Authors: David Alan Herzog, Edward Kohn
ISBN-13: 9780764563713, ISBN-10: 0764563718
Format: Paperback
Publisher: Wiley, John & Sons, Incorporated
Date Published: May 2001
Edition: (Non-applicable)
Ed Kohn is an outstanding educator and author, with over 33 years' experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at the Sherman Oaks Center for Enriched Studies. Formerly an instructor at Fairleigh Dickinson University, David Alan Herzog is the author of over 100 audio visual tides and computer programs and has written and edited several books in mathematics and science.
We take great notes—and make learning a snap When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core algebraic concepts—from linear equations, relations and functions, and rational expressions to radicals, quadratic systems, and factoring polynomials—and get the best possible grade. At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase—and zero in on the essential information you need to succeed. Study smarter @ cliffsnotes.com Free CliffsNote-A-Day tips Free test-taking tips and tricks Free test samples and schedules Free info on other test resources Plus hundreds of downloadable Cliffs titles 24 hours a day Make the grade with CliffsQuickReviews CliffsQuickReviews are available for more than 30 introductory level courses. See inside for a complete listing of these and other bestselling Cliffs titles.
Introduction | 1 | |
Why You Need This Book | 2 | |
How to Use This Book | 2 | |
Visit Our Web Site | 3 | |
Chapter 1 | Linear Sentences in One Variable | 5 |
Linear Equations | 5 | |
Formulas | 7 | |
Absolute Value Equations | 10 | |
Linear Inequalities | 12 | |
Compound Inequalities | 14 | |
Absolute Value Inequalities | 17 | |
Chapter 2 | Segments, Lines, and Inequallties | 22 |
Rectangular Coordinate System | 22 | |
Distance Formula | 24 | |
Midpoint Formula | 25 | |
Slope of a Line | 26 | |
Slope of Parallel and Perpendicular Lines | 28 | |
Equations of Lines | 29 | |
Graphs of Linear Inequalities | 35 | |
Chapter 3 | Linear Sentences in Two Variables | 41 |
Linear Equations: Solutions Using Graphing | 41 | |
Linear Equations: Solutions Using Substitution | 43 | |
Linear Equations: Solutions Using Eliminations | 44 | |
Linear Equations: Solutions Using Matrices | 47 | |
Linear Equations: Solutions Using Determinants | 48 | |
Linear Inequalities: Solutions Using Graphing | 51 | |
Chapter 4 | Linear Equations in Three Variables | 57 |
Linear Equations: Solutions Using Elimination | 57 | |
Linear Equations: Solutions Using Matrices | 61 | |
Linear Equations: Solutions Using Determinants | 64 | |
Chapter 5 | Polynomial Arithmetic | 70 |
Adding and Subtracting Polynomials | 70 | |
Monomial, binomial, and trinomial | 70 | |
Like terms or similar terms | 71 | |
Ascending and descending order | 72 | |
Multiplying Polynomials | 73 | |
Special Products of Binomials | 75 | |
Dividing Polynomials | 77 | |
Synthetic Division | 81 | |
Chapter 6 | Factoring Polynomials | 84 |
Greatest Common Factor | 84 | |
Difference of Squares | 85 | |
Sum or Difference of Cubes | 86 | |
Trinomials of the Form x[superscript 2] + bx + c | 88 | |
Trinomials of the Form ax[superscript 2] + bx + c | 89 | |
Square Trinomials | 91 | |
Factoring by Regrouping | 91 | |
Summary of Factoring Techniques | 92 | |
Solving Equations by Factoring | 93 | |
Chapter 7 | Rational Expressions | 97 |
Examples of Rational Expressions | 97 | |
Simplifying Rational Expressions | 98 | |
Multiplying Rational Expressions | 99 | |
Dividing Rational Expressions | 100 | |
Adding and Subtracting Rational Expressions | 101 | |
Complex Fractions | 105 | |
Solving Rational Equations | 107 | |
Proportion, Direct Variation, Inverse Variation, Joint Variation | 109 | |
Proportion | 119 | |
Direct variation | 110 | |
Inverse variation | 111 | |
Joint variation | 112 | |
Graphing Rational Functions | 113 | |
Chapter 8 | Relations and Functions | 118 |
Basic Definitions | 118 | |
Relation | 118 | |
Domain and range | 119 | |
Function | 121 | |
Function Notation | 123 | |
Compositions of Functions | 124 | |
Algebra of Functions | 125 | |
Inverse Functions | 126 | |
Chapter 9 | Polynomial Functions | 132 |
Polynomial Function | 132 | |
Remainder Theorem | 133 | |
Factor Theorem | 134 | |
Zeros of a Function | 135 | |
Rational Zero Theorem | 135 | |
Graphing Polynomial Functions | 137 | |
Chapter 10 | Radicals and Complex Numbers | 141 |
Radicals | 141 | |
Simplifying Radicals | 144 | |
Adding and Subtracting Radical Expressions | 144 | |
Multiplying Radical Expressions | 145 | |
Dividing Radical Expressions | 146 | |
Rationalizing the denominator | 147 | |
Conjugates | 148 | |
Rational Exponents | 148 | |
Complex Numbers | 149 | |
Chapter 11 | Quadratics in One Variable | 153 |
Quadratic Equations | 153 | |
Solving Quadratics by Factoring | 154 | |
Solving Quadratics by the Square Root Property | 154 | |
Solving Quadratics by Completing the Square | 155 | |
Solving Quadratics by the Quadratic Formula | 157 | |
Solving Equations in Quadratic Form | 159 | |
Solving Radical Equations | 160 | |
Solving Quadratic Inequalities | 165 | |
Chapter 12 | Conic Sections | 171 |
The Four Conic Sections | 171 | |
Circle | 172 | |
Parabola | 174 | |
Ellipse | 179 | |
Hyperbola | 185 | |
Chapter 13 | Quadratic Systems | 192 |
Systems of Equations Solved Algebraically | 192 | |
Systems of Equations Solved Graphically | 194 | |
Systems of Inequalities Solved Graphically | 196 | |
Chapter 14 | Exponential and Logarithmic Functions | 200 |
Exponential Functions | 200 | |
Logarithmic Functions | 204 | |
Properties of Logarithms | 207 | |
Exponential and Logarithmic Equations | 209 | |
Chapter 15 | Sequences and Series | 215 |
Definition and Examples of Sequences | 215 | |
Arithmetic Sequence | 217 | |
Arithmetic Series | 218 | |
Geometric Sequence | 219 | |
Geometric Series | 221 | |
Summation Notation | 223 | |
Chapter 16 | Additional Topics | 226 |
Factorials | 226 | |
Binomial Coefficients and the Binomial Theorem | 227 | |
Permutations | 229 | |
Combinations | 231 | |
Chapter 17 | Word Problems | 233 |
General Strategy | 233 | |
Simple Interest | 234 | |
Compound Interest | 235 | |
Mixture | 236 | |
Motion | 236 | |
Work | 239 | |
Arithmetic/Geometric Series | 241 | |
CQR Review | 244 | |
CQR Resource Center | 250 | |
Glossary | 253 | |
Index | 260 |