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| Prologue: Principles of Problem Solving | |
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| Prerequisites | |
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| Modeling the Real World | |
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| Real Numbers and Their Properties | |
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| The Real Number Line and Order | |
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| Integer Exponents | |
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| Rational Exponents and Radicals | |
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| Algebraic Expressions | |
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| Factoring Algebraic Expressions | |
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| Rational Expressions | |
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| Chapter P Review | |
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| Chapter P Test | |
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| Focus on Problem Solving: General Principles | |
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| Equations and Inequalities | |
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| Chapter Overview | |
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| Basic Equations | |
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| Modeling with Equations | |
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| Quadratic Equations | |
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| Complex Numbers | |
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| Other Types of Equations | |
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| Inequalities | |
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| Absolute Value Equations and Inequalities | |
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Chapter 1 Review | |
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Chapter 1 Test | |
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| Focus on Modeling: Making the Best Decisions | |
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| Coordinates and Graphs | |
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| Chapter Overview | |
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| The Coordinate Plane | |
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| Graphs of Equations in Two Variables | |
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| Graphing Calculators: Solving Equations Graphically | |
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| Lines | |
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| Modeling: Variation | |
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Chapter 2 Review | |
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Chapter 2 Test | |
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| Focus on Modeling: Fitting Lines to Data | |
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| Cumulative Review Test: Chapters 1 and 2 | |
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| Functions | |
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| Chapter Overview | |
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| What Is a Function? | |
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| Graphs of Functions | |
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| Getting Information from the Graph of a Function | |
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| Average Rate of Change of a Function | |
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| Transformations of Functions | |
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| Combining Functions | |
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| One-to-One Functions and Their Inverses | |
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Chapter 3 Review | |
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Chapter 3 Test | |
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| Focus on Modeling: Functions as Models | |
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| Polynomial and Rational Functions | |
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| Chapter Overview | |
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| Quadratic Functions and Models | |
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| Polynomial Functions and Their Graphs | |
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| Dividing Polynomials | |
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| Real Zeros of Polynomials | |
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| Complex Numbers | |
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| Complex Zeros and the Fundamental Theorem of Algebra | |
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| Rational Functions | |
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Chapter 4 Review | |
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Chapter 4 Test | |
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| Focus on Modeling: Fitting Polynomial Curves to Data | |
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| Exponential and Logarithmic Functions | |
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| Chapter Overview | |
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| Exponential Functions | |
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| The Natural Exponential Function | |
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| Logarithmic Functions | |
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| Laws of Logarithms | |
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| Exponential and Logarithmic Equations | |
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| Modeling with Exponential and Logarithmic Functions | |
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Chapter 5 Review | |
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| Chapter 5t Test | |
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| Focus on Modeling: Fitting Exponential and Power Curves to Data | |
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| Cumulative Review Test: Chapters 3, 4, and 5 | |
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| Trigonometric Functions: Right Triangle Approach | |
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| Chapter Overview | |
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| Angle Measure | |
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| Trigonometry of Right Triangles | |
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| Trigonometric Functions of Angles | |
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| Inverse Trigonometric Functions and Triangles | |
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| The Law of Sines | |
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| The Law of Cosines | |
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Chapter 6 Review | |
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Chapter 6 Test | |
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| Focus on Modeling: Surveying | |
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| Trigonometric Functions: Unit Circle Approach | |
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| Chapter Overview | |
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| The Unit Circle | |
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| Trigonometric Functions of Real Numbers | |
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| Trigonometric Graphs | |
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| More Trigonometric Graphs | |
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| Inverse Trigonometric Functions and Their Graphs | |
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| Modeling Harmonic Motion | |
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Chapter 7 Review | |
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Chapter 7 Test | |
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| Focus on Modeling: Fitting Sinusoidal Curves to Data | |
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| Analytic Trigonometry | |
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| Chapter Overview | |
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| Trigonometric Identities | |
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| Addition and Subtraction Formulas | |
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| Double-Angle, Half-Angle, and Sum-Product Identities | |
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| Basic Trigonometric Equations | |
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| More Trigonometric Equations | |
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Chapter 8 Review | |
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Chapter 8 Test | |
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| Focus on Modeling: Traveling and Standing Waves | |
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| Cumulative Review Test: Chapters 6, 7, and 8 | |
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| Polar Coordinates and Parametric Equations | |
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| Chapter Overview | |
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| Polar Coordinates | |
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| Graphs of Polar Equations | |
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| Polar Form of Complex Numbers; DeMoivre's Theorem | |
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| Plane Curves and Parametric Equations | |
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Chapter 9 Review | |
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Chapter 9 Test | |
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| Focus on Modeling: The Path of a Projectile | |
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| Vectors in Two and Three Dimensions | |
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| Chapter Overview | |
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| Vectors in Two Dimensions | |
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| The Dot Product | |
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| Three �Dimensional Coordinate Geometry | |
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| Vectors in Three Dimensions | |
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| The Cross Product | |
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| Equations of Lines and Planes | |
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Chapter 10 Review | |
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Chapter 10 Test | |
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| Focus on Modeling: Vector Fields | |
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| Cumulative Review Test: Chapters 9 and 10 | |
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| Systems of Equations and Inequalities | |
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| Chapter Overview | |
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| Systems of Linear Equations in Two Variables | |
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| Systems of Linear Equations in Several Variables | |
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| Systems of Linear Equations: Matrices | |
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| The Algebra of Matrices | |
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| Inverses of Matrices and Matrix Equations | |
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| Determinants and Cramer's Rule | |
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| Partial Fractions | |
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| Systems of Non-Linear Equations | |
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| Systems | |
