Schaum's Outline of Elementary Algebra (Schaum's Outline Series) / Edition 3

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This third edition of the perennial bestseller defines the recent changes in how the discipline is taught and introduces a new perspective on the discipline. New material in this third edition includes:

  • A modernized section on trigonometry
  • An introduction to mathematical modeling
  • Instruction in use of the graphing calculator
  • 2,000 solved problems
  • 3,000 supplementary practice problems and more

Schaum's Outlines contain hundreds of solutions to problems covered in any college course. This guide, which can be used with any text or can stand alone, contains at the beginning of each chapter a list of key definitions, a summary of major concepts, step by step solutions to dozens of problems, and additional practice problems.

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Product Details

  • ISBN-13: 9780071410830
  • Publisher: McGraw-Hill Companies, The
  • Publication date: 1/1/2004
  • Series: Schaum's Outline Series
  • Edition description: Third Edition
  • Edition number: 3
  • Pages: 400
  • Product dimensions: 8.12 (w) x 10.74 (h) x 0.44 (d)

Meet the Author

Philip A. Schmidt, Ph.D. is the director of the Mathaware Project, at Berea College. He is the author of several Schaum's Outlines.

Dr. Barnett Rich held a Ph.D. from Columbia University and a J.D. from NYU. Dr. Rich was the author of 23 books.

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Table of Contents

Chapter 1 From Arithemetic to Algebra 1
1. Representing Numbers by Letters 1
2. Interchanging Numbers in Addition 2
3. Interchanging Numbers in Multiplication 3
4. Symbolizing the Operations in Algebra 4
5. Expressing Addition and Subtraction Algebraically 5
6. Expressing Multiplication and Division Algebraically 6
7. Expressing Two or More Operations Algebraically 6
8. Order in Which Fundamental Operations Are Performed 8
9. The Uses of Parentheses: Changing the Order of Operations 9
10. Multiplying Factors in Terms: Numerical and Literal Coefficients 10
11. Repeated Multiplying of a Factor: Base, Exponent, and Power 11
12. Combining Like and Unlike Terms 13
Chapter 2 Simple Equations and Their Solutions 21
1. Kinds of Equalities: Equations and Identities 21
2. Translating Verbal Statements into Equations 22
3. Solving Simple Equations by Using Inverse Operations 23
4. Rules of Equality for Solving Equations 25
5. Using Division to Solve an Equation 26
6. Using Multiplication to Solve an Equation 28
7. Using Subtraction to Solve an Equation 30
8. Using Addition to Solve an Equation 31
9. Using Two or More Operations to Solve an Equation 32
Chapter 3 Signed Numbers 43
1. Understanding Signed Numbers: Positive and Negative Numbers 43
2. Using Number Scales for Signed Numbers 44
3. Adding Signed Numbers 48
4. Simplifying the Addition of Signed Numbers 50
5. Subtracting Signed Numbers 51
6. Multiplying Signed Numbers 53
7. Finding Powers of Signed Numbers 55
8. Dividing Signed Numbers 56
9. Evaluating Expressions Having Signed Numbers 58
Chapter 4 Introduction to Monomials and Polynomials 64
1. Understanding Monomials and Polynomials 64
2. Adding Monomials 65
3. Arranging and Adding Polynomials 66
4. Subtracting Monomials 67
5. Subtracting Polynomials 68
6. Using Parentheses and Other Grouping Symbols to Add or Subtract Polynomials 69
7. Multiplying Monomials and Powers of the Same Base 71
8. Multiplying a Polynomial by a Monomial 72
9. Multiplying Polynomials 73
10. Dividing Powers and Monomials 74
11. Dividing a Polynomial by a Monomial 76
12. Dividing a Polynomial by a Polynomial 77
Chapter 5 First-Degree Equations 86
1. Reviewing the Solution of First-Degree Equations Having Positive Roots 86
2. Solving First-Degree Equations Having Negative Solutions 88
3. Solving Equations by Transposing 90
4. Solving Equations Containing Parentheses 91
5. Solving Equations Containing One Fraction or Fractions Having the Same Denominator 92
6. Solving Equations Containing Fractions Having Different Denominators: Lowest Common Denominator 93
7. Solving Equations Containing Decimals 95
8. Solving Literal Equations 96
9. The Graphing Calculator 97
Chapter 6 Formulas 105
1. Points and Lines 105
2. Understanding Polygons, Circles, and Solids 106
3. Formulas for Perimeters and Circumferences: Linear Measure 111
4. Formulas for Areas: Square Measure 115
5. Formulas for Volumes: Cubic Measure 120
6. Deriving Formulas 124
7. Transforming Formulas 126
8. Finding the Value of an Unknown in a Formula 128
Chapter 7 Graphs of Linear Equations 137
1. Understanding Graphs 137
2. Graphing Linear Equations 141
3. Solving a Pair of Linear Equations Graphically 147
4. Deriving a Linear Equation from a Table of Values 150
5. Midpoint of a Segment 152
6. Distance between Two Points 153
Chapter 8 Introduction to Simultaneous Equations 163
1. Solving a Pair of Equations by Addition or Subtraction 163
2. Solving a Pair of Equations by Substitution 166
Chapter 9 Problem Solving and Mathematical Modeling 169
1. Number Problems Having One Unknown: Introduction to Problem Solving 169
2. Number Problems Having Two Unknowns 171
3. Consecutive-Integer Problems 173
4. Age Problems 175
5. Ratio Problems 176
6. Angle Problems 179
7. Perimeter Problems 182
8. Coin or Stamp Problems 185
9. Cost and Mixture Problems 187
10. Investment or Interest Problems 189
11. Motion Problems 191
12. Mathematical Modeling 197
Chapter 10 Products and Factoring 213
1. Understanding Factors and Products 213
2. Factoring a Polynomial Having a Common Monomial Factor 214
3. Squaring a Monomial 215
4. Finding the Square Root of a Monomial 216
5. Finding the Product of the Sum and Difference of Two Numbers 217
6. Factoring the Difference of Two Squares 218
7. Finding the Product of Two Binomials with Like Terms 219
8. Factoring Trinomials in Form of x[superscript 2] + bx + c 221
9. Factoring a Trinomial in Form of ax[superscript 2] + bx + c 222
10. Squaring a Binomial 223
11. Factoring a Perfect-Square Trinomial 223
12. Completely Factoring Polynomials 225
13. The Variable: Direct and Inverse Variation 226
14. Understanding Direct Variation: y = kx or y / x = k 227
15. Understanding Inverse Variation: xy = k 230
Chapter 11 Fractions 241
1. Understanding Fractions 241
2. Changing Fractions to Equivalent Fractions 243
3. Reciprocals and Their Uses 244
4. Reducing Fractions to Lowest Terms 246
5. Multiplying Fractions 248
6. Dividing Fractions 249
7. Adding or Subtracting Fractions Having the Same Denominator 250
8. Adding or Subtracting Fractions Having Different Denominators 251
9. Simplifying Complex Fractions 253
Chapter 12 Roots and Radicals 262
1. Understanding Roots and Radicals 262
2. Understanding Rational and Irrational Numbers 264
3. Finding the Square Root of a Number by Using a Graph 265
4. Finding the Square Root of a Number by Using a Table or Calculator 266
5. Simplifying the Square Root of a Product 267
6. Simplifying the Square Root of a Fraction 269
7. Adding and Subtracting Square Roots of Numbers 271
8. Multiplying Square Roots of Numbers 272
9. Dividing Square Roots of Numbers 273
10. Rationalizing the Denominator of a Fraction 274
11. Solving Radical Equations 276
Chapter 13 Quadratic Equations 284
1. Understanding Quadratic Equations in One Unknown 284
2. Solving Quadratic Equations by Factoring 285
3. Solving Incomplete Quadratic Equations 287
4. Solving a Quadratic Equation by Completing the Square 289
5. Solving a Quadratic Equation by Quadratic Formula 291
6. Solving Quadratic Equations Graphically 293
Chapter 14 The Pythagorean Theorem and Similar Triangles 301
1. Law of Pythagoras 301
2. Proportions: Equal Ratios 305
3. Similar Triangles 307
Chapter 15 Introduction to Trigonometry 315
1. Understanding Trigonometric Ratios 315
2. Trigonometric Functions of an Acute Angle 315
3. Trigonometric Functions of Complementary Angles 316
4. Trigonometric Functions of 30[degree], 45[degree], 60[degree] 316
Chapter 16 Introduction to Geometry 323
1. Solving Problems Graphically 323
2. Understanding the Slope of a Line 324
3. Understanding Congruent Triangles 326
4. Understanding Symmetry 330
5. Transformations 331
Appendix A Review of Arithmetic 343
1. The Whole Numbers 343
2. Fractions 345
3. Decimals 348
4. Reviewing Percents and Percentage 350
Appendix B The Use of Calculators 353
1. Using a Calculator to Perform the Fundamental Operations of Arithmetic 353
2. Introduction to the Graphing Calculator 354
Index 359
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