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| R. Review of Basic Concepts | |
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| Sets | |
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| Real Numbers and Their Properties | |
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| Polynomials | |
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| Factoring Polynomials | |
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| Rational Expressions | |
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| Rational Exponents | |
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| Radical Expressions | |
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| Equations and Inequalities | |
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| Linear Equations | |
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| Applications and Modeling with Linear Equations | |
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| Complex Numbers | |
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| Quadratic Equations | |
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| Applications and Modeling with Quadratic Equations | |
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| Other Types of Equations and Applications | |
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| Inequalities | |
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| Absolute Value Equations and Inequalities | |
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| Graphs and Functions | |
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| Rectangular Coordinates and Graphs | |
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| Circles | |
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| Functions | |
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| Linear Functions | |
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| Equations of Lines | |
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| Curve Fitting | |
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| Graphs of Basic Functions | |
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| Graphing Techniques | |
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| Function Operations and Composition | |
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| Polynomial and Rational Functions | |
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| Quadratic Functions and Models | |
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| Synthetic Division | |
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| Zeros of Polynomial Functions | |
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| Polynomial Functions: Graphs, Applications, and Models | |
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| Rational Functions: Graphs, Applications, and Models | |
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| Variation | |
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| Inverse, Exponential, and Logarithmic Functions | |
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| Inverse Functions | |
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| Exponential Functions | |
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| Logarithmic Functions | |
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| Evaluating Logarithms and the Change-of-Base Theorem | |
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| Exponential and Logarithmic Equations | |
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| Applications and Models of Exponential Growth and Decay | |
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| Trigonometric Functions | |
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| Angles | |
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| Trigonometric Functions | |
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| Evaluating Trigonometric Functions | |
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| Solving Right Triangles | |
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| The Circular Functions and Their Graphs | |
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| Radian Measure | |
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| The Unit Circle and Circular Functions | |
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| Graphs of the Sine and Cosine Functions | |
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| Translations of the Graphs of the Sine and Cosine Functions | |
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| Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions | |
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| Harmonic Motion | |
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| Trigonometric Identities and Equations | |
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| Fundamental Identities | |
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| Verifying Trigonometric Identities | |
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| Sum and Difference Identities | |
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| Double-Angle and Half-Angle Identities | |
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| Inverse Circular Functions | |
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| Trigonometric Equations | |
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| Equations Involving Inverse Trigonometric Functions | |
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| Applications of Trigonometry | |
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| The Law of Sines | |
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| The Law of Cosines | |
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| Vectors, Operations, and the Dot Product | |
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| Applications of Vectors | |
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| Trigonometric (Polar) Form of Complex Numbers | |
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| Products and Quotients | |
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| DeMoivre's Theorem | |
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| Powers and Roots of Complex Numbers | |
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| Polar Equations and Graphs | |
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| Parametric Equations, Graphs, and Applications | |
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| Systems and Matrices | |
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| Systems of Linear Equations | |
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| Matrix Solution of Linear Systems | |
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| Determinant Solution of Linear Systems | |
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| Partial Fractions | |
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| Nonlinear Systems of Equations | |
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| Systems of Inequalities and Linear Programming | |
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| Properties of Matrices | |
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| Matrix Inverses | |
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| Analytic Geometry | |
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| Parabolas | |
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| Ellipses | |
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| Hyperbolas | |
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| Summary of the Conic Sections | |
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| Further Topics in Algebra | |
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| Sequences and Series | |
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| Arithmetic Sequences and Series | |
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| Geometric Sequences and Series | |
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| The Binomial Theorem | |
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| Mathematical Induction | |
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| Counting Theory | |
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| Basics of Probability | |
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| Polar Form of Conic Sections | |
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| Rotation of Axes | |
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| Geometry Formulas | |
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| Glossary | |
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| Solutions to Selected Exercises | |
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| Answers to Selected Exercises | |
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| Index of Applications | |
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| Index | |