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Algebra and Trigonometry Structure and Method: Book 2 (Student Version) book cover, ISBN 9780395676103

Algebra and Trigonometry Structure and Method: Book 2 (Student Version)

by Thompson, Kay

ISBN13: 9780395676103
ISBN10: 039567610X
Additional ISBN(s): 9780395676110
Format: Hardcover
Copyright: 1994-04-01
Publisher: Houghton Mifflin College Div
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Table of Contents

Basic Concepts of Algebra

The Language of Algebra

Real Numbers and Their Graphs

1

(5)

Simplifying Expressions

6

(8)

Operating with Real Numbers

Basic Properties of Real Numbers

14

(7)

Sums and Differences

21

(6)

Products

27

(6)

Quotients

33

(4)

Solving Equations and Solving Problems

Solving Equations in One Variable

37

(6)

Words into Symbols

43

(6)

Problem Solving with Equations

49

(10)

Inequalities and Proof

Working with Inequalities

Solving Inequalities in One Variable

59

(6)

Solving Combined Inequalities

65

(4)

Problem Solving Using Inequalities

69

(4)

Working with Absolute Value

Absolute Value in Open Sentences

73

(3)

Solving Absolute Value Sentences Graphically

76

(5)

Proving Theorems

Theorems and Proofs

81

(7)

Theorems about Order and Absolute Value

88

(13)

Linear Equations and Functions

Linear Equations and Their Graphs

Open Sentences in Two Variables

101

(6)

Graphs of Linear Equations in Two Variables

107

(5)

The Slope of a Line

112

(6)

Finding an Equation of a Line

118

(6)

Linear Systems

Systems of Linear Equations in Two Variables

124

(7)

Problem Solving: Using Systems

131

(4)

Linear Inequalities in Two Variables

135

(6)

Functions and Relations

Functions

141

(5)

Linear Functions

146

(7)

Relations

153

(14)

Products and Factors of Polynomials

Working with Polynomials

Polynomials

167

(4)

Using Laws of Exponents

171

(3)

Multiplying Polynomials

174

(5)

Factors of Polynomials

Using Prime Factorization

179

(4)

Factoring Polynomials

183

(5)

Factoring Quadratic Polynomials

188

(6)

Applications of Factoring

Solving Polynomial Equations

194

(4)

Problem Solving Using Polynomial Equations

198

(4)

Solving Polynomial Inequalities

202

(9)

Rational Expressions

Using the Laws of Exponents

Quotients of Monomials

211

(5)

Zero and Negative Exponents

216

(5)

Scientific Notation and Significant Digits

221

(6)

Rational Expressions

Rational Algebraic Expressions

227

(5)

Products and Quotients of Rational Expressions

232

(3)

Sums and Differences of Rational Expressions

235

(3)

Complex Fractions

238

(4)

Problem Solving Using Fractional Equations

Fractional Coefficients

242

(5)

Fractional Equations

247

(12)

Irrational and Complex Numbers

Roots and Radicals

Roots of Real Numbers

259

(5)

Properties of Radicals

264

(6)

Sums of Radicals

270

(4)

Binomials Containing Radicals

274

(3)

Equations Containing Radicals

277

(6)

Real Numbers and Complex Numbers

Rational and Irrational Numbers

283

(5)

The Imaginary Number i

288

(4)

The Complex Numbers

292

(15)

Quadratic Equations and Functions

Solving Quadratic Equations

Completing the Square

307

(4)

The Quadratic Formula

311

(6)

Roots of Quadratic Equations

The Discriminant

317

(5)

Equations in Quadratic Form

322

(4)

Quadratic Functions and Their Graphs

Graphing y - k = a(x-h)2

326

(7)

Quadratic Functions

333

(5)

Writing Quadratic Equations and Functions

338

(13)

Variation and Polynomial Equations

Variation and Proportion

Direct Variation and Proportion

351

(7)

Inverse and Joint Variation

358

(6)

Polynomial Equations

Dividing Polynomials

364

(4)

Synthetic Division

368

(4)

The Remainder and Factor Theorems

372

(5)

Some Useful Theorems

377

(5)

Solving Polynomial Equations

Finding Rational Roots

382

(4)

Approximating Irrational Roots

386

(5)

Linear Interpolation

391

(10)

Analytic Geometry

Conic Sections: Circles and Parabolas

Distance and Midpoint Formulas

401

(6)

Circles

407

(5)

Parabolas

412

(6)

Conic Sections: Ellipses and Hyperbolas

Ellipses

418

(8)

Hyperbolas

426

(6)

More on Central Conics

432

(4)

Systems of Equations

The Geometry of Quadratic Systems

436

(3)

Solving Quadratic Systems

439

(5)

Systems of Linear Equations in Three Variables

444

(11)

Exponential and Logarithmic Functions

Exponential Functions

Rational Exponents

455

(4)

Real Number Exponents

459

(4)

Composition and Inverses of Functions

463

(5)

Logarithmic Functions

Definition of Logarithms

468

(5)

Laws of Logarithms

473

(5)

Applications

Applications of Logarithms

478

(5)

Problem Solving: Exponential Growth and Decay

483

(6)

The Natural Logarithm Function

489

(12)

Sequences and Series

Sequences

Types of Sequences

501

(6)

Arithmetic Sequences

507

(3)

Geometric Sequences

510

(8)

Series

Series and Sigma Notation

518

(7)

Sums of Arithmetic and Geometric Series

525

(6)

Infinite Geometric Series

531

(6)

Binomial Expansions

Powers of Binomials

537

(3)

The General Binomial Expansion

540

(9)

Triangle Trigonometry

Trigonometric Functions

Angles and Degree Measure

549

(6)

Trigonometric Functions of Acute Angles

555

(6)

Trigonometric Functions of General Angles

561

(7)

Values of Trigonometric Functions

568

(6)

Triangle Trigonometry

Solving Right Triangles

574

(6)

The Law of Cosines

580

(6)

The Law of Sines

586

(5)

Solving General Triangles

591

(6)

Areas of Triangles

597

(10)

Trigonometric Graphs; Identities

Circular Functions and Their Graphs

Radian Measure

607

(6)

Circular Functions

613

(6)

Periodicity and Symmetry

619

(5)

Graphs of the Sine and Cosine

624

(6)

Graphs of the Other Functions

630

(6)

Trigonometric Identities

The Fundamental Identities

636

(5)

Trigonometric Addition Formulas

641

(5)

Double-Angle and Half-Angle Formulas

646

(4)

Formulas for the Tangent

650

(9)

Trigonometric Applications

Vectors

Vector Operations

659

(7)

Vectors in the Plane

666

(9)

Polar Coordinates and Complex Numbers

Polar Coordinates

675

(5)

The Geometry of Complex Numbers

680

(5)

De Moivre's Theorem

685

(4)

Inverse Functions

The Inverse Cosine and Inverse Sine

689

(4)

Other Inverse Functions

693

(4)

Trigonometric Equations

697

(12)

Statistics and Probability

Statistics

Presenting Statistical Data

709

(4)

Analyzing Statistical Data

713

(6)

The Normal Distribution

719

(5)

Correlation

724

(6)

Counting

Fundamental Counting Principles

730

(4)

Permutations

734

(4)

Combinations

738

(5)

Probability

Sample Spaces and Events

743

(2)

Probability

745

(9)

Mutually Exclusive and Independent Events

754

(13)

Matrices and Determinants

Matrices

Definition of Terms

767

(3)

Addition and Scalar Multiplication

770

(4)

Matrix Multiplication

774

(5)

Applications of Matrices

779

(8)

Inverses of Matrices

Determinants

787

(3)

Inverses of Matrices

790

(4)

Working with Determinants

Expansion of Determinants by Minors

794

(4)

Properties of Determinants

798

(3)

Cramer's Rule

801

(9)

Tables

810

(22)

Explorations

832

(16)

Portfolio Projects

848

(20)

Appendix

A-1 Common Logarithms: Notation and Interpolation

856

(2)

A-2 Common Logarithms: Computation

858

(4)

A-3 Discrete Mathematics

862

(2)

A-4 Preparing for College Entrance Exams

864

(4)

Glossary

868

(10)

Index

878

Answers to Selected Exercises

Supplemental Materials

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