Algebra Know-It-All (Know It All)

✍ Scribed by Stan Gibilisco

• Publisher: McGraw-Hill/TAB Electronics
• Year: 2008
• Tongue: English
• Leaves: 746
• Edition: 1
• Category: Library

✦ Synopsis

Master algebra from the comfort of home! Want to “know it all” when it comes to algebra? Algebra Know-It-ALL gives you the expert, one-on-one instruction you need, whether you're new to algebra or you're looking to ramp up your skills. Providing easy-to-understand concepts and thoroughly explained exercises, math whiz Stan Gibilisco serves as your own private tutor-without the expense! His clear, friendly guidance helps you tackle the concepts and problems that confuse you the most and work through them at your own pace. Train your brain with ease! Algebra Know-It-ALL features: Icons to help you identify your current skill level Chapter-end quizzes and word problem/solution pairs to reinforce learning Worked-out answers to all practice exercises Extensive multiple-choice questions to prepare you for standardized tests “Extra Credit” and “Challenge” problems to stretch your skills Stan's expert guidance gives you the know-how to: Solve arithmetic problems without a calculator Convert fractions to decimal form and vice-versa Manipulate simple equations and inequalities Learn how coordinate systems work Make simple graphs Solve quadratic and cubic equations Understand complex-number solutions to equations Use logarithms and exponential functions Take college entrance examinations with confidence li>And much more!

✦ Table of Contents

Contents......Page 9
Preface......Page 15
Acknowledgment......Page 16
Part 1 Numbers, Sets, and Operations......Page 17
Fingers and Sticks......Page 19
Roman Numerals......Page 22
Hindu-Arabic Numerals......Page 24
The Counting Base......Page 27
Practice Exercises......Page 33
The Concept of a Set......Page 35
How Sets Relate......Page 38
Set Intersection......Page 43
Set Union......Page 46
Practice Exercises......Page 49
How Natural Numbers are Made......Page 51
Special Natural Numbers......Page 54
Natural Number Nontrivia......Page 58
The Integers......Page 61
Practice Exercises......Page 65
Moving Up and Down......Page 67
Identity, Grouping, and Signs......Page 71
The Commutative Law for Addition......Page 73
The Associative Law for Addition......Page 75
Practice Exercises......Page 79
Moving Out and In......Page 81
Identity, Grouping, and Signs......Page 86
The Commutative Law for Multiplication......Page 89
The Associative Law for Multiplication......Page 91
The Distributive Laws......Page 94
Practice Exercises......Page 97
“Messy” Quotients......Page 99
“Reducing” a Fraction or Ratio......Page 103
Multiplying and Dividing Fractions......Page 105
Adding and Subtracting Fractions......Page 107
Practice Exercises......Page 110
Powers of 10......Page 111
Terminating Decimals......Page 115
Endless Decimals......Page 117
Conversions......Page 120
Practice Exercises......Page 123
Integer Powers......Page 125
Reciprocal-of-Integer Powers......Page 128
Multiplying and Dividing with Exponents......Page 133
Multiple Powers......Page 135
Practice Exercises......Page 139
The Number Hierarchy......Page 140
More About Irrationals and Reals......Page 145
How Real Variables Behave......Page 149
More Rules for Real Variables......Page 152
Practice Exercises......Page 156
10 Review Questions and Answers......Page 158
Part 2 Linear Equations and Relations......Page 187
Equation Morphing Revisited......Page 189
Inequalities......Page 192
How Inequalities Behave......Page 195
Inequality Morphing......Page 199
Practice Exercises......Page 206
Constants, Sums, and Differences......Page 208
Products and Ratios......Page 212
Combinations of Operations......Page 214
Word Problems......Page 219
Practice Exercises......Page 223
Mapping “Territories”......Page 224
Types of Mappings......Page 227
Examples of Relations......Page 231
Examples of Functions......Page 234
Practice Exercises......Page 237
Two Number Lines......Page 239
Three Relations......Page 242
Three Functions......Page 248
Practice Exercises......Page 250
Slope-Intercept Form......Page 252
Point-Slope Form......Page 258
Equations from Graphs......Page 260
Practice Exercises......Page 265
Morph and Mix......Page 267
Double Elimination......Page 271
Rename and Replace......Page 274
Practice Exercises......Page 278
We Morphed, We Mixed, We Can Graph......Page 280
We Added, We Eliminated, We Can Graph......Page 283
We Renamed, We Replaced, We Can Graph......Page 287
We Couldn’t Solve, but We Can Graph......Page 291
Practice Exercises......Page 294
Eliminate One Variable......Page 297
Solve the Two-by-Two......Page 301
Substitute Back......Page 304
General Linear Systems......Page 306
Practice Exercises......Page 310
How to Build a Matrix......Page 312
Matrix Operations......Page 314
A Sample Problem......Page 316
Practice Exercises......Page 322
20 Review Questions and Answers......Page 324
Part 3 Nonlinear Equations and Relations......Page 363
The Square Root of –1......Page 365
The Imaginary Number Line......Page 367
Real + Imaginary = Complex......Page 371
Practice Exercises......Page 377
Second-Degree Polynomials......Page 379
Binomial Factor Form......Page 383
Completing the Square......Page 387
The Quadratic Formula......Page 391
Practice Exercises......Page 395
Complex Roots by Formula......Page 397
Imaginary Roots in Factors......Page 403
Conjugate Roots in Factors......Page 407
Practice Exercises......Page 411
Two Real Zeros......Page 412
One Real Zero......Page 418
No Real Zeros......Page 423
Practice Exercises......Page 428
Cube of Binomial......Page 429
Three Binomial Factors......Page 431
Binomial Times Trinomial......Page 435
Polynomial Equation of Third Degree......Page 438
Practice Exercises......Page 446
Binomial to the nth Power......Page 448
Binomial Factors......Page 451
Polynomial Standard Form......Page 454
Digging for Real Roots......Page 455
Practice Exercises......Page 461
Linear and Quadratic......Page 463
Two Quadratics......Page 467
Enter the Cubic......Page 472
Practice Exercises......Page 477
Linear and Quadratic......Page 479
Two Quadratics......Page 482
Enter the Cubic......Page 487
Practice Exercises......Page 491
What Is a Logarithm?......Page 495
How Logarithms Work......Page 498
What Is an Exponential?......Page 503
How Exponentials Work......Page 507
Practice Exercises......Page 512
30 Review Questions and Answers......Page 514
Final Exam......Page 561
Appendix A: Worked-Out Solutions to Exercises: Chapters 1 to 9......Page 603
Appendix B: Worked-Out Solutions to Exercises: Chapters 11 to 19......Page 635
Appendix C: Worked-Out Solutions to Exercises: Chapters 21 to 29......Page 679
Appendix D: Answers to Final Exam Questions......Page 732
Appendix E: Special Characters in Order of Appearance......Page 733
Suggested Additional Reading......Page 735
B......Page 737
C......Page 738
F......Page 739
I......Page 740
M......Page 741
N......Page 742
P......Page 743
R......Page 744
T......Page 745
Z......Page 746