Algebra II for Dummies

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Algebra II for Dummies

Format:  Paperback,

370 pages

Publisher: John Wiley & Sons Inc

Publish Date: Jul 2006

ISBN-13: 9780471775812

ISBN-10: 0471775819

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Besides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and possibly pursue further study in math.

"Algebra II For Dummies" is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems. This friendly guide shows you how to get up to speed on exponential functions, laws of logarithms, conic sections, matrices, and other advanced algebra concepts. In no time you'll have the tools you need to: Interpret quadratic functionsFind the roots of a polynomialReason with rational functionsExpose exponential and logarithmic functionsCut up conic sectionsSolve linear and non linear systems of equationsEquate inequalitiesSimplifyy complex numbersMake moves with matricesSort out sequences and sets

This straightforward guide offers plenty of multiplication tricks that only math teachers know. It also profiles special types of numbers, making it easy for you to categorize them and solve any problems without breaking a sweat. When it comes to understanding and working out algebraic equations, "Algebra II For Dummies" is all you need to succeed

Specifications

Author:
Publisher: John Wiley & Sons Inc
Publish Date: Jul 2006
ISBN-13: 9780471775812
ISBN-10: 0471775819
Format: Paperback
Number of Pages: 370
Shipping Weight (in pounds): 1.22
Product in Inches (L x W x H): 7.34 x 0.81 x 9.16
Walmart No.: 471775819

Chapter outline

Introductionp. 1
About This Bookp. 1
Conventions Used in This Bookp. 2
Foolish Assumptionsp. 2
How This Book Is Organizedp. 3
Icons Used in This Bookp. 5
Where to Go from Herep. 6
Homing in on Basic Solutionsp. 7
Going Beyond Beginning Algebrap. 9
Outlining Algebra Propertiesp. 10
Keeping order with the commutative propertyp. 10
Maintaining group harmony with the associative propertyp. 10
Distributing a wealth of valuesp. 11
Checking out an algebraic IDp. 12
Singing along in-versesp. 13
Ordering Your Operationsp. 13
Equipping Yourself with the Multiplication Property of Zerop. 14
Expounding on Exponential Rulesp. 15
Multiplying and dividing exponentsp. 15
Getting to the roots of exponentsp. 15
Raising or lowering the roof with exponentsp. 16
Making nice with negative exponentsp. 17
Implementing Factoring Techniquesp. 17
Factoring two termsp. 17
Taking on three termsp. 18
Factoring four or more terms by groupingp. 22
Toeing the Straight Line: Linear Equationsp. 23
Linear Equations: Handling the First Degreep. 23
Tackling basic linear equationsp. 24
Clearing out fractionsp. 25
Isolating different unknownsp. 26
Linear Inequalities: Algebraic Relationship Therapyp. 28
Solving basic inequalitiesp. 28
Introducing interval notationp. 29
Compounding inequality issuesp. 30
Absolute Value: Keeping Everything in Linep. 32
Solving absolute-value equationsp. 32
Seeing through absolute-value inequalityp. 34
Cracking Quadratic Equationsp. 37
Solving Simple Quadratics with the Square Root Rulep. 38
Finding simple square-root solutionsp. 38
Dealing with radical square-root solutionsp. 38
Dismantling Quadratic Equations into Factorsp. 39
Factoring binomialsp. 39
Factoring trinomialsp. 41
Factoring by groupingp. 42
Resorting to the Quadratic Formulap. 43
Finding rational solutionsp. 44
Straightening out irrational solutionsp. 44
Formulating huge quadratic resultsp. 45
Completing the Square: Warming Up for Conicsp. 46
Squaring up to solve a quadratic equationp. 46
Completing the square twice overp. 48
Getting Promoted to High-Powered Quadratics (without the Raise)p. 49
Handling the sum or difference of cubesp. 50
Tackling quadratic-like trinomialsp. 51
Solving Quadratic Inequalitiesp. 52
Keeping it strictly quadraticp. 53
Signing up for fractionsp. 54
Increasing the number of factorsp. 55
Rooting Out the Rational, Radical, and Negativep. 57
Acting Rationally with Fraction-Filled Equationsp. 57
Solving rational equations by tuning in your LCDp. 58
Solving rational equations with proportionsp. 62
Ridding Yourself of a Radicalp. 65
Squaring both sides of a radical equationp. 65
Calming two radicalsp. 67
Changing Negative Attitudes about Exponentsp. 68
Flipping negative exponents out of the picturep. 69
Factoring out negatives to solve equationsp. 70
Fooling Around with Fractional Exponentsp. 73
Combining terms with fractional exponentsp. 73
Factoring fractional exponentsp. 73
Solving equations by working with fractional exponentsp. 74
Graphing Your Way to the Good Lifep. 77
Coordinating Your Graphing Effortsp. 78
Identifying the parts of the coordinate planep. 78
Plotting from dot to dotp. 79
Streamlining the Graphing Process with Intercepts and Symmetryp. 80
Finding x- and y-interceptsp. 80
Reflecting on a graph's symmetryp. 82
Graphing Linesp. 84
Finding the slope of a linep. 85
Facing two types of equations for linesp. 86
Identifying parallel and perpendicular linesp. 88
Looking at 10 Basic Formsp. 89
Lines and quadraticsp. 90
Cubics and quarticsp. 90
Radicals and rationalsp. 91
Exponential and logarithmic curvesp. 92
Absolute values and circlesp. 93
Solving Problems with a Graphing Calculatorp. 93
Entering equations into graphing calculators correctlyp. 94
Looking through the graphing windowp. 96
Facing Off with Functionsp. 97
Formulating Function Factsp. 99
Defining Functionsp. 99
Introducing function notationp. 100
Evaluating functionsp. 100
Homing In on Domain and Rangep. 101
Determining a function's domainp. 101
Describing a function's rangep. 102
Betting on Even or Odd Functionsp. 104
Recognizing even and odd functionsp. 104
Applying even and odd functions to graphsp. 105
Facing One-to-One Confrontationsp. 106
Defining one-to-one functionsp. 106
Eliminating one-to-one violatorsp. 107
Going to Pieces with Piecewise Functionsp. 108
Doing pieceworkp. 108
Applying piecewise functionsp. 110
Composing Yourself and Functionsp. 111
Performing compositionsp. 112
Simplifying the difference quotientp. 113
Singing Along with Inverse Functionsp. 114
Determining if functions are inversesp. 114
Solving for the inverse of a functionp. 115
Sketching and Interpreting Quadratic Functionsp. 117
Interpreting the Standard Form of Quadraticsp. 117
Starting with "a" in the standard formp. 118
Following up with "b" and "cp. 119
Investigating Intercepts in Quadraticsp. 120
Finding the one and only y-interceptp. 120
Finding the x-interceptsp. 122
Going to the Extreme: Finding the Vertexp. 124
Lining Up along the Axis of Symmetryp. 126
Sketching a Graph from the Available Informationp. 127
Applying Quadratics to the Real Worldp. 129
Selling candlesp. 129
Shooting basketballsp. 130
Launching a water balloonp. 131
Staying Ahead of the Curves: Polynomialsp. 133
Taking a Look at the Standard Polynomial Formp. 133
Exploring Polynomial Intercepts and Turning Pointsp. 134
Interpreting relative value and absolute valuep. 135
Counting intercepts and turning pointsp. 136
Solving for polynomial interceptsp. 137
Determining Positive and Negative Intervalsp. 139
Using a sign-linep. 139
Interpreting the rulep. 141
Finding the Roots of a Polynomialp. 142
Factoring for polynomial rootsp. 143
Saving your sanity: The Rational Root Theoremp. 145
Letting Descartes make a ruling on signsp. 148
Synthesizing Root Findingsp. 149
Using synthetic division to test for rootsp. 150
Synthetically dividing by a binomialp. 153
Wringing out the Remainder (Theorem)p. 154
Relying on Reason: Rational Functionsp. 157
Exploring Rational Functionsp. 158
Sizing up domainp. 158
Introducing interceptsp. 159
Adding Asymptotes to the Rational Potp. 159
Determining the equations of vertical asymptotesp. 160
Determining the equations of horizontal asymptotesp. 160
Graphing vertical and horizontal asymptotesp. 161
Crunching the numbers and graphing oblique asymptotesp. 162
Accounting for Removable Discontinuitiesp. 164
Removal by factoringp. 164
Evaluating the removal restrictionsp. 165
Showing removable discontinuities on a graphp. 165
Pushing the Limits of Rational Functionsp. 166
Evaluating limits at discontinuitiesp. 168
Going to infinityp. 170
Catching rational limits at infinityp. 172
Putting It All Together: Sketching Rational Graphs from Cluesp. 173
Exposing Exponential and Logarithmic Functionsp. 177
Evaluating Exponential Expressionsp. 177
Exponential Functions: It's All About the Base, Babyp. 178
Observing the trends in basesp. 179
Meeting the most frequently used bases: 10 and ep. 180
Solving Exponential Equationsp. 182
Making bases matchp. 182
Recognizing and using quadratic patternsp. 184
Showing an "Interest" in Exponential Functionsp. 185
Applying the compound interest formulap. 185
Looking at continuous compoundingp. 188
Logging On to Logarithmic Functionsp. 189
Meeting the properties of logarithmsp. 189
Putting your logs to workp. 190
Solving Logarithmic Equationsp. 193
Setting log equal to logp. 193
Rewriting log equations as exponentialsp. 195
Graphing Exponential and Logarithmic Functionsp. 196
Expounding on the exponentialp. 196
Not seeing the logs for the treesp. 198
Conquering Conics and Systems of Equationsp. 201
Cutting Up Conic Sectionsp. 203
Cutting Up a Conep. 203
Opening Every Which Way with Parabolasp. 204
Looking at parabolas with vertices at the originp. 205
Observing the general form of parabola equationsp. 208
Sketching the graphs of parabolasp. 209
Converting parabolic equations to the standard formp. 212
Going Round and Round in Conic Circlesp. 213
Standardizing the circlep. 213
Specializing in circlesp. 214
Preparing Your Eyes for Solar Ellipsesp. 215
Raising the standards of an ellipsep. 216
Sketching an elliptical pathp. 218
Feeling Hyper about Hyperbolasp. 219
Including the asymptotesp. 220
Graphing hyperbolasp. 222
Identifying Conics from Their Equations, Standard or Notp. 223
Solving Systems of Linear Equationsp. 225
Looking at the Standard Linear-Systems Form and Its Possible Solutionsp. 225
Graphing Solutions of Linear Systemsp. 226
Pinpointing the intersectionp. 227
Toeing the same line twicep. 228
Dealing with parallel linesp. 228
Eliminating Systems of Two Linear Equations with Additionp. 229
Getting to an elimination pointp. 230
Recognizing solutions for parallel and coexisting linesp. 231
Solving Systems of Two Linear Equations with Substitutionp. 232
Variable substituting made easyp. 232
Identifying parallel and coexisting linesp. 233
Using Cramer's Rule to Defeat Unwieldy Fractionsp. 234
Setting up the linear system for Cramerp. 235
Applying Cramer's Rule to a linear systemp. 236
Raising Linear Systems to Three Linear Equationsp. 237
Solving three-equation systems with algebrap. 237
Settling for a generalized solution for linear combinationsp. 239
Upping the Ante with Increased Equationsp. 241
Applying Linear Systems to Our 3-D Worldp. 243
Using Systems to Decompose Fractionsp. 244
Solving Systems of Nonlinear Equations and Inequalitiesp. 247
Crossing Parabolas with Linesp. 247
Determining the point(s) where a line and parabola cross pathsp. 248
Dealing with a solution that's no solutionp. 250
Intertwining Parabolas and Circlesp. 251
Managing multiple intersectionsp. 252
Sorting out the solutionsp. 254
Planning Your Attack on Other Systems of Equationsp. 255
Mixing polynomials and linesp. 256
Crossing polynomialsp. 257
Navigating exponential intersectionsp. 259
Rounding up rational functionsp. 261
Playing Fair with Inequalitiesp. 264
Drawing and quartering inequalitiesp. 264
Graphing areas with curves and linesp. 265
Shifting into High Gear with Advanced Conceptsp. 267
Simplifying Complex Numbers in a Complex Worldp. 269
Using Your Imagination to Simplify Powers of ip. 270
Understanding the Complexity of Complex Numbersp. 271
Operating on complex numbersp. 272
Multiplying by the conjugate to perform divisionp. 273
Simplifying radicalsp. 275
Solving Quadratic Equations with Complex Solutionsp. 276
Working Polynomials with Complex Solutionsp. 278
Identifying conjugate pairsp. 278
Interpreting complex zerosp. 279
Making Moves with Matricesp. 281
Describing the Different Types of Matricesp. 282
Row and column matricesp. 282
Square matricesp. 283
Zero matricesp. 283
Identity matricesp. 284
Performing Operations on Matricesp. 284
Adding and subtracting matricesp. 285
Multiplying matrices by scalarsp. 286
Multiplying two matricesp. 286
Applying matrices and operationsp. 288
Defining Row Operationsp. 292
Finding Inverse Matricesp. 293
Determining additive inversesp. 294
Determining multiplicative inversesp. 294
Dividing Matrices by Using Inversesp. 299
Using Matrices to Find Solutions for Systems of Equationsp. 300
Making a List: Sequences and Seriesp. 303
Understanding Sequence Terminologyp. 303
Using sequence notationp. 304
No-fear factorials in sequencesp. 304
Alternating sequential patternsp. 305
Looking for sequential patternsp. 306
Taking Note of Arithmetic and Geometric Sequencesp. 309
Finding common ground: Arithmetic sequencesp. 309
Taking the multiplicative approach: Geometric sequencesp. 311
Recursively Defining Functionsp. 312
Making a Series of Movesp. 313
Introducing summation notationp. 314
Summing arithmeticallyp. 315
Summing geometricallyp. 316
Applying Sums of Sequences to the Real Worldp. 318
Cleaning up an amphitheaterp. 318
Negotiating your allowancep. 319
Bouncing a ballp. 320
Highlighting Special Formulasp. 322
Everything You Wanted to Know about Setsp. 323
Revealing Set Notationp. 323
Listing elements with a rosterp. 324
Building sets from scratchp. 324
Going for all (universal set) or nothing (empty set)p. 325
Subbing in with subsetsp. 325
Operating on Setsp. 327
Celebrating the union of two setsp. 327
Looking both ways for set intersectionsp. 328
Feeling complementary about setsp. 329
Counting the elements in setsp. 329
Drawing Venn You Feel Like Itp. 330
Applying the Venn diagramp. 331
Using Venn diagrams with set operationsp. 332
Adding a set to a Venn diagramp. 333
Focusing on Factorialsp. 336
Making factorial manageablep. 336
Simplifying factorialsp. 337
How Do I Love Thee? Let Me Count Up the Waysp. 338
Applying the multiplication principle to setsp. 338
Arranging permutations of setsp. 339
Mixing up sets with combinationsp. 343
Branching Out with Tree Diagramsp. 344
Picturing a tree diagram for a permutationp. 345
Drawing a tree diagram for a combinationp. 346
The Part of Tensp. 347
Ten Multiplication Tricksp. 349
Ten Special Types of Numbersp. 357
Indexp. 361

Book description

Besides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and possibly pursue further study in math.

Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems.

This friendly guide shows you how to get up to speed on exponential functions, laws of logarithms, conic sections, matrices, and other advanced algebra concepts. In no time you’ll have the tools you need to:

  • Interpret quadratic functions
  • Find the roots of a polynomial
  • Reason with rational functions
  • Expose exponential and logarithmic functions
  • Cut up conic sections
  • Solve linear and non linear systems of equations
  • Equate inequalities
  • Simplifyy complex numbers
  • Make moves with matrices
  • Sort out sequences and sets

This straightforward guide offers plenty of multiplication tricks that only math teachers know.

It also profiles special types of numbers, making it easy for you to categorize them and solve any problems without breaking a sweat. When it comes to understanding and working out algebraic equations, Algebra II For Dummies is all you need to succeed!

Customer Product Reviews

Rated 5 out of 5★ by 1reviewer.
Rated 5 out of 5★ by Excellent resource for struggling students I'm a father who completed Algebra I many years ago and never took Algebra II, and I have an 11th grade daughter who is struggling with Algebra II. I bought this book with the expectation that it would help me quickly get up to speed so that I could help my daughter understand what to do when presented with a problem on an assignment, quiz, test, etc. I had to apply myself, but within a couple of weeks, I was able to be an effective tutor for my daughter. This book clearly explains how to do things; it shows the procedure for solving problems in a way that is easy to understand. I must add, however, that if I had not had a good grasp of Algebra I, I don't think this book would have been the right solution for me. (I would have first needed to buy Algebra for Dummies.) 11/28/2012
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