Algebra One Summer Review Packet

Name: ___________________________________

Algebra One Summer Review Packet (2019)

Stevenson High School

This packet must be completed the summer before entering Algebra 1. These skills are necessary for a

successful year in this course. Please review the notes for each section and complete all subsequent practice

problems. Be sure to show all of your work. This packet must be completed in its entirety and be ready to be

submitted on the first day of school. A short quiz on these topics will be given on the first Friday of school. If

you’re stuck on something or need more practice, look it up online (Kahn Academy is a great practice

resource with videos). https://www.kutasoftware.com/free.html is also a great resource for free worksheets

and answer keys. Have a great summer—we’ll see you in the fall! ☺

Idea #1: Order of Operations

1. 7 + 54 ÷ 3(2)

2. 17 − 25 ÷ 4 + 6 3. 24 − 42 ∙ 3 + 15

4. (7−22)+17

−14+2∙5

5. 6∙4

4+32−1 6.

52−34

(23−5)∙(62÷9)

7. −|−9 − 10| + 122 ÷ 6 ∙ 3 8. 202 ÷ {3(5 − 9)2 + 2}

9. 84

12+ (5 − 72) − 72 ÷ 6 ∙ 2

Algebra One Summer Review Packet

Idea #2: Translating Words into Mathematical Symbols

Translate the following into phrases, equations, or inequalities. Let x represent the number.

10. The product of a number and 3 11. The difference between a number and 10

12. The quotient of a number and -5 13. Four subtracted from a number

14. The sum of twice a number and 7 15. The product of a number and 10, increased by 1

16. Four less than a number squared 17. Three times the difference of a number and 7 is 18

18. Four times a number divided by 8 is 3

19. Five times the sum of a number and 6 is 48

20. The prodcut of a number and 3 is the same as the sum of that number and six

21. Fifteen decreased by the quotient of a number and 3 is 20

22. Four less than the product of a number and 7 is eight more than that number

23. A number is at most 45

24. A number is at least 20

25. A number is no more than 26

26. A number is no less than 10

27. A number divided by 10 is less than 4

Algebra One Summer Review Packet

Idea #3: Substitution and Evaluating Expressions

Evaluate each expression using the variable replacements.

28. 5𝑥2 − 𝑦, 𝑤ℎ𝑒𝑛 𝑥 = 4 𝑎𝑛𝑑 𝑦 = 24 29. 3𝑥𝑦−4

7𝑥, 𝑤ℎ𝑒𝑛 𝑥 = 2 𝑎𝑛𝑑 𝑦 = 3

30. 𝑎2𝑏 − 𝑏2, 𝑤ℎ𝑒𝑛 𝑎 = 3 𝑎𝑛𝑑 𝑏 = −4 31. −𝑦2 − 3𝑥𝑦, 𝑤ℎ𝑒𝑛 𝑥 = −4 𝑎𝑛𝑑 𝑦 = 2

32. 𝑎2+𝑏2

𝑎−𝑏, 𝑤ℎ𝑒𝑛 𝑎 = 3 𝑎𝑛𝑑 𝑏 = 4 33. 𝑥2 − 2(𝑥 − 𝑦) − 𝑧3, 𝑤ℎ𝑒𝑛 𝑥 = 2, 𝑦 = −2,

𝑎𝑛𝑑 𝑧 = −3

• Substitute the variables with their given

values.

• Each time you substitute a variable with a

number, use parentheses around the number.

• Use Order of Operations to finish the problem.

Algebra One Summer Review Packet

Idea #4: The Real Number System

Name all the sets to which each number belongs.

34. 9 35. -4.2 36. √16

37. √5 38. 5

3 39.

8

2

40. −8

2 41.

√10

√10 42. 0

Algebra One Summer Review Packet

Idea #5: Distributive Property

Use the distributive property to rewrite the expression without parentheses.

43. 7(𝑥 + 4)

44. 2(𝑏 − 3) 45. −4(𝑦 + 3)

46. −5(𝑥 − 2)

47. −(𝑦 − 9) 48. 8(4 − 𝑏)

49. −4(−𝑤 − 10)

50. 5(2𝑚 − 3) 51. −3(2𝑥 − 4)

52. 𝑥(𝑦 + 4)

53. 𝑑(𝑐 − 4) 54. 2(𝑥 − 𝑦 + 8)

55. (3𝑥 − 3)6 56. (2 + 𝑡)(−2) 57. −(6𝑦 − 5)

Algebra One Summer Review Packet

Idea #6: Combining Like Terms

Simplify each expression below by combining like terms and using the distributive property when

needed.

58. 5𝑥 − 9𝑥 + 2 59. 3𝑞2 + 𝑞 − 𝑞2 60. 𝑐2 + 4𝑑2 − 7𝑑2

61. 5𝑥2 + 6𝑥 − 12𝑥2 − 9𝑥 + 2 62. 7𝑝 − 1 − 9𝑝 + 5

63. 5𝑥 + 7𝑦 − 𝑥 + 2𝑦 + 3𝑥

64. 26𝑎 + 2𝑏 − 4𝑎 + 10𝑏 65. −15𝑛5 + 4𝑛5

66. 8𝑘2 − 𝑘 − 5𝑘 + 7 − 2𝑘2

67. 𝑥2 + 2𝑥𝑦 − 7𝑥𝑦 + 4𝑦2

68. 5ℎ − 6 − 8 + 7ℎ 69. 4𝑥2 − 7 + 2𝑥 − 3𝑥2 + 8𝑥 − 6

70. 8(2𝑥 − 3) − 6𝑥

71. 9(2𝑘 − 4) − 2(7𝑘 − 2) 72. 6 + 8(4𝑤 − 7) − (2𝑤 + 1)

Algebra One Summer Review Packet

Idea #7: Fractions

Write each fraction in simplest form.

73. 8

20 74. −

6

18 75. −

12

42 76.

16

56

Write each improper fraction as a mixed number.

77. 19

6 78. −

26

3 79.

21

4 80. −

35

8

Write each mixed number as an improper fraction.

81. 31

5 82. 7

2

3 83. −2

11

13 84. −4

3

7

Algebra One Summer Review Packet

Add or subtract. Write all answers in simplest form.

85. 1

6+

4

6 86.

5

8−

3

8 87.

4

9−

1

9

88. 1

2+

1

8 89.

7

10+

1

3 90.

15

24−

7

12

91. 2

9− (−

5

18) 92.

5

8+ (−

1

20)

93. −5

6+ 1

2

9

94. 51

8− 2

3

4 95. −4

3

8− 2

5

6 96. 9

2

5+ 3

1

3

Algebra One Summer Review Packet

Multiply or divide. Write the answer as a fraction or mixed number in simplest form.

97. 1

2∙

1

2 98.

2

3∙

4

5

99. 3

7∙

7

9

100. 3

4∙

8

9 101. 1

2

3×

3

5 102. 3 × 2

5

9

103. 51

4× 1

1

7 104.

7

8÷

3

4 105.

5

12÷

1

2

106. 11

16÷ 1

1

2 107. 4

1

2÷

3

4 108. 7

1

5÷ 2

1

4

Algebra One Summer Review Packet

Idea #8: Basic Equation Solving

109. 𝑦 + 13 = 0 110. 𝑎 − 12 = 19 111. 𝑥 + 6 = −12

112. 𝑏 − 9 = 19 113. 8𝑥 = 24 114. −9𝑥 = 36

115. 𝑏

4= 7 116. 5𝑛 − 4 = 26 117. 16 − 𝑥 = −14

118. 2𝑥 + 4 = 18 119. 6 − 5𝑥 = 21 120. 𝑑

4− 11 = −16

Algebra One Summer Review Packet

Idea #9: Graphing a Line by Making a Table of Values

EXAMPLE: Graph 𝑦 = −4𝑥 + 8.

x 𝒚 = −𝟒𝒙 + 𝟖 y (𝒙, 𝒚)

4 𝑦 = −4(4) + 8 -8 (4, -8)

2 𝑦 = −4(2) + 8 0 (2, 0)

1 𝑦 = −4(1) + 8 4 (1, 4)

121. 𝑦 = 3𝑥 − 7

x 𝒚 = 𝟑𝒙 − 𝟕 y (𝒙, 𝒚)

4

1

0

122. 𝑦 = 2𝑥 − 1

x 𝒚 = 𝟐𝒙 − 𝟏 y (𝒙, 𝒚)

5

2

0

123. 𝑦 = 7 − 2𝑥

x 𝒚 = 𝟕 − 𝟐𝒙 y (𝒙, 𝒚)

7

5

3

STEPS:

1. Plug x-values into the original

equation to solve for y.

2. The x you plugged in and the y

value you solve for in step one

become your ordered pair.

3. Plot ordered pairs and draw in line

connecting points.

Algebra One Summer Review Packet

Idea #10: Find Slope on a Graph and Find Slope Using the Slope Formula

124.

125. 126. 127.

128. 129. 130.

131.

***Show work—show how you used the slope formula! 132. (19, −16), (−7, −15)

133. (1, −19), (−2, −7) 134. (−4,7), (−6. −4)

135. (17, −13), (17,8)

136. (19,3), (20,3) 137. (19, −2), (−11,10)

Algebra One Summer Review Packet