Download Welcome to the study of Algebra 2! Please note that this packet is a

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