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The Humongous Book of Algebra Problems

Book Description

When the numbers just don't add up...

Following in the footsteps of the successful The Humongous Books of Calculus Problems, bestselling author Michael Kelley has taken a typical algebra workbook, and made notes in the margins, adding missing steps and simplifying concepts and solutions. Students will learn how to interpret and solve 1000 problems as they are typically presented in algebra courses-and become prepared to solve those problems that were never discussed in class but always seem to find their way onto exams.

Annotations throughout the text clarify each problem and fill in missing steps needed to reach the solution, making this book like no other algebra workbook on the market.

Table of Contents

  1. Contents iii (1/2)
  2. Contents iii (2/2)
  3. Chapter 1: Arithmetic Fundamentals 1
    1. Number Classification 2
    2. Expressions Containing Signed Numbers 5
    3. Grouping Symbols 8
    4. Algebraic Properties 11 (1/2)
    5. Algebraic Properties 11 (2/2)
  4. Chapter 2: Rational Numbers 17
    1. Rational Number Notation 18
    2. Simplifying Fractions 23
    3. Combining Fractions 26 (1/3)
    4. Combining Fractions 26 (2/3)
    5. Combining Fractions 26 (3/3)
  5. Chapter 3: Basic Algebraic Expressions 37
    1. Translating Expressions 38
    2. Exponential Expressions 40
    3. Distributive Property 45
    4. Order of Operations 48
    5. Evaluating Expressions 51
  6. Chapter 4: Linear Equations in One Variable 55
    1. Adding and Subtracting to Solve an Equation 56
    2. Multiplying and Dividing to Solve an Equation 59
    3. Solving Equations Using Multiple Steps 61 (1/2)
    4. Solving Equations Using Multiple Steps 61 (2/2)
    5. Absolute Value Equations 70
    6. Equations Containing Multiple Variables 73
  7. Chapter 5: Graphing Linear Equations in Two Variables 77
    1. Number Lines and the Coordinate Plane 78
    2. Graphing with a Table of Values 83 (1/2)
    3. Graphing with a Table of Values 83 (2/2)
    4. Graphing Using Intercepts 90
    5. Calculating Slope of a Line 93 (1/2)
    6. Calculating Slope of a Line 93 (2/2)
    7. Graphing Absolute Value Equations 100
  8. Chapter 6: Linear Equations in Two Variables 105
    1. Point-Slope Form of a Linear Equation 106
    2. Slope-Intercept Form of a Linear Equation 110
    3. Graphing Lines in Slope-Intercept Form 113
    4. Standard Form of a Linear Equation 118
    5. Creating Linear Equations 121 (1/2)
    6. Creating Linear Equations 121 (2/2)
  9. Chapter 7: Linear Inequalities 127
    1. Inequalities in One Variable 128
    2. Graphing Inequalities in One Variable 132
    3. Compound Inequalities 135
    4. Absolute Value Inequalities 137
    5. Set Notation 140
    6. Graphing Inequalities in Two Variables 142
  10. Chapter 8: Systems of Linear Equations and Inequalities 147
    1. Graphing Linear Systems 148
    2. The Substitution Method 153 (1/2)
    3. The Substitution Method 153 (2/2)
    4. Variable Elimination 162 (1/2)
    5. Variable Elimination 162 (2/2)
    6. Systems of Inequalities 168
    7. Linear Programming 173 (1/2)
    8. Linear Programming 173 (2/2)
  11. Chapter 9: Matrix Operations and Calculations 181
    1. Anatomy of a Matrix 182
    2. Adding and Subtracting Matrices 183
    3. Multiplying Matrices 188
    4. Calculating Determinants 192 (1/2)
    5. Calculating Determinants 192 (2/2)
    6. Cramer’s Rule 200 (1/2)
    7. Cramer’s Rule 200 (2/2)
  12. Chapter 10: Applications of Matrix Algebra 207
    1. Augmented and Identity Matrices 208
    2. Matrix Row Operations 211
    3. Row and Reduced-Row Echelon Form 216 (1/3)
    4. Row and Reduced-Row Echelon Form 216 (2/3)
    5. Row and Reduced-Row Echelon Form 216 (3/3)
    6. Inverse Matrices 228 (1/2)
    7. Inverse Matrices 228 (2/2)
  13. Chapter 11: Polynomials 237
    1. Classifying Polynomials 238
    2. Adding and Subtracting Polynomials 239
    3. Multiplying Polynomials 244
    4. Long Division of Polynomials 246
    5. Synthetic Division of Polynomials 251 (1/2)
    6. Synthetic Division of Polynomials 251 (2/2)
  14. Chapter 12: Factoring Polynomials 257
    1. Greatest Common Factors 258 (1/2)
    2. Greatest Common Factors 258 (2/2)
    3. Factoring by Grouping 265
    4. Common Factor Patterns 267
    5. Factoring Quadratic Trinomials 270
  15. Chapter 13: Radical Expressions and Equations 275
    1. Simplifying Radical Expressions 276
    2. Rational Exponents 281
    3. Radical Operations 283
    4. Solving Radical Equations 288
    5. Complex Numbers 290
  16. Chapter 14: Quadratic Equations and Inequalities 295
    1. Solving Quadratics by Factoring 296
    2. Completing the Square 300
    3. Quadratic Formula 305 (1/2)
    4. Quadratic Formula 305 (2/2)
    5. Applying the Discriminant 312
    6. One-Variable Quadratic Inequalities 316 (1/2)
    7. One-Variable Quadratic Inequalities 316 (2/2)
  17. Chapter 15: Functions 323
    1. Relations and Functions 324
    2. Operations on Functions 326
    3. Composition of Functions 330
    4. Inverse Functions 335 (1/2)
    5. Inverse Functions 335 (2/2)
    6. Piecewise-Defined Functions 343
  18. Chapter 16: Graphing Functions 347
    1. Graphing with a Table of Values 348 (1/2)
    2. Graphing with a Table of Values 348 (2/2)
    3. Domain and Range of a Function 354 (1/2)
    4. Domain and Range of a Function 354 (2/2)
    5. Symmetry 360
    6. Fundamental Function Graphs365
    7. Graphing Functions Using Transformations 369
    8. Absolute Value Functions 374
  19. Chapter 17: Calculating Roots of Functions 379
    1. Identifying Rational Roots 380
    2. Leading Coefficient Test 384
    3. Descartes’ Rule of Signs 388
    4. Rational Root Test 390
    5. Synthesizing Root Identification Strategies 394
  20. Chapter 18: Logarithmic Functions 399
    1. Evaluating Logarithmic Expressions 400
    2. Graphs of Logarithmic Functions 402
    3. Common and Natural Logarithms 406
    4. Change of Base Formula 409
    5. Logarithmic Properties 412
  21. Chapter 19: Exponential Functions 417
    1. Graphing Exponential Functions 418
    2. Composing Exponential and Logarithmic Functions 423
    3. Exponential and Logarithmic Equations 426 (1/2)
    4. Exponential and Logarithmic Equations 426 (2/2)
    5. Exponential Growth and Decay 433 (1/2)
    6. Exponential Growth and Decay 433 (2/2)
  22. Chapter 20: Rational Expressions 439
    1. Simplifying Rational Expressions 440
    2. Adding and Subtracting Rational Expressions 444 (1/2)
    3. Adding and Subtracting Rational Expressions 444 (2/2)
    4. Multiplying and Dividing Rational Expressions 452
    5. Simplifying Complex Fractions 457
    6. Graphing Rational Functions 459 (1/2)
    7. Graphing Rational Functions 459 (2/2)
  23. Chapter 21: Rational Equations and Inequalities 465
    1. Proportions and Cross Multiplication 466
    2. Solving Rational Equations 470
    3. Direct and Indirect Variation 475
    4. Solving Rational Inequalities 479 (1/2)
    5. Solving Rational Inequalities 479 (2/2)
  24. Chapter 22: Conic Sections 487
    1. Parabolas 488 (1/2)
    2. Parabolas 488 (2/2)
    3. Circles 494
    4. Ellipses 499 (1/2)
    5. Ellipses 499 (2/2)
    6. Hyperbolas 506 (1/2)
    7. Hyperbolas 506 (2/2)
  25. Chapter 23: Word Problems 515
    1. Determining Unknown Values 516
    2. Calculating Interest 521
    3. Geometric Formulas 525
    4. Speed and Distance 529
    5. Mixture and Combination 534
    6. Work 538 (1/2)
    7. Work 538 (2/2)
  26. Appendix A: Algebraic Properties 545
  27. Appendix B: Important Graphs and Graph Transformations 547
  28. Appendix C: Key Algebra Formulas 551
  29. Index 555 (1/3)
  30. Index 555 (2/3)
  31. Index 555 (3/3)