ALGEBRA 2 CRA 2 REVIEW - Chapters 1-6 Answer Section

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1 ALGEBRA 2 CRA 2 REVIEW - Chapters 1-6 Answer Section MULTIPLE CHOICE 1. ANS: C 2. ANS: A 3. ANS: A OBJ: Using Vertex Form SHORT ANSWER 4. ANS: (x + 6)(x 2 6x + 36) OBJ: Solving Equations by Factoring 5. ANS: 3x(5x + 7) OBJ: Finding Common and Binomial Factors 6. ANS: 4( 2x 2 3x + 4) OBJ: Finding Common and Binomial Factors 7. ANS: (x + 6)(x + 8) OBJ: Finding Common and Binomial Factors 8. ANS: (3x + 5)(x + 7) OBJ: Finding Common and Binomial Factors 9. ANS: (5x + 3)(x 5) OBJ: Finding Common and Binomial Factors 10. ANS: (4x + 5) 2 OBJ: Factoring Special Expressions 11. ANS: (3x + 4)(3x 4) OBJ: Factoring Special Expressions 1

2 12. ANS: (x + 6)(x 2 6x + 36) OBJ: Solving Equations by Factoring 13. ANS: (x 2)(x + 2)(x 4)(x + 4) OBJ: Solving Equations by Factoring 14. ANS: 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ±5 OBJ: The Fundamental Theorem of Algebra 15. ANS: Distributive Commutative Associative Reverse Distributive Arithmetic Commutative 16. ANS: irrational numbers, real numbers OBJ: Graphing and Ordering Real Numbers 17. ANS: integers, rational numbers, real numbers OBJ: Graphing and Ordering Real Numbers 18. ANS: h < 64 in. OBJ: Solving and Graphing Inequalities 19. ANS: $5,275 at 4.2%, $7,225 at 6.2% OBJ: Writing Equations to Solve Problems 2

3 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: Graphing Relations 21. ANS: Yes; for each element in the domain there is exactly one element in the range. OBJ: Graphing Relations 22. ANS: OBJ: Graphing Linear Inequalities 3

4 23. ANS: OBJ: Solving Systems of Inequalities 24. ANS: OBJ: Solving Systems of Inequalities 4

5 25. ANS: OBJ: Solving Systems of Inequalities 26. ANS: 21 OBJ: Evaluating Algebraic Expressions 27. ANS: 1 OBJ: Evaluating Algebraic Expressions 28. ANS: 10x + 2y OBJ: Simplifying Algebraic Expressions 29. ANS: x = 0 or x = OBJ: Absolute Value Equations 30. ANS: 4 3 i, 4 3 i OBJ: Operations With Complex Numbers 31. ANS: t = S 4r 2 OBJ: Solving Equations 32. ANS: 7.5 cm by 22.5 cm OBJ: Writing Equations to Solve Problems 5

6 33. ANS: all real numbers OBJ: Solving and Graphing Inequalities 34. ANS: x 0 and x 3 OBJ: Compound Inequalities 35. ANS: x < 3 or x > 5 OBJ: Compound Inequalities 36. ANS: 1 x < 4 OBJ: Compound Inequalities 37. ANS: x 11 or x 8 OBJ: Absolute Value Inequalities 38. ANS: 18 < x < 8 OBJ: Absolute Value Inequalities 39. ANS: OBJ: Experimental Probability 40. ANS: 3 8 OBJ: Theoretical Probability 6

7 41. ANS: 20x 5 8x 4 ; quintic binomial OBJ: Exploring Polynomial Functions 42. ANS: OBJ: Identifying Functions 43. ANS: 1 3 OBJ: Graphing Linear Equations 44. ANS: 7 6 OBJ: Graphing Linear Equations 45. ANS: y + 4 = 1 (x + 6) 8 OBJ: Writing Equations of Lines 46. ANS: 3 5 OBJ: Writing Equations of Lines 47. ANS: 8 7 x + y = 61 7 OBJ: Writing Equations of Lines 48. ANS: y = 4 5 x OBJ: Writing Equations of Lines 49. ANS: y = 3x 6 OBJ: Writing Equations of Lines 50. ANS: x = 7 OBJ: Writing Equations of Lines 7

8 51. ANS: 4.1 OBJ: Writing and Interpreting a Direct Variation 52. ANS: h = 56t OBJ: Modeling Real-World Data 53. ANS: S = 230T 200; 2560 lb OBJ: Predicting With Linear Models 54. ANS: y = 2 3 x 4 OBJ: Translating Graphs Vertically 55. ANS: (0, 5) OBJ: Solving Systems by Substitution 56. ANS: dependent OBJ: Systems of Linear Equations 57. ANS: independent OBJ: Systems of Linear Equations 58. ANS: inconsistent OBJ: Systems of Linear Equations 59. ANS: (0, 2) OBJ: Solving Systems by Elimination 60. ANS: no solutions OBJ: Solving Systems by Elimination 61. ANS: infinite solutions OBJ: Solving Systems by Elimination 8

9 62. ANS: 5x 6y 30 OBJ: Graphing Linear Inequalities 63. ANS: OBJ: Graphing Two-Variable Absolute Value Inequalities 64. ANS: 1,000 units; $1300 OBJ: Finding Maximum and Minimum Values 65. ANS: y = 4x 2 + 2x 4 OBJ: Using Quadratic Models 66. ANS: y = 2(x + 3) 2 4 OBJ: Using Vertex Form 67. ANS: y = 2(x + 4) OBJ: Using Vertex Form 68. ANS: y = 3x OBJ: Using Vertex Form 69. ANS: y = 3(x + 2) OBJ: Using Vertex Form 9

10 70. ANS: 8, 1 OBJ: Solving by Factoring and Finding Square Roots 71. ANS: 1.47, 0.85 OBJ: Solving by Graphing 72. ANS: 1 9i OBJ: Operations With Complex Numbers 73. ANS: i OBJ: Operations With Complex Numbers 74. ANS: 10 2i 7 OBJ: Identifying Complex Numbers 75. ANS: 49 OBJ: Solving Equations by Completing the Square 76. ANS: y = (x + 5) 2 9 OBJ: Rewriting a Function by Completing the Square 77. ANS: P = (h 30) ; $30; $500 OBJ: Rewriting a Function by Completing the Square 78. ANS: 1 5, 2 OBJ: Using the Quadratic Formula 79. ANS: 1 4 ± 65 4 OBJ: Using the Quadratic Formula 80. ANS: quintic trinomial OBJ: Exploring Polynomial Functions 10

11 81. ANS: 4x(x 4)(x + 6) OBJ: The Factored Form of a Polynomial 82. ANS: x 2 + 2x 24 OBJ: The Factored Form of a Polynomial 83. ANS: x x 2 x + 9 OBJ: Using Synthetic Division 84. ANS: x x 2 x + 9 OBJ: Using Synthetic Division 85. ANS: f(x) = x 3 + 3x 2 16x 48 OBJ: Factors and Zeros of a Polynomial Function 86. ANS: f(x) = x 3 2x 2 19x + 20 OBJ: 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 x b. 13,830 bacteria OBJ: Using Quadratic Models 91. ANS: -1, -3, ANS: 4 complex roots; 0, 2 or 4 real roots OBJ: The Fundamental Theorem of Algebra 93. ANS: 6, 3, 2, 1, 1, 2, 3, 6 OBJ: The Rational Root Theorem 11

12 94. ANS: 5 1, OBJ: Irrational Root Theorem and Imaginary Root Theorem 95. ANS: 1, 3 2, ± 5i OBJ: The Fundamental Theorem of Algebra 12

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