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

Introduction to Algebra Variables and Equations Variables 1(5) Grouping Symbols 6(4) Equations 10(4) Applications and Problem Solving Translating Words into Symbols 14(5) Translating Sentences into Equations 19(4) Translating Problems into Equations 23(4) A Problem Solving Plan 27(4) Numbers on a Line Number Lines 31(5) Opposites and Absolute Values 36(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 45(4) Addition on a Number Line 49(5) Rules for Addition 54(5) Subtracting Real Numbers 59(6) Multiplication The Distributive Property 65(5) Rules for Multiplication 70(5) Problem Solving: Consecutive Integers 75(4) Division The Reciprocal of a Real Number 79(4) Dividing Real Numbers 83(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 95(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