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Honors
ALGeBRA 2
SUMMER REVIEW PACKET
DUE ON THE FIRST DAY OF SCHOOL
The problems in this packet are designed to help you review topics that you should have already
mastered and that are important to your success in your next level of mathematics.
It is your responsibility to understand these concepts and
be able to apply the necessary skills to solve these problems.
You will be held accountable for this material!
Do problems on a separate sheet of paper.
Show all your work for each problem.
You may want to work with one or more people on this,
however each student must submit her or his own packet.
All work must be completed and ready to turn in on the first day of school.
Rockville High School
Honors Algebra 2 Summer Review Packet
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Solve each linear equation.
1.
4.
4(3  x) = 2(x + 6)
3x  2(x + 1) = 0
2.
5.
2(3x + 6) + 8 = 6x
3(x + 2) + 1 = 2x + 7 + x
3.
3(4  x) = 12  3x
Solve each system of linear equations algebraically.
6.
 5x  4 y  6

 2 x  3 y  1
7.
 2 x  y  8

 y  3x  2
8.
  x  2 y  11

3 x  2 y  13
9.
 3x  2 y  5

 6 x  4 y  7
Solve each formula for the indicated variable.
10. P = 2(l + w) ; for l
11. d = rt ; for r
12.
cd
 a ; for c
2
13. V = lwh ; for h
Factor each polynomial completely.
14. x2  x  72
18. 2x2y  4xy  30y
15. 7x3  4x2 + 8x
19. x2  64
16. a2 + 20a + 64
20. 2x2 + 9x  5
17. 10m3n2  15m2n + 25m
21. x2 + 12x + 36
Solve each quadratic equation algebraically.
22. x2  3x = 10
25. 2x2  3x  2 = 0
23. 5m2 = 7m
26. z2 = 16
24. (2c + 1)(c + 3) = 0
27. r2 + 10r  9 = 0
Write the equation for each line.
28. thru (0, 1), slope = 1
31. vertical thru (5, 4)
y
4
3
32. thru (2, 3) and (7, 2)
29. thru (2, 3), slope =
y
34.
33. thru (3, 4) and (2, 4)
y
35.
x
30. thru (3, 1), slope = 0
36.
x
y
37.
x
x
38. thru (25, 40) and (100, 55)
Rockville High School
Honors Algebra 2 Summer Review Packet
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Graph, then state the domain and range. Use the grids on the last page of this packet.
39. y = 
3
x+4
4
43. y = (x  2)2 + 1
40. x  3y = 6
41. y = 5
42. x = 2
44. y = x2 + 6x + 1
45. y  32x
46. y ≤ 3x  2
47. x > 2
Simplify. When appropriate, write in standard form. All exponents should be positive.
48. (3x + 4x  7) + (2x  7x + 8)
2
2
49.
64 x3 y 2  16 x 2 y 3  32 x5 y 5
50. (39a4  4a3 + 2a2  a  7)  (10a4 + 3a3  2a2  a + 8)
8x2 y 2
51. 2x2z(3x  2z)
52. 3xy3(x  2y)
53. (3x2 + x  1)(2x  3)
54.
55. (8a3b2)(2a4b5)
56. (3x2y3z)3
5a 5bc 7
57. (15a4b2c)0
59. (3x + 7)(2x  5)
60. (x + 6)2
58.
3x3 y 2
6x
2 5
10 a 3b 2c 7
y
Simplify each radical expression. Give exact answers (no decimal approximations).
61.
32
62.
108
63.
3
5
64.
3
2
65.
3
3
66.
48xy5
67.
8  18  32
68.
21 14
69.
16a 3b 2
Using the matrices given, complete the indicated operations.
5  1
2
A

 3  2 0 
 5  3
B   0
2 
 1 4 
70. A + C
71. 2B
74. What are the dimensions of A?
Rockville High School
  1 3 0
C

  5 2 3
72. C  A
73. A + B
75. What is the order of B?
Honors Algebra 2 Summer Review Packet
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Rockville High School
Honors Algebra 2 Summer Review Packet