The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA II
Wednesday, August 16, 2017 — 12:30 to 3:30 p.m.
MODEL RESPONSE SET
Table of Contents
Question 25 . . . . . . . . . . . . . . . . . . . 2
Question 26 . . . . . . . . . . . . . . . . . . . 6
Question 27 . . . . . . . . . . . . . . . . . . 10
Question 28 . . . . . . . . . . . . . . . . . . 15
Question 29 . . . . . . . . . . . . . . . . . . 19
Question 30 . . . . . . . . . . . . . . . . . . 25
Question 31 . . . . . . . . . . . . . . . . . . 29
Question 32 . . . . . . . . . . . . . . . . . . 34
Question 33 . . . . . . . . . . . . . . . . . . 38
Question 34 . . . . . . . . . . . . . . . . . . 44
Question 35 . . . . . . . . . . . . . . . . . . 53
Question 36 . . . . . . . . . . . . . . . . . . 60
Question 37 . . . . . . . . . . . . . . . . . . 68
Question 25
25 Explain how can be evaluated using properties of rational exponents to result in an integer
answer.
()⫺8
4
3
Score 2: The student gave a complete and correct response.
Algebra II – August ’17 [2]
Question 25
25 Explain how can be evaluated using properties of rational exponents to result in an integer
answer.
()⫺8
4
3
Score 2: The student gave a complete and correct response.
Algebra II – August ’17 [3]
Question 25
25 Explain how can be evaluated using properties of rational exponents to result in an integer
answer.
()⫺8
4
3
Score 1: The student gave a correct justification, not an explanation.
Algebra II – August ’17 [4]
Question 25
25 Explain how can be evaluated using properties of rational exponents to result in an integer
answer.
()⫺8
4
3
Score 0: The student made multiple errors and did not provide an explanation.
Algebra II – August ’17 [5]
26 A study was designed to test the effectiveness of a new drug. Half of the volunteers received the
drug. The other half received a sugar pill. The probability of a volunteer receiving the drug and
getting well was 40%. What is the probability of a volunteer getting well, given that the volunteer
received the drug?
Algebra II – August ’17 [6]
Question 26
Score 2: The student gave a complete and correct response.
26 A study was designed to test the effectiveness of a new drug. Half of the volunteers received the
drug. The other half received a sugar pill. The probability of a volunteer receiving the drug and
getting well was 40%. What is the probability of a volunteer getting well, given that the volunteer
received the drug?
Algebra II – August ’17 [7]
Question 26
Score 2: The student gave a complete and correct response.
26 A study was designed to test the effectiveness of a new drug. Half of the volunteers received the
drug. The other half received a sugar pill. The probability of a volunteer receiving the drug and
getting well was 40%. What is the probability of a volunteer getting well, given that the volunteer
received the drug?
Algebra II – August ’17 [8]
Question 26
Score 1: The student gave a correct answer based on the drug column in the table, even though
there is no evidence to support the data in the sugar column.
Algebra II – August ’17 [9]
Question 26
Score 0: The student made an error confusing independence with conditional probability,
and substituted incorrectly for P(W), which is actually unknown.
26 A study was designed to test the effectiveness of a new drug. Half of the volunteers received the
drug. The other half received a sugar pill. The probability of a volunteer receiving the drug and
getting well was 40%. What is the probability of a volunteer getting well, given that the volunteer
received the drug?
Algebra II – August ’17 [10]
Question 27
Score 2: The student gave a complete and correct response.
27 Verify the following Pythagorean identity for all values of x and y:
(x
2
y
2
)
2
(x
2
y
2
)
2
(2xy)
2
Algebra II – August ’17 [11]
Question 27
Score 2: The student gave a complete and correct response.
27 Verify the following Pythagorean identity for all values of x and y:
(x
2
y
2
)
2
(x
2
y
2
)
2
(2xy)
2
Algebra II – August ’17 [12]
Question 27
Score 2: The student gave a complete and correct response given there are no domain restrictions
for addition and subtraction.
27 Verify the following Pythagorean identity for all values of x and y:
(x
2
y
2
)
2
(x
2
y
2
)
2
(2xy)
2
Algebra II – August ’17 [13]
Question 27
Score 1: The student made an error squaring 2xy.
27 Verify the following Pythagorean identity for all values of x and y:
(x
2
y
2
)
2
(x
2
y
2
)
2
(2xy)
2
Algebra II – August ’17 [14]
Question 27
Score 0: The student did not verify the identity for all values of x and y.
27 Verify the following Pythagorean identity for all values of x and y:
(x
2
y
2
)
2
(x
2
y
2
)
2
(2xy)
2
Algebra II – August ’17 [15]
Question 28
Score 2: The student gave a complete and correct response.
28 Mrs. Jones had hundreds of jelly beans in a bag that contained equal numbers of six different
flavors. Her student randomly selected four jelly beans and they were all black licorice. Her
student complained and said “What are the odds I got all of that kind?” Mrs. Jones replied,
“simulate rolling a die 250 times and tell me if four black licorice jelly beans is unusual.”
Explain how this simulation could be used to solve the problem.
Algebra II – August ’17 [16]
Question 28
Score 1: The student gave an incomplete explanation.
28 Mrs. Jones had hundreds of jelly beans in a bag that contained equal numbers of six different
flavors. Her student randomly selected four jelly beans and they were all black licorice. Her
student complained and said “What are the odds I got all of that kind?” Mrs. Jones replied,
“simulate rolling a die 250 times and tell me if four black licorice jelly beans is unusual.”
Explain how this simulation could be used to solve the problem.
Algebra II – August ’17 [17]
Question 28
Score 1: The student gave an incomplete explanation.
28 Mrs. Jones had hundreds of jelly beans in a bag that contained equal numbers of six different
flavors. Her student randomly selected four jelly beans and they were all black licorice. Her
student complained and said “What are the odds I got all of that kind?” Mrs. Jones replied,
“simulate rolling a die 250 times and tell me if four black licorice jelly beans is unusual.”
Explain how this simulation could be used to solve the problem.
Algebra II – August ’17 [18]
Question 28
Score 0: The student did not explain the simulation.
28 Mrs. Jones had hundreds of jelly beans in a bag that contained equal numbers of six different
flavors. Her student randomly selected four jelly beans and they were all black licorice. Her
student complained and said “What are the odds I got all of that kind?” Mrs. Jones replied,
“simulate rolling a die 250 times and tell me if four black licorice jelly beans is unusual.”
Explain how this simulation could be used to solve the problem.
Algebra II – August ’17 [19]
Question 29
Score 2: The student gave a complete and correct response.
29 While experimenting with her calculator, Candy creates the sequence 4, 9, 19, 39, 79, … .
Write a recursive formula for Candy’s sequence.
Determine the eighth term in Candy’s sequence.
Algebra II – August ’17 [20]
Question 29
Score 1: The student showed appropriate work to find 639.
29 While experimenting with her calculator, Candy creates the sequence 4, 9, 19, 39, 79, … .
Write a recursive formula for Candy’s sequence.
Determine the eighth term in Candy’s sequence.
Algebra II – August ’17 [21]
Question 29
Score 1: The student did not identify a
1
4.
29 While experimenting with her calculator, Candy creates the sequence 4, 9, 19, 39, 79, … .
Write a recursive formula for Candy’s sequence.
Determine the eighth term in Candy’s sequence.
Algebra II – August ’17 [22]
Question 29
Score 1: The student did not write a recursive formula.
29 While experimenting with her calculator, Candy creates the sequence 4, 9, 19, 39, 79, … .
Write a recursive formula for Candy’s sequence.
Determine the eighth term in Candy’s sequence.
Algebra II – August ’17 [23]
Question 29
Score 0: The student provided no correct work.
29 While experimenting with her calculator, Candy creates the sequence 4, 9, 19, 39, 79, … .
Write a recursive formula for Candy’s sequence.
Determine the eighth term in Candy’s sequence.
Algebra II – August ’17 [24]
Question 29
Score 0: The student did not provide a recursive formula and made a computational error.
29 While experimenting with her calculator, Candy creates the sequence 4, 9, 19, 39, 79, … .
Write a recursive formula for Candy’s sequence.
Determine the eighth term in Candy’s sequence.
Algebra II – August ’17 [25]
Question 30
Score 2: The student gave a complete and correct response.
30 In New York State, the minimum wage has grown exponentially. In 1966, the minimum wage was
$1.25 an hour and in 2015, it was $8.75. Algebraically determine the rate of growth to the
nearest percent.
Algebra II – August ’17 [26]
Question 30
Score 1: The student did not determine the rate of growth.
30 In New York State, the minimum wage has grown exponentially. In 1966, the minimum wage was
$1.25 an hour and in 2015, it was $8.75. Algebraically determine the rate of growth to the
nearest percent.
Algebra II – August ’17 [27]
Question 30
Score 1: The student made an error by subtracting 8.75 1.25.
30 In New York State, the minimum wage has grown exponentially. In 1966, the minimum wage was
$1.25 an hour and in 2015, it was $8.75. Algebraically determine the rate of growth to the
nearest percent.
Algebra II – August ’17 [28]
Question 30
Score 0: The student obtained a correct answer, but made multiple errors.
30 In New York State, the minimum wage has grown exponentially. In 1966, the minimum wage was
$1.25 an hour and in 2015, it was $8.75. Algebraically determine the rate of growth to the
nearest percent.
Algebra II – August ‘17 [29]
Question 31
Score 2: The student gave a complete and correct response.
31 Algebraically determine whether the function j(x) x
4
3x
2
4 is odd, even, or neither.
Algebra II – August ‘17 [30]
Question 31
Score 1: The student used a method other than algebraic.
31 Algebraically determine whether the function j(x) x
4
3x
2
4 is odd, even, or neither.
Algebra II – August ‘17 [31]
Question 31
Score 1: The student did not verify for all values of x.
31 Algebraically determine whether the function j(x) x
4
3x
2
4 is odd, even, or neither.
Algebra II – August ‘17 [32]
Question 31
Score 1: The student used a method other than algebraic.
31 Algebraically determine whether the function j(x) x
4
3x
2
4 is odd, even, or neither.
Algebra II – August ‘17 [33]
Question 31
Score 0: The student incorrectly justified an even function and used a method other than
algebraic.
31 Algebraically determine whether the function j(x) x
4
3x
2
4 is odd, even, or neither.
Algebra II – August ’17 [34]
Question 32
Score 2: The student gave a complete and correct response.
32 On the axes below, sketch a possible function p(x) (x a)(x b)(x c), where a, b, and c are
positive, a b, and p(x) has a positive y-intercept of d. Label all intercepts.
y
x
Algebra II – August ’17 [35]
Question 32
Score 1: The student did not label the intercept at –c.
32 On the axes below, sketch a possible function p(x) (x a)(x b)(x c), where a, b, and c are
positive, a b, and p(x) has a positive y-intercept of d. Label all intercepts.
Algebra II – August ’17 [36]
Question 32
Score 1: The student did not label the x-intercepts correctly.
32 On the axes below, sketch a possible function p(x) (x a)(x b)(x c), where a, b, and c are
positive, a b, and p(x) has a positive y-intercept of d. Label all intercepts.
y
x
Algebra II – August ’17 [37]
Question 32
Score 0: The student made multiple labeling errors.
32 On the axes below, sketch a possible function p(x) (x a)(x b)(x c), where a, b, and c are
positive, a b, and p(x) has a positive y-intercept of d. Label all intercepts.
Algebra II – August ’17 [38]
Question 33
33 Solve for all values of p:
3
2
33
p
pp
p
p
5
Score 4: The student gave a complete and correct response.
Algebra II – August ’17 [39]
Question 33
33 Solve for all values of p:
3
2
33
p
pp
p
p
5
Score 3: The student incorrectly rejected one of the solutions.
Algebra II – August ’17 [40]
33 Solve for all values of p:
3
2
33
p
pp
p
p
5
Score 2: The student made a transcription error in the first line of the solution and did not check
for extraneous solutions.
Question 33
Algebra II – August ’17 [41]
Question 33
33 Solve for all values of p:
3
2
33
p
pp
p
p
5
Score 2: The student wrote a correct quadratic equation in standard form.
Algebra II – August ’17 [42]
Question 33
33 Solve for all values of p:
3
2
33
p
pp
p
p
5
Score 1: The student wrote a correct quadratic expression.
Algebra II – August ’17 [43]
Question 33
33 Solve for all values of p:
3
2
33
p
pp
p
p
5
Score 0: The student did not show enough correct work to receive any credit.
Algebra II – August ’17 [44]
Question 34
Score 4: The student gave a complete and correct response.
34 Simon lost his library card and has an overdue library book. When the book was 5 days late, he
owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was
21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book.
Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book
is 60 days late.
Suppose the total amount Simon owes when the book is n days late can be determined by an
arithmetic sequence. Determine a formula for a
n
, the nth term of this sequence.
Algebra II – August ’17 [45]
Question 34
Score 4: The student gave a complete and correct response.
34 Simon lost his library card and has an overdue library book. When the book was 5 days late, he
owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was
21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book.
Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book
is 60 days late.
Suppose the total amount Simon owes when the book is n days late can be determined by an
arithmetic sequence. Determine a formula for a
n
, the nth term of this sequence.
Algebra II – August ’17 [46]
Question 34
Score 4: The student gave a complete and correct response.
34 Simon lost his library card and has an overdue library book. When the book was 5 days late, he
owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was
21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book.
Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book
is 60 days late.
Suppose the total amount Simon owes when the book is n days late can be determined by an
arithmetic sequence. Determine a formula for a
n
, the nth term of this sequence.
Algebra II – August ’17 [47]
Question 34
Score 3: The student wrote an expression for a
n
.
34 Simon lost his library card and has an overdue library book. When the book was 5 days late, he
owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was
21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book.
Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book
is 60 days late.
Suppose the total amount Simon owes when the book is n days late can be determined by an
arithmetic sequence. Determine a formula for a
n
, the nth term of this sequence.
Algebra II – August ’17 [48]
Question 34
Score 2: The student made a conceptual error writing the formula for a
n
by not adjusting the number
of common differences, but found an appropriate amount based on that error.
34 Simon lost his library card and has an overdue library book. When the book was 5 days late, he
owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was
21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book.
Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book
is 60 days late.
Suppose the total amount Simon owes when the book is n days late can be determined by an
arithmetic sequence. Determine a formula for a
n
, the nth term of this sequence.
Algebra II – August ’17 [49]
Question 34
Score 2: The student made a conceptual error writing the formula for a
n
by not adjusting the number
of common differences
, but found an appropriate amount based on that error.
34 Simon lost his library card and has an overdue library book. When the book was 5 days late, he
owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was
21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book.
Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book
is 60 days late.
Suppose the total amount Simon owes when the book is n days late can be determined by an
arithmetic sequence. Determine a formula for a
n
, the nth term of this sequence.
Algebra II – August ’17 [50]
Question 34
Score 1: The student correctly determined $16 without using a formula.
34 Simon lost his library card and has an overdue library book. When the book was 5 days late, he
owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was
21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book.
Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book
is 60 days late.
Suppose the total amount Simon owes when the book is n days late can be determined by an
arithmetic sequence. Determine a formula for a
n
, the nth term of this sequence.
Algebra II – August ’17 [51]
Question 34
Score 1: The student found the correct amount of money, but did not show any work.
34 Simon lost his library card and has an overdue library book. When the book was 5 days late, he
owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was
21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book.
Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book
is 60 days late.
Suppose the total amount Simon owes when the book is n days late can be determined by an
arithmetic sequence. Determine a formula for a
n
, the nth term of this sequence.
Algebra II – August ’17 [52]
Question 34
Score 0: The student did not show any correct work.
34 Simon lost his library card and has an overdue library book. When the book was 5 days late, he
owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was
21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book.
Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book
is 60 days late.
Suppose the total amount Simon owes when the book is n days late can be determined by an
arithmetic sequence. Determine a formula for a
n
, the nth term of this sequence.
Algebra II – August ’17 [53]
Question 35
35 a) On the axes below, sketch at least one cycle of a sine curve with an amplitude of 2, a midline
at , and a period of 2
π.
y
3
2
b) Explain any differences between a sketch of y 2 sin
()
and the sketch from
part a.
x
π
3
3
2
Score 4: The student gave a complete and correct response.
Algebra II – August ’17 [54]
Question 35
Score 3: The student did not label the sketch.
b) Explain any differences between a sketch of y 2 sin
()
and the sketch from
part a.
x
π
3
3
2
35 a) On the axes below, sketch at least one cycle of a sine curve with an amplitude of 2, a midline
at , and a period of 2
π.
y
3
2
Algebra II – August ’17 [55]
Question 35
Score 3: The student only received credit for the sketch.
35 a) On the axes below, sketch at least one cycle of a sine curve with an amplitude of 2, a midline
at , and a period of 2
π.
y
3
2
b) Explain any differences between a sketch of y 2 sin
()
and the sketch from
part a.
x
π
3
3
2
Algebra II – August ’17 [56]
Question 35
Score 2: The student made one graphing error with no explanation.
35 a) On the axes below, sketch at least one cycle of a sine curve with an amplitude of 2, a midline
at , and a period of 2
π.
y
3
2
b) Explain any differences between a sketch of y 2 sin
()
and the sketch from
part a.
x
π
3
3
2
Algebra II – August ’17 [57]
Question 35
Score 1: The student made two graphing errors with no explanation.
b) Explain any differences between a sketch of y 2 sin
()
and the sketch from
part a.
x
π
3
3
2
35 a) On the axes below, sketch at least one cycle of a sine curve with an amplitude of 2, a midline
at , and a period of 2
π.
y
3
2
Algebra II – August ’17 [58]
Question 35
Score 0: The student made several errors, and wrote an incorrect explanation.
b) Explain any differences between a sketch of y 2 sin
()
and the sketch from
part a.
x
π
3
3
2
35 a) On the axes below, sketch at least one cycle of a sine curve with an amplitude of 2, a midline
at , and a period of 2
π.
y
3
2
Algebra II – August ’17 [59]
Question 35
Score 0: The student gave a completely incorrect response.
b) Explain any differences between a sketch of y 2 sin
()
and the sketch from
part a.
x
π
3
3
2
35 a) On the axes below, sketch at least one cycle of a sine curve with an amplitude of 2, a midline
at , and a period of 2
π.
y
3
2
Algebra II – August ’17 [60]
Question 36
36 Using a microscope, a researcher observed and recorded the number of bacteria spores on a large
sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she
recorded is shown in the table below.
Using these data, write an exponential regression equation, rounding all values to the nearest
thousandth.
Hours (x)
Average Number
of Spores (y)
04
0.5 10
115
260
3 260
4 1130
6 16,380
Score 4: The student gave a complete and correct response.
The researcher knows that people are likely to suffer from food-borne illness if the number of
spores exceeds 100. Using the exponential regression equation, determine the maximum amount
of time, to the nearest quarter hour, that the meat can be kept at room temperature safely.
Algebra II – August ’17 [61]
Question 36
36 Using a microscope, a researcher observed and recorded the number of bacteria spores on a large
sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she
recorded is shown in the table below.
Using these data, write an exponential regression equation, rounding all values to the nearest
thousandth.
Hours (x)
Average Number
of Spores (y)
04
0.5 10
115
260
3 260
4 1130
6 16,380
Score 4: The student gave a complete and correct response.
The researcher knows that people are likely to suffer from food-borne illness if the number of
spores exceeds 100. Using the exponential regression equation, determine the maximum amount
of time, to the nearest quarter hour, that the meat can be kept at room temperature safely.
Algebra II – August ’17 [62]
Question 36
36 Using a microscope, a researcher observed and recorded the number of bacteria spores on a large
sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she
recorded is shown in the table below.
Using these data, write an exponential regression equation, rounding all values to the nearest
thousandth.
Hours (x)
Average Number
of Spores (y)
04
0.5 10
115
260
3 260
4 1130
6 16,380
Score 4: The student gave a complete and correct response.
The researcher knows that people are likely to suffer from food-borne illness if the number of
spores exceeds 100. Using the exponential regression equation, determine the maximum amount
of time, to the nearest quarter hour, that the meat can be kept at room temperature safely.
Algebra II – August ’17 [63]
Question 36
36 Using a microscope, a researcher observed and recorded the number of bacteria spores on a large
sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she
recorded is shown in the table below.
Using these data, write an exponential regression equation, rounding all values to the nearest
thousandth.
Hours (x)
Average Number
of Spores (y)
04
0.5 10
115
260
3 260
4 1130
6 16,380
Score 3: The student did not round to the nearest quarter hour.
The researcher knows that people are likely to suffer from food-borne illness if the number of
spores exceeds 100. Using the exponential regression equation, determine the maximum amount
of time, to the nearest quarter hour, that the meat can be kept at room temperature safely.
Algebra II – August ’17 [64]
Question 36
36 Using a microscope, a researcher observed and recorded the number of bacteria spores on a large
sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she
recorded is shown in the table below.
Using these data, write an exponential regression equation, rounding all values to the nearest
thousandth.
Hours (x)
Average Number
of Spores (y)
04
0.5 10
115
260
3 260
4 1130
6 16,380
Score 2: The student made an error rounding the coefficients and did not finish solving for x.
The researcher knows that people are likely to suffer from food-borne illness if the number of
spores exceeds 100. Using the exponential regression equation, determine the maximum amount
of time, to the nearest quarter hour, that the meat can be kept at room temperature safely.
Algebra II – August ’17 [65]
Question 36
36 Using a microscope, a researcher observed and recorded the number of bacteria spores on a large
sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she
recorded is shown in the table below.
Using these data, write an exponential regression equation, rounding all values to the nearest
thousandth.
Hours (x)
Average Number
of Spores (y)
04
0.5 10
115
260
3 260
4 1130
6 16,380
Score 2: The student made a computational error finding the regression equation and wrote 2.25
(based on their equation) without showing work.
The researcher knows that people are likely to suffer from food-borne illness if the number of
spores exceeds 100. Using the exponential regression equation, determine the maximum amount
of time, to the nearest quarter hour, that the meat can be kept at room temperature safely.
Algebra II – August ’17 [66]
Question 36
36 Using a microscope, a researcher observed and recorded the number of bacteria spores on a large
sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she
recorded is shown in the table below.
Using these data, write an exponential regression equation, rounding all values to the nearest
thousandth.
Hours (x)
Average Number
of Spores (y)
04
0.5 10
115
260
3 260
4 1130
6 16,380
Score 1: The student received credit for finding and correctly rounding the regression coefficients.
The researcher knows that people are likely to suffer from food-borne illness if the number of
spores exceeds 100. Using the exponential regression equation, determine the maximum amount
of time, to the nearest quarter hour, that the meat can be kept at room temperature safely.
Algebra II – August ’17 [67]
Question 36
36 Using a microscope, a researcher observed and recorded the number of bacteria spores on a large
sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she
recorded is shown in the table below.
Using these data, write an exponential regression equation, rounding all values to the nearest
thousandth.
Hours (x)
Average Number
of Spores (y)
04
0.5 10
115
260
3 260
4 1130
6 16,380
Score 0: The student showed no correct work.
The researcher knows that people are likely to suffer from food-borne illness if the number of
spores exceeds 100. Using the exponential regression equation, determine the maximum amount
of time, to the nearest quarter hour, that the meat can be kept at room temperature safely.
37 The value of a certain small passenger car based on its use in years is modeled by
V(t) 28482.698(0.684)
t
, where V(t) is the value in dollars and t is the time in years. Zach had
to take out a loan to purchase the small passenger car. The function Z(t) 22151.327(0.778)
t
,
where Z(t ) is measured in dollars, and t is the time in years, models the unpaid amount of Zach’s
loan over time.
Graph V(t) and Z(t) over the interval 0 t 5, on the set of axes below.
Algebra II – August ’17 [68]
Question 37
Score 6: The student gave a complete and correct response.
Algebra II – August ’17 [69]
Question 37
State where V(t) ⫽ Z(t), to the nearest hundredth, and interpret its meaning in the context of the
problem.
Zach takes out an insurance policy that requires him to pay a $3000 deductible in case of a
collision. Zach will cancel the collision policy when the value of his car equals his deductible.
To the nearest year, how long will it take Zach to cancel this policy? Justify your answer.
Algebra II – August ’17 [70]
Question 37
37 The value of a certain small passenger car based on its use in years is modeled by
V(t) 28482.698(0.684)
t
, where V(t) is the value in dollars and t is the time in years. Zach had
to take out a loan to purchase the small passenger car. The function Z(t) 22151.327(0.778)
t
,
where Z(t ) is measured in dollars, and t is the time in years, models the unpaid amount of Zach’s
loan over time.
Graph V(t) and Z(t) over the interval 0 t 5, on the set of axes below.
Score 5: The student wrote the answer to the second part as a coordinate pair.
Algebra II – August ’17 [71]
Question 37
State where V(t) ⫽ Z(t), to the nearest hundredth, and interpret its meaning in the context of the
problem.
Zach takes out an insurance policy that requires him to pay a $3000 deductible in case of a
collision. Zach will cancel the collision policy when the value of his car equals his deductible.
To the nearest year, how long will it take Zach to cancel this policy? Justify your answer.
Algebra II – August ’17 [72]
Question 37
37 The value of a certain small passenger car based on its use in years is modeled by
V(t) 28482.698(0.684)
t
, where V(t) is the value in dollars and t is the time in years. Zach had
to take out a loan to purchase the small passenger car. The function Z(t) 22151.327(0.778)
t
,
where Z(t ) is measured in dollars, and t is the time in years, models the unpaid amount of Zach’s
loan over time.
Graph V(t) and Z(t) over the interval 0 t 5, on the set of axes below.
Score 4: The student made one graphing error, then did not state where the graphs intersect.
Algebra II – August ’17 [73]
Question 37
State where V(t) ⫽ Z(t), to the nearest hundredth, and interpret its meaning in the context of the
problem.
Zach takes out an insurance policy that requires him to pay a $3000 deductible in case of a
collision. Zach will cancel the collision policy when the value of his car equals his deductible.
To the nearest year, how long will it take Zach to cancel this policy? Justify your answer.
Algebra II – August ’17 [74]
Question 37
37 The value of a certain small passenger car based on its use in years is modeled by
V(t) 28482.698(0.684)
t
, where V(t) is the value in dollars and t is the time in years. Zach had
to take out a loan to purchase the small passenger car. The function Z(t) 22151.327(0.778)
t
,
where Z(t ) is measured in dollars, and t is the time in years, models the unpaid amount of Zach’s
loan over time.
Graph V(t) and Z(t) over the interval 0 t 5, on the set of axes below.
Score 3: The student received credit for the graph and the contextual interpretation on the
second part.
Algebra II – August ’17 [75]
Question 37
State where V(t) ⫽ Z(t), to the nearest hundredth, and interpret its meaning in the context of the
problem.
Zach takes out an insurance policy that requires him to pay a $3000 deductible in case of a
collision. Zach will cancel the collision policy when the value of his car equals his deductible.
To the nearest year, how long will it take Zach to cancel this policy? Justify your answer.
Algebra II – August ’17 [76]
Question 37
37 The value of a certain small passenger car based on its use in years is modeled by
V(t) 28482.698(0.684)
t
, where V(t) is the value in dollars and t is the time in years. Zach had
to take out a loan to purchase the small passenger car. The function Z(t) 22151.327(0.778)
t
,
where Z(t ) is measured in dollars, and t is the time in years, models the unpaid amount of Zach’s
loan over time.
Graph V(t) and Z(t) over the interval 0 t 5, on the set of axes below.
Score 2: The student received credit for correctly drawing each graph.
Algebra II – August ’17 [77]
Question 37
State where V(t) ⫽ Z(t), to the nearest hundredth, and interpret its meaning in the context of the
problem.
Zach takes out an insurance policy that requires him to pay a $3000 deductible in case of a
collision. Zach will cancel the collision policy when the value of his car equals his deductible.
To the nearest year, how long will it take Zach to cancel this policy? Justify your answer.
Algebra II – August ’17 [78]
Question 37
37 The value of a certain small passenger car based on its use in years is modeled by
V(t) 28482.698(0.684)
t
, where V(t) is the value in dollars and t is the time in years. Zach had
to take out a loan to purchase the small passenger car. The function Z(t) 22151.327(0.778)
t
,
where Z(t ) is measured in dollars, and t is the time in years, models the unpaid amount of Zach’s
loan over time.
Graph V(t) and Z(t) over the interval 0 t 5, on the set of axes below.
Score 1: The student earned one point for the graph.
Algebra II – August ’17 [79]
Question 37
State where V(t) ⫽ Z(t), to the nearest hundredth, and interpret its meaning in the context of the
problem.
Zach takes out an insurance policy that requires him to pay a $3000 deductible in case of a
collision. Zach will cancel the collision policy when the value of his car equals his deductible.
To the nearest year, how long will it take Zach to cancel this policy? Justify your answer.
Algebra II – August ’17 [80]
Question 37
37 The value of a certain small passenger car based on its use in years is modeled by
V(t) 28482.698(0.684)
t
, where V(t) is the value in dollars and t is the time in years. Zach had
to take out a loan to purchase the small passenger car. The function Z(t) 22151.327(0.778)
t
,
where Z(t ) is measured in dollars, and t is the time in years, models the unpaid amount of Zach’s
loan over time.
Graph V(t) and Z(t) over the interval 0 t 5, on the set of axes below.
Score 0: The student made several graphing errors and showed no other correct work.
Algebra II – August ’17 [81]
Question 37
State where V(t) ⫽ Z(t), to the nearest hundredth, and interpret its meaning in the context of the
problem.
Zach takes out an insurance policy that requires him to pay a $3000 deductible in case of a
collision. Zach will cancel the collision policy when the value of his car equals his deductible.
To the nearest year, how long will it take Zach to cancel this policy? Justify your answer.
