TCSS Georgia
KEY
Milestones
Study Guide
for
Algebra I
1.
2.
3.
D.
C. x is the set of all non-negative integers.
4. 12√5
5. A. −𝟖𝟖√𝟔
6. C . 𝟖√𝟏𝟎
7. B .√25 + 1.75
8. D. √10 ● √8
9. 927 feet.
10. C = klw dollars
11. 3,960 feet per minute.
12. $14.60
13. Kilograms/meters 3
14. 480cm or 4.8m
15. D . 3,200 cm
16. B . 40 seconds
17. a. 1 b. 3n², n and 2
18. The 2 represents the two sets of length/width pairs.
19. C . –2n2 – n + 5
20. D . the area of a square with a side length of 8x
21. P = 16x + 20 units
22. 2x3 –x - 6
23. A = 8x² - 10x -3 square feet
24. C . 56x2 + 3x – 20
25. C . 50x + 11 units
26.B . 3x2 + 5x – 8
27. a = - 6
28. x. < 1
29. 17 weeks
30. No
31. r = 30
8
32. x = 𝑎
33. C . 2 hours
34. C . 10 miles
35. B. x > 1
36. B . Step 2
37. (3, 2)
38. (1, 1)
39. (3, 1)
40. No solution
41.
y = –x + 6
y = 2x – 3
x
y
x
y
-1
-5
-1
7
0
-3
0
6
1
-1
1
5
2
1
2
4
3
3
3
3
b. Yes, (3, 3)
d. Yes, at (3, 3)
42. Rebecca has 2 quarters and 3 nickels.
43. 200 minutes
44. No
45. Infinitely many
46. No solution.
47. D . (3, 1)
48. C . (2, 3)
49. x = 3
50. C . (5, 1)
51. A. 10
52. B . 6
53.
. B.
54. (0,8) (3,4) (6,0)
55.
56. The model is S(x) = 2x + 13, which will generate the amount Joe has saved after
x weeks.
57.B . f(n) = 7n – 4
58. f(n) = 2n + 15
59. f(7) = 13
60. g(x) = 3 – 5x
61. f(b) = -4b
62.
63. a. What is the reasonable domain of the function? Whole numbers
b. What is the cost of 2,000 items? $7,600
c. If costs must be kept below $10,000 this month, what is the greatest number of items
she can manufacture? X<3,846 items
64.
a. 𝑎1 = 1 𝑎3 = 9
b. The set of counting numbers (1,2,3,4,5……)
c. (1,3,9,27,81,243,….)
d. 3
65. Domain (1,2,3,4,5,…) range (3,7,11,15,19,…)
66. B. 𝑎𝑛 = 𝑎𝑛−1 + 2
67. B. 𝑎𝑛 = 𝑎𝑛−1 + 3
68. D . f(x) = 3x + 5
69. D . C = 3.14 × d
70. C . f(x) = 4x – 20
71. Some of its key features are
•
•
•
•
Domain: all real numbers
Range: all real numbers
x-intercept: 0
y-intercept: 0
•
•
•
Increasing: as x increases, f(x) increases
Decreasing: never
Positive: f(x) > 0 when x > 0
•
•
•
Negative: f(x) < 0 when x < 0
Rate of change: 1
End behavior: Decreases as x goes to -∞ and increases as x goes to ∞
72. Some of its key features are
•
•
•
•
•
•
•
Domain: all real numbers
Range: all real numbers
x-intercept:.0
y-intercept: 0
Increasing: Never
Decreasing: x (-∞, ∞)
Positive: f(x) is positive for x < 0
•
•
•
Negative: f(x) is negative for x > 0
Rate of change: - 1
End behavior: increases as x goes to -∞and decreases as x goes to ∞
73.
a.
b.
c.
28,000
16, that means the truck is fully paid off after 16 months of payments
decrease
74. A 0 ≤ x ≤ 6
75. It is a linear function, the domain is all real numbers, the y-intercept is -3, the x-intercept is 6,
the average rate of change is ½ ,
76. The graph of m(x) intersects both the x and y-axes at 0. The domain of all real numbers and range
of all real numbers. There is a constant rate of change and is decreasing.
77. C.
78. B . 10
79. a. 1, b. 3n², n and 2
80. (4a + 9)(4a – 9)
81. 2(3x – 1)(2x + 3)
82. D . (11x + 8y)(11x – 8y)
83. C . 3x2 + 2x + 18
84. C . 3(2xy – 7)(xy + 2)
85. 2 (x + 3) 2 – 17
86. 18 feet
87. -9 and 3
88. -1/2 and 3
3
89. A. − 2 and x = 1
90. D . (–5, –34)
91. B . (x + 4)2 – 46
92. C . 10 items and 60 items
93. r =0 and r = -h
94.
95.
a.
n(n + 1)= 132
b.
n = -12 and n = 11
96.
a.
𝑉
r =√𝜋ℎ
b. 5 inches
97.
98.
99.
100.
101.
102.
103.
A . 2 feet
C.
x=5
x = + 10
x = 1 and x = ¾
C . x = –2, x = 3
104.
105.
106.
107.
D.
C . x = –2, x = 7
C . 2.00 seconds
a.
b.
4x² + 20x +24=63.
7inches
a. $3,960
b. -40x² +400x + 3000
108.
c. $200
109. a. n(n + 1)
110. C . 2n2
b. 110
111.
112.
D . 5 seconds
A . P(x) = 2x2 – 20x – 5
113.
a. The graph of ½ f(x) is a vertical shrink of f(x) by a factor of ½
b. f(x) – 5 is a shift or vertical translation of the graph of f(x) down 5 units.
c. f (x - 2) + 1 is a shift or vertical translation of the graph of f(x)right 2 units and up 1 unit
114.
115.
116.
117.
118.
Odd
the graph of f(1/2 x) is a horizontal stretch of f(x) by a factor of 2
B . The graph of f(x) is shifted left 6 units.
C . f(x) = 6x2 – 2
D . The graph of g(x) is a vertical stretch of f(x) by a factor of 3 and a reflection across the xaxis.
119. a. 66 seconds b.0.97 and 2.97 seconds c. 66 feet d. 4 seconds e. 0< t < 4
120. a. The average rate of change represents the rate at which the company earns a profit.
b. $12,000 per month
c.
$29,000
121. A . 0 < t < 5
122. B
123. B . As x increases, f ( x) decreases. As x decreases, f ( x) decreases.
124.
125.
126. A . f(x) = x2 – 3x – 10
127. D . The ball represented by f(t) is in the air for about 4 seconds, and the ball
represented by g(t) is in the air for about 3 seconds.
128. $1,124.86
129. 1,600,000
130. C . 1,478
131. .
Part A: f(n) = 100(0.90)𝑛−1
Part B: The temperature starts at f(1) = 100. The variable r stands for the ratio between subsequent
temperatures, which is 0.90. f(n) = (0.90) f(n-1) for all n>1
132. D . f(n) = 6(3n – 1)
133. D . f(x) = 5x
134. f(x) = 3 x + 5
135.
a.
b.
Compare f(x) to 3f(x). The curve increases at a higher growth rate and has a different y-intercept.
Compare f(x) to f(3x). the curve increases at a higher rate than 3f(x), but has the same y-intercept
as f(x)
c.
d. 3f(x)
136. B . f(x) = 3(x + 5)
137. A. f(x) = 3x – 5
138. 4,374
139. g(x) = 2(x) + 1
140. f(b) = 4(b)
141.
142. a. 2 b. 2 c. 𝑎𝑛 = 𝑎1 (3)(𝑛−1)
d. 118,098
143.
a. 𝑎1=1 𝑎3=9
b. 1,2,3,4,5,……
c. 1,3,9,27,81,243,….
d. 3
144. Domain 1,2,3,4,5 range 3,7,63,255,1023.
145. A. 𝒂𝒏 = (𝟒)(𝒏−𝟏)
146. C . 1,000(0.80)x
147. C . C = 6d
148. D . f(x) = 100(12)x
149. a. no x or“t”intercept, y or A(t) intercept is 200 b. t> 0 c time cannot be negative d. A(t) >
200
150. Both have the same domain, range and y-intercept. One is exponential growth and the other decay
151. D . any whole number greater than or equal to 5
152. A . bounce 1
152. Quantity B will be 293.57 greater than Quantity A after 4 years.
153. B . y = 2(x – 1) + 2
154.
a. Make a scatter plot of the swan populations.
b. Exponential
c. 64
155. Given the sequence 7, 10, 13, 16, . . .
a.
b.
c.
linear
f(x) = 3x + 4
64
156.
157.
158. B.
159.
D.
160. A
.
x
0
1
2
3
4
y
0
3
9
27
81
161. D . The graph of f(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at
a point between 4 and 5, and then the graph of g(x) exceeds the graph of f(x).
162.
C . The graphs of exponential functions eventually exceed the graphs of linear and quadratic
functions.
163. D . The values of g(x) begin to exceed the values of f(x) within the interval [4, 5].
164.
165. B(p) = 24(3𝑝 )
𝟐
166. D.− 𝟑
167. 75 is the initial number of cells. The 2indicates that the number of cells doubles every minute.
168. g(x) + 6
169.
–
170. D . h(x) + 1 = x2 + 1 and p(x) – 1 = 2x –
171. B. –f(x)
1
172. a. whole numbers b. $7,600
173. Linear
𝟖
174. D . f(x) = 𝟓 (𝟓𝒙 )
175. C . f(x) = 4x – 20
3
176. B . f(x) = –x2 + 4
177.
178.
179.
180.
181.
a. whole numbers b. -40
a. 9 b. 111
D . any whole number such that 0 ≤P(t) ≤1,000
B . the time it took the rocket to return to the ground
a. Richard had the greater median earnings from tips. The difference in the median of the
earnings from tips is $10.
b. The difference in Josh’s interquartile range and Richards’s interquartile range is $1.
182.
183.
184. a. it appears to be skewed to the left with most of the intervals approaching 90 min
b. Last week;s distribution seems more skewed to the left than Last month’s. it is also more
asymmetric and Last month’s distribution appears to have the highest percentage of intervals
longer than 1 hour 30 minutes between eruptions. C. it shows that the geyser rarely erupts an
hour after its previous eruption and most visitors will have to wait more than 90 minutes to see
two eruptions.
185. C . The mean and median temperatures in Macon were higher than the mean and median
temperatures in Charlotte.
186. C . 10 to 16
187. B . The lower quartile is 44.
188. C . Class 3
189. B . Peter had one very low score in Week 2.
190. y = 0.38x + 0.99
191. A . bimodal
192. a. 75-80 minutes b. 1 minute 35 seconds
c. positive correlation
193. a. the fall b. 23% c. 10% d. That customers tend to purchase the larger drinks in the fall
and the smaller drinks in the spring and summer
194. A.
𝟑
195. D. 𝒚 = 𝟓 𝒙 + 𝟓
196. a. strong positive, 18-60 years c. $10,000-$70,000 d. no
197. a. yes, b. no, c. no, d. yes
198. The regression line for this table would be a good predictor of yearly income because the sum
of the error differences is zero.
199. C . 8
200. D . strong negative
201. D . After operating costs are paid at a toy shop, as more toys are sold, more money is made.
202. A . 3
203. B. $7.50
𝑷
204. D . w = − 𝒍
𝟐
205. B
206.
207.
208.
209.
𝑥
B f(x) = − 1
2
210.
211. D . g(x) = (x + 3) – 7
212. C . The slope is 6. This means that for every 1 additional tree, she can expect an average of
6 additional birds per acre. The y-intercept is 4. The average number of birds per acre in an
area with no trees is 4.
213. D . 73.6%
214.
215. 4 + √𝟕
216. C. -3
217. D . 5x2 + 7x
218.
219.
220.