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

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  • Edition: 1st
  • Format: Paperback
  • Copyright: 2008-07-11
  • Publisher: McGraw-Hill Education TAB
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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

Prefacep. xiii
Acknowledgmentp. xiv
Numbers, Sets, and Operations
Counting Methodsp. 3
Fingers and Sticksp. 3
Roman Numeralsp. 6
Hindu-Arabic Numeralsp. 8
The Counting Basep. 11
Practice Exercisesp. 17
The Language of Setsp. 19
The Concept of a Setp. 19
How Sets Relatep. 22
Set Intersectionp. 27
Set Unionp. 30
Practice Exercisesp. 33
Natural Numbers and Integersp. 35
How Natural Numbers are Madep. 35
Special Natural Numbersp. 38
Natural Number Nontriviap. 42
The Integersp. 45
Practice Exercisesp. 49
Addition and Subtractionp. 51
Moving Up and Downp. 51
Identity, Grouping, and Signsp. 55
The Commutative Law for Additionp. 57
The Associative Law for Additionp. 59
Practice Exercisesp. 63
Multiplication and Divisionp. 65
Moving Out and Inp. 65
Identity, Grouping, and Signsp. 70
The Commutative Law for Multiplicationp. 73
The Associative Law for Multiplicationp. 75
The Distributive Lawsp. 78
Practice Exercisesp. 81
Fractions Built of Integersp. 83
"Messy" Quotientsp. 83
"Reducing" a Fraction or Ratiop. 87
Multiplying and Dividing Fractionsp. 89
Adding and Subtracting Fractionsp. 91
Practice Exercisesp. 94
Decimal Fractionsp. 95
Powers of 10p. 95
Terminating Decimalsp. 99
Endless Decimalsp. 101
Conversionsp. 104
Practice Exercisesp. 107
Powers and Rootsp. 109
Integer Powersp. 109
Reciprocal-of-Integer Powersp. 112
Multiplying and Dividing with Exponentsp. 117
Multiple Powersp. 119
Practice Exercisesp. 123
Irrational and Real Numbersp. 124
The Number Hierarchyp. 124
More About Irrationals and Realsp. 129
How Real Variables Behavep. 133
More Rules for Real Variablesp. 136
Practice Exercisesp. 140
Review Questions and Answersp. 142
Linear Equations and Relations
Equations and Inequalitiesp. 173
Equation Morphing Revisitedp. 173
Inequalitiesp. 176
How Inequalities Behavep. 179
Inequality Morphingp. 183
Practice Exercisesp. 190
First-Degree Equations in One Variablep. 192
Constants, Sums, and Differencesp. 192
Products and Ratiosp. 196
Combinations of Operationsp. 198
Word Problemsp. 203
Practice Exercisesp. 207
Mappings, Relations, and Functionsp. 208
Mapping "Territories"p. 208
Types of Mappingsp. 211
Examples of Relationsp. 215
Examples of Functionsp. 218
Practice Exercisesp. 221
The Cartesian Planep. 223
Two Number Linesp. 223
Three Relationsp. 226
Three Functionsp. 232
Practice Exercisesp. 234
Graphs of Linear Relationsp. 236
Slope-Intercept Formp. 236
Point-Slope Formp. 242
Equations from Graphsp. 244
Practice Exercisesp. 249
Two-by-Two Linear Systemsp. 251
Morph and Mixp. 251
Double Eliminationp. 255
Rename and Replacep. 258
Practice Exercisesp. 262
Two-by-Two Linear Graphsp. 264
We Morphed, We Mixed, We Can Graphp. 264
We Added, We Eliminated, We Can Graphp. 267
We Renamed, We Replaced, We Can Graphp. 271
We Couldn't Solve, but We Can Graphp. 275
Practice Exercisesp. 278
Larger Linear Systemsp. 281
Eliminate One Variablep. 281
Solve the Two-by-Twop. 285
Substitute Backp. 288
General Linear Systemsp. 290
Practice Exercisesp. 294
The Matrix Morphing Gamep. 296
How to Build a Matrixp. 296
Matrix Operationsp. 298
A Sample Problemp. 300
Practice Exercisesp. 306
Review Questions and Answersp. 308
Nonlinear Equations and Relations
Imaginary and Complex Numbersp. 349
The Square Root of -1p. 349
The Imaginary Number Linep. 351
Real + Imaginary = Complexp. 355
Practice Exercisesp. 361
Quadratic Equations with Real Rootsp. 363
Second-Degree Polynomialsp. 363
Binomial Factor Formp. 367
Completing the Squarep. 371
The Quadratic Formulap. 375
Practice Exercisesp. 379
Quadratic Equations with Complex Rootsp. 381
Complex Roots by Formulap. 381
Imaginary Roots in Factorsp. 387
Conjugate Roots in Factorsp. 391
Practice Exercisesp. 395
Graphs of Quadratic Functionsp. 396
Two Real Zerosp. 396
One Real Zerop. 402
No Real Zerosp. 407
Practice Exercisesp. 412
Cubic Equations in Real Numbersp. 413
Cube of Binomialp. 413
Three Binomial Factorsp. 415
Binomial Times Trinomialp. 419
Polynomial Equation of Third Degreep. 422
Practice Exercisesp. 430
Polynomial Equations in Real Numbersp. 432
Binomial to the nth Powerp. 432
Binomial Factorsp. 435
Polynomial Standard Formp. 438
Digging for Real Rootsp. 439
Practice Exercisesp. 445
More Two-by-Two Systemsp. 447
Linear and Quadraticp. 447
Two Quadraticsp. 451
Enter the Cubicp. 456
Practice Exercisesp. 461
More Two-by-Two Graphsp. 463
Linear and Quadraticp. 463
Two Quadraticsp. 466
Enter the Cubicp. 471
Practice Exercisesp. 475
Logarithms and Exponentialsp. 479
What Is a Logarithm?p. 479
How Logarithms Workp. 482
What Is an Exponential?p. 487
How Exponentials Workp. 491
Practice Exercisesp. 496
Review Questions and Answersp. 498
Final Examp. 545
Worked-Out Solutions to Exercises: Chapters 1 to 9p. 587
Worked-Out Solutions to Exercises: Chapters 11 to 19p. 619
Worked-Out Solutions to Exercises: Chapters 21 to 29p. 663
Answers to Final Exam Questionsp. 716
Special Characters in Order of Appearancep. 717
Suggested Additional Readingp. 719
Indexp. 721
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