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Fundamentals | |

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Overview | |

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Real Numbers | |

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Exponents and Radicals | |

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Algebraic Expressions | |

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Discovery Project: Visualizing a Formula | |

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Fractional Expressions | |

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Equations | |

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Modeling with Equations | |

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Discovery Project: Equations through the Ages | |

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Inequalities | |

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Coordinate Geometry | |

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Graphing Calculators: Solving Equations and Inequalities Graphically | |

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Lines | |

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Modeling Variation | |

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Review | |

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Test | |

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Focus on Problem Solving: General Principles | |

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Functions | |

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Overview | |

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What is a Function? Graphs of Functions | |

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Discovery Project: Relations and Functions | |

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Increasing and Decreasing Functions: Average Rate of Change | |

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Transformations of Functions | |

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Quadratic Functions: Maxima and Minima | |

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Modeling with Functions | |

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Combining Functions | |

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Discovery | |

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Project: Iteration and Chaos | |

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One-to-One Functions and Their Inverses Review | |

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Test | |

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Focus on Modeling: Fitting Lines to Data | |

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Polynomial and Rational Functions | |

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Overview | |

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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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Discovery Project: Zeroing in on a Zero | |

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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 | |

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Focus on Modeling: Fitting Polynomials to Data | |

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Exponential and Logarithmic Functions | |

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Overview | |

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Exponential Functions | |

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Discovery Project: Exponential Explosion | |

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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 | |

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

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Trigonometric Functions of Real Numbers | |

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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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Discovery Project: Predator-Prey Models | |

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More Trigonometric Graphs | |

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Modeling Harmonic Motion | |

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Review | |

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Test | |

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Focus on Modeling: Fitting Sinusoidal Curves to Data | |

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Trigonometric Functions of Angles | |

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Overview | |

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Angle Measure | |

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Trigonometry of Right Triangles | |

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Discovery Project: Similarity | |

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Trigonometric Functions of Angles | |

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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 | |

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Focus on Modeling:Surveying | |

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Analytic Trigonometric | |

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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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Inverse Trigonometric Functions | |

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Discovery Project: Where to Sit at the Movies | |

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Trigonometric Equations | |

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Review | |

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Test | |

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Focus on Modeling: Traveling and Standing Waves | |

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Polar Coordinates and Vectors | |

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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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Discovery Project: Fractals | |

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Vectors | |

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The Dot Product | |

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Discovery Project: Sailing Against the Wind | |

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Review | |

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Test | |

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Focus on Modeling: Mapping the World | |

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Systems of Equations and Inequalities | |

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Overview | |

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Systems of Equations | |

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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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Discovery Project: Best Fit versus Exact Fit | |

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Systems of Linear Equations: Matrices | |

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The Algebra of Matrices | |

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Discovery Project: Will the Species Survive? Inverses of Matrices and Matrix Equations | |

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Discovery Project: Computer Graphics | |

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I Determinants and Cramer's Rule | |

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Partial Fractions | |

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Systems of Inequalities | |

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Review | |

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Test | |

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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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Discovery Project: Conics in Architecture Shifted Conics | |

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Rotation of Axes | |

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Discovery Project: Computer Graphics II | |

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Polar Equations of Conics | |

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Plane Curves and Parametric Equations | |

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Review | |

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Test | |

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Focus on Modeling: The Path of a Projectile | |

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Sequences and Series | |

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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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Discovery Project: Finding Patterns | |

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Mathematical Finance | |

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Mathematical Induction | |

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The Binomial Theorem | |

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Review | |

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Test | |

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Focus on Modeling: Modeling with Recursive Sequences | |

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Limits: A Preview of Calculus | |

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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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Discovery Project: Designing a Roller Coaster | |

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Limits at | |