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Contents
Table of Contents
BASIC CONCEPTS OF ALGEBRA
P.1 The Real Numbers and Their Properties
P.2 Integer Exponents and Scientific Notation
P.3 Polynomials
P.4 Factoring Polynomials
P.5 Rational Expressions
P.6 Rational Exponents and Radicals
Chapter P Review and Tests
Review Exercises
Practice Test
EQUATIONS AND INEQUALITIES
1.1 Linear Equations in One Variable
1.2 Applications of Linear Equations: Modeling
1.3 Quadratic Equations
1.4 Complex Numbers: Quadratic Equations with Complex Solutions
1.5 Solving Other Types of Equations
1.6 Inequalities
1.7 Equations and Inequalities Involving Absolute Value
Chapter 1 Review and Tests
Review Exercises
Practice Test A
Practice Test B
GRAPHS AND FUNCTIONS
2.1 The Coordinate Plane
2.2 Graphs of Equations
2.3 Lines
2.4 Functions
2.5 Properties of Functions
2.6 A Library of Functions
2.7 Transformations of Functions
2.8 Combining Functions; Composite Functions
2.9 Inverse Functions
Chapter 2 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—2
POLYNOMIAL AND RATIONAL FUNCTIONS
3.1 Quadratic Functions
3.2 Polynomial Functions
3.3 Dividing Polynomials
3.4 The Real Zeros of a Polynomial Function
3.5 The Complex Zeros of a Polynomial Function
3.6 Rational Functions
3.7 Variation
Chapter 3 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—3
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Rules of Logarithms
4.4 Exponential and Logarithmic Equations and Inequalities
4.5 Logarithmic Scales; Modeling
Chapter 4 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—4
TRIGONOMETRIC FUNCTIONS
5.1 Angles and Their Measure
5.2 Right-Triangle Trigonometry
5.3 Trigonometric Functions of Any Angle; The Unit Circle
5.4 Graphs of the Sine and Cosine Functions
5.5 Graphs of the Other Trigonometric Functions
5.6 Inverse Trigonometric Functions
Chapter 5 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—5
TRIGONOMETRIC IDENTITIES AND EQUATIONS
6.1 Trigonometric Identities
6.2 Sum and Difference Formulas
6.3 Double-Angle and Half-Angle Formulas
6.4 Product-to-Sum and Sum-to-Product Formulas
6.5 Trigonometric Equations I
6.6 Trigonometric Equations II
Chapter 6 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—6
APPLICATIONS OF TRIGONOMETRIC FUNCTIONS
7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Areas of Polygons Using Trigonometry
7.4 Vectors
7.5 The Dot Product
7.6 Polar Coordinates
7.7 Polar Form of Complex Numbers; DeMoivre's Theorem
Chapter 7 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—7
SYSTEMS OF EQUATIONS AND INEQUALITIES
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.3 Partial-Fraction Decomposition
8.4 Systems of Nonlinear Equations
8.5 Systems of Inequalities
8.6 Linear Programming
Chapter 8 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—8
MATRICES AND DETERMINANTS
9.1 Matrices and Systems of Equations
9.2 Matrix Algebra
9.3 The Matrix Inverse
9.4 Determinants and Cramer's Rule
Chapter 9 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—9
CONIC SECTIONS
10.1 Conic Sections: Overview
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
Chapter 10 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—10
FURTHER TOPICS IN ALGEBRA
11.1 Sequences and Series
11.2 Arithmetic Sequences; Partial Sums
11.3 Geometric Sequences and Series
11.4 Mathematical Induction
11.5 The Binomial Theorem
11.6 Counting Principles
11.7 Probability
Chapter 11 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—11
Answers to Selected Exercises Credits Index
