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Tables of Contents for Algebra for Students

Chapter/Section Title

Page #

Page Count

To The Student

ix

Review of the Real Number System

Basic Terms

1

10

Operations on Real Numbers

11

11

Properties of Real Numbers

22

9

Chaper 1 Test

28

3

Linear Equations and Inequalities

Linear Equations in One Variable

31

10

Formulas

41

5

Applications of Linear Equations

46

7

More Applications of Linear Equations

53

4

Linear Inequalities in One Variable

57

8

Set Operations and Compound Inequalities

65

5

Absolute Value Equations and Inequalities

70

11

Chaper 2 Test

78

3

Graphs, Linear Equations, and Functions

The Rectangular Coordinate System

81

11

The Slope of a Line

92

10

Linear Equations in Two Variables

102

10

Linear Inequalities in Two Variables

112

7

Introduction to Functions

119

11

Variation

130

12

Chaper 3 Test

137

5

Exponents and Polynomials

Integer Exponents and Scientific Notation

142

12

Addition and Subtraction of Polynomials

154

7

Polynomial Functions

161

7

Multiplication of Polynomials

168

8

Greatest Common Factors; Factoring by Grouping

176

5

Factoring Trinomials

181

7

Special Factoring

188

5

General Methods of Factoring

193

5

Solving Equations by Factoring

198

12

Chaper 4 Test

206

4

Rational Expressions

Rational Expressions and Functions; Multiplication and Division

210

9

Addition and Subtraction of Rational Expressions

219

6

Complex Fractions

225

5

Division of Polynomials

230

6

Graphs and Equations with Rational Expressions

236

7

Applications of Rational Expressions

243

12

Chaper 5 Test

252

3

Roots and Radicals

Rational Exponents and Radicals

255

8

Simplifying Radical Expressions

263

9

Addition and Subtraction of Radical Expressions

272

4

Multiplication and Division of Radical Expressions

276

7

Graphs and Equations with Radical Expressions

283

12

Complex Numbers

295

12

Chaper 6 Test

303

4

Quadratic Equations and Inequalities

Completing the Square

307

8

The Quadratic Formula

315

9

Equations Quadratic in Form

324

9

Formulas and Applications

333

7

Nonlinear Inequalities

340

9

Chaper 7 Test

347

2

Graphing Relations and Functions

The Algebra of Functions

349

9

Quadratic Functions; Translations

358

11

More About Parabolas; Applications

369

10

Symmetry; Increasing and Decreasing Functions

379

9

The Circle and the Ellipse

388

9

The Hyperbola; Conic Sections

397

6

Piecewise Linear Functions

403

14

Chaper 8 Test

413

4

Polynomial and Rational Functions

Synthetic Division

417

8

Zeros of Polynomial Functions

425

7

Graphs and Applications of Polynomial Functions

432

15

Graphs and Applications of Rational Functions

447

21

Chaper 9 Test

463

5

Inverse, Exponential, and Logarithmic Functions

Inverse Functions

468

7

Exponential Functions

475

8

Logarithmic Functions

483

7

Properties of Logarithms

490

5

Evaluating Logarithms

495

5

Exponential and Logarithmic Equations; Applications

500

15

Chaper 10 Test

510

5

Systems of Equations and Inequalities

Linear Systems of Equations in Two Variables

515

12

Linear Systems of Equations in Three Variables

527

6

Applications of Linear Systems of Equations

533

6

Nonlinear Systems of Equations

539

8

Second-Degree Inequalities, Systems of Inequalities, and Linear Programming

547

18

Chaper 11 Test

560

5

Matrices and Determinants

Matrix Solution of Linear Systems

565

8

Properties of Matrices

573

9

Determinants

582

8

Cramer's Rule

590

5

Matrix Inverses

595

14

Chaper 12 Test

606

3

Further Topics in Algebra

Sequences and Series

609

8

Arithmetic Sequences

617

9

Geometric Sequences

626

11

The Binomial Theorem

637

7

Mathematical Induction

644

5

Counting Theory

649

12

Basics of Probability

661

14

Chaper 13 Test

670

5

Answers to Chapter Tests

675