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A1© 2015 College Board. All rights reserved. SpringBoard Algebra 2, Unit 1 Practice
LeSSon 1-1 1. 65 5 15h 1 3
2. 4 hours; the cost of renting a bike for 4 hours is $63.
3. $13; it costs $78 to rent the bike for 5 hours since 15(5) 1 3 5 78. This is $13 more than Aaron has, 78 2 65 5 13.
4. B
5. a. No; there are 5 quarter-hour segments from 7:00 p.m. to 8:15 p.m. Using the equation c 5 40 1 4(5), c is $60.
b. Eliza should return the bike by 7:30 p.m. since 40 1 4(2) 5 48. She has enough money to keep the bike until 7:30 p.m.
LeSSon 1-2 6. number of Days Cost
1 $272 $473 $674 $875 $107
7. Sample answer: c 5 20d 1 7; c represents the cost of the bike rental, and d represents the number of days Susan rents the bike.
8.
1 2 3 4 5d
c
25
50
75
100
125
Cost
($)
Days
9. C
10. No; sample answer: Substituting 15 for d in the equation and solving for c shows that Barbara does not have enough money to rent the bike for 15 days.
LeSSon 1-3 11. a. x 5 210, x 5 24
2628210 24 22 0 2 4 6 8 10
b. x 5 6, x 5 7
2628210 24 22 0 2 4 6 8 10
c. x 5 2, x 5 10
2628210 24 22 0 2 4 6 8 10
d. x 5 28, x 5 22
2628210 24 22 0 2 4 6 8 10
12. 48 # s # 62
13. a. 1 , x , 9
2628210 24 22 0 2 4 6 8 10
b. x # 24 13
or x $ 1
2628210 24 22 0 2 4 6 8 10
c. 24 34
# x # 5 14
2628210 24 22 0 2 4 6 8 10
d. x , 26 or x . 23
2628210 24 22 0 2 4 6 8 10
14. D
15. |w 2 2| # 8; 6 # w # 10;
2628210 24 22 0 2 4 6 8 10
Answers to Algebra 2 Unit 1 Practice
A2© 2015 College Board. All rights reserved. SpringBoard Algebra 2, Unit 1 Practice
LeSSon 2-1
16. y 5 x34
1 2;
x
y
2223242526272829210 21
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10
1 2 3 4 5 6 7 8 9 10
17. B
18. f (e) 5 0.095e 1 1200
19.
10,000
20,000
30,000
40,000
50,000
1000
2000
3000
4000
5000
f (e)
e
Monthly Sales ($)
Julian’s Monthly Earnings
Mon
thly
Ear
ning
s ($
)
20. $8421.05; solve the equation 2000 5 0.095s 1 1200 for s.
LeSSon 2-2 21. a.
x
y
2223242526272829210 21
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10
1 2 3 4 5 6 7 8 9 10
b. Dashed line; . means that points on the boundary line are not included in the solution set.
c. Above the line; (0, 0) is not a solution, so the half-plane that does not include (0, 0) should be shaded.
22. x , 2
y # 2x
x
y
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10
1 2 3 4 5 6 7 8 9 10
y $ 23x 1 2
23. C
A3© 2015 College Board. All rights reserved. SpringBoard Algebra 2, Unit 1 Practice
24. a. Sample answer: (22, 1) and (3, 6).
b. Sample answer: (22, 1) does not satisfy the constraint y $ 23x 1 2 and (3, 6) does not satisfy the constraint x , 2.
25. x $ 1, y , 2, y $ x12
2 2
LeSSon 3-1 26. a. (1, 21)
x
y
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10
1 2 3 4 5 6 7 8 9 10
b. no solution
x
y
2223242526272829210 21
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10
1 2 3 4 5 6 7 8 9 10
c. (2, 0)
x
y
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10
1 2 3 4 5 6 7 8 9 10
d. infinitely many solutions
x
y
2223242526272829210 21
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10
1 2 3 4 5 6 7 8 9 10
27. a. (3, 1)
b. (7, 2)
c. infinitely many solutions
d. (2, 5)
28. a. (4, 27)
b. (4.5, 3)
c. (2, 23)
d. (10, 25)
A4© 2015 College Board. All rights reserved. SpringBoard Algebra 2, Unit 1 Practice
29. Sample answer: Multiply the first equation by 3 to
get 1 5
2 5
x yx y
1.2 1.5 7.51.2 3.5 2.5
. Then subtract the equation
to eliminate the variable x and get 5y 5 5.
30. C
LeSSon 3-2 31. a. (22, 4, 0)
b. (4, 3, 23)
c. (247
, 277
, 4) d. (1, 5, 21)
32. a. (2, 23, 22)
b. (1, 195
, 245 )
c. (23, 1, 5)
d. no solution
33. a. 1 1 5
1 1 5
1 1 5
c f vc f vc f v
10 12 3 103.506 8 15 125.5012 6 8 102.00
b. (3, 5, 4.5); A classic is $3, a fruit is $5, and a veggie is $4.50.
34. 4 pounds of peanuts, 2 pounds of cashews, and 4 pounds of raisins
35. B
LeSSon 3-3 36. B
37. 3 3 3
38. a. 2
3 2 37 3 61 10 18
b. 2
2 2 2
2 2
1 4 131 1 85 8 4
c.
2
4 9 914 10 03 5 3
d. 2
2 2
2 3 196 6 143 13 21
39. a. 2 2
2
9 316 2
b. 2
2 2
17 1 1518 14 10
c.
2
2 2
63
89
1015
d. not defined
40. a. No. The matrices are not the same dimensions.
b. Yes. The number of rows in G is the same as the number of columns in H.
LeSSon 3-4 41. B
42. a.
2
25
xy
1 12 1
2010
; (10, 30)
b.
5
xyz
2 3 13 3 12 4 1
485
; (4, 1, 27)
43. a.
1 5
1 5
x yx y
5.57.95 9.5 47.6
b.
5
xy
1 17.95 9.5
5.547.6
c. (3, 2.5)
d. Lori bought 3 pounds of cheddar and 2.5 or 212
pounds of Swiss for the party.
44. a.
5
phe
55 17 3312 10 1323 18 19
970335595
b. (10, 15, 5); During the sale, paperback books cost $10, hardcover books costs $15, and e-books cost $5.
45. Mari has 2 nickels, 5 dimes, and 35 quarters.
LeSSon 4-1 46. 23 # x , 12, [23, 12), {x | x ∈ , 23 # x , 12}
47. D
A5© 2015 College Board. All rights reserved. SpringBoard Algebra 2, Unit 1 Practice
48. a.
x
f (x)
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10
1 2 3 4 5 6 7 8 9 10
b.
x
f (x)
2223242526272829210 21
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10
1 2 3 4 5 6 7 8 9 10
domain: 2` , x , `, (2`, `), {x | x ∈ }; domain: x fi 1, (2`, 1) and (1, `), {x | x ∈, x fi 1};
range: 2` , y # 2, (2`, 2], { y | y ∈ , y # 2} range: 2` , y , 4, (2`, 4), { y | y ∈ , y , 4}
c.
x
f (x)
2223242526272829210 21
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10
1 2 3 4 5 6 7 8 9 10
d.
x
f (x)
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10
1 2 3 4 5 6 7 8 9 10
domain: 2` , x , `, (2`, `), {x | x ∈ }; domain: 2` , x , `, (2`, `), {x | x ∈ , x fi 21};
range: 22 , y # `, (22, `), { y | y ∈ , y . 22} range: 25 , y , `, (25, `), {y | y ∈ , y . 5}
49. h(23) 5 211, h(3) is undefined, h(30) 5 895
50. a. w (x) 5
25 if 0 , x # 50000.01x 2 25 if 5000 , x # 15,0000.005x 1 50 if 15,000 , x # 25,0000.0025x 1 112.5 if x . 25,000
A6© 2015 College Board. All rights reserved. SpringBoard Algebra 2, Unit 1 Practice
b.
10 20 30 40 50
50
100
150
200
250
Cost
($)
Water (thousands of gallons)
Water Charges
x
w(x)
c. Since the rate or charge for the water changes with the amount of consumption, the slope for each piece of the function is different.
d. $162.79; first determine the water consumption for a quarter of the year. Since there are 91.25 days in a quarter, the water consumption for a quarter is 247.2 gallons per day 3 91.25 days or 22,557 gallons. Next use the part of the piecewise function that corresponds to the range for the given number of gallons. Substituting 22,557 gallons for x in 0.0025x 1 112.5 5 $162.79.
LeSSon 4-2 51. a.
x
f(x)
22232425 21
2524232221
12345
1 2 3 4 5
b. f (2.4) 5 2, f (0.05) 5 0, f (23.6) 5 24
52. a.
x
h(x)
2223242526272829210 21
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10
1 2 3 4 5 6 7 8 9 10
b. domain: {x | x ∈ }; range: { y | y ∈ , y $ 0}
c. (3, 0)
d. f (x) 5
2 1 ,
2 $
x xx x
3 if 33 if 3
53. a. t(x) 5 45[x]
b.
1 2 3 4 5
45
90
135
180
225
Cost
($)
Hours
Cost of Tutort(x)
x
c. $90; $180
d. B
A7© 2015 College Board. All rights reserved. SpringBoard Algebra 2, Unit 1 Practice
54. a.
x
h(x)
22232425 21
2524232221
12345
1 2 3 4 5
b. h(0.3) 5 0, h(3) is undefined, h(1.1) 5 2, h(100) 5 3
55. $392; no. A step function is a piecewise function with a constant value throughout each interval of its domain. The value of this function changes with each hour. It is a piecewise function because there are two different rates based on the number of hours worked.
LeSSon 4-3 56. a. g (x) 5 2|x|
b. 5( )g x x13
c. g (x) 5 |x 2 5|
d. g (x) 5 4|x| 1 2
e. g (x) 5 22|x 1 1| 2 3
57. domain: {x | x ∈ }; range: { y | y ∈, y # 21}
58. f (x) 5 2|x 2 3| 1 1
59. C
60.
x
g(x)
2223242526272829210 21
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10
1 2 3 4 5 6 7 8 9 10
a vertical translation of 23, a horizontal translation
of 21, and a vertical shrink by 12
LeSSon 5-1 61. a. x 2 1 x 2 1
b. x 2 2 x 1 3
c. x 3 2 2x 2 1 x 2 2
d. 1
2
xx
12,
2
x fi 2
62. C
63. x 5 27, x 5 12; since both x 2 2 5x and 84 are equal to h(x), they are equal to each other. x 2 2 5x 5 84. Now set the equation equal to 0 and solve the trinomial for x.
x 2 2 5x 2 84 5 0(x 1 7)(x 2 12) 5 0
(x 1 7) 5 0 or (x 2 12) 5 0x 5 27 or x 5 12
64. a. m(x) 5 25,000 1 0.08x; p(x) 5 30,000 1 0.05x
b. The function (m 1 p)(x) represents the couple’s total annual earnings.
c. (m 1 p)(x) 5 55,000 1 0.13x
d. the couple’s annual earnings last year; $56,300
e. I could use (m 2 p)(x) to compare the annual earnings of Marty and his wife.
65. a. f(l ? w)(x) 5 (l 1 x)(w 1 x) 5 lw 1 lx 1 wx 1 x 2
b. 527 sq ft
LeSSon 5-2 66. y(x(z)) 5 6z 23; 21
67. The domain of the composite function is the range of k(l), all real numbers greater than or equal to 22.
68. a. c(h) 5 15 1 75h
b. domain: hours, range: dollars
c. The slope is 75. It means the cost will increase by $75 for each additional hour of repair time.
69. a. h(x) 5 0.75x
b. c(h(x)) 5 15 1 75(0.75x) 5 15 1 56.25x
c. C
70. The cost will not be the same; for each new location, you have to add the flat fee of $15.
A8© 2015 College Board. All rights reserved. SpringBoard Algebra 2, Unit 1 Practice
LeSSon 5-3 71. a. 9 b. 11
c. 16 d. 11
72. a. 34 b. 23
c. 23 d. 9
e. 25 f. 215
g. 2 h. 27
73. a. 4x 2 b. 2x 2
74. D
75. a. s(p) 5 0.75p
b. t(p) 5 1.07p
c. $361.13
LeSSon 6-1 76. 15
77. a. 522f x x( ) 13
1
b. g 21(x) 5 2x 1 6
c. 5 12h x x( ) 43
41
d. 522j x x( ) 4 32
1
78. B
79. a. 5 5k(15) 155
3; the map distance between two
points that are actually 15 kilometers apart is 3 centimeters.
b. k 21(a) 5 5a; the inverse function is the actual distance in kilometers between two points that are a centimeters apart on the map.
c. k 21(3) 5 5 ? 3 5 15 kilometers
80. f 21(8) 5 2
LeSSon 6-2
81. a. 512f x x( ) 23
;1 52 12f f x x( ( )) (3 2) 23
1
5 5x x33
b. g 21(x) 5 3x 2 12;
5 12g g x x( ( )) 3
13
41 2 12
5 x 1 12 2 12 5 x
82. D
83. a. f (x)
f 21 (x)
x
y
2223242526272829210 21
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10
1 2 3 4 5 6 7 8 9 10
b. f (x)
f 21 (x)
x
y
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1 2 3 4 5 6 7 8 9 10
A9© 2015 College Board. All rights reserved. SpringBoard Algebra 2, Unit 1 Practice
84. x 25 21 3 7 11
f 21( x) 0 2 4 6 8
or f21(x) 5 1x( 5)2
85. a.
x
y
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10
1 2 3 4 5 6 7 8 9 10
f 21 (x)
f (x)
b. f (x)
f 21 (x)
x
y
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1 2 3 4 5 6 7 8 9 10
