Introduction 1
About This Book 1
Foolish Assumptions 2
Icons Used in This Book 2
Beyond the Book 3
Where to Go from Here 3
Book 1: Starting Out With Numbers and Properties 5
Chapter 1: Assembling Your Tools: Number Systems 7
Identifying Numbers by Name 8
Realizing real numbers 8
Counting on natural numbers 8
Whittling out whole numbers 8
Integrating integers 9
Being reasonable: Rational numbers 9
Restraining irrational numbers 9
Picking out primes and composites 10
Zero: It’s Complicated 10
Imagining imaginary numbers 10
Coping with complex numbers 10
Placing Numbers on the Number Line 12
Speaking in Algebra 13
Being precise with words 13
Describing the size of an expression 15
Relating operations with symbols 15
Taking Aim at Algebra-Speak 17
Herding numbers with grouping symbols 17
Defining relationships 19
Taking on algebraic tasks 20
Practice Questions Answers and Explanations 22
Whaddya Know? Chapter 1 Quiz 23
Answers to Chapter 1 Quiz 25
Chapter 2: Deciphering Signs in Expressions 27
Assigning Numbers Their Place 27
Using the number line 28
Comparing positives and negatives with symbols 29
Zeroing in on Zero 31
Going in for Operations 32
Sorting out types of operations 32
Tackling the Basic Binary Operations 35
Adding signed numbers 35
Making a Difference with Signed Numbers 38
Multiplying Signed Numbers 40
Dividing Signed Numbers 41
Working with Nothing: Zero and Signed Numbers 42
Practice Questions Answers and Explanations 44
Whaddya Know? Chapter 2 Quiz 47
Answers to Chapter 2 Quiz 48
Chapter 3: Incorporating Algebraic Properties 49
Getting a Grip on Grouping Symbols 49
Spreading, Grouping, and Changing the Order 52
Distributing the wealth 52
Making Associations Work 53
Computing by Commuting 55
Relating Inverses and Identities 56
Investigating Inverses 56
Identifying Identities 58
Working with Factorial 59
Applying the Greatest Integer Function 60
Practice Question Answers and Explanations 62
Whaddya Know? Chapter 3 Quiz 66
Answers to Chapter 3 Quiz 67
Chapter 4: Coordinating Fractions and Decimals 69
Converting Improper Fractions and Mixed Numbers 70
Finding Fraction Equivalences 72
Rewriting fractions 72
Determining lowest terms 74
Making Proportional Statements 75
Finding Common Denominators 77
Creating common denominators from multiples of factors 78
Using the box method 80
Applying Fractional Operations 81
Adding and subtracting fractions 81
Multiplying and dividing fractions 83
Simplifying Complex Fractions 86
Performing Operations with Decimals 88
Changing Fractions to Decimals and Vice Versa 89
Making fractions become decimals 90
Rounding decimals 91
Writing decimals as equivalent fractions 91
Practice Question Answers and Explanations 94
Whaddya Know? Chapter 4 Quiz 101
Answers to Chapter 4 Quiz 103
Book 2: Operating On Operations 105
Chapter 5: Taming Rampaging Radicals 107
Simplifying Radical Terms 108
Working through Radical Expressions 109
Recognizing perfect square terms 109
Rewriting radical terms 110
Rationalizing Fractions 113
Managing Radicals as Exponential Terms 114
Using Fractional Exponents 116
Making the switch to fractional exponents 117
Simplifying expressions with exponents 118
Estimating Answers 119
Practice Questions Answers and Explanations 120
Whaddya Know? Chapter 5 Quiz 124
Answers to Chapter 5 Quiz 125
Chapter 6: Exploring Exponents 127
Powering up with Exponential Notation 127
Using Negative Exponents 130
Multiplying and Dividing Exponentials 132
Multiplying the same base 132
Multiplying the same power 133
Dividing with exponents 135
Raising Powers to Powers 137
Testing the Power of Zero 139
Writing Numbers with Scientific Notation 140
Practice Questions Answers and Explanations 143
Whaddya Know? Chapter 6 Quiz 145
Answers to Chapter 6 Quiz 146
Book 3: Making Things Simple by Simplifying 149
Chapter 7: Simplifying Algebraic Expressions 151
Addressing the Order of Operations 152
Adding and Subtracting Like Terms 154
Multiplying and Dividing Algebraically 157
Dealing with factors 157
Diving into dividing 158
Gathering Terms with Grouping Symbols 160
Evaluating Expressions 163
Checking Your Answers 165
Seeing if it makes sense 165
Plugging in values 166
Practice Questions Answers and Explanations 168
Whaddya Know? Chapter 7 Quiz 171
Answers to Chapter 7 Quiz 172
Chapter 8: Working with Numbers in Their Prime 175
Beginning with the Basics 176
Composing Composite Numbers 178
Writing Prime Factorizations 178
Dividing while standing on your head 178
Getting to the root of primes with a tree 180
Wrapping your head around the rules of divisibility 182
Making Use of a Prime Factor 185
Taking primes into account 185
Pulling out factors and leaving the rest 187
Practice Questions Answers and Explanations 190
Whaddya Know? Chapter 8 Quiz 194
Answers to Chapter 8 Quiz 195
Chapter 9: Specializing in Multiplication Matters 197
Distributing One Factor Over Many 198
Distributing Signs 200
Mixing It up with Numbers and Variables 201
Negative exponents yielding fractional answers 203
Working with Fractional Powers 205
Distributing More Than One Term 207
Distributing binomials 207
Distributing trinomials 209
Curses, Foiled Again — Or Not 210
Squaring Binomials 211
Multiplying the Sum and Difference of the Same Two Terms 212
Powering Up Binomials 213
Cubing binomials 213
Raising Binomials to Higher Powers 215
Creating the Sum and Difference of Cubes 217
Multiplying Conjugates 218
Practice Questions Answers and Explanations 220
Whaddya Know? Chapter 9 Quiz 225
Answers to Chapter 9 Quiz 226
Chapter 10: Dividing the Long Way to Simplify Algebraic Expressions 229
Dividing by a Monomial 229
Dividing by a Binomial 231
Dividing by Polynomials with More Terms 233
Simplifying Division Synthetically 235
Practice Questions Answers and Explanations 237
Whaddya Know? Chapter 10 Quiz 240
Answers to Chapter 10 Quiz 241
Book 4: Factoring 243
Chapter 11: Figuring on Factoring 245
Factoring out the Greatest Common Factor 245
Factoring out numbers 246
Factoring out variables 249
Unlocking combinations of numbers and variables 252
Using the Box Method 255
Changing Factoring into a Division Problem 257
Reducing Algebraic Fractions 258
Practice Questions Answers and Explanations 260
Whaddya Know? Chapter 11 Quiz 262
Answers to Chapter 11 Quiz 264
Chapter 12: Taking the Bite out of Binomial Factoring 267
Reining in Big and Tiny Numbers 268
Factoring the Difference of Squares 269
Factoring Differences and Sums of Cubes 271
Making Factoring a Multiple Mission 274
Practice Questions Answers and Explanations 277
Whaddya Know? Chapter 12 Quiz 279
Answers to Chapter 12 Quiz 280
Chapter 13: Factoring Trinomials and Special Polynomials 281
Recognizing the Standard Quadratic Expression 281
Focusing First on the Greatest Common Factor 283
Unwrapping the FOILing Package 284
The opening to unFOIL 284
Coming to the end of the FOIL roll 287
Factoring Quadratic-Like Trinomials 290
Factoring Trinomials Using More Than One Method 291
Factoring by Grouping 293
Putting All the Factoring Together and Making Factoring Choices 297
Combining unFOIL and the GCF 297
Grouping and unFOILing in the same package 298
Incorporating the Remainder Theorem 301
Synthesizing with synthetic division 302
Choosing numbers for synthetic division 303
Practice Questions Answers and Explanations 305
Whaddya Know? Chapter 13 Quiz 310
Answers to Chapter 13 Quiz 311
Book 5: Solving Linear And Polynomial Equations 313
Chapter 14: Establishing Ground Rules for Solving Equations 315
Creating the Correct Setup for Solving Equations 316
Setting up equations for further action 316
Making plans for solving equations 316
Keeping Equations Balanced 318
Balancing with binary operations 318
Squaring both sides and suffering the consequences 320
Taking a root of both sides 322
Solving with Reciprocals 323
Making a List and Checking It Twice 324
Doing a reality check 324
Thinking like a car mechanic when checking your work 325
Practice Problems Answers and Explanations 328
Whaddya Know? Chapter 14 Quiz 330
Answers to Chapter 14 Quiz 331
Chapter 15: Lining Up Linear Equations 333
Playing by the Rules 334
Using the Addition/Subtraction Property 334
Using the Multiplication/Division Property 336
Devising a method using division 336
Making the most of multiplication 337
Reciprocating the invitation 338
Putting Several Operations Together 339
Solving Linear Equations with Grouping Symbols 343
Nesting isn’t for the birds 343
Distributing first 343
Multiplying or dividing before distributing 346
Working with Proportions 349
Using the rules for proportions 349
Transforming fractional equations into proportions 351
Solving for Variables in Formulas 352
Practice Questions Answers and Explanations 355
Whaddya Know? Chapter 15 Quiz 363
Answers to Chapter 15 Quiz 364
Chapter 16: Muscling Up to Quadratic Equations 367
Using the Square-Root Rule 368
Factoring for a Solution 370
Zeroing in on the multiplication property of zero 370
Assigning the greatest common factor and multiplication property of zero to solving quadratics 372
Solving Quadratics with Three Terms 373
Using the Quadratic Formula 379
Completing the Square 383
Imagining the Worst with Imaginary Numbers 384
Practice Problems Answers and Explanations 387
Whaddya Know? Chapter 16 Quiz 392
Answers to Chapter 16 Quiz 393
Book 6: Dealing With Non-Polynomial Equations and Inequalities 395
Chapter 17: Yielding to Higher Powers 397
Queuing Up to Cubic Equations 397
Solving perfectly cubed equations 398
Working with the not-so-perfectly cubed 400
Going for the greatest common factor 401
Grouping cubes 404
Solving cubics with integers 405
Determining How Many Possible Roots 407
Applying the Rational Root Theorem 408
Using the Factor/Root Theorem 410
Solving by Factoring 411
Solving Powers That Are Quadratic-Like 412
Solving Synthetically 416
Practice Questions Answers and Explanations 420
Whaddya Know? Chapter 17 Quiz 426
Answers to Chapter 17 Quiz 427
Chapter 18: Reeling in Radical and Absolute Value Equations 429
Raising Both Sides to Solve Radical Equations 430
Powering up by squaring both sides 430
Raising to higher powers 433
Doubling the Fun with Radical Equations .435
Solving Absolute Value Equations 437
Making linear absolute value equations absolutely wonderful 437
Factoring absolute value equations for solutions 440
Checking for Absolute Value Extraneous Roots 441
Practice Questions Answers and Explanations 443
Whaddya Know? Chapter 18 Quiz 447
Answers to Chapter 18 Quiz 448
Chapter 19: Getting Even with Inequalities 449
Defining the Inequality Notation 450
Pointing in the right direction 450
Grappling with graphing inequalities 450
Using the Rules to Work on Inequality Statements 451
Rewriting Inequalities Using Interval Notation 453
Solving Linear Inequalities 455
Solving Quadratic Inequalities 457
Dealing with Polynomial and Rational Inequalities 460
Solving Absolute-Value Inequalities 463
Solving Complex Inequalities 465
Practice Questions Answers and Explanations 467
Whaddya Know? Chapter 19 Quiz 471
Answers to Chapter 19 Quiz 472
Book 7: Evaluating Formulas and Story Problems 475
Chapter 20: Facing Up to Formulas 477
Working with Formulas 477
Measuring Up 479
Finding out how long: Units of length 479
Putting the Pythagorean Theorem to work 482
Deciphering Perimeter, Area, and Volume 484
Using perimeter formulas to get around 484
Squaring off with area formulas 486
Soaring with Heron’s formula 488
Working with volume formulas 490
Getting Interested in Using Percent 492
Compounding interest formulas 492
Gauging taxes and discounts 495
Working out the Combinations and Permutations 497
Counting down to factorials 498
Counting on combinations 498
Ordering up permutations 500
Practice Questions Answers and Explanations 502
Whaddya Know? Chapter 20 Quiz 505
Answers to Chapter 20 Quiz 507
Chapter 21: Making Formulas Work in Basic Story Problems 509
Setting Up to Solve Story Problems 509
Applying the Pythagorean Theorem 511
Using Geometry to Solve Story Problems 513
Working around Perimeter, Area, and Volume 515
Parading out perimeter and arranging area 515
Adjusting the area 517
Pumping up the volume 519
Going ’Round in Circles 523
Putting Distance, Rate, and Time in a Formula 525
Going the distance with the distance-rate-time formula 525
Figuring distance plus distance 527
Equating distances 528
Figuring distance and fuel 529
Counting on Interest and Percent 530
Practice Questions Answers and Explanations 532
Whaddya Know? Chapter 21 Quiz 537
Answers to Chapter 21 Quiz 539
Chapter 22: Relating Values in Story Problems 541
Tackling Age Problems 542
Tackling Consecutive Integer Problems 543
Working Together on Work Problems 545
Throwing an Object into the Air 547
Practice Questions Answers and Explanations 550
Whaddya Know? Chapter 22 Quiz 553
Answers to Chapter 22 Quiz 554
Chapter 23: Measuring Up with Quality and Quantity Story Problems 555
Achieving the Right Blend with Mixture Problems 556
Concocting the Correct Solution 100% of the Time 559
Dealing with Money Problems 561
Investigating investments and interest 561
Going for the green: Money 564
Practice Questions Answers and Explanations 567
Whaddya Know? Chapter 23 Quiz 571
Answers to Chapter 23 Quiz 572
Book 8: Getting a Grip On Graphing 573
Chapter 24: Getting a Handle on Graphing 575
Thickening the Plot with Points 575
Interpreting ordered pairs 576
Actually Graphing Points 577
Sectioning Off by Quadrants 578
Graphing Lines 579
Using points to lay out lines 579
Going with the horizontal and vertical 581
Graphing Lines Using Intercepts 583
Computing Slopes of Lines 585
Sighting the slope 585
Formulating slope 587
Graphing with the Slope-Intercept Form 590
Changing to the Slope-Intercept Form 591
Writing Equations of Lines 592
Given a point and a slope 593
Given two points 593
Picking on Parallel and Perpendicular Lines 594
Finding Distances between Points 595
Finding Midpoints of Segments 597
Practice Questions Answers and Explanations 598
Whaddya Know? Chapter 24 Quiz 602
Answers to Chapter 24 Quiz 604
Chapter 25: Extending the Graphing Horizon 605
Finding the Intersections of Lines 605
Graphing for intersections 606
Substituting to find intersections 607
Graphing Parabolas and Circles 608
Curling Up with Parabolas 609
Trying out the basic parabola 609
Putting the vertex on an axis 610
Going around in circles with a circular graph 612
Plotting and Plugging in Polynomial Graphs 614
Investigating Graphs of Inequality Functions 618
Taking on Absolute-Value Function Graphs 620
Graphing with Transformations 621
Sliding and multiplying 622
Practice Questions Answers and Explanations 625
Whaddya Know? Chapter 25 Quiz 632
Answers to Chapter 25 Quiz 633
Chapter 26: Coordinating Systems of Equations and Graphing 639
Defining Solutions of Systems of Equations 639
Solving Systems of Linear Equations 641
Using elimination 641
Using substitution 642
Introducing intersections of lines 643
Solving Systems Involving Non-Linear Equations 644
Taking on Systems of Three Linear Equations 647
Practice Problems Answers and Explanations 648
Whaddya Know? Chapter 26 Quiz 651
Answers to Chapter 26 Quiz 652
Index 655
