Name ———————————————————————
CHAPTER
9
Date ————————————
Chapter Test A
For use after Chapter 9
Find the sum or difference.
Answers
1.
(4a 2 4a ) 1 (6a 1 5a )
3.
(3x 2 1 2x 2 2) 2 (5x 2 2 5x 1 6)
4.
(2h 2 7h 1 10) 1 (h 1 4h 1 7)
3
2
3
2
2
2.
(2y 2 4y) 2 (2y 1 2)
2
3
1.
2.
2
3.
In Exercises 5 and 6, use the following information.
4.
For 1990 through 2000, the number of fiction books F (in 10,000s) and
nonfiction books N (in 10,000s) borrowed from a library can be modeled by
F 5 0.01t2 1 0.09t 1 6
5.
6.
N 5 0.004t2 1 0.06t 1 4
7.
where t is the number of years since 1990.
5. Write an equation that gives the total number of books borrowed B
8.
from the library in a year from 1990 to 2000.
9.
6. What was the total number of books borrowed in 2000?
10.
Find the product.
9. (d 2 1 3d 1 2)(d 1 1)
11. (t 2 4)2
11.
8. (2w 2 3)(4w 2 7)
10. ( p 1 3)( p 2 3)
12.
12. (2s 2 5)(2s 1 5)
13.
14.
In humans, the gene B is for brown eyes, and the
gene b is for blue eyes. Any gene combination with
a B results in brown eyes. Suppose the parents have
the same gene combination Bb. The Punnett square
shows the possible gene combinations of the
offspring and the resulting eye color.
Father
In Exercises 13 and 14, use the following information.
Mother
B
b
15.
B
BB
Bb
16.
b
Bb
bb
13. What percent of the possible gene combinations of the offspring
result in blue eyes?
14. Show how you could use a polynomial to model the possible gene
combinations of the offspring.
Solve the equation.
15. (q 1 7)(q 2 4) 5 0
172
Algebra 1
Chapter 9 Assessment Book
16. (4z 2 1)(z 1 5) 5 0
Copyright © Holt McDougal. All rights reserved.
7. n(2n3 2 3n 1 2)
Name ———————————————————————
CHAPTER
9
Chapter Test A
Date ————————————
continued
For use after Chapter 9
Factor out the greatest common monomial factor.
Answers
17. 4c8 2 8c 5
17.
18. 6f 2g 3 1 12g
19. 2k 3 1 6k 2 2 14k
18.
Solve the equation.
20. 3m2 2 9m 5 0
21. 7u2 5 3u
19.
In Exercises 22 and 23, use the following information.
20.
A frog leaps from a lily pad in a pond into the air with an initial vertical
velocity of 20 feet per second. The height h (in feet) of the frog can be
modeled by h 5 216t 2 1 vt 1 s where t is the time (in seconds) the frog
has been in the air, v is the initial vertical velocity (in feet per second),
and s is the initial height.
21.
22.
23.
22. Write an equation that gives the height of the frog as a function of
the time (in seconds) since leaving the lily pad.
24.
23. After how many seconds does the frog land in the water?
25.
Factor the trinomial.
26.
24. x2 1 9x 1 14
25. y 2 2 y 2 12
26. 3m2 1 20m 1 12
27. Find the dimensions of the triangle that has an area of
27.
28.
30 square centimeters.
29.
(x 1 17) cm
Copyright © Holt McDougal. All rights reserved.
30.
Not drawn to scale
31.
x cm
Factor the polynomial completely.
32.
28. 3x 3 1 15x 2 1 18x
33.
29. 2s2 2 18
30. r(r 1 3) 1 7(r 1 3)
Solve the equation.
31. b4 2 3b3 2 10b2 5 0
32. j( j 1 3) 5 28
33. A small vegetable garden has an area
of 80 square feet. Its length is 2 feet
more than the width. Find the
dimensions of the garden.
x
x12
Algebra 1
Chapter 9 Assessment Book
173
Name ———————————————————————
CHAPTER
9
Date ————————————
Chapter Test B
For use after Chapter 9
Find the sum or difference.
Answers
1.
(4a3 2 2a 1 1) 2 (a3 2 2a 1 3)
1.
2.
(3x3 1 4x 1 14) 1 (24x2 1 21)
2.
3.
(3d 2 5d 3 1 2d 2) 2 (8d 3 1 6d 2 1)
3.
4. (23n 1 7n) 1 (4n3 2 2n2 1 12)
In Exercises 5 and 6, use the following information.
During the period 1985–2012, the projected enrollment B (in thousands of
students) in public schools and the projected enrollment R (in thousands of
students) in private schools can be modeled by
B 5 218.53t 2 1 975.8t 1 48,140
and
4.
5.
R 5 80.8t 1 8049
where t is the number of years since 1985.
6.
5. Write an equation that models the difference in the projected
enrollments for public schools and private schools as a function
of the number of years since 1985.
7.
8.
6. Find the difference in projected enrollments for public schools and
9.
private schools in 2005.
Find the product.
9.
(s2 1 6s 2 5)(5s 1 2)
11. (w 2 5)
2
8. ( y 1 4)(5y 2 3)
10. (4p 1 1)(4p 2 1)
10.
11.
2
12. (2b 1 3)
12.
In Exercises 13 and 14, use the following information.
13.
You are making an open box from a rectangular sheet of cardboard by
cutting squares 2 inches in length from each corner and folding up the
sides. The length of the sheet of cardboard is 8 inches more than the width.
2 in.
2 in.
13. Write a polynomial that represents the total volume of the open box.
14. Find the volume of the open box when the width of the sheet of
cardboard is 6 inches.
174
Algebra 1
Chapter 9 Assessment Book
14.
Copyright © Holt McDougal. All rights reserved.
7. 24c(29c 2 1 5c 1 8)
Name ———————————————————————
CHAPTER
9
Chapter Test B
Date ————————————
continued
For use after Chapter 9
Solve the equation.
Answers
15. (h 2 7)(2h 1 1) 5 0
15.
16. 4g 2 2 32g 5 0
16.
2
17. 3m 5 26m
17.
In Exercises 18 and 19, use the following information.
18.
The room and the hallway shown in the floor plan below have different
dimensions but the same area.
w11
Bedroom
Hall
19.
w
20.
21.
w22
3w
22.
18. Write an equation that relates the areas of the rooms.
23.
19. Find the value of w.
Factor the trinomial.
20. n2 2 14n 2 72
21. 2x 2 1 14x 2 45
22. 6k 2 2 k 2 12
24.
25.
Copyright © Holt McDougal. All rights reserved.
In Exercises 23 and 24, use the following information.
A juggler throws a ball from an initial height of 4 feet with an initial
vertical velocity of 30 feet per second. The height h (in feet) of the ball can
be modeled by h 5 216t 2 1 vt 1 s where t is the time (in seconds) the ball
has been in the air, v is the initial vertical velocity (in feet per second), and
s is the initial height.
23. Write an equation that gives the height (in feet) of the ball as a
function of the time (in seconds) since it left the juggler’s hand.
26.
27.
28.
29.
30.
24. If the juggler misses the ball, after how many seconds does it hit the
ground?
31.
Factor the polynomial completely.
25. x5 2 x 3
26. 5a(a 2 3) 2 7(a 2 3)
27. 9t 4 1 30t 3 1 25t 2
28. b 3 1 5b2 2 3b 2 15
32.
Solve the equation.
29. x 2 1 8x 1 15 5 0
30. 7y 2 2 5 5y 2
31. 72 5 32q2
32. u3 1 6u2 5 4u 1 24
Algebra 1
Chapter 9 Assessment Book
175
Name ———————————————————————
Date ————————————
Chapter Test C
CHAPTER
9
For use after Chapter 9
Find the sum or difference.
Answers
1.
(10p2 2 5p3 1 4 2 12p) 1 (8p3 2 4p2 1 5)
1.
2.
(24x 2y 2 5xy 2 y) 2 (25x 2y 1 6xy 1 3)
2.
3. (6cd 1 3c 1 9d) 1 (3cd 2 5d)
3.
In Exercises 4 and 5, use the following information.
During the period 1985–2012, the projected enrollment B (in thousands of
students) in public schools and the projected enrollment R (in thousands of
students) in private schools can be modeled by
B 5 218.53t 2 1 975.8t 1 48,140
and
4.
5.
R 5 80.8t 1 8049
where t is the number of years since 1985.
4. Write an equation that models the difference in the projected
enrollments for public schools and private schools as a function of
the number of years since 1985.
6.
7.
5. Describe the trend in the difference in projected enrollments for
public schools and private schools over time.
9.
1
8. (a 2 b)(5a 1 7b)
10. (7t 1 3u)(7t 2 3u)
2
7.
(3s 2 2 s 2 8)(4 2 s)
9. (5z 2 4)2
11.
1 3q 2 }12 21 3q 1 }12 2
10.
11.
12.
13.
In Exercises 12–14, use the following information.
You are making an open box from a rectangular sheet of cardboard by
cutting squares of equal length from each corner and folding up the sides.
The dimensions of the sheet of cardboard are 15 inches by 12 inches.
x in.
x in.
15 in.
12 in.
12. Write a polynomial that represents the total volume of the open box.
13. What is a reasonable domain for the function?
14. Find the volume of the open box when 2-inch squares are cut from
each corner.
176
Algebra 1
Chapter 9 Assessment Book
14.
Copyright © Holt McDougal. All rights reserved.
Find the product.
1
6. 6xy 2x2 2 3xy 1 } y 2
3
8.
Name ———————————————————————
CHAPTER
9
Chapter Test C
Date ————————————
continued
For use after Chapter 9
Find the zeros of the function.
15. f (x) 5 242x 2 2 14x
Answers
16. g(x) 5 210x 2 1 3x 1 27
17. The stopping distance of a car is modeled by the function
d 5 0.05r(r 1 2) where d is the stopping distance of the car
measured in feet and r is the speed of the car in miles per hour.
If skid marks left on the road are 48 feet long, how fast was the
car traveling?
Factor the trinomial.
16.
17.
18.
19.
18. x 2 2 14xy 2 51y 2
2
15.
20.
2
19. 4m 1 9mn 1 5n
21.
20. 2c3 2 7c 2d 1 3cd 2
22.
Find the dimension of the rectangle or triangle that has the
given area.
21. Area: 15 square meters
22. Area: 2.5 square centimeters
(2x 2 3) cm
23.
24.
25.
(2x 2 1) m
(2x 1 1) cm
(x 1 3) m
27.
Copyright © Holt McDougal. All rights reserved.
Factor the polynomial completely.
3
26.
28.
3
2
23. 36p 2 49p
24. 9y 1 30y 1 25y
25. uv 1 wx 2 wv 2 ux
26. 25a2 2 20ab3 1 4b6
27. 23c 2 1 75u2
28. x3 1 2x2 2 49x 2 98
29. A seagull flying over a lake drops a fish from a height of 81 feet.
29.
30.
31.
After how many seconds does the fish land in the water?
32.
Solve the equation.
30. 26w 3 5 2150w
31. x3 1 12 5 3x2 1 4x
33.
Write a polynomial equation with integral coefficients that has
the given roots.
32. 0, 22, and 1
2
33. 24 and }
3
Algebra 1
Chapter 9 Assessment Book
177
Chapter 9, continued
5. 4z2 1 z 2 18 6. p2 2 6p 2 7
4. 4n3 2 2n2 1 4n 1 12
7. 64m2 1 48m 1 9 8. 25y2 2 60y 1 36
5. D 5 218.53t 2 2 895t 1 40,091
9. w 2 1 4w
6. 14,779,000 students 7. 36c 3 2 20c 2 2 32c
1. 3x(4x 1 y) 2. 7ab(3b 1 5) 3. 9z2(1 2 2z)
4. 4p(1 2 2p) 5. (w 1 1)(w 1 14)
6. (m 2 10)(m 2 2) 7. (2k 2 1)(k 1 3)
8. (3b 1 1)(b 2 7) 9. (2y 1 5)(4y 1 3)
12. 4b2 1 12b 1 9
13. V 5 2(x 2 4)(x 1 4) 5 2x 2 2 32
1
14. 40 in.3 15. 2}, 7 16. 0, 8 17. 22, 0
2
1
10. 2(2d 1 5)(d 1 1) 11. 26, 4 12. 0, }
3
7
18. 3w(w 2 2) 5 w(w 1 1) 19. }
2
13. 3, 4 14. 22, 0 15. 2, 5 16. 23, 22
20. (n 2 18)(n 1 4) 21. 2(x 2 9)(x 2 5)
22. (3k 1 4)(2k 2 3) 23. h 5 216t 2 1 30t 1 4
Quiz 3
1. (x 1 9)(x 2 9) 2. (3z 1 11)(3z 2 11)
3. (10m 1 7n)(10m 2 7n) 4. (h 1 7)2
24. 2 sec 25. x 3(x 1 1)(x 2 1)
26. (a 2 3)(5a 2 7) 27. t 2(3t 1 5)2
10. 3(z 1 5)2 11. 2k(k 2 9)2
2
28. (b 2 5)(b2 2 3) 29. 25, 23 30. 1, }
5
3
31. 6} 32. 26, 62
2
12. (x 1 y)(x 1 2) 13. 25 14. 22, 2
Chapter Test C
5. (8t 2 1)2 6. 4(a2 1 b2) 7. 6(x 1 y)(x 2 y)
8. 5(m 1 2n)(m 2 2n) 9. x(x 2 5)(x 1 2)
15. 27, 0, 7 16. 0, 1, 5 17. 6 in. long by 2 in.
wide by 8 in. high
3
1. 10a 1 a
2
1. 3p3 1 6p2 2 12p 1 9 2. 9x2y 1 xy 2 y 1 3
3. 9cd 1 3c 1 4d
4. D 5 218.53t 2 2 895t 1 40,091
Chapter Test A
2
2. 3y 2 4y 2 2
2
3. 22x 1 7x 2 8 4. 3h2 2 3h 1 17
5. T 5 217.63t 2 1 3147.34t 1 29,544
Copyright © Holt McDougal. All rights reserved.
10. 16p2 2 1 11. w 2 2 10w 1 25
6. $47,254.40 7. 2n4 2 3n2 1 2n
8. 8w 2 2 26w 1 21 9. d 3 1 4d 2 1 5d 1 2
10. p2 2 9 11. t 2 2 8t 1 16 12. 4s2 2 25
2
2
13. 25% 14. 0.25B 1 0.5Bb 1 0.25b
1
4
15. 27, 4 16. 25, } 17. 4c 5(c 3 2 2)
18. 6f 2g 2(g 1 2) 19. 2k(k 2 1 6k 2 7) 20. 0, 3
3
21. 0, } 22. h 5 216t 2 1 20t 23. 1.25 seconds
7
5. The difference in the enrollments of public
schools and private schools is decreasing.
6. 12x 3y 2 18x 2y 2 1 2xy 3
7. 23s 3 1 13s 2 1 4s 2 32
8. 5a2 1 12ab 1 7b2 9. 25z 2 2 40z 1 16
1
10. 49t 2 2 9u2 11. 9q2 2 }
4
12. V 5 x(15 2 2x)(12 2 2x) 13. 0 ≤ x ≤ 6
3 9
1
14. 176 cubic inches 15. 0, 2} 16. 2}, }
3
2 5
17. 30 mi/h 18. (x 1 3y)(x 2 17y)
19. (4m 1 5n)(m 1 n) 20. c(2c 2 3d)(c 2 d)
24. (x 1 7)(x 1 2) 25. (y 2 4)( y 1 3)
21. 3 m by 5 m 22. 1 cm by 5 cm
26. (3m 1 2)(m 1 6) 27. 3 cm by 20 cm
23. p(6 2 7p)(6 1 7p) 24. y(3y 1 5)2
28. 3x(x 1 2)(x 1 3) 29. 2(s 1 3)(s 2 3)
25. (v 2 x)(u 2 w) 26. (5a 2 2b3)2
30. (r 1 7)(r 1 3) 31. 0, 22, 5 32. 27, 4
27. 23(5u 1 c)(5u 2 c)
33. 8 ft by 10 ft
1
28. (x 2 7)(x 1 7)(x 1 2) 29. 2 } sec
4
Chapter Test B
3
ANSWERS
8. 5y 2 1 17y 2 12 9. 5s3 1 32s2 2 13s 2 10
Quiz 2
30. 0, 65 31. 62, 3
3
2
1. 3a 2 2 2. 3x 2 4x 1 4x 1 35
32. Sample answer: x3 1 x2 2 2x 5 0
3. 213d 3 1 2d 2 2 3d 1 1
33. Sample answer: 3x2 1 10x 2 8 5 0
Algebra 1
Assessment Book
A23