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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 | |