Holt Algebra 1_chapter 11_standardized Test 1u6v5y
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Name ——————————————————————— CHAPTER
11
Date ————————————
Standardized Test A For use after Chapter 11
}
5. Which expression is equivalent to Ï 50 ?
Multiple Choice 1. The graph of which function is a vertical }
shrink of the graph y 5 Ï x ?
1 A y 5 }3 Ï x
}
}
}
B 5Ï10
A 5Ï 2
}
}
D 25Ï 2
C 10Ï5 }
B y 5 3 Ïx
}
}
D y 5 Ïx 2 3
C y 5 22 Ï x
}
in its simplest form? }
B 4Ï 10
}
}
D 5Ï 8
A 2Ï 10 2. The graph of which function is a vertical
translation 6 units up of the graph of } Ï y 5 x? }
}
B y 5 Ïx 1 6
}
D y 5 Ïx 1 6
A y 5 Ïx 2 6
3. The graph of which function is shown?
Y
}
7. Which expression is equivalent to
9
}2 ?
}
A 3x
B 3Ïx }
Ï3
3
C }x
D } x
simplest form?
}
3Ï 5 B } 5
3 A }5
/
Ïx
3 8. Which expression is equivalent to } } in its Ï5
Copyright © Holt McDougal. All rights reserved.
}
C 4Ï 5
}
C y 5 Ïx 2 6
}
6. Which expression is equivalent to Ï 20 p Ï 2
X
}
}
Ï15
3Ï 5
C } 25
D } 25
9. Which expression is equivalent to }
}
Ï18 2 Ï2 ?
}
A y 5 2Ï x 2 2
A 4
B 8
}
B y 5 2Ï x 1 2
}
}
C 2Ï 2
}
C y 5 2Ï x 2 2
D 8Ï 2
}
D y 5 2Ï x 1 22
10. Which expression is equivalent to }
4. How is the graph of f (x) 5 Ï x 1 1 related to }
the graph of g(x) 5 Ï x 1 4?
A It is a horizontal translation 3 units left of the graph of g. B It is a horizontal translation 3 units right of the graph of g. C It is a vertical translation 3 units down of the graph of g. D It is a vertical translation 3 units up of the graph of g.
}
}
Ï3 1 10 1 Ï12 2? }
B 12Ï 3
A 16 }
C 16Ï 3
}
D 10Ï 3 1 6
8 3 11. Which expression is equivalent to } } + } } Ïx Ïx
in its simplest form? } A 11x B 11Ïx 11 C } } Ïx
}
11Ïx
D } x Algebra 1 Chapter 11 Assessment Book
217
Name ———————————————————————
Standardized Test A
CHAPTER
11
For use after Chapter 11
}
12. Which expression is equivalent to 1 2 1 Ï 6 22
in its simplest form?
}
Gridded Response
in the equation } 2Ïx 1 6 5 10?
B 10 1 4Ï 6
C 4 1 2Ï6
continued
19. What is the value of x }
A 10
Date ————————————
}
D 4 1 5Ï 6
3}
3}
13. Which expression is equivalent to Ï 32 p Ï 2
in its simplest form?
A 4
B 8
3}
3}
C Ï 64
D 4Ï 16
Short Response
14. What is the solution of the equation
20. A map of your town is shown.
}
A 4
B 5
C 25
D 64
15. Given a right triangle with side lengths
18 and 24, what is the length of the hypotenuse? A 30
B 42
C 48
D 450
16. Which of the triangles with the given side
lengths is a right triangle? A 8, 10, 20
B 12, 16, 20
C 15, 30, 45
D 20, 25, 60
17. What is the midpoint of the line segment
with endpoints (3, 5) and (13, 9)? A (4, 11)
B (6, 9)
C (8, 7)
D (16, 24)
18. What is the distance between (2, 5) and
(6, 21)? }
A Ï10
}
C 2Ï 10
218
Algebra 1 Chapter 11 Assessment Book
}
B 2Ï 7
}
D 2Ï 13
Y
,IBRARY 0OST/FFICE -ARKET 3CHOOL 4RAIN3TATION 3TADIUM
X
You are at the post office and your friend is at the stadium. You want to meet at the place that is closest to the midpoint of the locations. At which location should you meet? Explain. Extended Response 21. A staircase is to be built in a building to
connect two floors that are 24 vertical feet apart. There will be 24 steps on the staircase. The horizontal distance of each step is 16 inches. a. What is the linear distance (in feet)
needed for the staircase? Explain. b. How far does a person travel by walking the full length of the staircase? Explain. c. How much further would a person walking the full length of the staircase travel if the linear distance found in part (a) is increased by 13 feet?
Copyright © Holt McDougal. All rights reserved.
4Ï x 2 4 5 16 ?
Name ———————————————————————
Date ————————————
Standardized Test B
CHAPTER
11
For use after Chapter 11 }
5. Which expression is equivalent to Ï 72 ?
Multiple Choice
}
1. The graph of which function is a vertical
}
}
A Ï70 1 Ï 2
B 6Ï 2
C 12
D 36
}
stretch of the graph y 5 Ï x ? 1
}
}
B y 5 5 1 Ïx
A y 5 }2 Ï x
}
}
D y 5 Ïx 1 3
C y 5 4 Ïx
}
in its simplest form? }
}
A 4Ï 3 2. The graph of which function is a horizontal
translation of 2 units to the left of the graph } y 5 Ïx ? }
A y 5 Ïx 2 2 }
C y 5 Ïx 2 2
}
B y 5 Ïx 1 2 }
D y 5 Ïx 1 2
3. The graph of which function is shown?
B 16Ï 3
}
}
C 2Ï12
D 12Ï 2
}
7. Which expression is equivalent to
16x
? Ï} 49
}
4Ï x
4x
A } 7
B } 49 }
}
4Ï x C } 7
Ï4x D } 7
y 22 22
}
2
6
10 x
8. Which expression is equivalent to
simplest form?
26
3 Ï32 } 3Ï 2 C } 4
9
Ï}32 in its
3 4Ï2 } 3Ï2 D } 8
B } }
A } }
210
}
}
A y 5 2Ï x 2 3 2 6
9. Which expression is equivalent to
}
Copyright © Holt McDougal. All rights reserved.
}
6. Which expression is equivalent to Ï 24 p Ï 2
B y 5 2Ï x 1 3 1 6
simplest form?
}
}
C y 5 2Ï x 2 3 1 6
}
x2 Ï 5 Ï6 } 2Ï x 5 C } 6
30Ïx
B } 6
A } }
}
D y 5 2Ï x 1 3 2 6 }
4. How is the graph of f(x) 5 Ï x 1 5 related to
Ï
5x2 6
} in its
}
xÏ 30
D } 6
}
the graph of g(x) 5 Ï x 2 5? A It is a vertical translation of 5 units up of the graph of g. B It is a vertical translation of 10 units up of the graph of g. C It is a horizontal translation of 5 units to the right of the graph of g. D It is a horizontal translation of 10 units to the right of the graph of g.
10. Which expression is equivalent to }
}
}
Ï 24 1 5Ï 6 2 Ï 54 ? }
}
A 10Ï 2
B 4Ï 6 }
}
C 5 2 Ï 24
D 10Ï 6
11. Which expression is equivalent to }
(3Ï5 2 2)2? }
A 49 2 12Ï5
}
C 30 2 12Ï5
}
B 4 2 3Ï 5
}
D 24 2 3Ï 5
Algebra 1 Chapter 11 Assessment Book
219
Name ———————————————————————
Standardized Test B
CHAPTER
11
Date ————————————
continued
For use after Chapter 11
2 5 12. Which expression is equivalent to } } } 2 } Ïr Ïr
in its simplest form?
3r A } r
19. What is the value of x
5r 2 2 B } r2 }
3Ï r
Gridded Response
in the equation } 4Ïx 1 5 1 2 5 18?
3 Ïr
C } r
D }}
15 13. Which expression is equivalent to } } } Ï6 2 Ï3
in its simplest form? }
15Ï9 3
}
}
}
B 5Ï6 1 5Ï 3
A 2} }
15Ï6 1 15Ï3 C 2}} 3
}
D 15Ï3
Short Response 14. What is the solution of the equation }
20. A map of your town is shown.
}
A Ï3
B 3
C 23
D 25
y 7
15. Given a right triangle with side lengths 7 and
5
Park (2, 5)
24, what is the length of the hypotenuse? A 25
B 31
C 62
16. Which of the triangles with the given side
lengths is not a right triangle? A 3, 4, 5
B 11, 60, 61
C 15, 20, 25
D 9, 39, 41
17. What is the midpoint of the line segment
with endpoints (23, 22) and (5, 24)? A (1, 23)
B (24, 21)
C (21, 3)
D (4, 1)
18. What is the distance between (5, 3.5) and
(22, 22.5)? }
C Ï85
220
Algebra 1 Chapter 11 Assessment Book
(3, 2) School
(0, 1) Stadium 23
21
1
3
(5, 3) Fountain (6, 1) Library 5
7
x
You are at the library. Your friend is at the park. You want to meet at the place that is closest to the midpoint of your locations. At which location should you meet? Explain. Extended Response 21. The vertical distance from the first floor of
a house to the second floor is 12 feet. The tread of each step is 12 inches and the riser is 6 inches. a. How many steps are needed? Explain.
}
A 2
3
D 625
B Ï 13
b. What is the linear distance (in feet)
D 13
needed for the staircase? Explain. c. If a railing is installed from the edge of the bottom step to the edge of the top step, how long of a rail is needed? Round your answer to the nearest inch.
Copyright © Holt McDougal. All rights reserved.
6Ïx 1 2 1 5 5 35?
Name ———————————————————————
Date ————————————
Standardized Test C
CHAPTER
11
For use after Chapter 11 }
5. Which expression is equivalent to Ï 192 ?
Multiple Choice
}
1. The graph of which function is a vertical }
1
D 16Ï 3
}
B y 5 }3 Ïx
1 } C y 5 }2 Ïx
}
C 8Ï3 4
}
B 8Ï 2
}
stretch of the graph y 5 Ï x ? A y 5 }3 Ïx
}
A 4Ï3
}
D y 5 2Ï x 1 5
6. Which expression is equivalent to }
}
Ï6x p 3Ï2x in its simplest form? }
A 36x
2. The graph of which function is a horizontal
translation 4 units to the right of the graph } y 5 Ïx ? }
}
A y 5 Ïx 2 4
B y 5 Ïx 1 4
}
}
C y 5 Ïx 2 4
D y 5 Ïx 1 4
B 6xÏ3
}
}
C 6Ï3x
D 12xÏ3
}
9x3 7. Which expression is equivalent to } ? 169
Ï
}
3x3
3Ï x
A } 13
B } 13
}
3. The graph of which function is shown? Y
}
3x2Ïx
3xÏx
C } 13
D } 13 }
8. Which expression is equivalent to
simplest form?
/
}
Ï39 B } 26
2 A } 13
X
}
}
Ï39
3
Ï}52 in its
Ï156
C } 52
D } 52
9. Which expression is equivalent to
A y 5 2Ï x 2 4 1 2 Copyright © Holt McDougal. All rights reserved.
}
}
}
}
Ï 75 2 4Ï 12 1 Ï 24 ?
}
B y 5 2Ï x 1 4 1 2
}
}
}
C y 5 2Ï x 1 2 2 4
}
}
}
D y 5 2Ï x 1 2 1 4 }
4. How is the graph of f(x) 5 Ï x 2 2 related to }
the graph of g(x) 5 Ï x 1 1?
10. Which expression is equivalent to }
}
Ï 2 1 23Ï 7 2 9 22 ? }
A It is a horizontal translation 3 units right of the graph of g.
A 144Ï2
B It is a horizontal translation 3 units left of the graph of g.
C 260Ï 14 1 81Ï 2
C It is a vertical translation 2 units down of the graph of g. D It is a vertical translation 3 units down of the graph of g.
}
D 3Ï 3 1 2Ï 6
C Ï3 1 2Ï 6
}
}
B 23Ï 3 1 4Ï6
A 23Ï 3 1 2Ï 6
}
}
B 252Ï2
}
}
}
}
D 144Ï2 1 54Ï 14
11. Which expression is equivalent to
3
5
} } in its simplest form? }2 } Ïx
Ïx
3
}
2Ï x x 5 2 3x C } } xÏx
A } 2
5 2 3x
B } x }
Ï x (5
2 3x)
D } 2 x
Algebra 1 Chapter 11 Assessment Book
221
Name ———————————————————————
Standardized Test C
CHAPTER
11
Date ————————————
continued
For use after Chapter 11
10 12. Which expression is equivalent to } } in 4 2 Ï7
its simplest form? }
}
22Ï7 A } 9
40 1 10Ï 7 B } 9 }
40 1 10Ï7
C 2} 33
}
Gridded Response 19. What is the value of x
in} the equation } Ï 5x 2 5 2Ï 4x 1 16 = 0?
8 1 2Ï 7
D } 13
6 13. Which expression is equivalent to } 3 } in its Ï25 simplest form? 3}
Ï30 5
3}
B }
A Ï6
3}
3}
6Ï5 C } 5
2Ï5 D } 25
Short Response 20. A map of your town is shown.
}
Ï18 2 3x 5 x? A 3 only
B 26 only
C 3 and 26
D 23 and 6
15. Given a right triangle with a side length
of 30 and a hypotenuse of 78, what is the length of the other leg? A 39
B 48
C 68
D 72
16. Which of the triangles with the given side
lengths is not a right triangle? A 12, 16, 20
B 21, 72, 75
C 24, 45, 51
D 25, 60, 75
17. What is the midpoint of the line segment
with endpoints (25, 7) and (4, 212)? 1
A 1 2}2, 24 2 9
5
C 1 2}2, 2}2 2
1
5
B 1 2}2 , 2}2 2 D (1, 24)
(212, 23)? }
}
C Ï202
222
Algebra 1 Chapter 11 Assessment Book
y 4
School (4, 2)
Stadium 2 (21, 3) 10 8 6 4 2 O
Train Station (22, 22)
2 4
2
4
6
8 10 x
Post Office (5, 22)
You are at the library and your friend is at the post office. You want to meet at the place that is closest to the midpoint of the locations. At which location should you meet? Explain. Extended Response 21. A staircase is to be built in a building to
connect two floors that are 26 vertical feet apart. Each step will have a height of 8 inches and a horizontal distance of 12 inches. a. How many steps are needed? Explain. b. What is the linear distance (in feet)
18. What is the distance between (23, 8) and
A 5Ï 10
Library (26, 3)
}
B Ï 106
}
D Ï 346
needed for the staircase? Explain. c. How far does a person travel by walking the full length of the staircase? Round to the nearest tenth of a foot. How much further would a person travel by walking the full length of the staircase if the linear distance found in part (b) is increased by 11 feet?
Copyright © Holt McDougal. All rights reserved.
14. What is/are the solution(s) of the equation
Chapter 11, continued }
}
}
23. 5Ï 2 24. Ï 85 25. (9, 4)
22. 31.6 m
}
26. (24, 1) 27. (0, 22) 28. 4Ï 2 units
ANSWERS
29. 100.5 square units
Chapter Test B 1.
1
; domain: x ≥ 0; range: y ≥ 23; The graph is a x vertical shrink and a shift 3 units down from the } graph of y 5 Ï x .
y 1
21 21
3
5
23 25
2.
y 1 1
3
5
23
; domain: x ≥ 22; range: y ≤ 0; The graph is a x reflection in the x-axis and a shift 2 units to the} left of the graph of y 5 Ï x .
}
3} πÏ2L Ï2 π 11. t 5 } 12. } sec 13. 7Ï t 2 1
4 2 3} 6aÏ25 3} 3} 14. } 15. Ï 900 1 Ï 30 1 1 16. 8 17. 9 5 18. 0, 3 19. 20 people 20. 10x 21. about 14 people 22. 3.1, 8.1 23. 36.3, 106.9, 112.9 }
24. 642.6 in.2 25. (210, 215); 6Ï 13 } 1 26. (1, 3); 2Ï 2 27. 22 28. } 2
1 29. y 5 } (x 2 1) 2
Standardized Test A 1. A 2. D 3. B 4. C 5. A 6. A 7. C 8. B 9. C 10. D 11. D 12. B 13. A 14. C 15. A 16. B 17. C 18. D 19. 19 20. Train station; It is closest to the midpoint of
}
}
3. 6a 2Ï 2a 4. 14Ï 2 5. 29Ï 3 } 2p } 2Ï3b 6. } 7. }3 8. 44 1 16Ï 7 b q } } 3} Ïh 5Ï 2 9. t 5 } 10. } sec 11. 2Ï 4 2 4 4 2 3} 3} Ï36a 12. } 13. 22Ï 5x 14. no solution 3 15. 2 16. 21, 3 17. 0.7 m 18. 4 in., 2 in.
7 25 5 19. } ft, } ft 20. 3, } 6 6 2
1
2
}
5 21. 2}, 21 2
1
}
2
}
22. (6, 22) 23. 2Ï 2 , 2Ï 10 , 4Ï 2 24. yes 25. 2 or 10 26. 3 or 21 27. Tower A
Chapter Test C
; domain: x ≥ 21; range: y ≥ 24; The graph is a 21 1 3 5 x vertical stretch, shift 1 21 unit to the left and 4 units down } from the graph of y 5 Ïx . y 2. ; domain: x ≥ 4; range: 6 y ≤ 2; The graph is a 2 reflection in the x-axis, a 22 2 6 10 x 22 vertical shrink, and a shift 4 units to the right and 2 26 units up from the graph of } y 5 Ïx . } 3. h ≥ 210; v ≥ 0 4. 22 cm 5. 9Ï 10
1.
y
1
6. 6a b
Ï 5x 2a 7. 22Ï2 8. } xy
}
2 5Ï
}
}
}
} 15 2 3Ï5 9. 15x 2 22yÏ x 1 8y 2 10. } 20
A28
Algebra 1 Assessment Book
(7, 4). It is 1 unit away and the distances to the other locations are greater than 1. 21. a. 32 ft; 24(16) 5 384 and 384 4 12 5 32 } b. 40 ft; Ï 242 1 322 5 40, c. 11 ft more Standardized Test B 1. C 2. D 3. A 4. B 5. B 6. A 7. C 8. D 9. D 10. B 11. A 12. C 13. B 14. C 15. A 16. D 17. A 18. C 19. 11 20. You would meet at the fountain. The midpoint between the two locations is the point (4, 3). The two locations closest to this point are the school and the library. You can use either the distance formula or your knowledge of right triangles to determine that the fountain is closest. 21. a. Twenty-four steps are needed. The height from floor to ceiling is 12 feet or 144 inches. If the riser of each step is 6 inches, you would need 24 steps to reach the second floor. b. 24 ft; Each step has a tread of 12 inches and there are 24 steps, so the linear distance would be 288 inches or 24 feet. c. A 322 inch rail is needed.
Standardized Test C 1. B 2. A 3. A 4. D 5. C 6. B 7. C 8. B 9. A 10. D 11. D 12. C 13. C 14. A 15. D 16. D 17. B 18. C 19. 21 20. Stadium; It is closest to the midpoint of }
(20.5, 1). It is Ï 4.25 , units away and the distances to the other locations are greater than that.
Copyright © Holt McDougal. All rights reserved.
}
Chapter 11, continued 21. a. 39 steps; 26 ft 5 312 in. and 312 4 8 5 39 b. 39 ft; Each step is one-foot long and there are 39 steps. c. 46.9 ft; 9.5 ft more
8.
; The domain and range are all nonzero real numbers.
y
1 23
x 1
21 21
1. D 2. B 3. C 4. E 5. D 6. B 7. B 8. B
ANSWERS
SAT/ACT Chapter Test
23
9. A 10. C 11. E 12. A 13. D 14. 9 15. 117 yd 16. 6
Performance Assessment 1. Complete answers should include: an
9. 3
Time (seconds)
explanation of each property of radicals; an example illustrating why there is no sum property of radicals; an example illustrating why there is no difference property of radicals. 2. a. ; Domain: 0 ≤ h ≤ 36 t
1 23
1
Quiz 2
1.0
1. x 2 3 2. x 1 9
0.5
3.
10
0 6 12 18 24 30 36 h Height (feet)
dropped it has a height of 0 feet; the object is at a height of 36 feet right before it is released. c. 36.03 units d. 32 ft e. 20 ft f. 1.06 sec g. Less time; The object is in the air for a total of 1.5 seconds, and it takes just over 1 second to fall the first 18 feet, which means it takes less than 0.5 second to fall the second 18 feet.
Chapter 12 1. direct variation 2. inverse variation
35 35 224 3. neither 4. y 5 }; } 5. y 5 }; 212 x 2 x 7 7 6. y 5 }; } x 2
; The domain and range are all nonzero real numbers.
y 6 2 2
10 6
2 22
y
2 2
10
x
210
2
26
26
6 x
26
33 5. x2 1 7x 2 4 6. x2 1 5x 1 4 1 } x+5 1 7. }; The excluded values are 21 and 1. x11 x23 8. }; The excluded value is 0. 2 12x3 9. }; The excluded value is 0. 5
Quiz 1
22 22
4.
y
6
b. (0, 1.5), (36, 0); 1.5 seconds after the object is
Copyright © Holt McDougal. All rights reserved.
21
1.5
0
7.
; The domain is all real numbers except x 5 21. The range is x all real numbers except y 5 0.
y
6
x
x25 10. }; The excluded values are 23 and 3. x23
Quiz 3 2(x 2 7) 7 4 1. } 2. } 3. } 4. 2x(x 2 5) 15x x x24 8x 1 7 2x 1 9 5. } 6. }} (x 1 8)(x 1 1) x26 7. 0 and 5 8. 0 and 2 9. 12 h
Chapter Test A 1. neither 2. direct variation
60 3. inverse variation 4. t 5 } n
5. 15 days
Algebra 1 Assessment Book
A29
11
Date ————————————
Standardized Test A For use after Chapter 11
}
5. Which expression is equivalent to Ï 50 ?
Multiple Choice 1. The graph of which function is a vertical }
shrink of the graph y 5 Ï x ?
1 A y 5 }3 Ï x
}
}
}
B 5Ï10
A 5Ï 2
}
}
D 25Ï 2
C 10Ï5 }
B y 5 3 Ïx
}
}
D y 5 Ïx 2 3
C y 5 22 Ï x
}
in its simplest form? }
B 4Ï 10
}
}
D 5Ï 8
A 2Ï 10 2. The graph of which function is a vertical
translation 6 units up of the graph of } Ï y 5 x? }
}
B y 5 Ïx 1 6
}
D y 5 Ïx 1 6
A y 5 Ïx 2 6
3. The graph of which function is shown?
Y
}
7. Which expression is equivalent to
9
}2 ?
}
A 3x
B 3Ïx }
Ï3
3
C }x
D } x
simplest form?
}
3Ï 5 B } 5
3 A }5
/
Ïx
3 8. Which expression is equivalent to } } in its Ï5
Copyright © Holt McDougal. All rights reserved.
}
C 4Ï 5
}
C y 5 Ïx 2 6
}
6. Which expression is equivalent to Ï 20 p Ï 2
X
}
}
Ï15
3Ï 5
C } 25
D } 25
9. Which expression is equivalent to }
}
Ï18 2 Ï2 ?
}
A y 5 2Ï x 2 2
A 4
B 8
}
B y 5 2Ï x 1 2
}
}
C 2Ï 2
}
C y 5 2Ï x 2 2
D 8Ï 2
}
D y 5 2Ï x 1 22
10. Which expression is equivalent to }
4. How is the graph of f (x) 5 Ï x 1 1 related to }
the graph of g(x) 5 Ï x 1 4?
A It is a horizontal translation 3 units left of the graph of g. B It is a horizontal translation 3 units right of the graph of g. C It is a vertical translation 3 units down of the graph of g. D It is a vertical translation 3 units up of the graph of g.
}
}
Ï3 1 10 1 Ï12 2? }
B 12Ï 3
A 16 }
C 16Ï 3
}
D 10Ï 3 1 6
8 3 11. Which expression is equivalent to } } + } } Ïx Ïx
in its simplest form? } A 11x B 11Ïx 11 C } } Ïx
}
11Ïx
D } x Algebra 1 Chapter 11 Assessment Book
217
Name ———————————————————————
Standardized Test A
CHAPTER
11
For use after Chapter 11
}
12. Which expression is equivalent to 1 2 1 Ï 6 22
in its simplest form?
}
Gridded Response
in the equation } 2Ïx 1 6 5 10?
B 10 1 4Ï 6
C 4 1 2Ï6
continued
19. What is the value of x }
A 10
Date ————————————
}
D 4 1 5Ï 6
3}
3}
13. Which expression is equivalent to Ï 32 p Ï 2
in its simplest form?
A 4
B 8
3}
3}
C Ï 64
D 4Ï 16
Short Response
14. What is the solution of the equation
20. A map of your town is shown.
}
A 4
B 5
C 25
D 64
15. Given a right triangle with side lengths
18 and 24, what is the length of the hypotenuse? A 30
B 42
C 48
D 450
16. Which of the triangles with the given side
lengths is a right triangle? A 8, 10, 20
B 12, 16, 20
C 15, 30, 45
D 20, 25, 60
17. What is the midpoint of the line segment
with endpoints (3, 5) and (13, 9)? A (4, 11)
B (6, 9)
C (8, 7)
D (16, 24)
18. What is the distance between (2, 5) and
(6, 21)? }
A Ï10
}
C 2Ï 10
218
Algebra 1 Chapter 11 Assessment Book
}
B 2Ï 7
}
D 2Ï 13
Y
,IBRARY 0OST/FFICE -ARKET 3CHOOL 4RAIN3TATION 3TADIUM
X
You are at the post office and your friend is at the stadium. You want to meet at the place that is closest to the midpoint of the locations. At which location should you meet? Explain. Extended Response 21. A staircase is to be built in a building to
connect two floors that are 24 vertical feet apart. There will be 24 steps on the staircase. The horizontal distance of each step is 16 inches. a. What is the linear distance (in feet)
needed for the staircase? Explain. b. How far does a person travel by walking the full length of the staircase? Explain. c. How much further would a person walking the full length of the staircase travel if the linear distance found in part (a) is increased by 13 feet?
Copyright © Holt McDougal. All rights reserved.
4Ï x 2 4 5 16 ?
Name ———————————————————————
Date ————————————
Standardized Test B
CHAPTER
11
For use after Chapter 11 }
5. Which expression is equivalent to Ï 72 ?
Multiple Choice
}
1. The graph of which function is a vertical
}
}
A Ï70 1 Ï 2
B 6Ï 2
C 12
D 36
}
stretch of the graph y 5 Ï x ? 1
}
}
B y 5 5 1 Ïx
A y 5 }2 Ï x
}
}
D y 5 Ïx 1 3
C y 5 4 Ïx
}
in its simplest form? }
}
A 4Ï 3 2. The graph of which function is a horizontal
translation of 2 units to the left of the graph } y 5 Ïx ? }
A y 5 Ïx 2 2 }
C y 5 Ïx 2 2
}
B y 5 Ïx 1 2 }
D y 5 Ïx 1 2
3. The graph of which function is shown?
B 16Ï 3
}
}
C 2Ï12
D 12Ï 2
}
7. Which expression is equivalent to
16x
? Ï} 49
}
4Ï x
4x
A } 7
B } 49 }
}
4Ï x C } 7
Ï4x D } 7
y 22 22
}
2
6
10 x
8. Which expression is equivalent to
simplest form?
26
3 Ï32 } 3Ï 2 C } 4
9
Ï}32 in its
3 4Ï2 } 3Ï2 D } 8
B } }
A } }
210
}
}
A y 5 2Ï x 2 3 2 6
9. Which expression is equivalent to
}
Copyright © Holt McDougal. All rights reserved.
}
6. Which expression is equivalent to Ï 24 p Ï 2
B y 5 2Ï x 1 3 1 6
simplest form?
}
}
C y 5 2Ï x 2 3 1 6
}
x2 Ï 5 Ï6 } 2Ï x 5 C } 6
30Ïx
B } 6
A } }
}
D y 5 2Ï x 1 3 2 6 }
4. How is the graph of f(x) 5 Ï x 1 5 related to
Ï
5x2 6
} in its
}
xÏ 30
D } 6
}
the graph of g(x) 5 Ï x 2 5? A It is a vertical translation of 5 units up of the graph of g. B It is a vertical translation of 10 units up of the graph of g. C It is a horizontal translation of 5 units to the right of the graph of g. D It is a horizontal translation of 10 units to the right of the graph of g.
10. Which expression is equivalent to }
}
}
Ï 24 1 5Ï 6 2 Ï 54 ? }
}
A 10Ï 2
B 4Ï 6 }
}
C 5 2 Ï 24
D 10Ï 6
11. Which expression is equivalent to }
(3Ï5 2 2)2? }
A 49 2 12Ï5
}
C 30 2 12Ï5
}
B 4 2 3Ï 5
}
D 24 2 3Ï 5
Algebra 1 Chapter 11 Assessment Book
219
Name ———————————————————————
Standardized Test B
CHAPTER
11
Date ————————————
continued
For use after Chapter 11
2 5 12. Which expression is equivalent to } } } 2 } Ïr Ïr
in its simplest form?
3r A } r
19. What is the value of x
5r 2 2 B } r2 }
3Ï r
Gridded Response
in the equation } 4Ïx 1 5 1 2 5 18?
3 Ïr
C } r
D }}
15 13. Which expression is equivalent to } } } Ï6 2 Ï3
in its simplest form? }
15Ï9 3
}
}
}
B 5Ï6 1 5Ï 3
A 2} }
15Ï6 1 15Ï3 C 2}} 3
}
D 15Ï3
Short Response 14. What is the solution of the equation }
20. A map of your town is shown.
}
A Ï3
B 3
C 23
D 25
y 7
15. Given a right triangle with side lengths 7 and
5
Park (2, 5)
24, what is the length of the hypotenuse? A 25
B 31
C 62
16. Which of the triangles with the given side
lengths is not a right triangle? A 3, 4, 5
B 11, 60, 61
C 15, 20, 25
D 9, 39, 41
17. What is the midpoint of the line segment
with endpoints (23, 22) and (5, 24)? A (1, 23)
B (24, 21)
C (21, 3)
D (4, 1)
18. What is the distance between (5, 3.5) and
(22, 22.5)? }
C Ï85
220
Algebra 1 Chapter 11 Assessment Book
(3, 2) School
(0, 1) Stadium 23
21
1
3
(5, 3) Fountain (6, 1) Library 5
7
x
You are at the library. Your friend is at the park. You want to meet at the place that is closest to the midpoint of your locations. At which location should you meet? Explain. Extended Response 21. The vertical distance from the first floor of
a house to the second floor is 12 feet. The tread of each step is 12 inches and the riser is 6 inches. a. How many steps are needed? Explain.
}
A 2
3
D 625
B Ï 13
b. What is the linear distance (in feet)
D 13
needed for the staircase? Explain. c. If a railing is installed from the edge of the bottom step to the edge of the top step, how long of a rail is needed? Round your answer to the nearest inch.
Copyright © Holt McDougal. All rights reserved.
6Ïx 1 2 1 5 5 35?
Name ———————————————————————
Date ————————————
Standardized Test C
CHAPTER
11
For use after Chapter 11 }
5. Which expression is equivalent to Ï 192 ?
Multiple Choice
}
1. The graph of which function is a vertical }
1
D 16Ï 3
}
B y 5 }3 Ïx
1 } C y 5 }2 Ïx
}
C 8Ï3 4
}
B 8Ï 2
}
stretch of the graph y 5 Ï x ? A y 5 }3 Ïx
}
A 4Ï3
}
D y 5 2Ï x 1 5
6. Which expression is equivalent to }
}
Ï6x p 3Ï2x in its simplest form? }
A 36x
2. The graph of which function is a horizontal
translation 4 units to the right of the graph } y 5 Ïx ? }
}
A y 5 Ïx 2 4
B y 5 Ïx 1 4
}
}
C y 5 Ïx 2 4
D y 5 Ïx 1 4
B 6xÏ3
}
}
C 6Ï3x
D 12xÏ3
}
9x3 7. Which expression is equivalent to } ? 169
Ï
}
3x3
3Ï x
A } 13
B } 13
}
3. The graph of which function is shown? Y
}
3x2Ïx
3xÏx
C } 13
D } 13 }
8. Which expression is equivalent to
simplest form?
/
}
Ï39 B } 26
2 A } 13
X
}
}
Ï39
3
Ï}52 in its
Ï156
C } 52
D } 52
9. Which expression is equivalent to
A y 5 2Ï x 2 4 1 2 Copyright © Holt McDougal. All rights reserved.
}
}
}
}
Ï 75 2 4Ï 12 1 Ï 24 ?
}
B y 5 2Ï x 1 4 1 2
}
}
}
C y 5 2Ï x 1 2 2 4
}
}
}
D y 5 2Ï x 1 2 1 4 }
4. How is the graph of f(x) 5 Ï x 2 2 related to }
the graph of g(x) 5 Ï x 1 1?
10. Which expression is equivalent to }
}
Ï 2 1 23Ï 7 2 9 22 ? }
A It is a horizontal translation 3 units right of the graph of g.
A 144Ï2
B It is a horizontal translation 3 units left of the graph of g.
C 260Ï 14 1 81Ï 2
C It is a vertical translation 2 units down of the graph of g. D It is a vertical translation 3 units down of the graph of g.
}
D 3Ï 3 1 2Ï 6
C Ï3 1 2Ï 6
}
}
B 23Ï 3 1 4Ï6
A 23Ï 3 1 2Ï 6
}
}
B 252Ï2
}
}
}
}
D 144Ï2 1 54Ï 14
11. Which expression is equivalent to
3
5
} } in its simplest form? }2 } Ïx
Ïx
3
}
2Ï x x 5 2 3x C } } xÏx
A } 2
5 2 3x
B } x }
Ï x (5
2 3x)
D } 2 x
Algebra 1 Chapter 11 Assessment Book
221
Name ———————————————————————
Standardized Test C
CHAPTER
11
Date ————————————
continued
For use after Chapter 11
10 12. Which expression is equivalent to } } in 4 2 Ï7
its simplest form? }
}
22Ï7 A } 9
40 1 10Ï 7 B } 9 }
40 1 10Ï7
C 2} 33
}
Gridded Response 19. What is the value of x
in} the equation } Ï 5x 2 5 2Ï 4x 1 16 = 0?
8 1 2Ï 7
D } 13
6 13. Which expression is equivalent to } 3 } in its Ï25 simplest form? 3}
Ï30 5
3}
B }
A Ï6
3}
3}
6Ï5 C } 5
2Ï5 D } 25
Short Response 20. A map of your town is shown.
}
Ï18 2 3x 5 x? A 3 only
B 26 only
C 3 and 26
D 23 and 6
15. Given a right triangle with a side length
of 30 and a hypotenuse of 78, what is the length of the other leg? A 39
B 48
C 68
D 72
16. Which of the triangles with the given side
lengths is not a right triangle? A 12, 16, 20
B 21, 72, 75
C 24, 45, 51
D 25, 60, 75
17. What is the midpoint of the line segment
with endpoints (25, 7) and (4, 212)? 1
A 1 2}2, 24 2 9
5
C 1 2}2, 2}2 2
1
5
B 1 2}2 , 2}2 2 D (1, 24)
(212, 23)? }
}
C Ï202
222
Algebra 1 Chapter 11 Assessment Book
y 4
School (4, 2)
Stadium 2 (21, 3) 10 8 6 4 2 O
Train Station (22, 22)
2 4
2
4
6
8 10 x
Post Office (5, 22)
You are at the library and your friend is at the post office. You want to meet at the place that is closest to the midpoint of the locations. At which location should you meet? Explain. Extended Response 21. A staircase is to be built in a building to
connect two floors that are 26 vertical feet apart. Each step will have a height of 8 inches and a horizontal distance of 12 inches. a. How many steps are needed? Explain. b. What is the linear distance (in feet)
18. What is the distance between (23, 8) and
A 5Ï 10
Library (26, 3)
}
B Ï 106
}
D Ï 346
needed for the staircase? Explain. c. How far does a person travel by walking the full length of the staircase? Round to the nearest tenth of a foot. How much further would a person travel by walking the full length of the staircase if the linear distance found in part (b) is increased by 11 feet?
Copyright © Holt McDougal. All rights reserved.
14. What is/are the solution(s) of the equation
Chapter 11, continued }
}
}
23. 5Ï 2 24. Ï 85 25. (9, 4)
22. 31.6 m
}
26. (24, 1) 27. (0, 22) 28. 4Ï 2 units
ANSWERS
29. 100.5 square units
Chapter Test B 1.
1
; domain: x ≥ 0; range: y ≥ 23; The graph is a x vertical shrink and a shift 3 units down from the } graph of y 5 Ï x .
y 1
21 21
3
5
23 25
2.
y 1 1
3
5
23
; domain: x ≥ 22; range: y ≤ 0; The graph is a x reflection in the x-axis and a shift 2 units to the} left of the graph of y 5 Ï x .
}
3} πÏ2L Ï2 π 11. t 5 } 12. } sec 13. 7Ï t 2 1
4 2 3} 6aÏ25 3} 3} 14. } 15. Ï 900 1 Ï 30 1 1 16. 8 17. 9 5 18. 0, 3 19. 20 people 20. 10x 21. about 14 people 22. 3.1, 8.1 23. 36.3, 106.9, 112.9 }
24. 642.6 in.2 25. (210, 215); 6Ï 13 } 1 26. (1, 3); 2Ï 2 27. 22 28. } 2
1 29. y 5 } (x 2 1) 2
Standardized Test A 1. A 2. D 3. B 4. C 5. A 6. A 7. C 8. B 9. C 10. D 11. D 12. B 13. A 14. C 15. A 16. B 17. C 18. D 19. 19 20. Train station; It is closest to the midpoint of
}
}
3. 6a 2Ï 2a 4. 14Ï 2 5. 29Ï 3 } 2p } 2Ï3b 6. } 7. }3 8. 44 1 16Ï 7 b q } } 3} Ïh 5Ï 2 9. t 5 } 10. } sec 11. 2Ï 4 2 4 4 2 3} 3} Ï36a 12. } 13. 22Ï 5x 14. no solution 3 15. 2 16. 21, 3 17. 0.7 m 18. 4 in., 2 in.
7 25 5 19. } ft, } ft 20. 3, } 6 6 2
1
2
}
5 21. 2}, 21 2
1
}
2
}
22. (6, 22) 23. 2Ï 2 , 2Ï 10 , 4Ï 2 24. yes 25. 2 or 10 26. 3 or 21 27. Tower A
Chapter Test C
; domain: x ≥ 21; range: y ≥ 24; The graph is a 21 1 3 5 x vertical stretch, shift 1 21 unit to the left and 4 units down } from the graph of y 5 Ïx . y 2. ; domain: x ≥ 4; range: 6 y ≤ 2; The graph is a 2 reflection in the x-axis, a 22 2 6 10 x 22 vertical shrink, and a shift 4 units to the right and 2 26 units up from the graph of } y 5 Ïx . } 3. h ≥ 210; v ≥ 0 4. 22 cm 5. 9Ï 10
1.
y
1
6. 6a b
Ï 5x 2a 7. 22Ï2 8. } xy
}
2 5Ï
}
}
}
} 15 2 3Ï5 9. 15x 2 22yÏ x 1 8y 2 10. } 20
A28
Algebra 1 Assessment Book
(7, 4). It is 1 unit away and the distances to the other locations are greater than 1. 21. a. 32 ft; 24(16) 5 384 and 384 4 12 5 32 } b. 40 ft; Ï 242 1 322 5 40, c. 11 ft more Standardized Test B 1. C 2. D 3. A 4. B 5. B 6. A 7. C 8. D 9. D 10. B 11. A 12. C 13. B 14. C 15. A 16. D 17. A 18. C 19. 11 20. You would meet at the fountain. The midpoint between the two locations is the point (4, 3). The two locations closest to this point are the school and the library. You can use either the distance formula or your knowledge of right triangles to determine that the fountain is closest. 21. a. Twenty-four steps are needed. The height from floor to ceiling is 12 feet or 144 inches. If the riser of each step is 6 inches, you would need 24 steps to reach the second floor. b. 24 ft; Each step has a tread of 12 inches and there are 24 steps, so the linear distance would be 288 inches or 24 feet. c. A 322 inch rail is needed.
Standardized Test C 1. B 2. A 3. A 4. D 5. C 6. B 7. C 8. B 9. A 10. D 11. D 12. C 13. C 14. A 15. D 16. D 17. B 18. C 19. 21 20. Stadium; It is closest to the midpoint of }
(20.5, 1). It is Ï 4.25 , units away and the distances to the other locations are greater than that.
Copyright © Holt McDougal. All rights reserved.
}
Chapter 11, continued 21. a. 39 steps; 26 ft 5 312 in. and 312 4 8 5 39 b. 39 ft; Each step is one-foot long and there are 39 steps. c. 46.9 ft; 9.5 ft more
8.
; The domain and range are all nonzero real numbers.
y
1 23
x 1
21 21
1. D 2. B 3. C 4. E 5. D 6. B 7. B 8. B
ANSWERS
SAT/ACT Chapter Test
23
9. A 10. C 11. E 12. A 13. D 14. 9 15. 117 yd 16. 6
Performance Assessment 1. Complete answers should include: an
9. 3
Time (seconds)
explanation of each property of radicals; an example illustrating why there is no sum property of radicals; an example illustrating why there is no difference property of radicals. 2. a. ; Domain: 0 ≤ h ≤ 36 t
1 23
1
Quiz 2
1.0
1. x 2 3 2. x 1 9
0.5
3.
10
0 6 12 18 24 30 36 h Height (feet)
dropped it has a height of 0 feet; the object is at a height of 36 feet right before it is released. c. 36.03 units d. 32 ft e. 20 ft f. 1.06 sec g. Less time; The object is in the air for a total of 1.5 seconds, and it takes just over 1 second to fall the first 18 feet, which means it takes less than 0.5 second to fall the second 18 feet.
Chapter 12 1. direct variation 2. inverse variation
35 35 224 3. neither 4. y 5 }; } 5. y 5 }; 212 x 2 x 7 7 6. y 5 }; } x 2
; The domain and range are all nonzero real numbers.
y 6 2 2
10 6
2 22
y
2 2
10
x
210
2
26
26
6 x
26
33 5. x2 1 7x 2 4 6. x2 1 5x 1 4 1 } x+5 1 7. }; The excluded values are 21 and 1. x11 x23 8. }; The excluded value is 0. 2 12x3 9. }; The excluded value is 0. 5
Quiz 1
22 22
4.
y
6
b. (0, 1.5), (36, 0); 1.5 seconds after the object is
Copyright © Holt McDougal. All rights reserved.
21
1.5
0
7.
; The domain is all real numbers except x 5 21. The range is x all real numbers except y 5 0.
y
6
x
x25 10. }; The excluded values are 23 and 3. x23
Quiz 3 2(x 2 7) 7 4 1. } 2. } 3. } 4. 2x(x 2 5) 15x x x24 8x 1 7 2x 1 9 5. } 6. }} (x 1 8)(x 1 1) x26 7. 0 and 5 8. 0 and 2 9. 12 h
Chapter Test A 1. neither 2. direct variation
60 3. inverse variation 4. t 5 } n
5. 15 days
Algebra 1 Assessment Book
A29
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