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R. Review of Basic Concepts R-1 Sets R-2 Real Numbers and Their Properties R-3 Polynomials R-4 Factoring Polynomials R-5 Rational Expressions R-6 Rational Exponents R-7 Radical Expressions 1. Equations and Inequalities 1-1 Linear Equations 1-2 Applications and Modeling with Linear Equations 1-3 Complex Numbers 1-4 Quadratic Equations 1-5 Applications and Modeling with Quadratic Equations 1-6 Other Types of Equations and Applications 1-7 Inequalities 1-8 Absolute Value Equations and Inequalities 2. Graphs and Functions 2-1 Rectangular Coordinates and Graphs 2-2 Circles 2-3 Functions 2-4 Linear Functions 2-5 Equations of Lines and Linear Models 2-6 Graphs of Basic Functions 2-7 Graphing Techniques 2-8 Function Operations and Composition 3. Polynomial and Rational Functions 3-1 Quadratic Functions and Models 3-2 Synthetic Division 3-3 Zeros of Polynomial Functions 3-4 Polynomial Functions: Graphs, Applications, and Models 3-5 Rational Functions: Graphs, Applications, and Models 3-6 Variation 4. Inverse, Exponential, and Logarithmic Functions 4-1 Inverse Functions 4-2 Exponential Functions 4-3 Logarithmic Functions 4-4 Evaluating Logarithms and the Change-of-Base Theorem 4-5 Exponential and Logarithmic Equations 4-6 Applications of Models of Exponential Growth and Decay 5. Trigonometric Functions 5-1 Angles 5-2 Trigonometric Functions 5-3 Trigonometric Function Values and Angle Measures 5-4 Solutions and Applications of Right Triangles 6. The Circular Functions and Their Graphs 6-1 Radian Measure 6-2 The Unit Circle and Circular Functions 6-3 Graphs of the Sine and Cosine Functions 6-4 Translations of the Graphs of the Sine and Cosine Functions 6-5 Graphs of the Tangent and Cotangent Functions 6-6 Graphs of the Secant and Cosecant Functions 6-7 Harmonic Motion 7. Trigonometric Identities and Equations 7-1 Fundamental Identities 7-2 Verifying Trigonometric Identities 7-3 Sum and Difference Identities 7-4 Double-Angle and Half-Angle Identities 7-5 Inverse Circular Functions 7-6 Trigonometric Equations 7-7 Equations Involving Inverse Trigonometric Functions 8. Applications of Trigonometry 8-1 The Law of Sines 8-2 The Law of Cosines 8-3 Geometrically Defined Vectors and Applications 8-4 Algebraically Defined Vectors and the Dot Product 8-5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients 8-6 De Moivre’s Theorem; Powers and Roots of Complex Numbers 8-7 Polar Equations and Graphs 8-8 Parametric Equations, Graphs, and Applications 9. Systems and Matrices 9-1 Systems of Linear Equations 9-2 Matrix Solution of Linear Systems 9-3 Determinant Solution of Linear Systems 9-4 Partial Fractions 9-5 Nonlinear Systems of Equations 9-6 Systems of Inequalities and Linear Programming 9-7 Properties of Matrices 9-8 Matrix Inverses 10. Analytic Geometry 10-1 Parabolas 10-2 Ellipses 10-3 Hyperbolas 10-4 Summary of the Conic Sections 11. Further Topics in Algebra 11-1 Sequences and Series 11-2 Arithmetic Sequences and Series 11-3 Geometric Sequences and Series 11-4 The Binomial Theorem 11-5 Mathematical Induction 11-6 Counting Theory 11-7 Basics of Probability Table of Contents
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