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Fundamentals | |

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Chapter Overview | |

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Real Numbers | |

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Exponents and Radicals | |

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Algebraic Expressions | |

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Fractional Expressions | |

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Equations | |

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Modeling with Equations | |

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Inequalities | |

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Coordinate Geometry | |

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Solving Equations and Inequalities Graphically | |

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Lines | |

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Modeling Variation | |

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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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Review | |

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TeSt. 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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Review | |

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TeSt. 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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Review | |

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TeSt. Focus on Modeling: Fitting Exponential and Power Curves to Data | |

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Cumulative Review Test: Chapters 2, 3, and 4 | |

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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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Review | |

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TeSt. Focus on Modeling: Fitting Sinusoidal Curves to Data | |

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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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Review | |

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TeSt. Focus on Modeling: Surveying | |

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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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Review | |

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TeSt. Focus on Modeling: Traveling and Standing Waves | |

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Cumulative Review Test: Chapters 5, 6, and 7 | |

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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 | |

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DeMoivre's Theorem | |

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Plane Curves and Parametric Equations | |

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Review | |

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TeSt. 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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Review | |

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TeSt. Focus on Modeling: Vector Fields | |

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Cumulative Review Test: Chapters 8 and 9 | |

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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 of Inequalities | |

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Review | |

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TeSt. Focus on Modeling: Linear Programming | |

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Analytic Geometry | |

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Overview | |

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Parabolas | |

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Ellipses | |

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Hyperbolas | |

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Shifted Conics | |

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Rotation of Axes | |

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Polar Equations of Conics | |

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Review | |

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TeSt. Focus on Modeling: Conics in Architecture | |

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Cumulative Review Test: Chapters 10 and 11 | |

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Sequences And Series | |

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Chapter Overview | |

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Sequences and Summation Notation | |

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Arithmetic Sequences | |

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Geometric Sequences | |

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Mathematics of Finance | |

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Mathematical Induction | |

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The Binomial Theorem | |

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Review | |

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TeSt. Focus on Modeling: Difference Equations | |

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Limits: A Preview Of Calculu.S | |

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Chapter Overview | |

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Finding Limits Numerically and Graphically | |

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Finding Limits Algebraically | |

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Tangent Lines and Derivatives | |

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Limits at Infinity: Limits of Sequences | |

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Areas | |

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Review | |

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TeSt. Appendix: Calculators and Calculations | |