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Welcome to the study of Algebra 2! Please note that this packet is a requirement for all students You work should be neat and legible. Show all work on the hand-out. If more space is needed you may use loose leaf paper. Purple Math is a great site and will provide you with examples and lessons to help you complete assignments. You can search topics in Google or YouTube for other help. Don’t buy anything; there is plenty of free help out there on the web. The booklet containing all of your assignments should be ready to turn in the first day of class. Come to class prepared to start working! A scientific or graphing calculator is a must for Algebra 2. We use Texas Instruments graphing calculators here at Mandarin High School. If you should buy a new TI (scientific or graphing) calculator, you should save the UPC for extra credit! Many stores will have them on sale in August. You will need the following materials starting your very first day: loose leaf paper graph paper pencils erasers TI-30XS calculator is required TI-83 or TI-84 calculator is preferred & will be of great assistance any other materials on your teacher’s syllabus The Algebra 2 teachers look forward to seeing you next August! SUMMER PREPERATORY WORK FOR ALGEBRA 2 This packet is REQUIRED and will count as a quiz grade during your 1st quarter of Algebra 2. Work MUST be shown in order to receive credit. TOPIC: VARIABLE AND VERBAL EXPRESSIONS. # 1 - 8: Write each as an algebraic expressions. 1. 𝑢 decreased by 17 2. 𝑥 increased by 6 3. The product of 𝑥 and 7 4. The sum of 𝑞 and 8 5. 6 squared 6. Twice 𝑞 7. The quotient of 18 and 𝑛 8. 𝑛 cubed TOPIC: ORDER OF OPERATIONS # 9 - 20: Evaluate each expression. Show each little step. (5 + 16) ÷ 7 – 2 10. 7 + 10 × 5 + 10 11. (6 + 25 – 7) ÷ 6 12. (6 – 4) × 49 ÷ 7 9. 13. (8 + 5) × 35 5 + 6 14. 27 + 2+3+4 3 15. 𝑝2 + 𝑚; use m = 1 and p = 5 16. 𝑦 2 – 𝑥; use x = 7, and y = 7 17. 𝑧(𝑥 + 𝑦); use x = 6, y = 8 , and z = 6 18. 𝑝3 + 0 + 𝑚; use m = 9, and p = 3 19. 𝑧 – (𝑦 ÷ 3 – 1); use y = 3, and z = 7 20. (𝑦 + 𝑥) ÷ 2 + 𝑥; use x = 1, and y = 1 TOPIC: COMBINING LIKE TERMS # 21 - 24: Simplify each expression. 21. 𝑛 – 4 – 9 22. −3𝑥 – 9 + 15𝑥 23. 5𝑛 + 3(6 + 7𝑛) 24. 5(−2𝑛 + 4) + 2(𝑛 + 3) TOPIC: ADDING AND SUBTRACTING POLYNOMIALS # 25 - 28: simplify each expression. 25. (5𝑝2 – 3) + (2𝑝2 – 3𝑝3 ) 26. (𝑎3 – 2𝑎2 ) – (3𝑎2 – 4𝑎3 ) 27. (4 + 2𝑛3 ) + (5𝑛3 + 2) 28. (4𝑟 3 + 3𝑟 4 ) – (𝑟 4 – 5𝑟 3 ) TOPIC: MULTIPLYING POLYNOMIALS # 29 - 32: Find each product. 29. 6𝑣(2𝑣 + 3) 30. −4(𝑣 + 1) 31. (𝑥 – 3)(6𝑥 – 2) 32. (8𝑝 – 2)(6𝑝 + 2) TOPIC: TWO-STEP EQUATIONS # 33 - 36: Solve each inequality. 33. −4 = 𝑟 − 20 5 35. 2(𝑛 + 5) = −2 34. −1 = 5+𝑥 6 36. −9𝑥 + 1 = −80 TOPIC: TWO-STEP INEQUALITIES # 37 - 40: Solve each inequality & graph its solution. 𝑚 3 37. 2𝑥 + 4 ≥ 24 38. 39. −3(𝑝 + 1) < −18 40. −𝑏 – 2 > 8 − 3 ≤ −6 TOPIC: MULTI-STEP EQUATIONS # 41 - 44: Solve each equation. 41. −(7 − 4𝑥) = 9 42. 5𝑛 + 34 = −2(1 – 7n) 43. 2(4𝑥 − 3) – 8 = 4 + 2𝑥 44. −3(4𝑥 + 3) + 4(6𝑥 + 1) = 43 TOPIC: MULTI-STEP INEQUALITIES # 45 - 48: Solve each inequality & graph its solution. 45. −3 − 6(4𝑥 + 6) > −111 46. 6 − 4(6𝑛 + 7) ≥ 122 47. 8𝑥 + 2𝑥 – 16 < −5𝑥 + 7𝑥 48. −1 – 6𝑥 – 6 ≥ −11 – 7𝑥 TOPIC: ABSOLUTE VALUE EQUATIONS # 49 - 52: Solve each equation. 49. |−3𝑝| = 15 50. |𝑘 − 10| = 3 51. |7 + 𝑝| = 7 52. 7|𝑛| = 56 TOPIC: GRAPHING LINES # 53 - 58: Sketch the graph of each line. 53. 𝑦 = 7 𝑥 2 −2 55. 𝑦 = −5 54. 𝑦 = −6𝑥 + 3 56. 𝑥 = 2 1 4 57. 𝑦 = − 𝑥 + 2 58. 𝑦 = 3𝑥 − 5 TOPIC: GRAPHING LINEAR INEQUALITIES # 59 - 62: Sketch the graph of each linear inequality. 3 𝑥 5 59. 𝑦 ≥ −3𝑥 + 4 60. 𝑦 ≤ 61. 𝑦 > −𝑥 − 5 62. 𝑦 < −4 −5 TOPIC: FINDING SLOPE FROM AN EQUATION # 63 - 66: Find the slope of each line. 5 63. 𝑦 = − 2 𝑥 − 5 64. 𝑦 = −4𝑥 + 1 65. 2𝑥 – 𝑦 = 1 66. 4𝑥 + 5𝑦 = −10 TOPIC: FINDING SLOPE FROM TWO POINTS # 67 - 70: Find the slope of the line through each pair of points. 67. (19, -16), (-7, -15) 68. (1, -19), (-2, -7) 69. (-4, 7), (-6, -4) 70. (20, 8), (9, 16) TOPIC: ADDING AND SUBTRACTING RADICAL EXPRESSIONS # 71 - 74: Simplify each expression. 71. −10√7 + 12√7 72. −3√15 − 4√15 73. −√12 + 3√3 74. 2√6 + 3√54 TOPIC: MULTIPLYING RADICAL EXPRESSIONS # 75 - 78: Simplify each expression. 75. √5 ∙ √10 76. 3√12 ∙ √6 77. √3(5 + √3) 78. 2√5(√6 + 2) TOPIC: SIMPLIFYING RATIONAL EXPRESSIONS # 79 - 82: Simplify each expression. 79. 81. 16𝑟 2 16𝑟 3 15𝑛 30𝑛2 80. 32𝑛2 24𝑛 82. − 36𝑥 3 42𝑥 TOPIC: FACTORING GENERAL TRINOMIALS # 83 – 90: Factor each trinomial. Example) 𝑥 2 + 3𝑥 + 2 Example) 𝑥 2 + 2𝑥 − 35 What two numbers multiply to make 2 and add to make 3? 2 and 1 What two numbers multiply to make -35 and add to make 2? 7 and -5 (𝑥 + 2)(𝑥 + 1) (𝑥 + 7 )(𝑥 − 5) Example) 𝑥 2 − 11𝑥 + 28 Example) 𝑥 2 − 4𝑥 − 5 What two numbers multiply to make 28 and add to make -11? -7 and -4 What two numbers multiply to make -5 and add to make -4? -5 and 1 (𝑥 − 7)(𝑥 − 4) (𝑥 − 5)(𝑥 + 1) 83. 𝑥 2 + 8𝑥 + 12 84. 𝑥 2 − 11𝑥 + 24 85. 𝑥 2 − 7𝑥 − 10 86. 𝑥 2 − 10𝑥 + 20 87. 𝑥 2 + 3𝑥 − 18 88. 𝑥 2 − 3𝑥 − 4 89. 𝑥 2 + 2𝑥 + 1 90. 𝑥 2 + 3𝑥 − 15