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Basic Concepts of Algebra | |
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The Real Numbers and Their Properties | |
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Integer Exponents and Scientific Notation | |
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Polynomials | |
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Factoring Polynomials | |
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Rational Expressions | |
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Rational Exponents and Radicals | |
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Topics in Geometry | |
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Chapter P. Summary | |
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Chapter P. Review Exercises | |
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Chapter P. Practice Test | |
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Equations and Inequalities | |
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Linear Equations in One Variable | |
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Applications of Linear Equations | |
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Complex Numbers | |
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Quadratic Equations | |
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Solving Other Types of Equations | |
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Linear Inequalities | |
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Equations and Inequalities Involving Absolute Value | |
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Chapter 1. Summary | |
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Chapter 1. Review Exercises | |
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Chapter 1. Practice Test A | |
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Chapter 1. Practice Test B | |
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Graphs and Functions | |
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The Coordinate Plane | |
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Graphs of Equations | |
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Lines | |
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Relations and Functions | |
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Properties of Functions | |
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A Library of Functions | |
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Transformations of Functions | |
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Combining Functions; Composite Functions | |
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Inverse Functions | |
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Chapter 2. Summary | |
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Chapter 2. Review Exercises | |
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Chapter 2. Practice Test A | |
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Chapter 2. Practice Test B | |
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Cumulative Review Chapters. P-2 | |
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Polynomial and Rational Functions | |
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Quadratic Functions | |
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Polynomial Functions | |
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Dividing Polynomials | |
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The Real Zeros of a Polynomial Function | |
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The Complex Zeros of a Polynomial Function | |
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Rational Functions | |
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Polynomial and Rational Inequalities | |
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Variation | |
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Chapter 3: Summary | |
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Chapter 3: Review Exercises | |
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Chapter 3: Practice Test A | |
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Chapter 3: Practice Test B | |
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Cumulative Review Chapters P-3 | |
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Exponential and Logarithmic Functions | |
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Exponential Functions | |
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The Natural Exponential Function | |
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Logarithmic Functions | |
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Rules of Logarithms | |
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Exponential and Logarithmic Equations | |
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Chapter 4: Summary | |
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Chapter 4: Review Exercises | |
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Chapter 4: Practice Test A | |
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Chapter 4: Practice Test B | |
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Cumulative Review Chapters P-4 | |
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Trigonometric Functions Angles and Their Measure | |
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Right Triangle Trigonometry | |
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Trigonometric Functions of Any Angle; Unit Circle | |
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Graphs of the Sine and Cosine Functions | |
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Graphs of the Other Trigonometric Functions | |
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Inverse Trigonometric Functions | |
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Chapter 5: Summary | |
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Chapter 5: Review Exercises | |
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Chapter 5: Practice Test A | |
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Chapter 5: Chapter Test B | |
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Cumulative Review Chapters P-5 | |
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Trigonometric Identities | |
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Verifying Identities | |
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Sum and Difference Identities | |
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Double-Angle and Half-Angle Identities | |
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Product-to-Sum and Sum-to-Product Identities | |
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Trigonometric Equations I | |
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Trigonometric Equations II | |
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Chapter 6: Summary | |
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Chapter 6: Review Exercises | |
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Chapter 6: Practice Test A | |
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Chapter 6: Practice Test B | |
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Cumulative Review Chapters P-6 | |
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Applications of Trigonometric Functions | |
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The Law of Sines | |
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The Law of Sines: Ambiguous Case | |
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The Law of Cosines | |
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Area of a Triangle | |
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Vectors | |
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The Dot Product | |
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Polar Coordinates | |
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Polar Form of Complex Numbers; DeMoivre's Theorem | |
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Chapter 7: Summary | |
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Chapter 7: Review Exercises | |
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Chapter 7: Practice Test A | |
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Chapter 7: Practice Test B | |
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Cumulative Review Chapters P-7 | |
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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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Systems of Nonlinear Equations | |
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Systems of Inequalities | |
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Linear Programming | |
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Partial-Fraction Decomposition | |
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Chapter 8: Summary | |
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Chapter 8: Review Exercises | |
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Chapter 8: Practice Test A | |
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Chapter 8: Practice Test B | |
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Cumulative Review Chapters P-8 | |
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Matrices and Determinants | |
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Matrices and Systems of Equations | |
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Matrix Algebra | |
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The Matrix Inverse | |
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Determinants and Cramer's Rule | |
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Chapter 9: Summary | |
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Chapter 9: Review Exercises | |
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Chapter 9: Practice Test A | |
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Chapter 9: Practice Test B | |
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Cumulative Review Chapters P-9 | |
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Conic Sections | |
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Conic Sections: Overview | |
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The Parabola | |
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The Ellipse | |
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The Hyperbola | |
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Chapter 10: Summary | |
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Chapter 10: Review Exercises | |
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Chapter 10: Practice Test A | |
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Chapter 10: Practice Test B | |
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Cumulative Review Chapters P-10 | |
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Further Topics in Algebra | |
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Sequences and Series | |
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Arithmetic Sequences; Partial Sums | |
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Geometric Sequences and Series | |
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Mathematical Induction | |
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The Binomial Theorem | |
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Counting Principles | |
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Probability | |
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Chapter 11: Summary | |
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Chapter 11: Review Exercises | |
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Chapter 11: Practice Test A | |
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Chapter 11: Practice Test B | |
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Cumulative Review Chapters P-11 | |
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Answers to Selected Exercises | |
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Credits | |
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Index of Applications | |
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Index | |