Systems of Linear Equations in Two Variables | |
| |
| |
| Systems of Linear Equations in Several Variables | |
| |
| |
| Discovery Project: Best Fit versus Exact Fit | |
| |
| |
| Systems of Linear Equations: Matrices | |
| |
| |
| The Algebra of Matrices | |
| |
| |
| Discovery Project: Will the Species Survive | |
| |
| |
| Inverses of Matrices and Matrix Equations | |
| |
| |
| Discovery Project: Computer Graphics | |
| |
| |
| I Determinantsand Cramer's Rule | |
| |
| |
| Partial Fractions | |
| |
| |
| Systems of Inequalities | |
| |
| |
| Chapter 10 Review | |
| |
| |
| Chapter 10 Test | |
| |
| |
| Focus on Modeling: Linear Programming | |
| |
| |
| |
| Analytic Geometry | |
| |
| |
| Parabolas | |
| |
| |
| Ellipses | |
| |
| |
| Hyperbolas | |
| |
| |
| Discovery Project: Conics in Architecture | |
| |
| |
| Shifted Conics | |
| |
| |
| Rotation of Axes | |
| |
| |
| Discovery Project: Computer Graphics II | |
| |
| |
| Polar Equations of Conics | |
| |
| |
| Plane Curves and Parametric Equations | |
| |
| |
| Chapter 11 Review | |
| |
| |
| Chapter 11 Test | |
| |
| |
| Focus on Modeling: The Path of a Projectile | |
| |
| |
| |
| Sequences And Series | |
| |
| |
| Sequences and Summation Notation | |
| |
| |
| Arithmetic Sequences | |
| |
| |
| Geometric Sequences | |
| |
| |
| Discovery Project: Finding Patterns | |
| |
| |
| Mathematics of Finance | |
| |
| |
| Mathematical Induction | |
| |
| |
| The Binomial Theorem | |
| |
| |
| Chapter 12 Review | |
| |
| |
| Chapter 12 Test | |
| |
| |
| Focus on Modeling: Modeling with Recursive Sequences | |
| |
| |
| |
| Counting And Probability | |
| |
| |
| Counting Principles | |
| |
| |
| Permutations and Combinations | |
| |
| |
| Probability | |
| |
| |
| Discovery Project: Small Samples, Big Results | |
| |
| |
| Binomial Probability | |
| |
| |
| Expected Value | |
| |
| |
| Chapter 13 Review | |
| |
| |
| Chapter 13 Test | |
| |
| |
| Focus on Modeling: The Monte Carlo Method | |