Algebra Structure and Method, Grades 8-11 Book 1: Mcdougal Littell Structure & Method,9780395977224

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

by
ISBN13: 9780395977224
ISBN10: 0395977223
Format: Hardcover
Pub. Date: 1999-01-13
Publisher(s): Holt McDougal
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Table of Contents

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

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