2019-2020 Algebra Summer Assignment – Mrs. Fussner’s class ONLY

You must show all work to earn full credit. This assignment will be due Friday, August 23, 2019. It will be worth 50

points. All of these skills are necessary to be successful in Algebra Honors. Algebra is the study of mathematical symbols

and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. There will be a test on

these topics at the beginning of the year. Please follow criteria for credit shown below. You may write on the back of

your notebook paper. Do NOT write on this worksheet. - Mrs. Fussner

PART 1 - Fractions

Find the reciprocal of the number.

1. 7 2. 14

1 3.

12

7 4. 1

8

5

Add or subtract without using a calculator. Write the answer as a fraction or mixed number in simplest form.

5. 6

4

6

1

6. 8

3

8

5

7. 9

1

9

4

8. 12

3

12

5

9. 8

1

2

1

10. 10

1

5

3

11. 3

1

10

7

12. 12

7

24

15

13. 4

32

8

15

14. 2

1

7

31

15. 6

52

8

34

16. 4

3

7

3

17. 10

7

2

17

18. 3

12

9

55

19. 16

31

8

54

20. 3

13

5

29

Multiply or divide without using a calculator. Write the answer as a fraction or mixed number in simplest

form.

21. 1

2×

1

2

22. 2

3×

4

5

23. 5

8×

4

15

24. 3

7×

7

9

25. 7

8÷

3

4

26. 5

12÷

1

2

27. 4

5÷

2

3

28. 11

16÷ 1

1

2

29. 41

2÷

3

4

30. 21

4÷ 1

1

3

31. 3

4×

8

9

32. 12

3×

3

5

Compare the two numbers. Write the answer using , or =.

33. -16.82 and -14.09

34. 0.40506 and 0.00456

35. 7

13 𝑎𝑛𝑑

3

13

36. 171

4 𝑎𝑛𝑑 17

2

8

37. 7

10𝑎𝑛𝑑

3

4

38. −5

9 𝑎𝑛𝑑 −

15

27

Write the numbers in order from least to greatest.

39. −45,617, −45,242, −40,099, −40,071

40. −23.12, -23.5, -24, -23.08, -24.01

41. 4

5,

8

3,

6

5,

3

1

42. 7

3,

10

3,

4

3,

2

3,

5

3

43. 4

115,

6

514,

3

115,

9

714

44. −7

8, −

5

4, −1

1

3, −

5

12

45. You need a piece of trim that is 65

8 yards

long for a craft project. You have a piece of

trim that is 63

4 yards long. Is the trim you

have long enough?

PART 2 – Integers/Order of Operations/Evaluate Expressions

Solve without using a calculator.

46. –2 + 3

47. –5 + 4

48. –7 – (–3)

49. –14 – 6

50. 6 + (–8)

51. 12 + (–7)

52. –8 + (–1)

53. –3(–4)

54. 24

−6

55. 5(–18)

56. 17(–4)

57. −21

−7

58. 81

−9

59. 45 – (–27)

60. −8

−4

* P. E. M./D. (whichever comes first from left to right), A./S. (whichever comes first from left to right) Evaluate the expression, you may use a calculator but MUST show every step of work.

61. 180 − (30 + 45)

62. (8 − 2) ∙ 180

63. 16 + 4 ∙ 2 − 3

64. 82 + (−6)2

65. −7 + 23 − 9

66. 9(7 − 2)2

67. 1

2(100 − 74)

68. 76

375

69. 3

4∙ 24 + 42 − 1

Evaluate the expression when x = 3. You may use a calculator but MUST show every step of work.

70. −3𝑥2

71. (−3𝑥)2

72. 𝑥(𝑥 − 7)

73. 𝑥+2

𝑥−2

74. 𝑥2 − 7𝑥 + 6

75. (𝑥−2)∙180

𝑥

76. 𝑥2 + 25

77. −2𝑥 − 18

78. (𝑥 + 2)(𝑥 −2)

PART 3 – Writing Expression/Simplifying Expressions

Simplify:

79. 2(𝑎 + 4)

80. (2𝑘 + 1)7

81. – (−3𝑥 + 2)

82. (7 − 2𝑧)𝑧

83. 𝑦(𝑦 − 9)

84. (𝑗 − 1)(−3)

85. 4𝑏(𝑏 + 3)

86. −2(𝑛 − 6)

87. – 𝑚 + 4 + 7𝑚

88. 6𝑥 −9x + x

89. 𝑥2 − 2𝑥 + 7𝑥 − 14

90. 𝑎2 + 3𝑎 + 3𝑎 + 9

91. 3 − (2𝑥 − 7)

92. 8 + 3(𝑦 − 4)

93. 6ℎ − 3ℎ(ℎ + 1)

94. 2(𝑥 + 4𝑥) − 7

Write an algebraic expression, equation or inequality (Do Not Solve) 95. Three more than twice a number is ten

96. Five decreased by a number

97. A number squared minus six is less than fourteen

98. Forty less than a number

99. Two times the sum of a number and twelve

100. Four times the difference of a number and eight

101. The product of a nine and a number is thirty-six

102. Ten is 50% of a number

103. Seven less than twice a number is twenty

PART 4 – Solving Equations and Inequalities

Solve the equation. You may use a calculator but MUST show every step of work.

104. 2𝑥 + 3 = 11

105. 4𝑥 − 2 = 10

106. 7 + 2𝑥 = 17

107. 3𝑦 − 4 = 20

108. 𝑥

7+ 2 = 1

109. 21 − 2𝑧 = −2𝑧 + 1

110. 10 − 𝑥 = −16

111. 6 −3𝑎

2= −6

112. 3

8𝑥 − 6 = 18

113. 3 = 5 +1

4𝑥

114. 3𝑟 − (2𝑟 − 21) = 21 + 𝑟

115. 5(𝑧 + 3) = 30

116. 44 + 4𝑔 = 5𝑔 − 8 − 𝑔

117. 4(𝑡 − 7) + 6 = 30

118. 85 =1

2(226 − 𝑥)

119. 5x + 9 = 3x + 1

120. 14 + 7n = 14n + 28

121. 22(g 1) = 2g + 8

122. d + 12 3d = 5d 6

123. 4(m 2) = 2(3m + 3)

124. (4y 8) = 2(y + 4)

125. 5a 2(4a + 5) = 7a

126. 11w + 2(3w 1) = 15w

127. 4(3 5p) = 5(3p +3)

Solve the inequality.

128. 11x + 13 ≥ -9

129. 6x – 10 < 6 – 2x

130. 3(x – 2) – 2x > 16

131. 6x + 10 > 8 – (x + 14)

132. -5x – 2(x + 3) ≤ 8

133. 3x + 8 ≤ 2(x – 4) – 2(1 – x)

134. 3(2x – 4) -2(x + 1) > 10

135. −3

2𝑥 + 3 ≤ 12

136. -8x – 3 < 18 – x

Write an inequality for each graph.

137.

138.

139.

140.

PART 5 – The Coordinate Plane

Identify the slope for each graph below.

150. 152.

151. 153.

Tell what point is located at each ordered pair.

141. (3, –2)

142. (–7, –8)

143. (2, 3)

144. (–4, 4)

145. (–5, 5)

146. (–5, 0)

Write the ordered pair for each given point & name the

quadrant it is in.

147. E

148. M

149. C

154. 155.

Identify the slope for each table below.

156. 157. 158. 159.

Identify the slope from the points below.

160. (1, -3) and (4, 2) 161. (7, 2) and (-1, 2) 162. (0, 3) and (6, 6)

Identify the slope for each equation

163. y = 4x – 6 164. y= -4 165. y= 6 + ½ x

PART 6 – Measurement & Proportions

Convert to the given unit:

166. 5 ft. = _______in

167. 20 m = ________ cm

168. 450 cm = ________m

169. 48 in = ________ ft.

170. 14 ft2 = _________ in2

171. 288 in2 = _______ ft2

172. 50 m2 = ________cm2

173. 3000 cm2 = ________m2

174. 𝑥

7=

10

14

175. 15

𝑥=

3

4

176. 𝑥

7=

10

14

177. 𝑥+1

10=

2

4

178. 5

6=

𝑥−2

𝑥+3

179. 2

3=

15

𝑥

180. 𝑥

8=

5

12

X Y

1 -3

2 3

4 7

8 15

10 19

X Y

-2 7

-1 4

0 1

1 -2

2 -5

X Y

-2 3

-1 3

0 3

1 3

2 3

X Y

-3 11

1 9

3 8

7 6

9 5

Solve for x:

PART 7 – Geometry

Fill in each blank with the correct formula.

181. the area of a circle: A = _______________________

182. the area of a triangle: A = _______________________

183. the area of a parallelogram: A = _______________________

184. the circumference of a circle: C = _______________________

Find the area & perimeter (or circumference) of each figure.

185. 186. 187. 188.

189. 190. 191. 192. a square with a

side of 10 mm

193. a circle with a 194. a rectangle with 195. a circle with a radius of 12 ft. length = 14 ft and diameter of 22 yd. width = 17 ft

196. Suzanne is making a frame for an 8-inch by 10-inch photo. How much wood does she need for the frame?

197. The diameter of a quarter is 24 mm. What is the quarter’s circumference?

198. The floor of our classroom is 50 feet by 75 feet. What is the area of our floor?

Use the figure below to answer questions 199 and 200.

199. What is the perimeter of this compound figure?

200. What is the area of this compound figure?

8 ft

16 ft

4 ft

10 ft

6 ft 8 ft

4 in 14 m 13 m

10 m 9 cm

9 cm

5 yd

10 yd

9 yd

13 ft

14 ft 15 ft

5 ft

6 ft

100 cm