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. 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
(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. 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. (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. 6𝑣(2𝑣 + 3)
30. −4(𝑣 + 1)
31. (𝑥 – 3)(6𝑥 – 2)
32. (8𝑝 – 2)(6𝑝 + 2)
TOPIC: TWO-STEP EQUATIONS
33. −4 =
𝑟
−
20
5
35. 2(𝑛 + 5) = −2
34. −1 =
5+𝑥
6
36. −9𝑥 + 1 = −80
TOPIC: TWO-STEP INEQUALITIES
𝑚
3
37. 2𝑥 + 4 ≥ 24
38.
39. −3(𝑝 + 1) < −18
40. −𝑏 – 2 > 8
− 3 ≤ −6
TOPIC: MULTI-STEP EQUATIONS
41. −(7 − 4𝑥) = 9
42. 5𝑛 + 34 = −2(1 – 7n)
43. 2(4𝑥 − 3) – 8 = 4 + 2𝑥
44. −3(4𝑥 + 3) + 4(6𝑥 + 1) = 4
TOPIC: MULTI-STEP INEQUALITIES
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: SOLVE A SYSTEM OF EQUATIONS
48.)
𝑥 − 2𝑦 = 3
3𝑥 + 𝑦 = −5
49.)
2𝑥 + 3𝑦 = 4
4𝑥 + 6𝑦 = 9
TOPIC: GRAPHING LINES
49. 𝑦 =
7
𝑥
2
−2
51. 𝑦 = −5
50. 𝑦 = −6𝑥 + 3
52. 𝑥 = 2
54. 𝑦 = 3𝑥 − 5
53. 𝑦 =
1
−4𝑥
+2
TOPIC: GRAPHING LINEAR INEQUALITIES
# 59 - 62: Sketch the graph of each linear inequality.
3
𝑥
5
55. 𝑦 ≥ −3𝑥 + 4
56. 𝑦 ≤
57. 𝑦 > −𝑥 − 5
58. 𝑦 < −4
−5
TOPIC: FINDING SLOPE FROM AN EQUATION
# 63 - 66: Find the slope of each line.
5
59. 𝑦 = − 2 𝑥 − 5
60. 𝑦 = −4𝑥 + 1
61. 2𝑥 – 𝑦 = 1
62. 4𝑥 + 5𝑦 = −10
TOPIC: FINDING SLOPE FROM TWO POINTS
63. (19, -16), (-7, -15)
64. (1, -19), (-2, -7)
65. (-4, 7), (-6, -4)
66. (20, 8), (9, 16)
TOPIC: SIMPLIFYING RADICAL EXPRESSIONS
A.)
√25
68.)
√49𝑥 4
B.)
√24𝑥 2 𝑦 6
70.)
√32𝑥 3
C.)
√20𝑥 8 𝑦 5
72.)
√27𝑥 6 𝑦 5 𝑧 4
TOPIC: ADDING AND SUBTRACTING RADICAL EXPRESSIONS
67. −10√7 + 12√7
68. −3√15 − 4√15
69. −√12 + 3√3
70. 2√6 + 3√54
TOPIC: MULTIPLYING RADICAL EXPRESSIONS
71. √5 ∙ √10
72. 3√12 ∙ √6
73. √3(5 + √3)
73.) 2√5(√6 + 2)
TOPIC: SIMPLIFYING EXPRESSIONS WITH EXPONENTS
79
𝑥2𝑦5
80.
𝑎3
𝑎2
81.
12𝑥 4 𝑦 2
6𝑦 6 𝑥 4
82.
𝑧 −3
83.
(𝑥 3 )4
84.
(𝑎2 𝑏 7 )3
83.
4𝑎 −3 𝑏5
16𝑎3 𝑏−2
85.
6𝑚2 (𝑛5 )3
8𝑛8 𝑚7
TOPIC: SOLVE USING THE QUADRATIC FORMULA
𝒙=
−𝒃±√𝒃𝟐 −𝟒𝒂𝒄
𝟐𝒂
86.
𝑦 = 4𝑥 2 + 𝑥 − 1
87.
𝑦 = 𝑥 2 − 2𝑥 + 3
88.
𝑦 = −𝑥 2 − 7𝑥 − 8
89.
𝑦 = 2𝑥 2 + 3𝑥 − 4
TOPIC: FACTORING GENERAL TRINOMIALS
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)
72. 𝑥 2 + 8𝑥 + 12
73. 𝑥 2 − 11𝑥 + 24
74. 𝑥 2 − 7𝑥 − 10
75. 𝑥 2 − 10𝑥 + 20
76. 𝑥 2 + 3𝑥 − 18
77. 𝑥 2 − 3𝑥 − 4
78. 𝑥 2 + 2𝑥 + 1
79. 𝑥 2 + 3𝑥 − 1