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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.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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| Trigonometic Functions Of Angles | |
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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 Trigonometry | |
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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; 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 I | |
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| 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 Infini | |