Algebra Structure and Method, Grades 8-11 Book 1: Mcdougal Littell Structure & Method

ISBN 13:
9780395977224
ISBN 10:
0395977223
Format: Hardcover
Copyright: 01/13/1999
Publisher: Holt McDougal

Note: Not guaranteed to come with supplemental materials (access cards, study guides, lab manuals, CDs, etc.)

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Introduction to Algebra

Variables and Equations

Variables

(5)

Grouping Symbols

(4)

Equations

(4)

Applications and Problem Solving

Translating Words into Symbols

(5)

Translating Sentences into Equations

(4)

Translating Problems into Equations

(4)

A Problem Solving Plan

(4)

Numbers on a Line

Number Lines

(5)

Opposites and Absolute Values

(9)

Explorations Exploring Density of Real Numbers 685

Technology Calculator Key-In 13

Special Topics Application / Energy Consumption 5 Challenge 9, 35 Reading Algebra xiv, 26 Biographical Note 30 Career Note / Bilingual Math Teacher 40

Reviews and Tests Mixed Review 5, 9, 12, 18, 22, 26, 29, 35, 39 Self-Test 13, 30, 39 Chapter Summary 40 Chapter Review 41 Chapter Test 42 Maintaining Skills 43

Working with Real Numbers

Addition and Subtraction

Basic Assumptions

(4)

Addition on a Number Line

(5)

Rules for Addition

(5)

Subtracting Real Numbers

(6)

Multiplication

The Distributive Property

(5)

Rules for Multiplication

(5)

Problem Solving: Consecutive Integers

(4)

Division

The Reciprocal of a Real Number

(4)

Dividing Real Numbers

(12)

Explorations Exploring Addition of Integers 686 Exploring Subtraction of Integers 687

Technology Calculator Key-In 58, 82 Computer Key-In 87

Special Topics Challenge 48, 53, 69 Reading Algebra 64 Application / Understanding Product Prices 74 Historical Note 87

Reviews and Tests Mixed Review 48, 53, 58, 63, 69, 73, 78, 82, 86 Self-Tests 63, 78, 86 Chapter Summary 88 Chapter Review 89 Chapter Test 90 Cumulative Review 91 Maintaining Skills 92 Preparing for College Entrance Exams 93

Solving Equations and Problems

Transforming Equations

Transforming Equations: Addition and Subtraction

(7)

Transforming Equations: Multiplication and Division

102

(5)

Using Several Transformations

107

(5)

Solving Problems

Using Equations to Solve Problems

112

(4)

Equations with the Variable on Both Sides

116

(5)

Extending Your Problem Solving Skills

Problem Solving: Using Charts

121

(5)

Cost, Income, and Value Problems

126

(4)

Proof in Algebra

130

(11)

Explorations Exploring Ways to Solve Equations 688

Technology Calculator Key-In 106, 111 Computer Exercises 111, 120, 129

Special Topics Application / Car Loans 101 Historical Note 115 Career Note / Astronomer 125

Reviews and Tests Mixed Review 100, 106, 110, 115, 120, 125, 129, 133 Self-Tests 111, 120, 134 Chapter Summary 134 Chapter Review 135 Chapter Test 136 Cumulative Review 137 Maintaining Skills 138 Mixed Problem Solving 139

Polynomials

Addition and Subtraction

Exponents

141

(5)

Adding and Subtracting Polynomials

146

(6)

Multiplication

Multiplying Monomials

152

(3)

Powers of Monomials

155

(3)

Multiplying Polynomials by Monomials

158

(3)

Multiplying Polynomials

161

(4)

Problem Solving

Transforming Formulas

165

(2)

Rate-Time-Distance Problems

167

(5)

Area Problems

172

(3)

Problems Without Solutions

175

(10)

Explorations Exploring Monomial and Binomial Products 689

Technology Computer Exercises 145, 151 Calculator Key-In 145

Special Topic Biographical Note 145

Reviews and Tests Mixed Review 144, 150, 154, 157, 160, 164, 166, 171, 174 Self-Tests 151, 164, 177 Chapter Summary 178 Chapter Review 178 Chapter Test 180 Cumulative Review 181 Maintaining Skills 182 Preparing for College Entrance Exams 183

Factoring Polynomials

Quotients and Factoring

Factoring Integers

185

(4)

Dividing Monomials

189

(5)

Monomial Factors of Polynomials

194

(6)

Products and Factors

Multiplying Binomials Mentally

200

(4)

Differences of Two Squares

204

(4)

Squares of Binomials

208

(5)

Factoring Patterns

Factoring Pattern for x2 + bx + c, c positive

213

(4)

Factoring Pattern for x2 + bx + c, c negative

217

(3)

Factoring Pattern for ax2 + bx + c

220

(4)

General Factoring and Its Application

Factoring by Grouping

224

(3)

Using Several Methods of Factoring

227

(3)

Solving Equations by Factoring

230

(4)

Using Factoring to Solve Problems

234

(13)

Explorations Exploring Polynomial Factors 691

Technology Computer Exercises 187, 203 Computer Key-In 188 Calculator Key-In 1993, 203

Special Topics Challenge 188, 223 Career Note / Draftsperson 229 Historical Note 239 Sums and Differences of Cubes 239

Reviews and Tests Mixed Review 187, 193, 199, 203, 207, 212, 216, 219, 223, 226, 229, 233, 238 Self-Tests 199, 212, 223, 238 Chapter Summary 240 Chapter Review 240 Chapter Test 242 Cumulative Review 243 Maintaining Skills 244 Mixed Problem Solving 245

Fractions

Algebraic Fractions

Simplifying Fractions

247

(4)

Multiplying Fractions

251

(4)

Dividing Fractions

255

(4)

Adding and Subtracting Fractions

Least Common Denominators

259

(5)

Adding and Subtracting Fractions

264

(6)

Polynomial Division

Mixed Expressions

270

(4)

Polynomial Long Division

274

(13)

Explorations Exploring GCF and LCM 692

Technology Computer Exercises 250, 273 Calculator Key-In 258 Computer Key-In 263

Special Topics Challenge 254, 263, 273 Biographical Note 269 Complex Fractions 278

Reviews and Tests Mixed Review 250, 254, 258, 262, 268, 273, 277 Self-Tests 258, 269, 277 Chapter Summary 280 Chapter Review 280 Chapter Test 282 Cumulative Review 283 Maintaining Skills 284 Preparing for College Entrance Exams 285

Applying Fractions

Ratio and Proportion

Ratios

287

(6)

Proportions

293

(5)

Fractional Equations

Equations with Fractional Coefficients

298

(6)

Fractional Equations

304

(5)

Percent Problems

Percents

309

(6)

Percent Problems

315

(6)

Mixture and Work Problems

Mixture Problems

321

(5)

Work Problems

326

(5)

Problems Involving Exponents

Negative Exponents

331

(5)

Scientific Notation

336

(13)

Explorations Exploring Applications of Proportions 693

Technology Computer Exercises 319 Calculator Key-In 341

Special Topics Challenge 292 Application / Units of Measurement in Problem Solving 302 Historical Note 303 Career Note / Electrical Engineer 341

Reviews and Tests Mixed Review 292, 297, 301, 308, 314, 320, 325, 330, 335, 340 Self-Tests 297, 308, 320, 330, 341 Chapter Summary 342 Chapter Review 342 Chapter Test 344 Cumulative Review 345 Maintaining Skills 346 Mixed Problem Solving 347

Introduction to Functions

Using Two Variables

Equations in Two Variables

349

(4)

Points, Lines, and their Graphs

353

(7)

Linear Equations

Slope of a Line

360

(6)

The Slope-Intercept Form of a Linear Equation

366

(5)

Determining an Equation of a Line

371

(3)

Functions

Functions Defined by Tables and Graphs

374

(5)

Functions Defined by Equations

379

(4)

Linear and Quadratic Functions

383

(8)

Variation

Direct Variation

391

(6)

Inverse Variation

397

(16)

Explorations Exploring Linear Equations 694

Technology Computer Exercises 352, 382, 388, 402 Computer Graphing Ideas 354, 357, 367, 368, 384, 386, 387, 399, 694 Computer Key-In 359 Calculator Key-In 365, 403

Special Topics Historical Note 359 Perpendicular Lines 370 Career Note / Statistician 377 Application / Line of Best Fit 378 Challenge 382 Relations 389 Biographical Note 396 Reading Algebra 404

Reviews and Tests Mixed Review 352, 358, 365, 369, 373, 377, 382, 387, 396, 402 Self-Tests 358, 373, 388, 403 Chapter Summary 405 Chapter Review 405 Chapter Test 407 Cumulative Review 409 Maintaining Skills 410 Preparing for College Entrance Exams 411

Systems of Linear Equations

Solving Systems of Linear Equations

The Graphing Method

413

(4)

The Substitution Method

417

(4)

Solving Problems with Two Variables

421

(5)

The Addition-or-Subtraction Method

426

(4)

Multiplication with the Addition-or-Subtraction Method

430

(8)

Applications

Wind and Water Current Problems

438

(6)

Puzzle Problems

444

(13)

Explorations Exploring Systems of Linear Equations 695

Technology Computer Exercises 416, 436 Computer Graphing Ideas 414, 415, 695

Special Topics Career Note / Nutritionist 425 Challenge 425, 437 Biographical Note 443 Historical Note 450

Reviews and Tests Mixed Review 416, 420, 425, 429, 436, 443, 449 Self-Tests 437, 450 Chapter Summary 450 Chapter Review 451 Chapter Test 452 Cumulative Review 453 Maintaining Skills 454 Mixed Problem Solving 455

Inequalities

Inequalities in One Variable

Order of Real Numbers

457

(5)

Solving Inequalities

462

(7)

Solving Problems Involving Inequalities

469

(9)

Combining Open Sentences

Solving Combined Inequalities

478

(4)

Absolute Value in Open Sentences

482

(4)

Absolute Values of Products in Open Sentences

486

(4)

Inequalities in Two Variables

Graphing Linear Inequalities

490

(5)

Systems of Linear Inequalities

495

(12)

Explorations Exploring Properties of Equality and Order 696

Technology Computer Exercises 460, 481 Computer Graphing Ideas 494 Calculator Key-In 498

Special Topics Biographical Note 461 Reading Algebra 468 Challenge 475 Intersection and Union of Sets 476 Historical Note 477 Career Note / Pharmacist 489 The Graph of y = |ax + b| + c 494 Application / Linear Programming 499

Reviews and Tests Mixed Review 461, 467, 475, 481, 485, 488, 494, 498 Self-Tests 475, 489, 498 Chapter Summary 501 Chapter Review 501 Chapter Test 502 Cumulative Review 503 Maintaining Skills 504 Preparing for College Entrance Exams 505

Rational and Irrational Numbers

Rational Numbers

Properties of Rational Numbers

507

(5)

Decimal Forms of Rational Numbers

512

(5)

Rational Square Roots

517

(4)

Irrational Numbers

Irrational Square Roots

521

(4)

Square Roots of Variable Expressions

525

(4)

The Pythagorean Theorem

529

(8)

Radical Expressions

Multiplying, Dividing, and Simplifying Radicals

537

(3)

Adding and Subtracting Radicals

540

(4)

Multiplication of Binomials Containing Radicals

544

(3)

Simple Radical Equations

547

(14)

Explorations Exploring Decimals 697 Exploring Irrational Numbers 698

Technology Calculator Key-In 528, 554 Computer Exercises 532

Special Topics Challenge 520, 534, 536 Historical Note 523 Irrationality of √2 524 Career Note / Operations Research Analyst 528 The Distance Formula 535 Biographical Note 542 Proving Divisibility Tests 543 Fractional Exponents 551

Reviews and Tests Mixed Review 511, 516, 520, 523, 528, 534, 539, 542, 546, 550 Self-Tests 520, 534, 550 Chapter Summary 554 Chapter Review 555 Chapter Test 556 Cumulative Review 557 Maintaining Skills 558 Mixed Problem Solving 559

Quadratic Functions

Quadratic Equations

Quadratic Equations with Perfect Squares

561

(3)

Completing the Square

564

(3)

The Quadratic Formula

567

(5)

Graphs of Quadratic Equations: The Discriminant

572

(4)

Using Quadratic Equations

Methods of Solution

576

(3)

Solving Problems Involving Quadratic Equations

579

(5)

Variation

Direct and Inverse Variation Involving Squares

584

(4)

Joint and Combined Variation

588

(12)

Explorations Exploring Quadratic Equations 700

Technology Computer Exercises 570, 575 Computer Graphing Ideas 700

Special Topics Imaginary Numbers 570 Biographical Note 578 Quadratic Inequalities 581 Application / Boyle's Gas Law 583 Application / Illumination 593

Reviews and Tests Mixed Review 563, 566, 570, 575, 578, 581, 587, 592 Self-Tests 575, 582, 594 Chapter Summary 594 Chapter Review 595 Chapter Test 596 Cumulative Review 597 Preparing for College Entrance Exams 599

Looking Ahead

Probability

Sample Spaces and Events

600

(3)

Probability

603

(3)

Statistics

Frequency Distributions

606

(5)

Presenting Statistical Data

611

(5)

Geometry

Points, Lines, and Angles

616

(3)

Pairs of Angles

619

(2)

Triangles

621

(3)

Similar Triangles

624

(3)

Trigonometry

Trigonometric Ratios

627

(3)

Values of Trigonometric Ratios

630

(3)

Problem Solving Using Trigonometry

633

(6)

Technology Computer Graphing Ideas 607

Special Topics Measures of Variation 609 Application / Misuse of Statistics 614 Challenge 632

Reviews and Tests Summary 637 Review 637

Extra Practice: Skills

639

(26)

Problem Solving

665

(16)

Tables

681

(4)

Explorations

685

(16)

Portfolio Projects

701

(8)

Appendix 1: Preparing for College Entrance Exams

709

(4)

Appendix 2: Point-Slope Form

713

(2)

Appendix 3: Inductive and Deductive Reasoning

715

(3)

Appendix 4: Hypothesis and Conclusion

718

(2)

Appendix 5: Indirect Reasoning

720

(1)

Glossary of Properties

721

(2)

Glossary of Terms

723

(10)

Index

733

(10)

Acknowledgements

743

Answers to Selected Exercises

Algebra Structure and Method, Grades 8-11 Book 1: Mcdougal Littell Structure & Method

9780395977224

0395977223

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