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Table of Content | Table of ContentsP. Prerequisites: Fundamental Concepts of AlgebraP.1 Algebraic Expressions, Mathematical Models, and Real NumbersP.2 Exponents and Scientific NotationP.3 Radicals and Rational ExponentsP.4 PolynomialsP.5 Factoring PolynomialsP.6 Rational ExpressionsP.7 EquationsP.8 Modeling with EquationsP.9 Linear Inequalities and Absolute Value InequalitiesSummary, Review, and TestReview ExercisesChapter P Test1. Functions and Graphs1.1 Graphs and Graphing Utilities1.2 Basics of Functions and Their Graphs1.3 More on Functions and Their Graphs1.4 Linear Functions and Slope1.5 More on Slope1.6 Transformations of Functions1.7 Combinations of Functions; Composite Functions1.8 Inverse Functions1.9 Distance and Midpoint Formulas; Circles1.10 Modeling with Functions2. Polynomial and Rational Functions2.1 Complex Numbers2.2 Quadratic Functions2.3 Polynomial Functions and Their Graphs2.4 Dividing Polynomials; Remainder and Factor Theorems2.5 Zeros of Polynomial Functions2.6 Rational Functions and Their Graphs2.7 Polynomial and Rational Inequalities2.8 Modeling Using Variation3. Exponential and Logarithmic Functions3.1 Exponential Functions3.2 Logarithmic Functions3.3 Properties of Logarithms3.4 Exponential and Logarithmic Equations3.5 Exponential Growth and Decay; Modeling Data4. Trigonometric Functions4.1 Angles and Radian Measure4.2 Trigonometric Functions: The Unit Circle4.3 Right Triangle Trigonometry4.4 Trigonometric Functions of Any Angle4.5 Graphs of Sine and Cosine Functions4.6 Graphs of Other Trigonometric Functions4.7 Inverse Trigonometric Functions4.8 Applications of Trigonometric Functions5. Analytic Trigonometry5.1 Verifying Trigonometric Identities5.2 Sum and Difference Formulas5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas5.4 Product-to-Sum and Sum-to-Product Formulas5.5 Trigonometric Equations6. Additional Topics in Trigonometry6.1 The Law of Sines6.2 The Law of Cosines6.3 Polar Coordinates6.4 Graphs of Polar Equations6.5 Complex Numbers in Polar Form; DeMoivre's Theorem6.6 Vectors6.7 The Dot Product7. Systems of Equations and Inequalities7.1 Systems of Linear Equations in Two Variables7.2 Systems of Linear Equations in Three Variables7.3 Partial Fractions7.4 Systems of Nonlinear Equations in Two Variables7.5 Systems of Inequalities7.6 Linear Programming8. Matrices and Determinants8.1 Matrix Solutions to Linear Systems8.2 Inconsistent and Dependent Systems and Their Applications8.3 Matrix Operations and Their Applications8.4 Multiplicative Inverses of Matrices and Matrix Equations8.5 Determinants and Cramer's Rule9. Conic Sections and Analytic Geometry9.1 The Ellipse9.2 The Hyperbola9.3 The Parabola9.4 Rotation of Axes9.5 Parametric Equations9.6 Conic Sections in Polar Coordinates10. Sequences, Induction, and Probability10.1 Sequences and Summation Notation10.2 Arithmetic Sequences10.3 Geometric Sequences and Series10.4 Mathematical Induction10.5 The Binomial Theorem10.6 Counting Principles, Permutations, and Combinations10.7 Probability11. Introduction to Calculus11.1 Finding Limits Using Tables and Graphs11.2 Finding Limits Using Properties of Limits11.3 Limits and Continuity11.4 Introduction to Derivatives |
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