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Table of Contents

P. Prerequisites: Fundamental Concepts of Algebra

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers

P.2 Exponents and Scientific Notation

P.3 Radicals and Rational Exponents

P.4 Polynomials

Mid-Chapter Check Point

P.5 Factoring Polynomials

P.6 Rational Expressions

SUMMARY, REVIEW, AND TEST

REVIEW EXERCISES

CHAPTER P TEST

1. Equations and Inequalities

1.1 Graphs and Graphing Utilities

1.2 Linear Equations and Rational Equations

1.3 Models and Applications

1.4 Complex Numbers

1.5 Quadratic Equations

Mid-Chapter Check Point

1.6 Other Types of Equations

1.7 Linear Inequalities and Absolute Value Inequalities

SUMMARY, REVIEW, AND TEST

REVIEW EXERCISES

CHAPTER 1 TEST

2. Functions and Graphs

2.1 Basics of Functions and Their Graphs

2.2 More on Functions and Their Graphs

2.3 Linear Functions and Slope

2.4 More on Slope

Mid-Chapter Check Point

2.5 Transformations of Functions

2.6 Combinations of Functions; Composite Functions

2.7 Inverse Functions

2.8 Distance and Midpoint Formulas; Circles

SUMMARY, REVIEW, AND TEST

REVIEW EXERCISES

CHAPTER 2 TEST

CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-2)

3. Polynomial and Rational Functions

3.1 Quadratic Functions

3.2 Polynomial Functions and Their Graphs

3.3 Dividing Polynomials; Remainder and Factor Theorems

3.4 Zeros of Polynomial Functions

Mid-Chapter Check Point

3.5 Rational Functions and Their Graphs

3.6 Polynomial and Rational Inequalities

3.7 Modeling Using Variation

SUMMARY, REVIEW, AND TEST

REVIEW EXERCISES

CHAPTER 3 TEST

CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-3) 410

4. Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

Mid-Chapter Check Point

4.4 Exponential and Logarithmic Equations

4.5 Exponential Growth and Decay; Modeling Data

SUMMARY, REVIEW, AND TEST

REVIEW EXERCISES

CHAPTER 4 TEST

CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-4)

5. Systems of Equations and Inequalities

5.1 Systems of Linear Equations in Two VariTables

5.2 Systems of Linear Equations in Three VariTables

5.3 Partial Fractions

5.4 Systems of Nonlinear Equations in Two VariTables

Mid-Chapter Check Point

5.5 Systems of Inequalities

5.6 Linear Programming

SUMMARY, REVIEW, AND TEST

REVIEW EXERCISES

CHAPTER 5 TEST

CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-5)

6. Matrices and Determinants

6.1 Matrix Solutions to Linear Systems

6.2 Inconsistent and Dependent Systems and Their Applications

6.3 Matrix Operations and Their Applications

Mid-Chapter Check Point

6.4 Multiplicative Inverses of Matrices and Matrix Equations

6.5 Determinants and Cramer’s Rule

SUMMARY, REVIEW, AND TEST

REVIEW EXERCISES

CHAPTER 6 TEST

CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-6)

7. Conic Sections

7.1 The Ellipse

7.2 The Hyperbola

Mid-Chapter Check Point

7.3 The Parabola

SUMMARY, REVIEW, AND TEST

REVIEW EXERCISES

CHAPTER 7 TEST

CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-7)

8. Sequences, Induction, and Probability

8.1 Sequences and Summation Notation

8.2 Arithmetic Sequences

8.3 Geometric Sequences and Series

Mid-Chapter Check Point

8.4 Mathematical Induction

8.5 The Binomial Theorem

8.6 Counting Principles, Permutations, and Combinations

8.7 Probability

SUMMARY, REVIEW, AND TEST

REVIEW EXERCISES

CHAPTER 8 TEST

CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-8)

Appendix: Where Did That Come From? Selected Proofs

Answers to Selected Exercises