Students and professionals alike must tap into their knowledge of algebra everyday, whether it's for the SATs, college courses, or even the workplace.
Author Larry Stephens presents a super-accessible approach to the subject that even the most math-phobic student can follow, featuring simplified rules and techniques based on real-world problems that use the principles of algebra for their solutions.
Algebra for the Utterly Confused offers a user-friendly, logical, step-by-step approach to the fundamentals of algebra, integrating contemporary software as one of the key tools to assist in the solutions of the problems, including MINITAB, Excel spreadsheets, and Maple.
- Handy icons help students visualize concepts and techniques
- More than 200 solved problems and examples aid students in working out algebraic solutions
- Summary of key points for every chapter reinforces covered topics
Author(s): Larry J. Stephens
Series: Utterly Confused Series
Edition: 1
Publisher: McGraw-Hill
Year: 2000
Language: English
Commentary: 50739
Pages: 241
Copyright......Page 5
Contents......Page 7
A Special Message to the Utterly Confused Algebra Student......Page 9
Icons......Page 11
How to Study Algebra......Page 13
General Guidelines for Effective Algebra Study......Page 14
Test-Taking Strategies......Page 15
Preface......Page 17
CHAPTER 1 Basic Algebra Concepts Review......Page 21
Real Numbers System......Page 22
Four Fundamental Operations Involving Fractions......Page 24
Four Fundamental Operations Involving Signed Numbers......Page 27
Scientific and Exponential Notation......Page 29
Prime Factorization......Page 31
Algebraic Variables......Page 32
Operations with Algebraic Expressions......Page 33
Factoring......Page 35
Solving Equations......Page 36
Questions......Page 39
Answers......Page 41
CHAPTER 2 Properties of Numbers......Page 43
Distributive Property......Page 44
Additive Inverse......Page 45
Multiplicative Inverse......Page 46
Additive Identity......Page 47
Commutative Law of Addition......Page 48
Associative Law of Addition......Page 49
Multiplication Property of Zero......Page 50
Questions......Page 52
Answers......Page 53
CHAPTER 3 Functions......Page 55
Function, Domain, and Range......Page 56
One-to-One Function......Page 57
Rectangular Coordinate System......Page 58
Linear Functions......Page 60
Inverse Function......Page 62
Questions......Page 66
Answers......Page 68
CHAPTER 4 Linear Functions and Linear Equations......Page 69
Linear Functions......Page 70
Slope of a Straight Line......Page 71
x- and y-Intercepts of a Straight Line......Page 72
Parallel and Perpendicular Lines......Page 73
Linear Equations......Page 74
Questions......Page 77
Answers......Page 78
CHAPTER 5 Linear Inequalities......Page 79
Linear Inequality in One Variable......Page 80
Addition and Multiplication Properties of Inequalities......Page 81
Linear Inequality in Two Variables......Page 83
Graphical Representation of the Solution Set for a Linear Inequality in Two Variables......Page 85
Answers......Page 88
CHAPTER 6 Absolute Values......Page 89
Absolute Value of a Signed Number......Page 90
Graph of the Absolute Value Function......Page 91
Solving Equations Containing the Absolute Value Function......Page 92
Equations Involving Absolute Values......Page 95
Inequalities Involving Absolute Values......Page 97
Answers......Page 100
CHAPTER 7 Systems of Linear Equations......Page 101
Solution to a System of Two Equations in Two Unknowns......Page 102
Graphical Solution to a System of Two Equations in Two Unknowns......Page 103
Addition/Subtraction Method for Solving a System of Equations......Page 106
Linear Programming......Page 109
System of Three Equations in Three Unknowns......Page 112
Systems of Equations and Multiple Regression......Page 114
Questions......Page 116
Answers......Page 117
CHAPTER 8 Polynomials......Page 119
Polynomial in One Variable......Page 120
Addition and Subtraction of Polynomials......Page 122
Multiplication of Polynomials......Page 125
Division of Polynomials......Page 128
Polynomial Equations......Page 129
Graphs of Polynomials......Page 131
Answers......Page 134
CHAPTER 9 Quadratic Functions and Equations......Page 135
Quadratic Function......Page 136
Maximum Value of a Quadratic Function......Page 137
Minimum Value for a Quadratic Function......Page 138
Quadratic Equations......Page 140
Quadratic Equations with Non-Real Number Solutions......Page 142
Graphs of Quadratic Functions......Page 144
Answers......Page 147
CHAPTER 10 Roots, Radicals, and Complex Numbers......Page 149
Cube Roots......Page 150
Higher-Order Roots......Page 152
Four Fundamental Operations Involving Radicals......Page 154
Operations on Complex Numbers......Page 155
Polynomials with Both Real and Imaginary Roots......Page 157
Answers......Page 160
CHAPTER 11 Rational Expressions......Page 161
Rational Expressions......Page 162
Multiplying Rational Expressions......Page 164
Dividing Rational Expressions......Page 166
Addition and Subtraction of Rational Expressions......Page 167
Solving Equations Containing Rational Expressions......Page 169
Questions......Page 171
Answers......Page 172
CHAPTER 12 Exponential and Logarithmic Functions......Page 173
Exponential Functions......Page 174
Logarithm Function......Page 177
Common and Natural Logarithms......Page 178
Technology and Exponential/Logarithmic Functions......Page 179
Properties of Logarithms......Page 180
Questions......Page 185
Answers......Page 186
CHAPTER 13 Equations of Second Degree and Their Graphs......Page 187
Circles......Page 188
Ellipses......Page 193
Hyperbolas......Page 197
Asymptotes for Hyperbolas......Page 199
Parabolas......Page 201
Answers......Page 202
CHAPTER 14 Sequences and Series......Page 203
Sequences and Series......Page 204
Arithmetic Sequences and Series......Page 205
Geometric Sequences and Series......Page 207
Sum of an Infinite Geometric Sequence......Page 210
Summing Powers of Natural Numbers......Page 212
Questions......Page 213
Answers......Page 214
CHAPTER 15 Combinatorics, Binomial Series, and Probability......Page 215
Combinations and Permutations......Page 216
Binomial Series......Page 220
Experiments, Sample Spaces, and Events......Page 223
Combining Events......Page 225
Basic Definitions of Probability......Page 227
Solving Probability Problems Having Equally Likely Outcomes......Page 230
Questions......Page 233
Answers......Page 234
Index......Page 237
About the Author......Page 241
