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Accelerated Algebra 2
Summer Assignment
Name____________________
2012
Show work for every problem!!
1. Without a calculator perform the following operations. Write each answer in simplest form.
1 1
27 6
!
a) +
b)
8 6
33 22
7 3
+
10 4
d)
9 1
!
11 3
3
2
e) !2 + 3
8
5
f)
1 1
+
8 6
c)
2. Without a calculator simplify each expression.
a) 8 ! ("3) + 5
c) !4 + 9 ÷ (!3)
b) 8 ÷ 2 ! 3 " 4
d) 1 ! (1 ! 5) 2 ÷ (!8)
3. Name the property of real numbers shown by each equation.
a) 19.49 (1) = 19.49
c) (7 ! a )b = 7b ! ab
b) !8 + 5 = 5 + (!8)
Simplify
4.
2(8 " 3)
+ 2(8 "12)
7"5
5. 6(a "1) " 3(2a + 1)
!
6. (3y 2 " 2y + 5) + 2(y 2 " y + 2)
!
7. (5x 2 " 3x + 1) " 3(x 2 + 2x)
!
8. (4b " 2)(b "1)
!
9. (b 2 + 2bc + c 2 )(b " c)
!
10. (3 " 2t) 2
!
!
d)
2 5
! =1
5 2
11. (g 3 + 27) ÷ (g + 3)
12. (21ab 3 "18a 2b 2 + 3a 3b) ÷ ("3ab)
!
13. 4(d " 2) + 2(d + e) " 6(e "1)
!
14. [5(2a "1) + (a " 4)] " 2[12a " ("a + 1)]
!
15. (2m " n)(m + n)
!
Factor completely
!
16. 24 x 3 " 3a 2
17. 9b 2 "1
!
!
18. 4de 2 " 2def
19. f 2 " f " 6
!
20. g 2 "12g + 36
!
21. h " hij
!
22. 36k 2 " 5k "1
!
23. 3m 2 " 27
!
24. n 4 " 25n 2 + 144
!
25. 2 p 6 "18
!
!
26. 18t 3 + 39t 2 "15t
27. 80v5 " 5v
!
!
41.
!
!
42.
32
1
16x 2
4
28.
2 z + 12
z + 10 z + 24
29.
3g 2 h4 9 gh3
÷
12 x 4 3x 4 y
30.
9 x2 −1 6 x2 + 2 x
÷
3x + 1
6x − 2
31.
32.
2
1
1
−
x+ y x− y
t2
1
−
2
t −1 t + 1
Solve
33. 2 z − 1 = 3 z + 4
34. 4k = 3(4k − 3)
35.
2a 3a 17
+ + =0
5
5 10
36.
w w +1
−
=1
3
2
37.
1
1
1
−
=
2d 5d 10
38.
2
5
+1 =
2a + 5
3
39.
16
4
−
= 1 3x − 1 1 − 3x
40. t 2 = 19t − 84
41. 2w2 + 5w + 3 = 0 42.
42 43. 2
1
2
!
44.
1
5
!
45.
5
2 7
!
!
!
!
46.
8 " 64
47. 4 72 " 3 36
(
)(
On a separate sheet of graph paper, graph each equation.
49. 3x + y = "1
!
!
1
50. y = " x + 4
2
51. 2x + y = 6
!
52. 3x " 5y = 15
53. x + 4 y = "8
!
!
54. 5x = 20
!
Solve each system.
55.
!
)
48. 2 5 + 3 2 5 " 3
x"y =0
3x " 2y = 1
!
!
56.
x " 2y = 16
x + y = 10
57.
3x " 2y = 4
2x + 3y = 7
58. Find the slope and y-intercept of the graph of 6x "12y = 5 .
!
59. Find the value of b for which the graph of 4 x " by = 5 contains the point ( 3,1) .
!
!
Find an equation in standard form of the line meeting the given conditions.
60. Slope=2; containing the point ("1,"1) .
!
3
61. Slope= " ; containing the point (0,5)
4
!
!
62. If f (m) = 2m 2 " 3m + 1, find:
a.
!
f ("2)
b. f (0)
!
c. f (5)
!
63. If g(t) = t 3 " 4t , find:
!
a. g(10)
!
!
b. g("1)
!
c. g("3)
On !
a separate sheet of graph paper, graph the solution set.
64. 3 " 2y > 16
!
!
!
65. 4 x + 1 " 9
66. 3x " y < 5
67. Nancy has 4 times as much money as Juan. If Nancy gives Juan 39 cents, they
would then have equal amounts. What is that new amount?
68. The Coffee Market made a blend of two grades of coffee, one worth $2.00 per
kilogram and the other worth $2.80 per kilogram. If 80 kilograms of the blend is to sell
for $2.20 per kilogram, how many kilograms of each coffee did the market use?
69. Given a triangle with area of 42 square centimeters, find its base and altitude if
together they measure 19 centimeters.
70. A plan left Akron at 12 noon flying west at 250 kilometers per hour. At 2 PM
another plane left the same airport, flying west at 350 kilometers per hour. At what time
did the second plane overtake the first?
71. The sum of the digits in a 2-digit numeral is 12. The units digit is twice the tens
digit. Find the numeral.