The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA II
Thursday, August 16, 2018 — 12:30 to 3:30 p.m., only
MODEL RESPONSE SET
Table of Contents
Question 25 . . . . . . . . . . . . . . . . . . 2
Question 26 . . . . . . . . . . . . . . . . . . 7
Question 27. . . . . . . . . . . . . . . . . 12
Question 28. . . . . . . . . . . . . . . . . 16
Question 29. . . . . . . . . . . . . . . . . 21
Question 30. . . . . . . . . . . . . . . . . 26
Question 31. . . . . . . . . . . . . . . . . 30
Question 32. . . . . . . . . . . . . . . . . 35
Question 33. . . . . . . . . . . . . . . . . 41
Question 34. . . . . . . . . . . . . . . . . 46
Question 35. . . . . . . . . . . . . . . . . 54
Question 36. . . . . . . . . . . . . . . . . 60
Question 37 . . . . . . . . . . . . . . . . . 67
Algebra II – August ’18 [2]
Question 25
25 Over the set of integers, factor the expression x
4
⫺ 4x
2
⫺ 12.
Score 2: The student gave a complete and correct response.
Algebra II – August ’18 [3]
Question 25
25 Over the set of integers, factor the expression x
4
⫺ 4x
2
⫺ 12.
Score 2: The student gave a complete and correct response.
Algebra II – August ’18 [4]
Question 25
25 Over the set of integers, factor the expression x
4
⫺ 4x
2
⫺ 12.
Score 1: The student factored correctly, but then went on to solve an equation.
Algebra II – August ’18 [5]
Question 25
25 Over the set of integers, factor the expression x
4
⫺ 4x
2
⫺ 12.
Score 1: The student initially factored correctly, but showed incorrect work beyond the correct
answer.
Algebra II – August ’18 [6]
Question 25
25 Over the set of integers, factor the expression x
4
⫺ 4x
2
⫺ 12.
Score 0: The student did not do enough correct work to receive any credit.
Algebra II – August ’18 [7]
Question 26
26 Express the fraction in simplest radical form.
2
16
3
2
4
1
4
x
x
()
Score 2 The student gave a complete and correct response.
Algebra II – August ’18 [8]
Question 26
26 Express the fraction in simplest radical form.
2
16
3
2
4
1
4
x
x
()
Score 2: The student gave a complete and correct response.
Algebra II – August ’18 [9]
Question 26
26 Express the fraction in simplest radical form.
2
16
3
2
4
1
4
x
x
()
Score 1: The student did not simplify completely.
Algebra II – August ’18 [10]
Question 26
26 Express the fraction in simplest radical form.
2
16
3
2
4
1
4
x
x
()
Score 1: The student applied the exponent to 2x instead of x.
Algebra II – August ’18 [11]
Question 26
26 Express the fraction in simplest radical form.
2
16
3
2
4
1
4
x
x
()
Score 0: The student made multiple errors applying exponent rules.
Algebra II – August ’18 [12]
Question 27
27 The world population was 2560 million people in 1950 and 3040 million in 1960 and can be
modeled by the function p(t) ⫽ 2560e
0.017185t
, where t is time in years after 1950 and p(t) is the
population in millions. Determine the average rate of change of p(t) in millions of people per year,
from 4
≤
t
≤
8. Round your answer to the nearest hundredth.
Score 2: The student gave a complete and correct response.
Algebra II – August ’18 [13]
Question 27
27 The world population was 2560 million people in 1950 and 3040 million in 1960 and can be
modeled by the function p(t) ⫽ 2560e
0.017185t
, where t is time in years after 1950 and p(t) is the
population in millions. Determine the average rate of change of p(t) in millions of people per year,
from 4
≤
t
≤
8. Round your answer to the nearest hundredth.
Score 1: The student made a substitution error when finding the average rate of change.
Algebra II – August ’18 [14]
Question 27
27 The world population was 2560 million people in 1950 and 3040 million in 1960 and can be
modeled by the function p(t) ⫽ 2560e
0.017185t
, where t is time in years after 1950 and p(t) is the
population in millions. Determine the average rate of change of p(t) in millions of people per year,
from 4
≤
t
≤
8. Round your answer to the nearest hundredth.
Score 1: The student failed to divide by four before rounding.
Algebra II – August ’18 [15]
Question 27
27 The world population was 2560 million people in 1950 and 3040 million in 1960 and can be
modeled by the function p(t) ⫽ 2560e
0.017185t
, where t is time in years after 1950 and p(t) is the
population in millions. Determine the average rate of change of p(t) in millions of people per year,
from 4
≤
t
≤
8. Round your answer to the nearest hundredth.
Score 0: The student made an error evaluating p(8) and rounded incorrectly.
Algebra II – August ’18 [16]
Question 28
Score 2: The student gave a complete and correct response.
28 The scores of a recent test taken by 1200 students had an approximately normal distribution with
a mean of 225 and a standard deviation of 18. Determine the number of students who scored
between 200 and 245.
Algebra II – August ’18 [17]
Question 28
Score 2: The student gave a complete and correct response.
28 The scores of a recent test taken by 1200 students had an approximately normal distribution with
a mean of 225 and a standard deviation of 18. Determine the number of students who scored
between 200 and 245.
Algebra II – August ’18 [18]
Question 28
Score 1: The student failed to determine the number of students.
28 The scores of a recent test taken by 1200 students had an approximately normal distribution with
a mean of 225 and a standard deviation of 18. Determine the number of students who scored
between 200 and 245.
Algebra II – August ’18 [19]
Question 28
Score 1: The student did not show enough work to determine the number of students.
28 The scores of a recent test taken by 1200 students had an approximately normal distribution with
a mean of 225 and a standard deviation of 18. Determine the number of students who scored
between 200 and 245.
Algebra II – August ’18 [20]
Question 28
Score 0: The student did not show enough correct work to receive any credit.
28 The scores of a recent test taken by 1200 students had an approximately normal distribution with
a mean of 225 and a standard deviation of 18. Determine the number of students who scored
between 200 and 245.
Algebra II – August ’18 [21]
Question 29
Score 2: The student gave a complete and correct response.
29 Algebraically solve for x:
⫺
⫹
⫹⫽⫺
3
3
1
26
1
2x
x
Algebra II – August ’18 [22]
Question 29
Score 2: The student gave a complete and correct response.
29 Algebraically solve for x:
⫺
⫹
⫹⫽⫺
3
3
1
26
1
2x
x
Algebra II – August ’18 [23]
Question 29
Score 1: The student failed to properly distribute the three.
29 Algebraically solve for x:
⫺
⫹
⫹⫽⫺
3
3
1
26
1
2x
x
Algebra II – August ’18 [24]
Question 29
Score 1: The student lost a solution by dividing by x.
29 Algebraically solve for x:
⫺
⫹
⫹⫽⫺
3
3
1
26
1
2x
x
Algebra II – August ’18 [25]
Question 29
Score 0: The student did not show enough correct work to receive any credit.
29 Algebraically solve for x:
⫺
⫹
⫹⫽⫺
3
3
1
26
1
2x
x
Algebra II – August ’18 [26]
Question 30
Score 2: The student gave a complete and correct response.
t(x)
x
30 Graph t(x) ⫽ 3sin(2x) ⫹ 2 over the domain [0,2π] on the set of axes below.
Algebra II – August ’18 [27]
Question 30
Score 1: The student made a graphing error.
t(x)
x
30 Graph t(x) ⫽ 3sin(2x) ⫹ 2 over the domain [0,2π] on the set of axes below.
Algebra II – August ’18 [28]
Question 30
Score 0: The student made multiple graphing errors.
t(x)
x
30 Graph t(x) ⫽ 3sin(2x) ⫹ 2 over the domain [0,2π] on the set of axes below.
Algebra II – August ’18 [29]
Question 30
Score 0: The student made multiple graphing errors.
t(x)
x
30 Graph t(x) ⫽ 3sin(2x) ⫹ 2 over the domain [0,2π] on the set of axes below.
Algebra II – August ’18 [30]
Question 31
Score 2: The student gave a complete and correct response.
31 Solve the following system of equations algebraically.
x
2
⫹ y
2
⫽ 400
y ⫽ x ⫺ 28
Algebra II – August ’18 [31]
Question 31
Score 2: The student gave a complete and correct response.
31 Solve the following system of equations algebraically.
x
2
⫹ y
2
⫽ 400
y ⫽ x ⫺ 28
Algebra II – August ’18 [32]
Question 31
Score 1: The student failed to find the corresponding y-values.
31 Solve the following system of equations algebraically.
x
2
⫹ y
2
⫽ 400
y ⫽ x ⫺ 28
Algebra II – August ’18 [33]
Question 31
Score 1: The student correctly determined 2x
2
⫺ 56x ⫹ 384 ⫽ 0.
31 Solve the following system of equations algebraically.
x
2
⫹ y
2
⫽ 400
y ⫽ x ⫺ 28
Algebra II – August ’18 [34]
Question 31
Score 0: The student made a conceptual error and only found a value for x.
31 Solve the following system of equations algebraically.
x
2
⫹ y
2
⫽ 400
y ⫽ x ⫺ 28
Algebra II – August ’18 [35]
Question 32
Score 2: The student gave a complete and correct response.
32 Some smart-phone applications contain “in-app” purchases, which allow users to purchase special
content within the application. A random sample of 140 users found that 35 percent made in-app
purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the
samples make in-app purchases. The approximately normal results are shown below.
Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth,
for the simulated results. In the given context, explain what this value represents.
0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52
5
0
10
15
20
25
Mean = 0.350
SD = 0.042
Proportion of In-App Purchases
Algebra II – August ’18 [36]
Question 32
Score 1: The student did not refer to the given context.
32 Some smart-phone applications contain “in-app” purchases, which allow users to purchase special
content within the application. A random sample of 140 users found that 35 percent made in-app
purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the
samples make in-app purchases. The approximately normal results are shown below.
Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth,
for the simulated results. In the given context, explain what this value represents.
0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52
5
0
10
15
20
25
Mean = 0.350
SD = 0.042
Proportion of In-App Purchases
Algebra II – August ’18 [37]
Question 32
Score 1: The student did not provide an explanation.
32 Some smart-phone applications contain “in-app” purchases, which allow users to purchase special
content within the application. A random sample of 140 users found that 35 percent made in-app
purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the
samples make in-app purchases. The approximately normal results are shown below.
Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth,
for the simulated results. In the given context, explain what this value represents.
0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52
5
0
10
15
20
25
Mean = 0.350
SD = 0.042
Proportion of In-App Purchases
Algebra II – August ’18 [38]
Question 32
Score 1: The student stated an incorrect margin of error, but provided an appropriate
explanation.
32 Some smart-phone applications contain “in-app” purchases, which allow users to purchase special
content within the application. A random sample of 140 users found that 35 percent made in-app
purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the
samples make in-app purchases. The approximately normal results are shown below.
Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth,
for the simulated results. In the given context, explain what this value represents.
0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52
5
0
10
15
20
25
Mean = 0.350
SD = 0.042
Proportion of In-App Purchases
Algebra II – August ’18 [39]
Question 32
Score 0: The student made a rounding error stating the margin of error and gave an incorrect
explanation.
32 Some smart-phone applications contain “in-app” purchases, which allow users to purchase special
content within the application. A random sample of 140 users found that 35 percent made in-app
purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the
samples make in-app purchases. The approximately normal results are shown below.
Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth,
for the simulated results. In the given context, explain what this value represents.
0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52
5
0
10
15
20
25
Mean = 0.350
SD = 0.042
Proportion of In-App Purchases
Algebra II – August ’18 [40]
Question 32
Score 0: The student did not show enough correct work to get any credit.
32 Some smart-phone applications contain “in-app” purchases, which allow users to purchase special
content within the application. A random sample of 140 users found that 35 percent made in-app
purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the
samples make in-app purchases. The approximately normal results are shown below.
Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth,
for the simulated results. In the given context, explain what this value represents.
0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52
5
0
10
15
20
25
Mean = 0.350
SD = 0.042
Proportion of In-App Purchases
Algebra II – August ’18 [41]
Question 33
Score 4: The student gave a complete and correct response.
33 Solve the following system of equations algebraically for all values of x, y, and z.
2x ⫹ 3y ⫺ 4z ⫽⫺1
x ⫺ 2y ⫹ 5z ⫽ 3
⫺4x ⫹ y ⫹ z ⫽ 16
Algebra II – August ’18 [42]
Question 33
Score 3: The student made one computational error solving for x.
33 Solve the following system of equations algebraically for all values of x, y, and z.
2x ⫹ 3y ⫺ 4z ⫽⫺1
x ⫺ 2y ⫹ 5z ⫽ 3
⫺4x ⫹ y ⫹ z ⫽ 16
Algebra II – August ’18 [43]
Question 33
Score 2: The student made two or more computational errors.
33 Solve the following system of equations algebraically for all values of x, y, and z.
2x ⫹ 3y ⫺ 4z ⫽⫺1
x ⫺ 2y ⫹ 5z ⫽ 3
⫺4x ⫹ y ⫹ z ⫽ 16
Algebra II – August ’18 [44]
Question 33
Score 1: The student only made two equations eliminating the same variable.
33 Solve the following system of equations algebraically for all values of x, y, and z.
2x ⫹ 3y ⫺ 4z ⫽⫺1
x ⫺ 2y ⫹ 5z ⫽ 3
⫺4x ⫹ y ⫹ z ⫽ 16
Algebra II – August ’18 [45]
Question 33
Score 0: The student did not do enough correct work to receive a credit.
33 Solve the following system of equations algebraically for all values of x, y, and z.
2x ⫹ 3y ⫺ 4z ⫽⫺1
x ⫺ 2y ⫹ 5z ⫽ 3
⫺4x ⫹ y ⫹ z ⫽ 16
Algebra II – August ’18 [46]
Question 34
Score 4: The student gave a complete and correct response.
34 Evaluate j(⫺1) given j(x) ⫽ 2x
4
⫺ x
3
⫺35x
2
⫹ 16x ⫹ 48. Explain what your answer tells you about
x ⫹ 1 as a factor.
Algebraically find the remaining zeros of j(x).
Algebra II – August ’18 [47]
Question 34
Score 3: The student did not find the remaining zeros algebraically.
34 Evaluate j(⫺1) given j(x) ⫽ 2x
4
⫺ x
3
⫺35x
2
⫹ 16x ⫹ 48. Explain what your answer tells you about
x ⫹ 1 as a factor.
Algebraically find the remaining zeros of j(x).
Algebra II – August ’18 [48]
Question 34
Score 3: The student omitted one of the zeros.
34 Evaluate j(⫺1) given j(x) ⫽ 2x
4
⫺ x
3
⫺35x
2
⫹ 16x ⫹ 48. Explain what your answer tells you about
x ⫹ 1 as a factor.
Algebraically find the remaining zeros of j(x).
Algebra II – August ’18 [49]
Question 34
Score 2: The student did not evaluate j(⫺1) and made a transcription error writing the answers.
34 Evaluate j(⫺1) given j(x) ⫽ 2x
4
⫺ x
3
⫺35x
2
⫹ 16x ⫹ 48. Explain what your answer tells you about
x ⫹ 1 as a factor.
Algebraically find the remaining zeros of j(x).
Algebra II – August ’18 [50]
Question 34
Score 2: The student did not find the remaining zeros.
34 Evaluate j(⫺1) given j(x) ⫽ 2x
4
⫺ x
3
⫺35x
2
⫹ 16x ⫹ 48. Explain what your answer tells you about
x ⫹ 1 as a factor.
Algebraically find the remaining zeros of j(x).
Algebra II – August ’18 [51]
Question 34
Score 1: The student received one credit for an explanation based on a calculation error.
34 Evaluate j(⫺1) given j(x) ⫽ 2x
4
⫺ x
3
⫺35x
2
⫹ 16x ⫹ 48. Explain what your answer tells you about
x ⫹ 1 as a factor.
Algebraically find the remaining zeros of j(x).
Algebra II – August ’18 [52]
Question 34
Score 1: The student only received credit for evaluating j(⫺1) correctly.
34 Evaluate j(⫺1) given j(x) ⫽ 2x
4
⫺ x
3
⫺35x
2
⫹ 16x ⫹ 48. Explain what your answer tells you about
x ⫹ 1 as a factor.
Algebraically find the remaining zeros of j(x).
Algebra II – August ’18 [53]
Question 34
Score 0: The student used a graphical method and did not find the correct zeros.
34 Evaluate j(⫺1) given j(x) ⫽ 2x
4
⫺ x
3
⫺35x
2
⫹ 16x ⫹ 48. Explain what your answer tells you about
x ⫹ 1 as a factor.
Algebraically find the remaining zeros of j(x).
Algebra II – August ’18 [54]
Question 35
Score 4: The student gave a complete and correct response.
35 Determine, to the nearest tenth of a year, how long it would take an investment to double at a
3
3
__
4
% interest rate, compounded continuously.
Algebra II – August ’18 [55]
Question 35
Score 4: The student gave a complete and correct response.
35 Determine, to the nearest tenth of a year, how long it would take an investment to double at a
3
3
__
4
% interest rate, compounded continuously.
Algebra II – August ’18 [56]
Question 35
Score 3: The student made one rounding error.
35 Determine, to the nearest tenth of a year, how long it would take an investment to double at a
3
3
__
4
% interest rate, compounded continuously.
Algebra II – August ’18 [57]
Question 35
Score 2: The student wrote an incorrect equation, but showed appropriate work.
35 Determine, to the nearest tenth of a year, how long it would take an investment to double at a
3
3
__
4
% interest rate, compounded continuously.
Algebra II – August ’18 [58]
Question 35
Score 1: The student wrote an incorrect equation and provided insufficient work to determine
18.8.
35 Determine, to the nearest tenth of a year, how long it would take an investment to double at a
3
3
__
4
% interest rate, compounded continuously.
Algebra II – August ’18 [59]
Question 35
Score 0: The student did not do enough correct work to receive any credit.
35 Determine, to the nearest tenth of a year, how long it would take an investment to double at a
3
3
__
4
% interest rate, compounded continuously.
Algebra II – August ’18 [60]
Question 36
Score 4: The student gave a complete and correct response.
36 To determine if the type of music played while taking a quiz has a relationship to results,
16 students were randomly assigned to either a room softly playing classical music or a room softly
playing rap music. The results on the quiz were as follows:
Classical: 74, 83, 77, 77, 84, 82, 90, 89
Rap: 77, 80, 78, 74, 69, 72, 78, 69
John correctly rounded the difference of the means of his experimental groups as 7. How did John
obtain this value and what does it represent in the given context? Justify your answer.
To determine if there is any significance in this value, John rerandomized the 16 scores into two
groups of 8, calculated the difference of the means, and simulated this process 250 times as shown
below.
Does the simulation support the theory that there may be a significant difference in quiz scores?
Explain.
Classical vs. Rap
Difference of the Means
Frequency
⫺5 0⫺55
Algebra II – August ’18 [61]
Question 36
Score 3: The student provided insufficient evidence for a significant difference.
John correctly rounded the difference of the means of his experimental groups as 7. How did John
obtain this value and what does it represent in the given context? Justify your answer.
Does the simulation support the theory that there may be a significant difference in quiz scores?
Explain.
36 To determine if the type of music played while taking a quiz has a relationship to results,
16 students were randomly assigned to either a room softly playing classical music or a room softly
playing rap music. The results on the quiz were as follows:
Classical: 74, 83, 77, 77, 84, 82, 90, 89
Rap: 77, 80, 78, 74, 69, 72, 78, 69
To determine if there is any significance in this value, John rerandomized the 16 scores into two
groups of 8, calculated the difference of the means, and simulated this process 250 times as shown
below.
Classical vs. Rap
Difference of the Means
Frequency
⫺5 0⫺55
Algebra II – August ’18 [62]
Question 36
Score 2: The student only received credit for the first part.
36 To determine if the type of music played while taking a quiz has a relationship to results,
16 students were randomly assigned to either a room softly playing classical music or a room softly
playing rap music. The results on the quiz were as follows:
Classical: 74, 83, 77, 77, 84, 82, 90, 89
Rap: 77, 80, 78, 74, 69, 72, 78, 69
John correctly rounded the difference of the means of his experimental groups as 7. How did John
obtain this value and what does it represent in the given context? Justify your answer.
To determine if there is any significance in this value, John rerandomized the 16 scores into two
groups of 8, calculated the difference of the means, and simulated this process 250 times as shown
below.
Does the simulation support the theory that there may be a significant difference in quiz scores?
Explain.
Classical vs. Rap
Difference of the Means
Frequency
⫺5 0⫺55
Algebra II – August ’18 [63]
Question 36
Score 2: The student received partial credit for each part.
36 To determine if the type of music played while taking a quiz has a relationship to results,
16 students were randomly assigned to either a room softly playing classical music or a room softly
playing rap music. The results on the quiz were as follows:
Classical: 74, 83, 77, 77, 84, 82, 90, 89
Rap: 77, 80, 78, 74, 69, 72, 78, 69
John correctly rounded the difference of the means of his experimental groups as 7. How did John
obtain this value and what does it represent in the given context? Justify your answer.
To determine if there is any significance in this value, John rerandomized the 16 scores into two
groups of 8, calculated the difference of the means, and simulated this process 250 times as shown
below.
Does the simulation support the theory that there may be a significant difference in quiz scores?
Explain.
Classical vs. Rap
Difference of the Means
Frequency
⫺5 0⫺55
Algebra II – August ’18 [64]
Question 36
Score 1: The student received partial credit for the first part.
36 To determine if the type of music played while taking a quiz has a relationship to results,
16 students were randomly assigned to either a room softly playing classical music or a room softly
playing rap music. The results on the quiz were as follows:
Classical: 74, 83, 77, 77, 84, 82, 90, 89
Rap: 77, 80, 78, 74, 69, 72, 78, 69
John correctly rounded the difference of the means of his experimental groups as 7. How did John
obtain this value and what does it represent in the given context? Justify your answer.
To determine if there is any significance in this value, John rerandomized the 16 scores into two
groups of 8, calculated the difference of the means, and simulated this process 250 times as shown
below.
Does the simulation support the theory that there may be a significant difference in quiz scores?
Explain.
Classical vs. Rap
Difference of the Means
Frequency
⫺5 0⫺55
Algebra II – August ’18 [65]
Question 36
Score 1: The student received partial credit for the first part.
36 To determine if the type of music played while taking a quiz has a relationship to results,
16 students were randomly assigned to either a room softly playing classical music or a room softly
playing rap music. The results on the quiz were as follows:
Classical: 74, 83, 77, 77, 84, 82, 90, 89
Rap: 77, 80, 78, 74, 69, 72, 78, 69
John correctly rounded the difference of the means of his experimental groups as 7. How did John
obtain this value and what does it represent in the given context? Justify your answer.
To determine if there is any significance in this value, John rerandomized the 16 scores into two
groups of 8, calculated the difference of the means, and simulated this process 250 times as shown
below.
Does the simulation support the theory that there may be a significant difference in quiz scores?
Explain.
Classical vs. Rap
Difference of the Means
Frequency
⫺5 0⫺55
Algebra II – August ’18 [66]
Question 36
Score 0: The student did not show enough correct work to receive any credit.
To determine if there is any significance in this value, John rerandomized the 16 scores into two
groups of 8, calculated the difference of the means, and simulated this process 250 times as shown
below.
Does the simulation support the theory that there may be a significant difference in quiz scores?
Explain.
Classical vs. Rap
Difference of the Means
Frequency
⫺5 0⫺55
36 To determine if the type of music played while taking a quiz has a relationship to results,
16 students were randomly assigned to either a room softly playing classical music or a room softly
playing rap music. The results on the quiz were as follows:
Classical: 74, 83, 77, 77, 84, 82, 90, 89
Rap: 77, 80, 78, 74, 69, 72, 78, 69
John correctly rounded the difference of the means of his experimental groups as 7. How did John
obtain this value and what does it represent in the given context? Justify your answer.
Algebra II – August ’18 [67]
Question 37
37 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a
fifteen-year period. The company represents its revenue and costs as a function of time, in years, x,
using the given functions.
R(x) ⫽ 550x
3
⫺ 12,000x
2
⫹ 83,000x ⫹ 7000
C(x) ⫽ 880x
3
⫺ 21,000x
2
⫹ 150,000x ⫺ 160,000
The company’s profits can be represented as the difference between its revenue and costs.
Write the profit function, P(x), as a polynomial in standard form.
Score 6: The student gave a complete and correct response.
Algebra II – August ’18 [68]
Question 37 continued.
Graph y ⫽ P(x) on the set of axes below over the domain 2
≤
x
≤
16.
Over the given domain, state when the company was the least profitable and the most profitable,
to the nearest year. Explain how you determined your answer.
y
x
Algebra II – August ’18 [69]
Question 37
37 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a
fifteen-year period. The company represents its revenue and costs as a function of time, in years, x,
using the given functions.
R(x) ⫽ 550x
3
⫺ 12,000x
2
⫹ 83,000x ⫹ 7000
C(x) ⫽ 880x
3
⫺ 21,000x
2
⫹ 150,000x ⫺ 160,000
The company’s profits can be represented as the difference between its revenue and costs.
Write the profit function, P(x), as a polynomial in standard form.
Score 5: The student misunderstood the meaning of the independent variable.
Algebra II – August ’18 [70]
Question 37 continued.
Graph y ⫽ P(x) on the set of axes below over the domain 2
≤
x
≤
16.
Over the given domain, state when the company was the least profitable and the most profitable,
to the nearest year. Explain how you determined your answer.
y
x
Algebra II – August ’18 [71]
Question 37
37 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a
fifteen-year period. The company represents its revenue and costs as a function of time, in years, x,
using the given functions.
R(x) ⫽ 550x
3
⫺ 12,000x
2
⫹ 83,000x ⫹ 7000
C(x) ⫽ 880x
3
⫺ 21,000x
2
⫹ 150,000x ⫺ 160,000
The company’s profits can be represented as the difference between its revenue and costs.
Write the profit function, P(x), as a polynomial in standard form.
Score 5: The student made an error finding P(x).
Algebra II – August ’18 [72]
Question 37 continued.
Graph y ⫽ P(x) on the set of axes below over the domain 2
≤
x
≤
16.
Over the given domain, state when the company was the least profitable and the most profitable,
to the nearest year. Explain how you determined your answer.
y
x
Algebra II – August ’18 [73]
Question 37
37 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a
fifteen-year period. The company represents its revenue and costs as a function of time, in years, x,
using the given functions.
R(x) ⫽ 550x
3
⫺ 12,000x
2
⫹ 83,000x ⫹ 7000
C(x) ⫽ 880x
3
⫺ 21,000x
2
⫹ 150,000x ⫺ 160,000
The company’s profits can be represented as the difference between its revenue and costs.
Write the profit function, P(x), as a polynomial in standard form.
Score 4: The student received one credit each for P(x), the graph, 5, and 13.
Algebra II – August ’18 [74]
Question 37 continued.
Graph y ⫽ P(x) on the set of axes below over the domain 2
≤
x
≤
16.
Over the given domain, state when the company was the least profitable and the most profitable,
to the nearest year. Explain how you determined your answer.
y
x
Algebra II – August ’18 [75]
Question 37
37 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a
fifteen-year period. The company represents its revenue and costs as a function of time, in years, x,
using the given functions.
R(x) ⫽ 550x
3
⫺ 12,000x
2
⫹ 83,000x ⫹ 7000
C(x) ⫽ 880x
3
⫺ 21,000x
2
⫹ 150,000x ⫺ 160,000
The company’s profits can be represented as the difference between its revenue and costs.
Write the profit function, P(x), as a polynomial in standard form.
Score 3: The student received credit for finding P(x), 5, and 13.
Algebra II – August ’18 [76]
Question 37 continued.
Graph y ⫽ P(x) on the set of axes below over the domain 2
≤
x
≤
16.
Over the given domain, state when the company was the least profitable and the most profitable,
to the nearest year. Explain how you determined your answer.
y
x
Algebra II – August ’18 [77]
Question 37
37 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a
fifteen-year period. The company represents its revenue and costs as a function of time, in years, x,
using the given functions.
R(x) ⫽ 550x
3
⫺ 12,000x
2
⫹ 83,000x ⫹ 7000
C(x) ⫽ 880x
3
⫺ 21,000x
2
⫹ 150,000x ⫺ 160,000
The company’s profits can be represented as the difference between its revenue and costs.
Write the profit function, P(x), as a polynomial in standard form.
Score 2: The student received one credit for P(x) and only one credit for graphing P(x) outside
the domain.
Algebra II – August ’18 [78]
Question 37 continued.
Graph y ⫽ P(x) on the set of axes below over the domain 2
≤
x
≤
16.
Over the given domain, state when the company was the least profitable and the most profitable,
to the nearest year. Explain how you determined your answer.
y
x
Algebra II – August ’18 [79]
Question 37
37 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a
fifteen-year period. The company represents its revenue and costs as a function of time, in years, x,
using the given functions.
R(x) ⫽ 550x
3
⫺ 12,000x
2
⫹ 83,000x ⫹ 7000
C(x) ⫽ 880x
3
⫺ 21,000x
2
⫹ 150,000x ⫺ 160,000
The company’s profits can be represented as the difference between its revenue and costs.
Write the profit function, P(x), as a polynomial in standard form.
Score 1: The student only found P(x) correctly.
Algebra II – August ’18 [80]
Question 37 continued.
Graph y ⫽ P(x) on the set of axes below over the domain 2
≤
x
≤
16.
Over the given domain, state when the company was the least profitable and the most profitable,
to the nearest year. Explain how you determined your answer.
y
x
Algebra II – August ’18 [81]
Question 37
37 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a
fifteen-year period. The company represents its revenue and costs as a function of time, in years, x,
using the given functions.
R(x) ⫽ 550x
3
⫺ 12,000x
2
⫹ 83,000x ⫹ 7000
C(x) ⫽ 880x
3
⫺ 21,000x
2
⫹ 150,000x ⫺ 160,000
The company’s profits can be represented as the difference between its revenue and costs.
Write the profit function, P(x), as a polynomial in standard form.
Score 0: The student made a computational error finding P(x) and showed no further correct
work.
Algebra II – August ’18 [82]
Question 37 continued.
Graph y ⫽ P(x) on the set of axes below over the domain 2
≤
x
≤
16.
Over the given domain, state when the company was the least profitable and the most profitable,
to the nearest year. Explain how you determined your answer.
y
x
