Name____________________________

Show all work on separate paper. For multi-step problems, work vertically. Write your name in pen at the top of each page. Use graph paper for all graphs. If you have any questions during the summer, email the teacher at juhernandez@nlmusd.org. Allow at least 48 hours for a response. The completed problem set is due at the beginning of the first day of class.

Your first test will be on concepts and problems from the summer project.

Simplify. Assume no denominator equals zero.

1.

6 3 13 4 5

5 2 6 13 4

p 2 7 p 18

23. 2 p 13 p 22

2. (–4k6q2p10) ÷ (2kq4q7)

3.

(2w 2 k 4 ) 3

( wk 5 ) 2 ( w 4 k 2 )

4. (3–1m2n–3) –1(6m2n) –2

5. (7x2 – 3)(2x – 4)

a

4

2n 3 9 n 2 7 n n 4 3n 3 4n 2

6b 12 (2 b) 2

25.

b 2 7b 2 28

24.

b 3a 2b

3 4

3

26.

6.

3

7. (5a – 3)

8. (6a3 – 7a2 – 7a + 6) ÷ (3a – 2)

9. (2p4–7p3–13p2+29–12) ÷ (p2–5p+3)

10. (c3k – 2)2

Factor.

11.

12.

13.

14.

162pr5s2 + 36p3r6s – 90p2r3s r2 – 20r + 64 r2 + 16r – 45

10y2 + 11y + 3

k 2 121m 2

15.

169

100

16. 81x2 – 12x +

17.

18.

19.

20.

21.

22.

4

3

y 4 10 y 2 9 y 2 2 y 3

2 y2 y 6 y 3y 2

2 1

a b

1 3

27.

a b b

28. b 4 b 1 b4 Solve.

29. 8(5c – 4)= –2(8 + 6c)

30. 4+w=

6(3 2w)

5

31. (a + 1)(2a–1) – (a – 1)(2a + 1) = –18

4

9

2

6a + 3a – 45a

2ab4 – 2a

2x3 – 6x2y + 9x – 27y

125 a 3 -27

216 z 3 125a 3

25 – x12a

Simplify.

32.

4 x10 y 2

289

33.

180

34. 72c 5 d 5

35.

48 16 x 2

36.

a 4 x b8 y

37.

5

3 y 27a 3b 6 5 9b 9 a 2

2

58. 16

175

39.

2

59. 64 3

1 2

5 3

343 3

60.

8

50 y 3

41.

61. 16 4

2

5

2 y8

62. 32 5

9

42. 2 108 27 3 125

5

5

44. 6 7 5 6 7 5

3

3

45. 11 2 6 11 2 6

5 10

5

9

2

3 2

364a 3b 6 3

65.

125 y 9

2

4

1

66. c 3 c 3 2c 3

5 6

46.

47.

3

25 2

63.

9

4 2 e 64. y 3

e

3

1

43.

80 2 24

125

2

5

5

2

10

40.

2 y 56. x y w

57. Simplify.

48

38.

1 y Solve.

2 11

48.

3c 7

50.

4

x y

5m

k

7

53. 16

54. m

12

2

2 z

5

5

2c 3 7

69. 25 7 m 5 4

5m

51. c d

Rewrite without any exponents.

52. 18

67.

68.

Rewrite using exponents.

49.

1

2

1

3

7

2

n

55. m k

76. 55 23 (7 r ) 2

77. 2 p 2 9 p 0

78. 2k 2 6 5k 5

70. 3 t 6 7

71. c 5 4c 1

72. m 3 m 4

73. 0 25 p 2

18

49

75. 8 2( x 1) 2

74. 0 t 2

76. a 4 2a 2 4 0

77. r 4 7r 2 12 0

78. w3 2w2 49w 98 0

79.

80.

81.

82.

83.

Find the slope between (4, 6) and (–2, 8).

A line contains the points (a,b) and (a + b, c + b). What is the slope of the line?

Find the x- and y-intercepts of the line 6y – 3x + 5 = 0.

What is the slope of all lines parallel to 4y – 2x + 1 = 0?

What is the slope of all lines perpendicular to 4y + 9x = 0?

Write the equation of the line.

84. Slope = 3, contains (–4, 5)

85. Contains (4, 6) and (–2, 3)

86. Slope = 0, passes through (–4, –5)

87. Undefined slope, contains (–11, 4)

5

x3

2

89. Passes through (–4 , –8) and is parallel to y + 5x – 3 = 0

90. Write the equation of the line that passes through (–2 , 4 ) and ( 5 , 4 ). Graph the line.

91. Write the equation of the line that passes through (–2 , 0 ) and ( 0 , 4 ). Graph the line.

7

9

92. Write the equation of the line that passes through 3, and 3, . Graph the line.

2

2

93. Write an equation for a circle with r = 5, centered at the origin. Graph the circle.

94. Write an equation for an ellipse passing through ( 0 , 2 ) and ( 4 , 0 )