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Your complete guide to acing Algebra II
Do quadratic equations make you queasy? Does the mere thought of logarithms make you feel lethargic? You're not alone! Algebra can induce anxiety in the best of us, especially for the masses that have never counted math as their forte. But here's the good news: you no longer have to suffer through statistics, sequences, and series alone. Algebra II For Dummies takes the fear out of this math course and gives you easy-to-follow, friendly guidance on everything you'll encounter in the classroom and arms you with the skills and confidence you need to score high at exam time.
Gone are the days that Algebra II is a subject that only the serious 'math' students need to worry about. Now, as the concepts and material covered in a typical Algebra II course are consistently popping up on standardized tests like the SAT and ACT, the demand for advanced guidance on this subject has never been more urgent. Thankfully, this new edition of Algebra II For Dummies answers the call with a friendly and accessible approach to this often-intimidating subject, offering you a closer look at exponentials, graphing inequalities, and other topics in a way you can understand.
* Examine exponentials like a pro
* Find out how to graph inequalities
* Go beyond your Algebra I knowledge
* Ace your Algebra II exams with ease
Whether you're looking to increase your score on a standardized test or simply succeed in your Algebra II course, this friendly guide makes it possible.
Your complete guide to acing Algebra II
Do quadratic equations make you queasy? Does the mere thought of logarithms make you feel lethargic? You're not alone! Algebra can induce anxiety in the best of us, especially for the masses that have never counted math as their forte. But here's the good news: you no longer have to suffer through statistics, sequences, and series alone. Algebra II For Dummies takes the fear out of this math course and gives you easy-to-follow, friendly guidance on everything you'll encounter in the classroom and arms you with the skills and confidence you need to score high at exam time.
Gone are the days that Algebra II is a subject that only the serious 'math' students need to worry about. Now, as the concepts and material covered in a typical Algebra II course are consistently popping up on standardized tests like the SAT and ACT, the demand for advanced guidance on this subject has never been more urgent. Thankfully, this new edition of Algebra II For Dummies answers the call with a friendly and accessible approach to this often-intimidating subject, offering you a closer look at exponentials, graphing inequalities, and other topics in a way you can understand.
* Examine exponentials like a pro
* Find out how to graph inequalities
* Go beyond your Algebra I knowledge
* Ace your Algebra II exams with ease
Whether you're looking to increase your score on a standardized test or simply succeed in your Algebra II course, this friendly guide makes it possible.
Mary Jane Sterling was a lecturer in mathematics for more than 35 years, teaching courses in algebra, calculus, and linear programming. She is the author ofAlgebra I For Dummies, Trigonometry For Dummies, Algebra Workbook For Dummies, and Trigonometry Workbook For Dummies.
Introduction 1
About This Book 1
Foolish Assumptions 2
Icons Used in This Book 3
Beyond the Book 4
Where to Go from Here 4
Part 1: Homing In On Basic Solutions 5
Chapter 1: Going Beyond Beginning Algebra 7
Outlining Algebraic Properties 8
Keeping order with the commutative property 8
Maintaining group harmony with the associative property 9
Distributing a wealth of values 9
Checking out an algebraic ID 10
Singing along in-verses 11
Ordering Your Operations 11
Zeroing in on the Multiplication Property of Zero 12
Expounding on Exponential Rules 13
Multiplying and dividing exponents 13
Getting to the roots of exponents 14
Raising or lowering the roof with exponents 14
Making nice with negative exponents 15
Implementing Factoring Techniques 15
Factoring two terms 16
Taking on three terms 17
Factoring four or more terms by grouping 19
Chapter 2: Toeing the Straight Line: Linear Equations 21
Linear Equations: Handling the First Degree 21
Tackling basic linear equations 22
Clearing out fractions 23
Isolating different unknowns 24
Linear Inequalities: Algebraic Relationship Therapy 25
Solving linear inequalities 26
Introducing interval notation 27
Compounding inequality issues 28
Absolute Value: Keeping Everything in Line 30
Solving absolute value equations 31
Seeing through absolute value inequality 31
Chapter 3: Conquering Quadratic Equations 35
Implementing the Square Root Rule 36
Dismantling Quadratic Equations into Factors 37
Factoring binomials 37
Factoring trinomials 39
Factoring by grouping 40
Resorting to the Quadratic Formula 41
Finding rational solutions 42
Straightening out irrational solutions 42
Formulating huge quadratic results 43
Completing the Square: Warming Up for Conics 43
Squaring up a quadratic equation 44
Completing the square twice over 45
Tackling Higher-Powered Polynomials 46
Handling the sum or difference of cubes 47
Tackling quadratic-like trinomials 48
Solving Quadratic Inequalities 49
Keeping inequality strictly quadratic 50
Signing up for fractions 52
Increasing the number of factors 53
Considering absolute value inequalities 53
Chapter 4: Rooting Out the Rational, Radical, and Negative 55
Acting Rationally with Fraction-Filled Equations 56
Systematically solving rational equations 56
Solving rational equations with proportions 60
Ridding Yourself of a Radical 61
Squaring both sides of a radical equation 62
Calming two radicals 63
Changing Negative Attitudes about Exponents 65
Flipping negative exponents out of the picture 65
Factoring out negatives to solve equations 66
Fooling Around with Fractional Exponents 68
Combining terms with fractional exponents 69
Factoring fractional exponents 69
Solving equations by working with fractional exponents 70
Chapter 5: Graphing Your Way to the Good Life 73
Coordinating Your Graphing Efforts 74
Identifying the parts of the coordinate plane 74
Plotting from dot to dot 75
Streamlining the Graphing Process with Intercepts and Symmetry 76
Finding x- and y-intercepts 77
Reflecting on a graph's symmetry 78
Graphing Lines 80
Finding the slope of a line 81
Facing two types of equations for lines 82
Identifying parallel and perpendicular lines 85
Looking at 10 Basic Forms 86
Lines and quadratics 86
Cubics and quartics 87
Radicals and rationals 87
Exponential and logarithmic curves 88
Absolute values and circles 89
Solving Problems with a Graphing Calculator 89
Entering equations into graphing calculators correctly 90
Looking through the graphing window 92
Part 2: Facing Off With Functions 95
Chapter 6: Formulating Function Facts 97
Defining Functions 98
Introducing function notation 98
Evaluating functions 98
Homing In on Domain and Range 99
Determining a function's domain 99
Describing a function's range 100
Betting on Even or Odd Functions 102
Recognizing even and odd functions 102
Applying even and odd functions to graphs 103
Facing One-to-One Confrontations 104
Defining one-to-one functions 104
Eliminating one-to-one violators 105
Going to Pieces with Piecewise Functions 106
Doing piecework 107
Applying piecewise functions 108
Composing Yourself and Functions 110
Performing compositions 110
Simplifying the difference quotient 111
Singing Along with Inverse Functions 112
Determining if functions are inverses 112
Solving for the inverse of a function 113
Chapter 7: Sketching and Interpreting Quadratic Functions 115
Interpreting the Standard Form of Quadratics 116
Starting with "a" in the standard form 116
Following up with "b" and "c" 117
Investigating Intercepts in Quadratics 118
Finding the one and only y-intercept 119
Finding the x-intercepts 120
Going to the Extreme: Finding the Vertex 123
Lining Up along the Axis of Symmetry 124
Sketching a Graph from the Available Information 125
Applying Quadratics to the Real World 127
Selling candles 127
Shooting basketballs 128
Launching a water balloon 130
Chapter 8: Staying Ahead of the Curves: Polynomials 133
Taking a Look at the Standard Polynomial Form 134
Exploring Polynomial Intercepts and Turning Points 134
Interpreting relative value and absolute value 135
Counting intercepts and turning points 135
Solving for polynomial intercepts 138
Determining Positive and Negative Intervals 139
Using a sign-line 140
Interpreting the rule 141
Finding the Roots of a Polynomial 143
Factoring for polynomial roots 143
Saving your sanity: The Rational Root Theorem 145
Letting Descartes make a ruling on signs 148
Synthesizing Root Findings 150
Using synthetic division to test for roots 150
Synthetically dividing by a binomial 153
Wringing out the Remainder (Theorem) 154
Chapter 9: Reasoning with Rational Functions 157
Exploring Rational Functions 158
Sizing up domain 158
Introducing intercepts 159
Adding Asymptotes to the Rational Pot 160
Determining the equations of vertical asymptotes 160
Determining the equations of horizontal asymptotes 161
Graphing vertical and horizontal asymptotes 161
Crunching the numbers and graphing oblique asymptotes 163
Accounting for Removable Discontinuities 164
Removal by factoring 164
Evaluating the removal restrictions 165
Showing removable discontinuities on a graph 165
Pushing the Limits of Rational Functions 167
Evaluating limits at discontinuities 168
Going to infinity 170
Catching rational limits at infinity 172
Putting It All Together: Sketching Rational Graphs from Clues 173
Chapter 10: Exposing Exponential and Logarithmic Functions 177
Evaluating Exponential Expressions 178
Exponential Functions: It's All about the Base, Baby 179
Observing the trends in bases 179
Meeting the most frequently used bases: 10 and e 180
Solving Exponential Equations 182
Making bases match 182
Recognizing and using quadratic patterns 184
Showing an "Interest" in Exponential Functions 186
Applying the compound interest formula 186
Looking at continuous compounding 188
Logging On to Logarithmic Functions 189
Meeting the properties of logarithms 190
Putting your logs to work 191
Solving Logarithmic Equations 193
Setting log equal to log 194
Rewriting log equations as exponentials 195
Graphing Exponential and Logarithmic Functions 196
Expounding on the exponential 196
Not seeing the logs for the trees 198
Part 3: Conquering Conics And Systems Of Equations 203
Chapter 11: Cutting Up Conic Sections 205
Cutting Up a Cone 206
Opening Every Which Way with Parabolas 206
Looking at parabolas with vertices at the origin 207
Observing the general form of parabola equations 210
Sketching the graphs of parabolas 211
Converting parabolic equations to the standard form 214
Going Round and Round in Conic Circles 215
Standardizing the circle 215
Specializing in circles 217
Preparing Your Eyes for Solar Ellipses 218
Raising the standards of an ellipse 218
Sketching an elliptical path 221
Feeling Hyper about Hyperbolas 222
Including the asymptotes 223
Graphing hyperbolas 224
Identifying Conics from Their Equations, Standard or Not 227
Chapter 12: Solving Systems of Linear Equations 229
Looking at the Standard Linear-Systems Form and Its Possible Solutions 230
Graphing Solutions of Linear Systems 230
Pinpointing the intersection 231
Toeing the same line twice 232
Dealing with parallel lines 232
Solving Systems of Two Linear Equations by Using Elimination 233
Getting to the point with elimination 234
Recognizing solutions indicating parallel or coexisting...
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
Introduction 1Part 1: Homing in on Basic Solutions 5Chapter 1: Going Beyond Beginning Algebra 7Chapter 2: Toeing the Straight Line: Linear Equations 21Chapter 3: Conquering Quadratic Equations 35Chapter 4: Rooting Out the Rational
Radical and Negative |
| ISBN-13: | 9781119543145 |
| ISBN-10: | 1119543142 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Sterling, Mary Jane |
| Hersteller: | John Wiley & Sons Inc |
| Maße: | 235 x 191 x 22 mm |
| Von/Mit: | Mary Jane Sterling |
| Erscheinungsdatum: | 01.03.2019 |
| Gewicht: | 0,525 kg |
Mary Jane Sterling was a lecturer in mathematics for more than 35 years, teaching courses in algebra, calculus, and linear programming. She is the author ofAlgebra I For Dummies, Trigonometry For Dummies, Algebra Workbook For Dummies, and Trigonometry Workbook For Dummies.
Introduction 1
About This Book 1
Foolish Assumptions 2
Icons Used in This Book 3
Beyond the Book 4
Where to Go from Here 4
Part 1: Homing In On Basic Solutions 5
Chapter 1: Going Beyond Beginning Algebra 7
Outlining Algebraic Properties 8
Keeping order with the commutative property 8
Maintaining group harmony with the associative property 9
Distributing a wealth of values 9
Checking out an algebraic ID 10
Singing along in-verses 11
Ordering Your Operations 11
Zeroing in on the Multiplication Property of Zero 12
Expounding on Exponential Rules 13
Multiplying and dividing exponents 13
Getting to the roots of exponents 14
Raising or lowering the roof with exponents 14
Making nice with negative exponents 15
Implementing Factoring Techniques 15
Factoring two terms 16
Taking on three terms 17
Factoring four or more terms by grouping 19
Chapter 2: Toeing the Straight Line: Linear Equations 21
Linear Equations: Handling the First Degree 21
Tackling basic linear equations 22
Clearing out fractions 23
Isolating different unknowns 24
Linear Inequalities: Algebraic Relationship Therapy 25
Solving linear inequalities 26
Introducing interval notation 27
Compounding inequality issues 28
Absolute Value: Keeping Everything in Line 30
Solving absolute value equations 31
Seeing through absolute value inequality 31
Chapter 3: Conquering Quadratic Equations 35
Implementing the Square Root Rule 36
Dismantling Quadratic Equations into Factors 37
Factoring binomials 37
Factoring trinomials 39
Factoring by grouping 40
Resorting to the Quadratic Formula 41
Finding rational solutions 42
Straightening out irrational solutions 42
Formulating huge quadratic results 43
Completing the Square: Warming Up for Conics 43
Squaring up a quadratic equation 44
Completing the square twice over 45
Tackling Higher-Powered Polynomials 46
Handling the sum or difference of cubes 47
Tackling quadratic-like trinomials 48
Solving Quadratic Inequalities 49
Keeping inequality strictly quadratic 50
Signing up for fractions 52
Increasing the number of factors 53
Considering absolute value inequalities 53
Chapter 4: Rooting Out the Rational, Radical, and Negative 55
Acting Rationally with Fraction-Filled Equations 56
Systematically solving rational equations 56
Solving rational equations with proportions 60
Ridding Yourself of a Radical 61
Squaring both sides of a radical equation 62
Calming two radicals 63
Changing Negative Attitudes about Exponents 65
Flipping negative exponents out of the picture 65
Factoring out negatives to solve equations 66
Fooling Around with Fractional Exponents 68
Combining terms with fractional exponents 69
Factoring fractional exponents 69
Solving equations by working with fractional exponents 70
Chapter 5: Graphing Your Way to the Good Life 73
Coordinating Your Graphing Efforts 74
Identifying the parts of the coordinate plane 74
Plotting from dot to dot 75
Streamlining the Graphing Process with Intercepts and Symmetry 76
Finding x- and y-intercepts 77
Reflecting on a graph's symmetry 78
Graphing Lines 80
Finding the slope of a line 81
Facing two types of equations for lines 82
Identifying parallel and perpendicular lines 85
Looking at 10 Basic Forms 86
Lines and quadratics 86
Cubics and quartics 87
Radicals and rationals 87
Exponential and logarithmic curves 88
Absolute values and circles 89
Solving Problems with a Graphing Calculator 89
Entering equations into graphing calculators correctly 90
Looking through the graphing window 92
Part 2: Facing Off With Functions 95
Chapter 6: Formulating Function Facts 97
Defining Functions 98
Introducing function notation 98
Evaluating functions 98
Homing In on Domain and Range 99
Determining a function's domain 99
Describing a function's range 100
Betting on Even or Odd Functions 102
Recognizing even and odd functions 102
Applying even and odd functions to graphs 103
Facing One-to-One Confrontations 104
Defining one-to-one functions 104
Eliminating one-to-one violators 105
Going to Pieces with Piecewise Functions 106
Doing piecework 107
Applying piecewise functions 108
Composing Yourself and Functions 110
Performing compositions 110
Simplifying the difference quotient 111
Singing Along with Inverse Functions 112
Determining if functions are inverses 112
Solving for the inverse of a function 113
Chapter 7: Sketching and Interpreting Quadratic Functions 115
Interpreting the Standard Form of Quadratics 116
Starting with "a" in the standard form 116
Following up with "b" and "c" 117
Investigating Intercepts in Quadratics 118
Finding the one and only y-intercept 119
Finding the x-intercepts 120
Going to the Extreme: Finding the Vertex 123
Lining Up along the Axis of Symmetry 124
Sketching a Graph from the Available Information 125
Applying Quadratics to the Real World 127
Selling candles 127
Shooting basketballs 128
Launching a water balloon 130
Chapter 8: Staying Ahead of the Curves: Polynomials 133
Taking a Look at the Standard Polynomial Form 134
Exploring Polynomial Intercepts and Turning Points 134
Interpreting relative value and absolute value 135
Counting intercepts and turning points 135
Solving for polynomial intercepts 138
Determining Positive and Negative Intervals 139
Using a sign-line 140
Interpreting the rule 141
Finding the Roots of a Polynomial 143
Factoring for polynomial roots 143
Saving your sanity: The Rational Root Theorem 145
Letting Descartes make a ruling on signs 148
Synthesizing Root Findings 150
Using synthetic division to test for roots 150
Synthetically dividing by a binomial 153
Wringing out the Remainder (Theorem) 154
Chapter 9: Reasoning with Rational Functions 157
Exploring Rational Functions 158
Sizing up domain 158
Introducing intercepts 159
Adding Asymptotes to the Rational Pot 160
Determining the equations of vertical asymptotes 160
Determining the equations of horizontal asymptotes 161
Graphing vertical and horizontal asymptotes 161
Crunching the numbers and graphing oblique asymptotes 163
Accounting for Removable Discontinuities 164
Removal by factoring 164
Evaluating the removal restrictions 165
Showing removable discontinuities on a graph 165
Pushing the Limits of Rational Functions 167
Evaluating limits at discontinuities 168
Going to infinity 170
Catching rational limits at infinity 172
Putting It All Together: Sketching Rational Graphs from Clues 173
Chapter 10: Exposing Exponential and Logarithmic Functions 177
Evaluating Exponential Expressions 178
Exponential Functions: It's All about the Base, Baby 179
Observing the trends in bases 179
Meeting the most frequently used bases: 10 and e 180
Solving Exponential Equations 182
Making bases match 182
Recognizing and using quadratic patterns 184
Showing an "Interest" in Exponential Functions 186
Applying the compound interest formula 186
Looking at continuous compounding 188
Logging On to Logarithmic Functions 189
Meeting the properties of logarithms 190
Putting your logs to work 191
Solving Logarithmic Equations 193
Setting log equal to log 194
Rewriting log equations as exponentials 195
Graphing Exponential and Logarithmic Functions 196
Expounding on the exponential 196
Not seeing the logs for the trees 198
Part 3: Conquering Conics And Systems Of Equations 203
Chapter 11: Cutting Up Conic Sections 205
Cutting Up a Cone 206
Opening Every Which Way with Parabolas 206
Looking at parabolas with vertices at the origin 207
Observing the general form of parabola equations 210
Sketching the graphs of parabolas 211
Converting parabolic equations to the standard form 214
Going Round and Round in Conic Circles 215
Standardizing the circle 215
Specializing in circles 217
Preparing Your Eyes for Solar Ellipses 218
Raising the standards of an ellipse 218
Sketching an elliptical path 221
Feeling Hyper about Hyperbolas 222
Including the asymptotes 223
Graphing hyperbolas 224
Identifying Conics from Their Equations, Standard or Not 227
Chapter 12: Solving Systems of Linear Equations 229
Looking at the Standard Linear-Systems Form and Its Possible Solutions 230
Graphing Solutions of Linear Systems 230
Pinpointing the intersection 231
Toeing the same line twice 232
Dealing with parallel lines 232
Solving Systems of Two Linear Equations by Using Elimination 233
Getting to the point with elimination 234
Recognizing solutions indicating parallel or coexisting...
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
Introduction 1Part 1: Homing in on Basic Solutions 5Chapter 1: Going Beyond Beginning Algebra 7Chapter 2: Toeing the Straight Line: Linear Equations 21Chapter 3: Conquering Quadratic Equations 35Chapter 4: Rooting Out the Rational
Radical and Negative |
| ISBN-13: | 9781119543145 |
| ISBN-10: | 1119543142 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Sterling, Mary Jane |
| Hersteller: | John Wiley & Sons Inc |
| Maße: | 235 x 191 x 22 mm |
| Von/Mit: | Mary Jane Sterling |
| Erscheinungsdatum: | 01.03.2019 |
| Gewicht: | 0,525 kg |
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