ALGEBRA 2 CRA 2 REVIEW - Chapters 1-6 Answer Section MULTIPLE CHOICE 1. ANS: C 2. ANS: A 3. ANS: A OBJ: 5-3.1 Using Vertex Form SHORT ANSWER 4. ANS: (x + 6)(x 2 6x + 36) OBJ: 6-4.2 Solving Equations by Factoring 5. ANS: 3x(5x + 7) OBJ: 5-4.1 Finding Common and Binomial Factors 6. ANS: 4( 2x 2 3x + 4) OBJ: 5-4.1 Finding Common and Binomial Factors 7. ANS: (x + 6)(x + 8) OBJ: 5-4.1 Finding Common and Binomial Factors 8. ANS: (3x + 5)(x + 7) OBJ: 5-4.1 Finding Common and Binomial Factors 9. ANS: (5x + 3)(x 5) OBJ: 5-4.1 Finding Common and Binomial Factors 10. ANS: (4x + 5) 2 OBJ: 5-4.2 Factoring Special Expressions 11. ANS: (3x + 4)(3x 4) OBJ: 5-4.2 Factoring Special Expressions 1
12. ANS: (x + 6)(x 2 6x + 36) OBJ: 6-4.2 Solving Equations by Factoring 13. ANS: (x 2)(x + 2)(x 4)(x + 4) OBJ: 6-4.2 Solving Equations by Factoring 14. ANS: 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ±5 OBJ: 6-6.1 The Fundamental Theorem of Algebra 15. ANS: Distributive Commutative Associative Reverse Distributive Arithmetic Commutative 16. ANS: irrational numbers, real numbers OBJ: 1-1.1 Graphing and Ordering Real Numbers 17. ANS: integers, rational numbers, real numbers OBJ: 1-1.1 Graphing and Ordering Real Numbers 18. ANS: h < 64 in. OBJ: 1-4.1 Solving and Graphing Inequalities 19. ANS: $5,275 at 4.2%, $7,225 at 6.2% OBJ: 1-3.2 Writing Equations to Solve Problems 2
20. ANS: Ï domain: 1, 1 Ô 2, 3 Ì 2, 2 Ô ÓÔ Ô Ï range: 1, 0, 1 2, 3 Ô Ô Ì ÓÔ 2 Ô OBJ: 2-1.1 Graphing Relations 21. ANS: Yes; for each element in the domain there is exactly one element in the range. OBJ: 2-1.1 Graphing Relations 22. ANS: OBJ: 2-7.1 Graphing Linear Inequalities 3
23. ANS: OBJ: 3-3.1 Solving Systems of Inequalities 24. ANS: OBJ: 3-3.1 Solving Systems of Inequalities 4
25. ANS: OBJ: 3-3.1 Solving Systems of Inequalities 26. ANS: 21 OBJ: 1-2.1 Evaluating Algebraic Expressions 27. ANS: 1 OBJ: 1-2.1 Evaluating Algebraic Expressions 28. ANS: 10x + 2y OBJ: 1-2.2 Simplifying Algebraic Expressions 29. ANS: x = 0 or x = 2 2 3 OBJ: 1-5.1 Absolute Value Equations 30. ANS: 4 3 i, 4 3 i OBJ: 5-6.2 Operations With Complex Numbers 31. ANS: t = S 4r 2 OBJ: 1-3.1 Solving Equations 32. ANS: 7.5 cm by 22.5 cm OBJ: 1-3.2 Writing Equations to Solve Problems 5
33. ANS: all real numbers OBJ: 1-4.1 Solving and Graphing Inequalities 34. ANS: x 0 and x 3 OBJ: 1-4.2 Compound Inequalities 35. ANS: x < 3 or x > 5 OBJ: 1-4.2 Compound Inequalities 36. ANS: 1 x < 4 OBJ: 1-4.2 Compound Inequalities 37. ANS: x 11 or x 8 OBJ: 1-5.2 Absolute Value Inequalities 38. ANS: 18 < x < 8 OBJ: 1-5.2 Absolute Value Inequalities 39. ANS: 11 20 OBJ: 1-6.1 Experimental Probability 40. ANS: 3 8 OBJ: 1-6.2 Theoretical Probability 6
41. ANS: 20x 5 8x 4 ; quintic binomial OBJ: 6-1.1 Exploring Polynomial Functions 42. ANS: 2 4 7 OBJ: 2-1.2 Identifying Functions 43. ANS: 1 3 OBJ: 2-2.1 Graphing Linear Equations 44. ANS: 7 6 OBJ: 2-2.1 Graphing Linear Equations 45. ANS: y + 4 = 1 (x + 6) 8 OBJ: 2-2.2 Writing Equations of Lines 46. ANS: 3 5 OBJ: 2-2.2 Writing Equations of Lines 47. ANS: 8 7 x + y = 61 7 OBJ: 2-2.2 Writing Equations of Lines 48. ANS: y = 4 5 x + 22 5 OBJ: 2-2.2 Writing Equations of Lines 49. ANS: y = 3x 6 OBJ: 2-2.2 Writing Equations of Lines 50. ANS: x = 7 OBJ: 2-2.2 Writing Equations of Lines 7
51. ANS: 4.1 OBJ: 2-3.1 Writing and Interpreting a Direct Variation 52. ANS: h = 56t + 158 OBJ: 2-4.1 Modeling Real-World Data 53. ANS: S = 230T 200; 2560 lb OBJ: 2-4.2 Predicting With Linear Models 54. ANS: y = 2 3 x 4 OBJ: 2-6.1 Translating Graphs Vertically 55. ANS: (0, 5) OBJ: 3-2.1 Solving Systems by Substitution 56. ANS: dependent OBJ: 3-1.1 Systems of Linear Equations 57. ANS: independent OBJ: 3-1.1 Systems of Linear Equations 58. ANS: inconsistent OBJ: 3-1.1 Systems of Linear Equations 59. ANS: (0, 2) OBJ: 3-2.2 Solving Systems by Elimination 60. ANS: no solutions OBJ: 3-2.2 Solving Systems by Elimination 61. ANS: infinite solutions OBJ: 3-2.2 Solving Systems by Elimination 8
62. ANS: 5x 6y 30 OBJ: 2-7.1 Graphing Linear Inequalities 63. ANS: OBJ: 2-7.2 Graphing Two-Variable Absolute Value Inequalities 64. ANS: 1,000 units; $1300 OBJ: 5-2.2 Finding Maximum and Minimum Values 65. ANS: y = 4x 2 + 2x 4 OBJ: 5-1.2 Using Quadratic Models 66. ANS: y = 2(x + 3) 2 4 OBJ: 5-3.1 Using Vertex Form 67. ANS: y = 2(x + 4) 2 + 3 OBJ: 5-3.1 Using Vertex Form 68. ANS: y = 3x 2 + 3 OBJ: 5-3.1 Using Vertex Form 69. ANS: y = 3(x + 2) 2 + 2 OBJ: 5-3.1 Using Vertex Form 9
70. ANS: 8, 1 OBJ: 5-5.1 Solving by Factoring and Finding Square Roots 71. ANS: 1.47, 0.85 OBJ: 5-5.2 Solving by Graphing 72. ANS: 1 9i OBJ: 5-6.2 Operations With Complex Numbers 73. ANS: 27 + 5i OBJ: 5-6.2 Operations With Complex Numbers 74. ANS: 10 2i 7 OBJ: 5-6.1 Identifying Complex Numbers 75. ANS: 49 OBJ: 5-7.1 Solving Equations by Completing the Square 76. ANS: y = (x + 5) 2 9 OBJ: 5-7.2 Rewriting a Function by Completing the Square 77. ANS: P = (h 30) 2 + 500; $30; $500 OBJ: 5-7.2 Rewriting a Function by Completing the Square 78. ANS: 1 5, 2 OBJ: 5-8.1 Using the Quadratic Formula 79. ANS: 1 4 ± 65 4 OBJ: 5-8.1 Using the Quadratic Formula 80. ANS: quintic trinomial OBJ: 6-1.1 Exploring Polynomial Functions 10
81. ANS: 4x(x 4)(x + 6) OBJ: 6-2.1 The Factored Form of a Polynomial 82. ANS: x 2 + 2x 24 OBJ: 6-2.1 The Factored Form of a Polynomial 83. ANS: x 3 + 19x 2 x + 9 OBJ: 6-3.2 Using Synthetic Division 84. ANS: x 3 + 19x 2 x + 9 OBJ: 6-3.2 Using Synthetic Division 85. ANS: f(x) = x 3 + 3x 2 16x 48 OBJ: 6-2.2 Factors and Zeros of a Polynomial Function 86. ANS: f(x) = x 3 2x 2 19x + 20 OBJ: 6-2.2 Factors and Zeros of a Polynomial Function 87. ANS: 2:3 88. ANS: 3:7 89. ANS: 3/5 90. ANS: a. P = 0.38x 2 2.45x + 5.10 b. 13,830 bacteria OBJ: 5-1.2 Using Quadratic Models 91. ANS: -1, -3, 2 92. ANS: 4 complex roots; 0, 2 or 4 real roots OBJ: 6-6.1 The Fundamental Theorem of Algebra 93. ANS: 6, 3, 2, 1, 1, 2, 3, 6 OBJ: 6-5.1 The Rational Root Theorem 11
94. ANS: 5 1, 4 + 7 OBJ: 6-5.2 Irrational Root Theorem and Imaginary Root Theorem 95. ANS: 1, 3 2, ± 5i OBJ: 6-6.1 The Fundamental Theorem of Algebra 12