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

by Holt Mcdougal

• ISBN13: 9780395977224
• ISBN10: 0395977223
• Additional ISBN(s): 9780395461402, 9780395676080
• Format: Hardcover
• Copyright: 1999-01-13
• Publisher: Holt McDougal
• More Book Details

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