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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