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The Rectangular Coordinate System, Lines, and Circles | |

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The Rectangular Coordinate System | |

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Circles | |

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Lines | |

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Parallel and Perpendicular Lines | |

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Functions | |

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Relations and Functions | |

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Properties of a Function's Graph | |

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Graphs of Basic Functions; Piecewise Functions | |

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Transformations of Functions | |

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The Algebra of Functions; Composite Functions | |

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One-to-One Functions; Inverse Functions | |

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Polynomial and Rational Functions | |

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Quadratic Functions | |

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Applications and Modeling of Quadratic Functions | |

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The Graphs of Polynomial Functions | |

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Synthetic Division; The Remainder and Factor Theorems | |

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The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra | |

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Rational Functions and Their Graphs | |

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Variation | |

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Exponential and Logarithmic Functions and Equations | |

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Exponential Functions | |

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The Natural Exponential Function | |

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Logarithmic Functions | |

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Properties of Logarithms | |

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Exponential and Logarithmic Equations | |

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Applications of Exponential and Logarithmic Functions | |

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An Introduction to Trigonometric Functions | |

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Angles: Degree and Radian Measure | |

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Applications of Radian Measure | |

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The Unit Circle | |

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Trigonometric Functions of General Angles | |

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Right Triangle Trigonometry | |

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The Graphs of Trigonometric Functions | |

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The Graphs of Sine and Cosine | |

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More on Graphs of Sine and Cosine; Phase Shift | |

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The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions | |

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Inverse Trigonometric Functions I | |

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Inverse Trigonometric Functions II | |

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Trigonometric Identities, Formulas, and Equations | |

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Trigonometric Identities | |

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The Sum and Difference Formulas | |

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The Double-Angle and Half-Angle Formulas | |

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The Product-to-Sum and Sum-to-Product Formulas | |

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Trigonometric Equations | |

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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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Area of Triangles | |

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Polar Equations, Complex Numbers, and Vectors | |

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Polar Coordinates and Polar Equations | |

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The Graphs of Polar Equations | |

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Complex Numbers; DeMoivre's Theorem | |

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Vectors | |

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The Dot Product | |

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Conic Sections | |

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The Parabola | |

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The Ellipse | |

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The Hyperbola | |

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Systems of Equations and Inequalities | |

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Systems of Linear Equations in Two Variables | |

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Systems of Linear Equations in Three Variables | |

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Inconsistent and Dependent Linear Systems in Three Variables | |

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Partial Fraction Decomposition | |

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Systems of Nonlinear Equations | |

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Systems of Inequalities | |

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Matrices | |

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Matrix Operations | |

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Inverses of Matrices and Matrix Equations | |

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Determinants and Cramer's Rule | |

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Sequences and Series; Counting and Probability | |

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Introduction to 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 Inductions | |

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The Theory of Counting | |

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An Introduction to Probability | |

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Real Numbers | |

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The Order of Operations and Algebraic Expressions | |

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The Laws of Exponents; Radicals | |

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Polynomials | |

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Factoring Polynomials | |

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Rational Expressions | |

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Linear Equations | |

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Applications of Linear Equations | |

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Complex Numbers | |

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Quadratic Equations | |

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Applications of Quadratic Equations | |

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Other Types of Equations | |

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Linear Inequalities | |

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Absolute Value Equations and Inequalities | |

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Polynomial and Rational Inequalities | |

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Degree, Minute, Second Form and Degree Decimal Form | |

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Triangles | |

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Conic Section Proofs | |