Review of Basic Concepts | |

Sets | |

Real Numbers and Their Properties | |

Polynomials | |

Factoring Polynomials | |

Rational Expressions | |

Rational Exponents | |

Radical Expressions | |

Equations and Inequalities | |

Linear Equations | |

Applications and Modeling with Linear Equations | |

Complex Numbers | |

Quadratic Equations | |

Applications and Modeling with Quadratic Equations | |

Other Types of Equations and Applications | |

Inequalities | |

Absolute Value Equations and Inequalities | |

Graphs and Functions | |

Rectangular Coordinates and Graphs | |

Circles.Functions.Linear Functions | |

Equations of Lines; Curve Fitting | |

Graphs of Basic Functions | |

Graphing Techniques | |

Function Operations and Composition | |

Polynomial and Rational Functions.Quadratic Functions and Models | |

Synthetic Division | |

Zeros of Polynomial Functions | |

Polynomial Functions: Graphs, Applications, and Models | |

Rational Functions: Graphs, Applications, and Models | |

Variation | |

Inverse, Exponential, and Logarithmic Functions | |

Inverse Functions | |

Exponential Functions | |

Logarithmic Functions | |

Evaluating Logarithms and the Change-of-Base Theorem | |

Exponential and Logarithmic Equations | |

Applications and Models of Exponential Growth and Decay | |

Trigonometric Functions.Angles | |

Trigonometric Functions | |

Evaluating Trigonometric Functions | |

Solving Right Triangles | |

The Circular Functions and Their Graphs | |

Radian Measure | |

The Unit Circle and Circular Functions | |

Graphs of the Sine and Cosine Functions | |

Translations of the Graphs of the Sine and Cosine Functions | |

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

Harmonic Motion | |

Trigonometric Identities and Equations | |

Fundamental Identities | |

Verifying Trigonometric Identities | |

Sum and Difference Identities | |

Double-Angleand Half-Angle Identities | |

Inverse Circular Functions | |

Trigonometric Equations | |

Equations Involving Inverse Trigonometric Functions | |

Applications of Trigonometry | |

The Law of Sines | |

The Law of Cosines | |

Vectors, Operations, and the Dot Product | |

Applications of Vectors | |

Trigonometric (Polar) Form of Complex Numbers; Products and Quotients | |

DeMoivre's Theorem; Powers and Roots of Complex Numbers | |

Polar Equations and Graphs | |

Parametric Equations, Graphs, and Applications | |

Systems and Matrices | |

Systems of Linear Equations | |

Matrix Solution of Linear Systems | |

Determinant Solution of Linear Systems | |

Partial Fractions | |

Nonlinear Systems of Equations | |

Systems of Inequalities and Linear Programming | |

Properties of Matrices.Matrix Inverses | |

Analytic Geometry | |

Parabolas | |

Ellipses | |

Hyperbolas | |

Summary of the Conic Sections | |

Further Topics in Algebra | |

Sequences and Series | |

Arithmetic Sequences and Series | |

Geometric Sequences and Series | |

The Binomial Theorem | |

Mathematical Induction | |

Counting Theory | |

Basics of Probability | |

Polar Form of Conic Sections | |

Appendix | |

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