Algebra Know-It-ALL Beginner to Advanced, and Everything in Between

by Gibilisco, Stan

• ISBN13: 9780071546171
• ISBN10: 0071546170
• eBook ISBN(s): 9780071546188
• Edition: 1st
• Format: Paperback
• Copyright: 2008-07-11
• Publisher: McGraw Hill TAB
• More Book Details
• Purchase Benefits

Summary

McGraw-Hill's new "Know-it-ALL" series makes you feel like you've got a private tutor This inviting tutorial guide provides all the benefits of a textbook without the high price and technical verbiage. The author provides an extensive selection of multiple-choice questions to coach you in taking standardized tests. All practice problems are complemented by fully worked-out answers with explanations. For those who firmly grasp the subject matter, "extra credit" questions reinforce their mastery.

Author Biography

Stan Gibilisco is one of McGraw-Hill's most prolific and popular authors. His clear, reader-friendly writing style makes his books accessible to a wide audience, and his experience as an electronics engineer, researcher, and mathematician makes him an ideal editor for reference books and tutorials. Stan has authored several titles for the McGraw-Hill Demystified library of home-schooling and self-teaching volumes, along with more than 30 other books and dozens of magazine articles. His work has been published in several languages. Booklist named his McGraw-Hill Encyclopedia of Personal Computing one of the "Best References of 1996," and named his Encyclopedia of Electronics one of the "Best References of the 1980s."

Table of Contents

Preface	p. xiii
Acknowledgment	p. xiv
Numbers, Sets, and Operations
Counting Methods	p. 3
Fingers and Sticks	p. 3
Roman Numerals	p. 6
Hindu-Arabic Numerals	p. 8
The Counting Base	p. 11
Practice Exercises	p. 17
The Language of Sets	p. 19
The Concept of a Set	p. 19
How Sets Relate	p. 22
Set Intersection	p. 27
Set Union	p. 30
Practice Exercises	p. 33
Natural Numbers and Integers	p. 35
How Natural Numbers are Made	p. 35
Special Natural Numbers	p. 38
Natural Number Nontrivia	p. 42
The Integers	p. 45
Practice Exercises	p. 49
Addition and Subtraction	p. 51
Moving Up and Down	p. 51
Identity, Grouping, and Signs	p. 55
The Commutative Law for Addition	p. 57
The Associative Law for Addition	p. 59
Practice Exercises	p. 63
Multiplication and Division	p. 65
Moving Out and In	p. 65
Identity, Grouping, and Signs	p. 70
The Commutative Law for Multiplication	p. 73
The Associative Law for Multiplication	p. 75
The Distributive Laws	p. 78
Practice Exercises	p. 81
Fractions Built of Integers	p. 83
"Messy" Quotients	p. 83
"Reducing" a Fraction or Ratio	p. 87
Multiplying and Dividing Fractions	p. 89
Adding and Subtracting Fractions	p. 91
Practice Exercises	p. 94
Decimal Fractions	p. 95
Powers of 10	p. 95
Terminating Decimals	p. 99
Endless Decimals	p. 101
Conversions	p. 104
Practice Exercises	p. 107
Powers and Roots	p. 109
Integer Powers	p. 109
Reciprocal-of-Integer Powers	p. 112
Multiplying and Dividing with Exponents	p. 117
Multiple Powers	p. 119
Practice Exercises	p. 123
Irrational and Real Numbers	p. 124
The Number Hierarchy	p. 124
More About Irrationals and Reals	p. 129
How Real Variables Behave	p. 133
More Rules for Real Variables	p. 136
Practice Exercises	p. 140
Review Questions and Answers	p. 142
Linear Equations and Relations
Equations and Inequalities	p. 173
Equation Morphing Revisited	p. 173
Inequalities	p. 176
How Inequalities Behave	p. 179
Inequality Morphing	p. 183
Practice Exercises	p. 190
First-Degree Equations in One Variable	p. 192
Constants, Sums, and Differences	p. 192
Products and Ratios	p. 196
Combinations of Operations	p. 198
Word Problems	p. 203
Practice Exercises	p. 207
Mappings, Relations, and Functions	p. 208
Mapping "Territories"	p. 208
Types of Mappings	p. 211
Examples of Relations	p. 215
Examples of Functions	p. 218
Practice Exercises	p. 221
The Cartesian Plane	p. 223
Two Number Lines	p. 223
Three Relations	p. 226
Three Functions	p. 232
Practice Exercises	p. 234
Graphs of Linear Relations	p. 236
Slope-Intercept Form	p. 236
Point-Slope Form	p. 242
Equations from Graphs	p. 244
Practice Exercises	p. 249
Two-by-Two Linear Systems	p. 251
Morph and Mix	p. 251
Double Elimination	p. 255
Rename and Replace	p. 258
Practice Exercises	p. 262
Two-by-Two Linear Graphs	p. 264
We Morphed, We Mixed, We Can Graph	p. 264
We Added, We Eliminated, We Can Graph	p. 267
We Renamed, We Replaced, We Can Graph	p. 271
We Couldn't Solve, but We Can Graph	p. 275
Practice Exercises	p. 278
Larger Linear Systems	p. 281
Eliminate One Variable	p. 281
Solve the Two-by-Two	p. 285
Substitute Back	p. 288
General Linear Systems	p. 290
Practice Exercises	p. 294
The Matrix Morphing Game	p. 296
How to Build a Matrix	p. 296
Matrix Operations	p. 298
A Sample Problem	p. 300
Practice Exercises	p. 306
Review Questions and Answers	p. 308
Nonlinear Equations and Relations
Imaginary and Complex Numbers	p. 349
The Square Root of -1	p. 349
The Imaginary Number Line	p. 351
Real + Imaginary = Complex	p. 355
Practice Exercises	p. 361
Quadratic Equations with Real Roots	p. 363
Second-Degree Polynomials	p. 363
Binomial Factor Form	p. 367
Completing the Square	p. 371
The Quadratic Formula	p. 375
Practice Exercises	p. 379
Quadratic Equations with Complex Roots	p. 381
Complex Roots by Formula	p. 381
Imaginary Roots in Factors	p. 387
Conjugate Roots in Factors	p. 391
Practice Exercises	p. 395
Graphs of Quadratic Functions	p. 396
Two Real Zeros	p. 396
One Real Zero	p. 402
No Real Zeros	p. 407
Practice Exercises	p. 412
Cubic Equations in Real Numbers	p. 413
Cube of Binomial	p. 413
Three Binomial Factors	p. 415
Binomial Times Trinomial	p. 419
Polynomial Equation of Third Degree	p. 422
Practice Exercises	p. 430
Polynomial Equations in Real Numbers	p. 432
Binomial to the nth Power	p. 432
Binomial Factors	p. 435
Polynomial Standard Form	p. 438
Digging for Real Roots	p. 439
Practice Exercises	p. 445
More Two-by-Two Systems	p. 447
Linear and Quadratic	p. 447
Two Quadratics	p. 451
Enter the Cubic	p. 456
Practice Exercises	p. 461
More Two-by-Two Graphs	p. 463
Linear and Quadratic	p. 463
Two Quadratics	p. 466
Enter the Cubic	p. 471
Practice Exercises	p. 475
Logarithms and Exponentials	p. 479
What Is a Logarithm?	p. 479
How Logarithms Work	p. 482
What Is an Exponential?	p. 487
How Exponentials Work	p. 491
Practice Exercises	p. 496
Review Questions and Answers	p. 498
Final Exam	p. 545
Worked-Out Solutions to Exercises: Chapters 1 to 9	p. 587
Worked-Out Solutions to Exercises: Chapters 11 to 19	p. 619
Worked-Out Solutions to Exercises: Chapters 21 to 29	p. 663
Answers to Final Exam Questions	p. 716
Special Characters in Order of Appearance	p. 717
Suggested Additional Reading	p. 719
Index	p. 721
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