Standardized Test Practice - Cumulative, Chapter 8
Read each question. Then fill in the correct answer on the answer document provided by your teacher or
on a sheet of paper.
1. Greg’s father can mow the lawn on his riding mower in 45 minutes. It takes Greg 1 hour 45 minutes to mow the
lawn with a push mower. Which of the following rational equations can be solved for the number of minutes t it
would take them to mow the lawn working together?
A
B
C
D
SOLUTION: The correct choice is C.
2. The total cost of reserving a campsite varies directly as the number of nights the site is rented, as shown in the table.
Which equation represents the direct variation?
F y = x + 24
G y = 24x
H
J y = 96x
SOLUTION: The equation y = 24x represents the direct variation. So, the correct choice is G.
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3. In which direction must the graph of
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be shifted to produce the graph of SOLUTION: Standardized
Practice
The correctTest
choice
is C. - Cumulative, Chapter 8
2. The total cost of reserving a campsite varies directly as the number of nights the site is rented, as shown in the table.
Which equation represents the direct variation?
F y = x + 24
G y = 24x
H
J y = 96x
SOLUTION: The equation y = 24x represents the direct variation. So, the correct choice is G.
3. In which direction must the graph of
be shifted to produce the graph of A up
B down
C right
D left
SOLUTION: The graph of
is shifted upwards by 2 units to product the graph of . So, the correct choice is A.
4. Which of the following is not an asymptote of the rational function
F f (x) = 0
G x = –7
H x Manual
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J f (x) = 1
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SOLUTION: The graph of
is shifted upwards by 2 units to product the graph of Standardized Test Practice - Cumulative, Chapter 8
. So, the correct choice is A.
4. Which of the following is not an asymptote of the rational function
F f (x) = 0
G x = –7
Hx=7
J f (x) = 1
SOLUTION: The vertical asymptotes of the rational function are at x = −7 and at x = 7.
The horizontal asymptote is at f (x) = 0. Thus, f (x) = 1 is not an asymptote of the rational function
.
The correct choice is J.
5. Simplify the complex fraction.
A
B
C
D
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The horizontal asymptote is at f (x) = 0. Thus, f (x) = 1 is not an asymptote of the rational function
.
The correctTest
choice
is J. - Cumulative, Chapter 8
Standardized
Practice
5. Simplify the complex fraction.
A
B
C
D
SOLUTION: The correct choice is C.
6. A ball was thrown upward with an initial velocity of 16 feet per second from the top of a building 128 feet high. Its
2
height h in feet above the ground t seconds later will be h = 128 + 16t – 16t .
Which is the best conclusion about the ball’s action?
F The ball stayed above 128 feet for more than 3 seconds.
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G The ball returned to the ground in less than 4 seconds.
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The correctTest
choice
is C. - Cumulative, Chapter 8
Standardized
Practice
6. A ball was thrown upward with an initial velocity of 16 feet per second from the top of a building 128 feet high. Its
2
height h in feet above the ground t seconds later will be h = 128 + 16t – 16t .
Which is the best conclusion about the ball’s action?
F The ball stayed above 128 feet for more than 3 seconds.
G The ball returned to the ground in less than 4 seconds.
H The ball traveled a greater distance going up than it did going down.
J The ball traveled less than 128 feet in 3.4 seconds.
SOLUTION: The ball returned to the ground in less than 4 seconds. The correct choice is G.
7. Which of these equations describes a relationship in which every negative real number x corresponds to a
nonnegative real number y?
A y = –x
By =x
C y = x2
Dy =x
3
SOLUTION: The correct choice is A.
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
8. Martha is putting a stone walkway around the garden pictured at the right. About how many feet of stone are
needed?
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SOLUTION: The correctTest
choice
is A. - Cumulative, Chapter 8
Standardized
Practice
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
8. Martha is putting a stone walkway around the garden pictured at the right. About how many feet of stone are
needed?
SOLUTION: Use the Pythagorean theorem to find x.
Therefore, about 56.8 feet of stone are needed to put a stone walkway.
9. GRIDDED RESPONSE Elaine had some money saved for a week-long vacation. The first day of the vacation she
spent $125 on food and a hotel. On the second day, she was given $80 from her sister for expenses. Elaine then had
$635 left for the rest of the vacation. How much money, in dollars, did she begin the vacation with?
SOLUTION: Let Elaine begin the vacation with x dollars.
Therefore, Elaine begin the vacation with $680.
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10. Carlos wants to print 800 one-page flyers for his landscaping business. He has a printer that is capable of printing 8
pages per minute. His business partner has another printer that prints 10 pages per minute.
Therefore, about 56.8 feet of stone are needed to put a stone walkway.
Standardized
Test Practice - Cumulative, Chapter 8
9. GRIDDED RESPONSE Elaine had some money saved for a week-long vacation. The first day of the vacation she
spent $125 on food and a hotel. On the second day, she was given $80 from her sister for expenses. Elaine then had
$635 left for the rest of the vacation. How much money, in dollars, did she begin the vacation with?
SOLUTION: Let Elaine begin the vacation with x dollars.
Therefore, Elaine begin the vacation with $680.
10. Carlos wants to print 800 one-page flyers for his landscaping business. He has a printer that is capable of printing 8
pages per minute. His business partner has another printer that prints 10 pages per minute.
a. How long would it take Carlos’ printer to print all the flyers? How long would it take his partner’s printer?
b. Set up a rational equation that can be used to find the number of minutes t it would take to print all 800 flyers if
both printers are used simultaneously.
c. Solve the equation you wrote in part b. How long would it take both printers to print all the flyers if they print
simultaneously? Round to the nearest minute.
SOLUTION: a.
For Carlos’, it would take 100 minutes to print all the flyers.
For Carlos’ business partner, it would take 80 minutes to print all the flyers.
b.
c.
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It would take about 44 minutes to print all the flyers if they print simultaneously.
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Therefore, Test
Elaine
begin the
vacation with Chapter
$680.
Standardized
Practice
- Cumulative,
8
10. Carlos wants to print 800 one-page flyers for his landscaping business. He has a printer that is capable of printing 8
pages per minute. His business partner has another printer that prints 10 pages per minute.
a. How long would it take Carlos’ printer to print all the flyers? How long would it take his partner’s printer?
b. Set up a rational equation that can be used to find the number of minutes t it would take to print all 800 flyers if
both printers are used simultaneously.
c. Solve the equation you wrote in part b. How long would it take both printers to print all the flyers if they print
simultaneously? Round to the nearest minute.
SOLUTION: a.
For Carlos’, it would take 100 minutes to print all the flyers.
For Carlos’ business partner, it would take 80 minutes to print all the flyers.
b.
c.
It would take about 44 minutes to print all the flyers if they print simultaneously.
0.02t
, where P is
11. GRIDDED RESPONSE The population of a country can be modeled by the equation P(t) = 40e
the population in millions and t is the number of years since 2005. When will the population be 400 million?
SOLUTION: Substitute 400 for P in the equation
.
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It would take
about
44 minutes
to print allChapter
the flyers8if they print simultaneously.
Standardized
Test
Practice
- Cumulative,
0.02t
, where P is
11. GRIDDED RESPONSE The population of a country can be modeled by the equation P(t) = 40e
the population in millions and t is the number of years since 2005. When will the population be 400 million?
SOLUTION: Substitute 400 for P in the equation
.
Therefore, the population will be 400 million in the year 2120.
12. What is the area of the shaded region of the rectangle expressed as a polynomial in simplest form?
SOLUTION: The width of the shaded region in terms of x is
.
The length of the shaded region in terms of x is
.
13. GRIDDED RESPONSE Suppose y varies inversely as x and y = 4 when x = 12. What is y when x is 5? Round to
the nearest tenth.
SOLUTION: eSolutions Manual - Powered by Cognero
Substitute x = 5 in the relation
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.
Standardized Test Practice - Cumulative, Chapter 8
13. GRIDDED RESPONSE Suppose y varies inversely as x and y = 4 when x = 12. What is y when x is 5? Round to
the nearest tenth.
SOLUTION: Substitute x = 5 in the relation
.
Record your answers on a sheet of paper. Show your work.
14. Use the graph of the rational function to answer each question.
a. Describe the vertical and horizontal asymptotes of the graph.
b. Write the equation of the rational function. Explain how you found your answer.
SOLUTION: a. Sample answer: vertical asymptotes at x = −4 and x = 4; horizontal asymptote at y = 0.
b.
15. Consider the polynomial function
4
3
2
f (x) = 3x + 19x + 7x – 11x – 2.
a. What is the degree of the function?
b. What is the leading coefficient of the function?
c. Evaluate f (1), f (–2), and f (2a). Show your work.
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SOLUTION: a.
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b.
Standardized
Test Practice - Cumulative, Chapter 8
15. Consider the polynomial function
4
3
2
f (x) = 3x + 19x + 7x – 11x – 2.
a. What is the degree of the function?
b. What is the leading coefficient of the function?
c. Evaluate f (1), f (–2), and f (2a). Show your work.
SOLUTION: a. The degree of the function is 4.
b. The leading coefficient of the function is 3.
c.
Therefore, f (1) = 16.
Therefore, f (−2) = −56.
Substitute 2a for x in f (x).
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