Standardized Test Practice - Cumulative, Chapter 7
Read each question. Then fill in the correct answer on the answer document provided by your teacher or
on a sheet of paper.
1. What is the y-intercept of the exponential function below?
x
y =4 – 1
A0
B1
C2
D3
SOLUTION: Substitute 0 for x in the equation
.
The y-intercept of the function is 0. The correct choice is A.
2. Suppose there are only 3500 birds of a particular endangered species left on an island and the population decreases
at a rate of about 5% each year. The logarithmic function
predicts how many years t it will be for
the population to decease to a number p . About how long will it take for the population to reach 3000 birds?
F 2 years
G 3 years
H 5 years
J 8 years
SOLUTION: Substitute p = 3000 in the function
.
Use a calculator to find the value of t.
It will take about 3 years for the population to reach 3000 birds. So the correct choice is G.
3. Suppose a certain bacteria duplicates to reproduce itself every 20 minutes. If you begin with one cell of the bacteria,
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how many will there be after 2 hours?
A2
B6
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Use a calculator to find the value of t.
Standardized
Test Practice - Cumulative, Chapter 7
It will take about 3 years for the population to reach 3000 birds. So the correct choice is G.
3. Suppose a certain bacteria duplicates to reproduce itself every 20 minutes. If you begin with one cell of the bacteria,
how many will there be after 2 hours?
A2
B6
C 32
D 64
SOLUTION: Substitute 2.079 for k, 2 for k, 1 for a in the equation
.
There will be 64 bacteria after 2 hours. So the correct choice is D.
4. Lucas determined that the total cost C to rent a car could be represented by the equation C = 0.35m + 125, where m
is the number of miles that he drives. If the total cost to rent the car was $363, how many miles did he drive?
F 125
G 238
H 520
J 680
SOLUTION: Substitute 363 for C in the equation
and solve for m.
He drove 680 miles. So the correct choice is J.
5. Which of the following best describes the graph of 3y = 4x – 3 and 8y = –6x – 5?
A The
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y-intercept.
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B The lines have the same x-intercept.
C The lines are perpendicular.
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Standardized
Test Practice - Cumulative, Chapter 7
He drove 680 miles. So the correct choice is J.
5. Which of the following best describes the graph of 3y = 4x – 3 and 8y = –6x – 5?
A The lines have the same y-intercept.
B The lines have the same x-intercept.
C The lines are perpendicular.
D The lines are parallel.
SOLUTION: The slope of the line 3y = 4x – 3 is 4/3.
Find the slope of the line 8y = –6x – 5.
The slope of the line 8y = –6x – 5 is –3/4.
The product of the slopes of two lines is –1. Therefore, the lines are perpendicular. So the correct choice is C.
6. Graph y = log5 x.
F
G
H
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Standardized Test Practice - Cumulative, Chapter 7
H
J
SOLUTION: Convert the logarithmic equation to the exponential equation.
Find the x-intercept of the graph.
Substitute 0 for y to find the x-intercept of the graph.
Therefore, the x-intercept of the graph is 1.
The graph in the option H only intersects the x-axis at x = 1. So the correct choice is H.
7. Ray’s Book Store sells two used books for $7.99. The total cost c of purchasing n books can be found by –
A multiplying n by c.
B multiplying n by 5.
C multiplying n by the cost of 1 book.
D dividing n by c.
SOLUTION: multiplying n by the cost of 1 book
The correct choice is C.
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
8. The function
is graphed below. What is the domain of the function?
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D dividing n by c.
SOLUTION: multiplyingTest
n by Practice
the cost of- Cumulative,
1 book
Standardized
Chapter 7
The correct choice is C.
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
8. The function
is graphed below. What is the domain of the function?
SOLUTION: The function
is defined for all values of x. The domain of the function is all real numbers.
9. Suzanne bought a new car this year for $33,750. The value of the car is expected to decrease by 10.5% per year.
What will be the approximate value of the car 6 years after Suzanne purchased it? Show your work.
SOLUTION: After 6 years, the approximate value of the car would be about $17,347.
10. Julio is solving the system of equations 8x – 2y = 12 and –15x + 2y = –19 by using elimination. His work is shown
below.
The solution is (–1, –10).
a. What error does Julio make?
b. What is the correct solution of the system of equations? Show your work.
SOLUTION: a. He make a sign error when he combines the equations; 12 + (–19) = –7, not 7.
b.
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Standardized
Test Practice - Cumulative, Chapter 7
After 6 years, the approximate value of the car would be about $17,347.
10. Julio is solving the system of equations 8x – 2y = 12 and –15x + 2y = –19 by using elimination. His work is shown
below.
The solution is (–1, –10).
a. What error does Julio make?
b. What is the correct solution of the system of equations? Show your work.
SOLUTION: a. He make a sign error when he combines the equations; 12 + (–19) = –7, not 7.
b.
The solution is (1, –2).
2
11. GRIDDED RESPONSE If f (x) = 3x and g(x) = x – 1, what is the value of f (g(–3))?
SOLUTION: –2 –6
–1 8
12. Simplify (–2a b )(–3a b ).
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SOLUTION: Page 6
Standardized Test Practice - Cumulative, Chapter 7
–2 –6
–1 8
12. Simplify (–2a b )(–3a b ).
SOLUTION: 13. GRIDDED RESPONSE For what value of x would the rectangle below have an area of 48 square units?
SOLUTION: The length of the rectangle cannot be negative. So the value of x is 12.
Record your answers on a sheet of paper. Show your work.
14. Suppose the number of whitetail deer in a particular region has increased at an annual rate of about 10% since 1995.
There were 135,000 deer in 1995.
a. Write a function to model the number of whitetail deer after t years.
b. About how many whitetail deer inhabited the region in 2000? Round your answer to the nearest hundred deer.
SOLUTION: a.
Here, N is the number of deer and t is the number of years since 1995.
b. 2000 – 1995 = 5
Substitute 5 for t in the function
.
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Therefore,
217,400
deer
inhabited in the region in 2000.
15. Sandy inherited $250,000 from her aunt in 1992. She invested the money and increased it as shown in the table
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Standardized
Test Practice - Cumulative, Chapter 7
The length of the rectangle cannot be negative. So the value of x is 12.
Record your answers on a sheet of paper. Show your work.
14. Suppose the number of whitetail deer in a particular region has increased at an annual rate of about 10% since 1995.
There were 135,000 deer in 1995.
a. Write a function to model the number of whitetail deer after t years.
b. About how many whitetail deer inhabited the region in 2000? Round your answer to the nearest hundred deer.
SOLUTION: a.
Here, N is the number of deer and t is the number of years since 1995.
b. 2000 – 1995 = 5
Substitute 5 for t in the function
.
Therefore, about 217,400 deer inhabited in the region in 2000.
15. Sandy inherited $250,000 from her aunt in 1992. She invested the money and increased it as shown in the table
below.
a. Write an exponential function that could be used to predict the amount of money A after investing for t years.
b. If the money continues to grow at the same rate, in what year will it be worth $500,000?
SOLUTION: a.
b. Substitute $500,000 for A(t) in the function
.
Therefore,
invested
money
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will be worth $500,000 in the year 2012.
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Standardized
Cumulative,
7 in 2000.
Therefore, Test
aboutPractice
217,400 -deer
inhabited inChapter
the region
15. Sandy inherited $250,000 from her aunt in 1992. She invested the money and increased it as shown in the table
below.
a. Write an exponential function that could be used to predict the amount of money A after investing for t years.
b. If the money continues to grow at the same rate, in what year will it be worth $500,000?
SOLUTION: a.
b. Substitute $500,000 for A(t) in the function
.
Therefore, the invested money will be worth $500,000 in the year 2012.
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