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Get a handle on pre-calculus in a pinch!
If you're tackling pre-calculus and want to up your chances of doing your very best, this hands-on workbook is just what you need to grasp and retain the concepts that will help you succeed. Inside, you'll get basic content review for every concept, paired with examples and plenty of practice problems, ample workspace, step-by-step solutions, and thorough explanations for each and every problem.
In Pre-Calculus Workbook For Dummies, you'll also get free access to a quiz for every chapter online! With all of the lessons and practice offered, you'll memorize the most frequently used formulas, see how to avoid common mistakes, understand tricky trig proofs, and get the inside scoop on key concepts such as quadratic equations.
Get ample review before jumping into a calculus course
Supplement your classroom work with easy-to-follow guidance
Make complex formulas and concepts more approachable
Be prepared to further your mathematics studies
Whether you're enrolled in a pre-calculus class or you're looking for a refresher as you prepare for a calculus course, this is the perfect study companion to make it easier.
Auteur
Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of Trigonometry For Dummies and Finite Math For Dummies.
Texte du rabat
Review key concepts Conquer pre-calculus with practice problems galore! If you're tackling pre-calculus and want to up your chances of doing your very best, this hands-on workbook is just what you need to grasp and retain the concepts that will help you succeed. Inside, you'll get an in-time review for every concept, paired with examples and plenty of practice problems, ample workspace, step-by-step solutions, and thorough explanations for each and every problem. Inside...
Résumé
Get a handle on pre-calculus in a pinch!
If you're tackling pre-calculus and want to up your chances of doing your very best, this hands-on workbook is just what you need to grasp and retain the concepts that will help you succeed. Inside, you'll get basic content review for every concept, paired with examples and plenty of practice problems, ample workspace, step-by-step solutions, and thorough explanations for each and every problem.
In Pre-Calculus Workbook For Dummies, you'll also get free access to a quiz for every chapter online! With all of the lessons and practice offered, you'll memorize the most frequently used formulas, see how to avoid common mistakes, understand tricky trig proofs, and get the inside scoop on key concepts such as quadratic equations.
Contenu
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
Part 1: Setting the Foundation: The Nuts And Bolts of Pre-Calculus 5
Chapter 1: Preparing for Pre-Calculus 7
Reviewing Order of Operations: The Fun in Fundamentals 8
Keeping Your Balance While Solving Equalities 10
When Your Image Really Counts: Graphing Equalities and Inequalities 12
Graphing with two points 12
Graphing by using the slope-intercept form 13
Graphing inequalities 14
Using Graphs to Find Distance, Midpoint, and Slope 15
Finding the distance 15
Calculating the midpoint 16
Discovering the slope 16
Answers to Problems on Fundamentals 19
Chapter 2: Real Numbers Come Clean 25
Solving Inequalities 25
Expressing Inequality Solutions in Interval Notation 28
Radicals and Exponents Just Simplify! 30
Getting Out of a Sticky Situation, or Rationalizing 33
Answers to Problems on Real Numbers 35
Chapter 3: Controlling Functions by Knowing Their Function 39
Using Both Faces of the Coin: Even and Odd 40
Leaving the Nest: Transforming Parent Graphs 42
Quadratic functions 42
Square root functions 42
Absolute value functions 43
Cubic functions 43
Cube root functions 44
Steeper or flatter 44
Translations 46
Reflections 46
Combinations of transformations 46
Graphing Rational Functions 49
Piecing Together Piecewise Functions 52
Combining Functions 54
Evaluating Composition of Functions 55
Working Together: Domain and Range 57
Unlocking the Inverse of a Function: Turning It Inside Out 59
Answers to Problems on Functions 61
Chapter 4: Searching for Roots 75
Factoring a Factorable Quadratic 75
Solving a Quadratic Polynomial Equation 78
Completing the square 78
Quadratic formula 79
Solving High-Order Polynomials 80
Factoring by grouping 80
Determining positive and negative roots: Descartes' Rule of Signs 81
Counting on imaginary roots 81
Getting the rational roots 81
Finding roots through synthetic division 82
Using Roots to Create an Equation 84
Graphing Polynomials 85
Answers to Problems on Roots and Degrees 89
Chapter 5: Exponential and Logarithmic Functions 95
Working with Exponential Functions 95
Eagerly Engaging Edgy Logarithmic Solutions 98
Making Exponents and Logs Work Together 101
Using Exponents and Logs in Practical Applications 103
Answers to Problems on Exponential and Logarithmic Functions 106
Part 2: Trig is the Key: Basic Review, The Unit Circle, and Graphs 113
Chapter 6: Basic Trigonometry and the Unit Circle 115
Finding the Six Trigonometric Ratios 115
Solving Word Problems with Right Triangles 118
Unit Circle and the Coordinate Plane: Finding Points and Angles 121
Finding Ratios from Angles on the Unit Circle 124
Solving Trig Equations 127
Making and Measuring Arcs 129
Answers to Problems on Basic Trig and the Unit Circle 131
Chapter 7: Graphing and Transforming Trig Functions 137
Getting a Grip on Periodic Graphs 137
Parent Graphs and Transformations: Sine and Cosine 138
Tangent and Cotangent: More Family Members 141
Generations: Secant and Cosecant 143
Answers to Problems on Graphing and Transforming Trig Functions 147 <p&g...