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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 ï¿½Dimensional 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 | |