Algebra 2 Summer Math Packet - The Bear Creek School€¦ ·  · 2017-05-30Algebra 2 Summer Math Packet. This is the summer review packet for students entering Algebra 2. Review

Algebra 2 Summer Math PacketThis is the summer review packet for students entering Algebra 2.

Review packets are designed to help you prepare for your next math class.

Instructions:

• Start review packets 2 weeks prior to the start of the school year.• Spend approximately an hour per day working through the packet.• Expect to turn in the completed packet on the first day of class.• An answer key is provided, however, ensure your work is shown to receive full credit.• You may write your answer directly on this sheet or staple additional work to this packet.• You are expected to use your notes from Algebra 1 and Geometry. There are textbooks in

the school library if you need to come to look up concepts from your previous classes thatyou may have forgotten.

Remember: This packet is for your benefit and is intended to help you succeed as you move through more advanced math classes.

Name: _______________________________

Algebra 2 Summer Math Packet

• Please do not use a calculator! Name -----------

For this review, you will need your class notes taken in Algebra 1 to use as a reference. You will also need several formulas:

• the quadratic formula, for solving equations of the form ax2 +bx+ c = 0

-b ± .Jb2 - 4ac

x =

2a • the slope formula for two points in the plane: (x1,y1) and (x2,y2)

m = Y2 -y1X2 -XI

• the standard form for the equation of a line: Ax+ By= C, where A,B, & C areintegers and A > 0

• the slope-intercept form of a line: y = mx + b• the fact that parallel lines have the same slopes and perpendicular lines have

slopes that are opposite reciprocals (m1 *m2 = -1) Note: * is used formultiplication.

• The properties: commutative, associative, distributive, etc.

• The distance formula: d = �( x2 - x1 )2

+ (y2 - Yi )2

Show as much work as possible for each problem. The answers are at the back of

the packet, so you must show work to earn the credit, but please check your answers as you work.

1) Insert=,<,> to make a true7 3

statement - ? - -16 10

2) Give the slope of the line thatcontains (1, 4) and (4, 4).

3) Evaluate (5s + 5t)2 for s = -4 andt = 2.

6 5 4) Find the solution: -- = --

w - 3 w+3

5) Multiply: (x + 6)(x - 7)

6) Solve and graph on the numberline: 3(x + 2) > 5x + 18

Algebra 2 Summer Math Packet 7) Find the value of 2x2 + x + 3 when

x = 3.

8) Arrange in order of decreasingmagnitude and write using >

- -

6. 782, 6.782, 6.782

9) Which property does the followingstatement illustrate?(a+ b)c = (b + a)c

10) Write the standard form of theequation of the line passing throughthe point (2, 5) and perpendicular tothe line 4x - y = 2.

8 ll)Graph: y=-x-4

7

-10 .......... ._.__..__.__,.__._.....,_.,__,,_..,__ -10 10

2 12)True or False. The set of natural

numbers is. {l, 2, 3, 4, ... }

13)True or False. A rational number

can be expressed as the quotient ab

where b * 0

14)Graph: 2x + y = 4

y

-10 ......_......,__.......__......,_.......,_,.............,_..__._ -10 10

15)The number: -5, belongs to whichof the following sets?(circle all that apply)

natural numbers, whole numbers,integers, rational numbers,irrational numbers, real numbers

16)Does the number -12-satisfy theequation 2 = 14 - x? Show yourwork.

17)If y = 2x2 + 5x + 4, find y whena) X = -3

b) x = 0

X

Algebra 2 Summer Math Packet 4

18)Ify= -x+4, find ywhen7

a) X = - 35

b) X = 7

19) Multiply: (5x + 2y)2

20)Multiply: (4x + 7)(2x + 1)

2l)Multiply: (x - l)(x + 9)

22) Graph y = 3x - 9

-10 I...J..-aL..J...J....L..J.-1....L..L..l.....t.....L....L...!....1.-J....!.-J-J...J

-10 10

23) Solve for a: Sa= 6{4a- [4a + (2a - 5)]}

24)Evaluate the formula:X

W = - for X = 3, y = 5, Z = 3 yz

25)Simplify:(3p3 -2) - (3p + 1) + (4p3 + 5p)

3

26) Find the slope of the line passingthrough the points (-2, 7) and (-4, 2).

27)Solve for x: 2x + 9 = 27

28)A line has a slope m = 2. Determinewhether the line through (5,4) and(3, 5) is parallel or perpendicular tothe first line.

29)Solve and graph on the numberline: 7(x + 5) > 9x + 37

Algebra 2 Summer Math Packet

30)Graph: x-y = 1

,.Y5

-5� 5

31)Simplify: -2(9- 4) - 3( -6-6)

1 32)Graph: y = -x-1

4

5

-5

� y

�5 5

33)Solve for x: 3(x + 2) = -7

X

34)Is ! a solution of the equation: 7

7x - 3 = 5? Show your work.

35) Simplify: -2.9 - (-6.8) + 6.6

X

36) Classify J4 as rational or

irrational.

37)Multiply: -6.2 * 4.7

4

38)The number .Ju belongs to which

of the following sets? (circle thecorrect sets of numbers)Natural numbers, whole numbers,integers, rational numbers,

irrational numbers, real numbers

39)Multiply: (x + 7)(x - 7)

40)Determine whether the graphs ofy = -3x + 5 and 2x - 6y = 9 areparallel or perpendicular lines .

41)Solve for y: 3.5 = 0.7y

42) The line through A (-4, 5) andB (2, y) is perpendicular to a line

with slope 1. Find y.

Algebra 2 Summer Math Packet

43)Graph: 3x- 8y = -24

44)Is 2 a solution of the equation3

3x + 3 = - 4? Show your work.

45)Simplify: 648 + (6 * 9 + 3)

46)Graph: 3x + y = 3

,lY

5

-5·-5

47)Graph: lxl � 5

X

5

X

7 448)Multiply: -*-

8 3

49) Multiply: (2x + 3)2

5

50) What property is illustrated by thefact that 73 + 0 = 73?

51)Does the number 4 satisfy theequation: 11 = 15 - x? Show yourwork.

52)Evaluate 2y2(x + y) when x = 5, andy= 2.

53)Divide:4

+ (-2.)5 15

54)Simplify: 618-101

55) Write the slope-intercept form ofthe equation of the line passingthrough the point (5,0) and parallelto the line y = -4x - 2.

Algebra 2 Summer Math Packet

2 56) Graph: y = --x- 33 ,Y

5

X

-5

-5 5

57)Simplify: (6+(-9))(24+(-72))-3- 9 3-6

58) Find the pair of parallel lines:a. -y+ 3x = 8 b. 3x + y = 8 c. -y = 3x + 8

59) Multiply: (5x - 2)(3x - 7)

60) Simplify: (10+ 3 * 6 + 3-6) + 5

61) Which property is illustrated bythe following statement? (2*7)= (7 *2)

62) Give the slope of the line thatcontains (8, 9) and (8, 8).

6

63) What property is illustrated by thefact that (36 + 19) + 28 = 36 + (19 + 28)

64) Simplify: (5w4 - 1) - (6w3 + 6) + (6w4 - 4w3)

65) Factor: w2 - 8w + 16

66) Factor: 3x3 - 6x2 - 9x

67) Factor: 16r2 + 40r + 25 (Hint: thisis a perfect square!)

68) Simplify: -3.Jsi

69) Solve using the quadratic formula:x2 + 6x + 4 = 0

70) Multiply: (7p2 - 3p + 4)(8p - 6)

Algebra 2 Summer Math Packet

71) Simplify: S(x-S)5(x-2)6

4 20(x- 5)9 (x-2)

72) Solve by factoring:x2 - 13x + 12 = 0

73)Factor by grouping:3x2 + 12x + x + 4

74)Solve using the quadratic formula:x2 = 5x- 2

7 5) Solve the system by substitution:{ 3x+2y=-1 y= 2x-4

4d+de76) Factor and simplify: 9d

77) Solve the system by substitution:{y = 4x-5 y=5x

78) Simplify: 7-Ju'i

{4x+ 3y=-1479) Solve the system: 8x-2y=12

80) Simplify: 2J6 + 7 J6 - 3J6

81) Factor: x2 + 5x + 6

82) Factor: x2- 64

83) Simplify: 6Ji + sJi - sJi

8(x-1)7 (x-7)8 84) Simplify: 40(x- 1)9(x-7)3

85) Is the ordered pair (-3, -3) a solution of the system of equations:{-3x+4y=-3 Show your work.4x-5y= 3

Algebra 2 Summer Math Packet

86) Factor and simplify:-9x

x-x2

87) Factor: 5x3 - 5x2 - 30x

88) Solve: 6x + 4 = 22

89)Determine whether the ordered pair(1, 5) is a solution of the system of

{y=-5x

equations: . 3x+y= 2

3 90)Solve: -x +I= 0

5

91)Solve by factoring: x2 - 7x + 10 = 0

92)Find the distance between thepoints (-2, 3) and (4, 10)

93)Solve: 4 + 8x = -20

94)Multiply: 3x(x2 - 2x -4)

95)Multiply: 4(x2 + 2x + 3)

96)Solve: 3(x + 2) = 4

97) Solve the system by substitution:

{x-4y= 2

X =-I+ y

{3x+2y=-5

98) Solve the system:6x+4y= 11

99)Solve: x + 4 2: 6

100) 7 -x < 5

Answer Key: Algebra 2 Summer Math Packet

1. 716

> − 310

2. 𝑚𝑚 = 0

3. 100

4. 𝑤𝑤 = −33

5. 𝑥𝑥2 − 𝑥𝑥 − 42

6. 𝑥𝑥 < −6

7. 𝑥𝑥 = 24 8. 6.782���� > 6.682� > 6.782

9. Commutative property of addition

10. 𝑥𝑥 + 4𝑦𝑦 = 22

11.

12. True

13. True

14.

15. Integers, rational numbers, real numbers 16. No, 2 ≠ 26

17. a) 𝑦𝑦 = 7 b) 𝑦𝑦 = 4

18. a) 𝑦𝑦 = −16 b) 𝑦𝑦 = 8

19. 25𝑥𝑥2 + 20𝑥𝑥𝑦𝑦 + 4𝑦𝑦2

20. 8𝑥𝑥2 + 18𝑥𝑥 + 7

21. 𝑥𝑥2 + 8𝑥𝑥 − 9

22.

23. 𝑎𝑎 = 32

24. 𝑤𝑤 = 1

5

25. 7𝑝𝑝3 + 2𝑝𝑝 − 3

26. 𝑚𝑚 = 5

2

27. 𝑥𝑥 = 9

28. Perpendicular

29. 𝑥𝑥 < −1

Answer Key: Algebra 2 Summer Math Packet

30.

31. 26 32.

33. 𝑥𝑥 = −133

34. Yes, 5 = 5

35. 10.5

36. Rational

37. −29.14

38. Irrational numbers, real numbers

39. 𝑥𝑥2 − 49

40. Perpendicular

41. 𝑦𝑦 = 5

42. 𝑦𝑦 = −1

43.

44. No, 10 ≠ −4 45. 36

46.

47.

48. 76

49. 4𝑥𝑥2 + 12𝑥𝑥 + 9

50. Identity property of addition or addition

property of zero

51. Yes, 11 = 11

52. 56

53. −127

54. 12

55. 𝑦𝑦 = −4𝑥𝑥 + 20

Answer Key: Algebra 2 Summer Math Packet

56.

57. 4 58. 𝑏𝑏 & 𝑐𝑐

59. 15𝑥𝑥2 − 41𝑥𝑥 + 14

60. 2

61. Commutative property of multiplication

62. Undefined (or no slope)

63. Associative property of addition

64. 11𝑤𝑤4 − 10𝑤𝑤3 − 7

65. (𝑤𝑤 − 4)2

66. 3𝑥𝑥(𝑥𝑥 − 3)(𝑥𝑥 + 1)

67. (4𝑟𝑟 + 5)2

68. −27

69. 𝑥𝑥 = −3 ± √5

70. 56𝑝𝑝3 − 66𝑝𝑝2 + 50𝑝𝑝 − 24

71. (𝑥𝑥−2)2

4(𝑥𝑥−5)4

72. 𝑥𝑥 = 12, 𝑥𝑥 = 1

73. (𝑥𝑥 + 4)(3𝑥𝑥 + 1)

74. 𝑥𝑥 = 5±√172

75. 𝑥𝑥 = 1,𝑦𝑦 = −2

76. 4+𝑒𝑒9

77. 𝑥𝑥 = −5,𝑦𝑦 = −25

78. 28√7

79. 𝑥𝑥 = 14

,𝑦𝑦 = −5

80. 6√6

81. (𝑥𝑥 + 3)(𝑥𝑥 + 2)

82. (𝑥𝑥 + 8)(𝑥𝑥 − 8)

83. 6√2

84. (𝑥𝑥−7)5

5(𝑥𝑥−1)2

85. Yes

86. − 9

1−𝑥𝑥= 9

𝑥𝑥−1

87. 5𝑥𝑥(𝑥𝑥 − 3)(𝑥𝑥 + 2)

88. 𝑥𝑥 = 3

89. No

90. 𝑥𝑥 = −5

3

91. 𝑥𝑥 = 5, 𝑥𝑥 = 2

92. √85

93. 𝑥𝑥 = −3

94. 3𝑥𝑥3 − 6𝑥𝑥2 − 12𝑥𝑥

95. 4𝑥𝑥2 + 8𝑥𝑥 + 12

96. 𝑥𝑥 = −2

3

97. 𝑥𝑥 = −2,𝑦𝑦 = −1

98. No solution

99. 𝑥𝑥 ≥ 2 100. 𝑥𝑥 > 2