Algebra II Workbook For Dummies

Table of Contents

Introduction     1
About This Book     1
Conventions Used in This Book     1
Foolish Assumptions     2
How This Book Is Organized     2
Homing In on the Basics     2
Functions     3
Conics and Systems of Equations     3
Other Good Stuff: Lists, Arrays, and Imaginary Numbers     3
The Part of Tens     3
Icons Used in This Book     3
Where to Go from Here     4
Homing In on the Basics     5
Going Beyond Beginning Algebra     7
Good Citizenship: Following the Order of Operations and Other Properties     7
Specializing in Products and FOIL     9
Variables on the Side: Solving Linear Equations     10
Dealing with Linear Absolute Value Equations     11
Greater Math Skills: Equalizing Linear Inequalities     13
Answers to Problems on Going Beyond Beginning Algebra     15
Handling Quadratic (and Quadratic-Like) Equations and Inequalities     19
Finding Reasonable Solutions with Radicals     19
Unfoiled Again! Successfully Factoring for Solutions     20
Your Bag of Tricks: Factoring Multiple Ways     23
Keeping Your Act Together:Factoring by Grouping     24
Resorting to the Quadratic Formula     25
Solving Quadratics by Completing the Square     26
Working with Quadratic-Like Equations     28
Checking Out Quadratic Inequalities     29
Answers to Problems on Quadratic (and Quadratic-Like) Equations and Inequalities     31
Rooting Out the Rational, the Radical, and the Negative     39
Doing Away with Denominators with an LCD     39
Simplifying and Solving Proportions     41
Wrangling with Radicals     43
Changing Negative Attitudes toward Negative Exponents     44
Divided Powers: Solving Equationswith Fractional Exponents     46
Answers to Problems on Rooting Out the Rational, the Radical, and the Negative     47
Graphing for the Good Life     53
Coordinating Axes, Coordinates of Points, and Quadrants     53
Crossing the Line: Using Intercepts and Symmetry to Graph     56
Graphing Lines Using Slope-Intercept and Standard Forms     58
Graphing Basic Polynomial Curves     60
Grappling with Radical and Absolute Value Equations     62
Enter the Machines: Using a Graphing Calculator     65
Answers to Problems on Graphing for the Good Life      68
Functions     77
Formulating Functions     79
Evaluating Functions     79
Determining the Domain and Range of a Function     80
Recognizing Even, Odd, and One-to-One Functions     82
They Come in Pieces: Working through Piecewise Functions     83
Composing Functions and Simplifying the Difference Quotient     84
Solving for Inverse Functions     86
Answers to Problems on Formulating Functions     89
Specializing in Quadratic Functions     95
Finding Intercepts and the Vertex of a Parabola     95
Applying Quadratics to Real-Life Situations     97
Graphing Parabolas     99
Answers to Problems on Quadratic Functions     102
Plugging In Polynomials     107
Finding Basic Polynomial Intercepts     107
Digging Up More-Difficult Polynomial Roots with Factoring     109
Determining Where a Function Is Positive or Negative     110
Graphing Polynomials     112
Possible Roots and Where to Find Them: The Rational Root Theorem and Descartes's Rule     115
Getting Real Results with Synthetic Division and the Remainder Theorem     117
Connecting the Factor Theorem with a Polynomial's Roots     119
Answers to Problems on Plugging In Polynomials     121
Acting Rationally with Functions     127
Determining Domain and Intercepts of Rational Functions     127
Introducing Vertical and Horizontal Asymptotes     129
Getting a New Slant with Oblique Asymptotes     130
Removing Discontinuities     131
Going the Limit: Limits at a Number and Infinity     132
Graphing Rational Functions     135
Answers to Problems on Rational Functions     140
Exposing Exponential and Logarithmic Functions     147
Evaluating e-Expressions and Powers of e     147
Solving Exponential Equations     149
Making Cents: Applying Compound Interest and Continuous Compounding     150
Checking Out the Properties of Logarithms     152
Presto-Chango: Expanding and Contracting Expressions with Log Functions     154
Solving Logarithmic Equations     155
They Ought to Be in Pictures: Graphing Exponential and Logarithmic Functions     157
Answers to Problems on Exponential and Logarithmic Functions     161
Conies and Systems of Equations     169
Any Way You Slice It: Conic Sections     171
Putting Equations of Parabolas in Standard Form     171
Shaping Up: Determining the Focus and Directrix of a Parabola     173
Back to the Drawing Board: Sketching Parabolas     175
Writing the Equations of Circles and Ellipses in Standard Form     177
Determining Foci and Vertices of Ellipses     180
Rounding Out Your Sketches: Circles and Ellipses     181
Hyperbola: Standard Equations and Foci     183
Determining the Asymptotes and Intercepts of Hyperbolas     185
Sketching the Hyperbola     186
Answers to Problems on Conic Sections     189
Solving Systems of Linear Equations     197
Solving Two Linear Equations Algebraically     197
Using Cramer's Rule to Defeat Unruly Fractions     199
A Third Variable: Upping the Systems to Three Linear Equations     200
A Line by Any Other Name: Writing Generalized Solution Rules     202
Decomposing Fractions Using Systems     203
Answers to Problems on Systems of Equations     206
Solving Systems of Non-Linear Equations and Inequalities     211
Finding the Intersections of Lines and Parabolas     211
Crossing Curves: Finding the Intersections of Parabolas and Circles     213
Appealing to a Higher Power: Dealing with Exponential Systems     214
Solving Systems of Inequalities      215
Answers to Problems on Solving Systems of Non-Linear Equations and Inequalities     218
Other Good Stuff: Lists, Arrays, and Imaginary Numbers     225
Getting More Complex with Imaginary Numbers     227
Simplifying Powers of i     227
Not Quite Brain Surgery: Doing Operations on Complex Numbers     228
"Dividing" Complex Numbers with a Conjugate     230
Solving Equations with Complex Solutions     231
Answers to Problems on Complex Numbers     233
Making Headway with Matrices     235
Describing Dimensions and Types of Matrices     235
Adding, Subtracting, and Doing Scalar Multiplication on Matrices     236
Trying Times: Multiplying Matrices by Each Other     238
The Search for Identity: Finding Inverse Matrices     239
Using Matrices to Solve Systems of Equations     243
Answers to Problems on Matrices     245
Going Out of Sequence with Sequences and Series     249
Writing the Terms of a Sequence     249
Differences and Multipliers: Working with Special Sequences     251
Backtracking: Constructing Recursively Defined Sequences     252
Using Summation Notation     253
Finding Sums with Special Series      255
Answers to Problems on Sequences and Series     258
Everything You Ever Wanted to Know about Sets and Counting     261
Writing the Elements of a Set from Rules or Patterns     261
Get Together: Combining Sets with Unions, Intersections, and Complements     263
Multiplication Countdowns: Simplifying Factorial Expressions     264
Checking Your Options: Using the Multiplication Property     266
Counting on Permutations When Order Matters     267
Mixing It Up with Combinations     268
Raising Binomials to Powers: Investigating the Binomial Theorem     270
Answers to Problems on Sets and Counting     272
The Part of Tens     277
Ten Basic Graphs     279
Putting Polynomials in Their Place     279
Lining Up Front and Center     280
Being Absolutely Sure with Absolute Value     280
Graphing Reciprocals of x and x2     281
Rooting Out Square Root and Cube Root     282
Growing Exponentially with a Graph     283
Logging In on Logarithmic Graphing     283
Ten Special Sequences and Their Sums     285
Adding As Easy As One, Two, Three     285
Summing Up the Squares     285
Finding the Sum of the Cubes     286
Not Being at Odds with Summing Odd Numbers     286
Evening Things Out by Adding Up Even Numbers     286
Adding Everything Arithmetic     287
Geometrically Speaking     287
Easing into a Sum for e     288
Signing In on the Sine     288
Powering Up on Powers of 2     289
Adding Up Fractions with Multiples for Denominators     289
Index     291