ALGEBRA II

The Unversity of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

ALGEBRA II

Wednesday, June 21, 2023 — 9:15 a.m. to 12:15 p.m.,

MODEL RESPONSE SET

Table of Contents

Question 25 . . . . . . . . . . . . . . . . . . . 2

Question 26 . . . . . . . . . . . . . . . . . . . 8

Question 27 . . . . . . . . . . . . . . . . . . 15

Question 28 . . . . . . . . . . . . . . . . . . 20

Question 29 . . . . . . . . . . . . . . . . . . 25

Question 30 . . . . . . . . . . . . . . . . . . 30

Question 31 . . . . . . . . . . . . . . . . . . 36

Question 32 . . . . . . . . . . . . . . . . . . 42

Question 33 . . . . . . . . . . . . . . . . . . 48

Question 34 . . . . . . . . . . . . . . . . . . 57

Question 35 . . . . . . . . . . . . . . . . . . 67

Question 36 . . . . . . . . . . . . . . . . . . 76

Question 37 . . . . . . . . . . . . . . . . . . 83

Question 25

Algebra II – June ’23 [2]

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

Algebra II – June ’23 [10]

The business office of a local college wishes to determine the methods of payment that will be

used by students when buying books at the beginning of a semester. Explain how the office can

gather an appropriate sample that minimizes bias.

Score 2: The student gave a complete and correct response.

Question 25

Algebra II – June ’23 [3]

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

Algebra II – June ’23 [10]

The business office of a local college wishes to determine the methods of payment that will be

used by students when buying books at the beginning of a semester. Explain how the office can

gather an appropriate sample that minimizes bias.

Score 2: The student gave a complete and correct response.

Question 25

Algebra II – June ’23 [4]

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

Algebra II – June ’23 [10]

The business office of a local college wishes to determine the methods of payment that will be

used by students when buying books at the beginning of a semester. Explain how the office can

gather an appropriate sample that minimizes bias.

Score 1: The student did not survey an appropriate sample.

Question 25

Algebra II – June ’23 [5]

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

Algebra II – June ’23 [10]

The business office of a local college wishes to determine the methods of payment that will be

used by students when buying books at the beginning of a semester. Explain how the office can

gather an appropriate sample that minimizes bias.

Score 1: The student did not describe a random selection process.

Question 25

Algebra II – June ’23 [6]

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

Algebra II – June ’23 [10]

The business office of a local college wishes to determine the methods of payment that will be

used by students when buying books at the beginning of a semester. Explain how the office can

gather an appropriate sample that minimizes bias.

Score 0: The student did not show enough correct work to receive any credit.

Question 25

Algebra II – June ’23 [7]

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

Algebra II – June ’23 [10]

The business office of a local college wishes to determine the methods of payment that will be

used by students when buying books at the beginning of a semester. Explain how the office can

gather an appropriate sample that minimizes bias.

Score 0: The student did not show enough correct work to receive any credit.

Question 26

Algebra II – June ’23 [8]

Algebra II – June ’23 [11] [OVER]

26 Determine the solution of

5 x 2 1 algebraically.

Score 2: The student gave a complete and correct response.

Question 26

Algebra II – June ’23 [9]

Algebra II – June ’23 [11] [OVER]

26 Determine the solution of

5 x 2 1 algebraically.

Score 2: The student gave a complete and correct response.

Question 26

Algebra II – June ’23 [10]

Algebra II – June ’23 [11] [OVER]

26 Determine the solution of

5 x 2 1 algebraically.

Score 1: The student did not reject 21.

Question 26

Algebra II – June ’23 [11]

Algebra II – June ’23 [11] [OVER]

26 Determine the solution of

5 x 2 1 algebraically.

Score 1: The student incorrectly found the square root of 4.

Question 26

Algebra II – June ’23 [12]

Algebra II – June ’23 [11] [OVER]

26 Determine the solution of

5 x 2 1 algebraically.

Score 1: The student made an error nding x, but then rejected correctly.

Question 26

Algebra II – June ’23 [13]

Algebra II – June ’23 [11] [OVER]

26 Determine the solution of

5 x 2 1 algebraically.

Score 0: The student made a computational error and did not reject correctly.

Question 26

Algebra II – June ’23 [14]

Algebra II – June ’23 [11] [OVER]

26 Determine the solution of

5 x 2 1 algebraically.

Score 0: The student did not do enough correct work to receive any credit.

Question 27

Algebra II – June ’23 [15]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 2: The student gave a complete and correct response.

Question 27

Algebra II – June ’23 [16]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 2: The student gave a complete and correct response.

Question 27

Algebra II – June ’23 [17]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 1: The student gave an incomplete explanation.

Question 27

Algebra II – June ’23 [18]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 0: The student did not give enough of an explanation to receive any credit.

Question 27

Algebra II – June ’23 [19]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 0: The student stated decrease and wrote an incomplete explanation.

Question 28

Algebra II – June ’23 [20]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 2: The student gave a complete and correct response.

Question 28

Algebra II – June ’23 [21]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 1: The student used 23 for x.

Question 28

Algebra II – June ’23 [22]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 1: The student found the correct answer with no correct work.

Question 28

Algebra II – June ’23 [23]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 0: The student did not show enough correct work to receive any credit.

Question 28

Algebra II – June ’23 [24]

Algebra II – June ’23 [12]

27 The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function

P(t) 5 37e

0.0532t

. Determine whether the population is increasing or decreasing over time. Explain

your reasoning.

28 The polynomial function g(x) 5 x

1 ax

2 5x 1 6 has a factor of (x 2 3). Determine the

value of a.

Score 0: The student did not show any appropriate work.

Question 29

Algebra II – June ’23 [25]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 2: The student gave a complete and correct response.

Question 29

Algebra II – June ’23 [26]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 1: The student wrote an explicit formula.

Question 29

Algebra II – June ’23 [27]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 1: The student did not state a

Question 29

Algebra II – June ’23 [28]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 0: The student did not show enough correct work to receive any credit.

Question 29

Algebra II – June ’23 [29]

Score 0: The student wrote an incorrect explicit formula.

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Question 30

Algebra II – June ’23 [30]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 2: The student gave a complete and correct response.

Question 30

Algebra II – June ’23 [31]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 2: The student gave a complete and correct response.

Question 30

Algebra II – June ’23 [32]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 1: The student made a transcription error.

Question 30

Algebra II – June ’23 [33]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 1: The student multiplied by 2 instead of dividing by 2.

Question 30

Algebra II – June ’23 [34]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 0: The student did not show enough correct work to receive any credit.

Question 30

Algebra II – June ’23 [35]

Algebra II – June ’23 [13] [OVER]

29 Write a recursive formula for the sequence 189, 63, 21, 7, … .

30 Solve algebraically for x to the nearest thousandth:

0.49x

5 15

Score 0: The student did not show enough correct work to receive any credit.

Question 31

Algebra II – June ’23 [36]

Algebra II – June ’23 [14]

31 For all values of x for which the expression is defined, write the expression below in simplest form.

1 x

2 18x 2 9

3x 2 x

Score 2: The student gave a complete and correct response.

Question 31

Algebra II – June ’23 [37]

Algebra II – June ’23 [14]

31 For all values of x for which the expression is defined, write the expression below in simplest form.

1 x

2 18x 2 9

3x 2 x

Score 1: The student made a factoring error.

Question 31

Algebra II – June ’23 [38]

Algebra II – June ’23 [14]

31 For all values of x for which the expression is defined, write the expression below in simplest form.

1 x

2 18x 2 9

3x 2 x

Score 1: The student did not leave the answer in simplest form.

Question 31

Algebra II – June ’23 [39]

Algebra II – June ’23 [14]

31 For all values of x for which the expression is defined, write the expression below in simplest form.

1 x

2 18x 2 9

3x 2 x

Score 1: The student only factored the numerator correctly.

Question 31

Algebra II – June ’23 [40]

Algebra II – June ’23 [14]

31 For all values of x for which the expression is defined, write the expression below in simplest form.

1 x

2 18x 2 9

3x 2 x

Score 0: The student did not show enough correct work to receive any credit.

Question 31

Algebra II – June ’23 [41]

Algebra II – June ’23 [14]

31 For all values of x for which the expression is defined, write the expression below in simplest form.

1 x

2 18x 2 9

3x 2 x

Score 0: The student made multiple errors.

Question 32

Algebra II – June ’23 [42]

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Score 2: The student gave a complete and correct response.

Question 32

Algebra II – June ’23 [43]

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Score 2: The student gave a complete and correct response.

Question 32

Algebra II – June ’23 [44]

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Score 1: The student wrote an incomplete explanation.

Question 32

Algebra II – June ’23 [45]

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Score 1: The student gave an incomplete explanation.

Question 32

Algebra II – June ’23 [46]

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Score 0: The student did not show enough relevant course-level work to receive any credit.

Question 32

Algebra II – June ’23 [47]

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Algebra II – June ’23 [15] [OVER]

32 An app design company believes that the proportion of high school students who have purchased

apps on their smartphones in the past 3 months is 0.85. A simulation of 500 samples of 150 students

was run based on this proportion and the results are shown below.

Mean = 0.852

SD = 0.029

0.775 0.800 0.825 0.850

Proportion

0.875 0.900

Frequency

Suppose a sample of 150 students from your high school showed that 88% of students had

purchased apps on their smartphones in the past 3 months. Based on the simulation, would the

results from your high school give the app design company reason to believe their assumption is

incorrect? Explain.

Score 0: The student did not show enough relevant course-level work to receive any credit.

Question 33

Algebra II – June ’23 [48]

Algebra II – June ’23 [16]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

33 Patricia creates a cubic polynomial function, p(x

), with a leading coefficient of 1. The zeros of the

function are 2, 3, and 26. Write an equation for p(x).

Sketch y 5 p(x) on the set of axes below.

Score 4: The student gave a complete and correct response.

Question 33

Algebra II – June ’23 [49]

Algebra II – June ’23 [16]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

33 Patricia creates a cubic polynomial function, p(x

), with a leading coefficient of 1. The zeros of the

function are 2, 3, and 26. Write an equation for p(x).

Sketch y 5 p(x) on the set of axes below.

Score 4: The student gave a complete and correct response.

Question 33

Algebra II – June ’23 [50]

Algebra II – June ’23 [16]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

33 Patricia creates a cubic polynomial function, p(x

), with a leading coefficient of 1. The zeros of the

function are 2, 3, and 26. Write an equation for p(x).

Sketch y 5 p(x) on the set of axes below.

Score 3: The student incorrectly wrote one of the factors as x 2 6.

Question 33

Algebra II – June ’23 [51]

Algebra II – June ’23 [16]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

33 Patricia creates a cubic polynomial function, p(x

), with a leading coefficient of 1. The zeros of the

function are 2, 3, and 26. Write an equation for p(x).

Sketch y 5 p(x) on the set of axes below.

Score 3: The student wrote an expression, not an equation for p(x). The student drew an acceptable

sketch through the zeros with appropriate end behavior.

Question 33

Algebra II – June ’23 [52]

Algebra II – June ’23 [16]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

33 Patricia creates a cubic polynomial function, p(x

), with a leading coefficient of 1. The zeros of the

function are 2, 3, and 26. Write an equation for p(x).

Sketch y 5 p(x) on the set of axes below.

Score 2: The student only received credit for the equation.

Question 33

Algebra II – June ’23 [53]

Algebra II – June ’23 [16]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

33 Patricia creates a cubic polynomial function, p(x

), with a leading coefficient of 1. The zeros of the

function are 2, 3, and 26. Write an equation for p(x).

Sketch y 5 p(x) on the set of axes below.

Score 2: The student did not write an equation for p(x) and made one graphing error.

Question 33

Algebra II – June ’23 [54]

Algebra II – June ’23 [16]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

33 Patricia creates a cubic polynomial function, p(x

), with a leading coefficient of 1. The zeros of the

function are 2, 3, and 26. Write an equation for p(x).

Sketch y 5 p(x) on the set of axes below.

Score 1: The student received one credit for the sketch.

Question 33

Algebra II – June ’23 [55]

Algebra II – June ’23 [16]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

33 Patricia creates a cubic polynomial function, p(x

), with a leading coefficient of 1. The zeros of the

function are 2, 3, and 26. Write an equation for p(x).

Sketch y 5 p(x) on the set of axes below.

Score 1: The student received one credit for the sketch.

Question 33

Algebra II – June ’23 [56]

Algebra II – June ’23 [16]

Part III

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. Utilize the information provided for each question to determine your answer.

Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct

numerical answer with no work shown will receive only 1 credit. All answers should be

written in pen, except for graphs and drawings, which should be done in pencil. [

16]

33 Patricia creates a cubic polynomial function, p(x

), with a leading coefficient of 1. The zeros of the

function are 2, 3, and 26. Write an equation for p(x).

Sketch y 5 p(x) on the set of axes below.

Score 0: The student did not show enough relevant course-level work to receive any credit.

Question 34

Algebra II – June ’23 [57]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 4: The student gave a complete and correct response.

Question 34

Algebra II – June ’23 [58]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 4: The student gave a complete and correct response.

Question 34

Algebra II – June ’23 [59]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 3: The student did not round the conditional probability.

Question 34

Algebra II – June ’23 [60]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 3: The student did not indicate a positive response to indicate independence.

Question 34

Algebra II – June ’23 [61]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 2: The student received no credit for the conditional probability.

Question 34

Algebra II – June ’23 [62]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 2: The student received no credit for determining independence.

Question 34

Algebra II – June ’23 [63]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 2: The student made an error in the numerator of the conditional probability and an error

calculating independence.

Question 34

Algebra II – June ’23 [64]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 1: The student received one credit for the exact conditional probability, but showed no

further correct work.

Question 34

Algebra II – June ’23 [65]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 1: The student found the conditional probability of the reversed conditions but showed no

further correct work.

Question 34

Algebra II – June ’23 [66]

Algebra II – June ’23 [17] [OVER]

34 A public radio station held a fund-raiser. The table below summarizes the donor category and

method of donation.

Donor Category

Supporter Patron

Method of

Donation

Phone calls 400 672

Online 1200 2016

To the nearest thousandth, find the probability that a randomly selected donor was categorized as

a supporter, given that the donation was made online.

Do these data indicate that being a supporter is independent of donating online? Justify your

answer.

Score 0: The student did not nd a conditional probability and did not show enough relevant

course-level work to receive any credit.

Question 35

Algebra II – June ’23 [67]

Algebra II – June ’23 [18]

35 Algebraically solve the system:

(x 2 2)

1 (y 2 3)

5 20

y 5 22x 1 7

Score 4: The student gave a complete and correct response.

Question 35

Algebra II – June ’23 [68]

Algebra II – June ’23 [18]

35 Algebraically solve the system:

(x 2 2)

1 (y 2 3)

5 20

y 5 22x 1 7

Score 4: The student gave a complete and correct response.

Question 35

Algebra II – June ’23 [69]

Algebra II – June ’23 [18]

35 Algebraically solve the system:

(x 2 2)

1 (y 2 3)

5 20

y 5 22x 1 7

Score 3: The student found only one solution.

Question 35

Algebra II – June ’23 [70]

Algebra II – June ’23 [18]

35 Algebraically solve the system:

(x 2 2)

1 (y 2 3)

5 20

y 5 22x 1 7

Score 3: The student received credit for both x-values.

Question 35

Algebra II – June ’23 [71]

Algebra II – June ’23 [18]

35 Algebraically solve the system:

(x 2 2)

1 (y 2 3)

5 20

y 5 22x 1 7

Score 2: The student wrote a correct quadratic in standard form.

Question 35

Algebra II – June ’23 [72]

Algebra II – June ’23 [18]

35 Algebraically solve the system:

(x 2 2)

1 (y 2 3)

5 20

y 5 22x 1 7

Score 2: The student solved correctly but used a method other than algebraic.

Question 35

Algebra II – June ’23 [73]

Algebra II – June ’23 [18]

35 Algebraically solve the system:

(x 2 2)

1 (y 2 3)

5 20

y 5 22x 1 7

Score 1: The student made one computational error when attempting to put the equation in

standard form, but showed no further correct work.

Question 35

Algebra II – June ’23 [74]

Algebra II – June ’23 [18]

35 Algebraically solve the system:

(x 2 2)

1 (y 2 3)

5 20

y 5 22x 1 7

Score 0: The student did not show enough correct course-level work to receive any credit.

Question 35

Algebra II – June ’23 [75]

Algebra II – June ’23 [18]

35 Algebraically solve the system:

(x 2 2)

1 (y 2 3)

5 20

y 5 22x 1 7

Score 0: The student did not show enough course-level work to receive any credit.

Question 36

Algebra II – June ’23 [76]

Algebra II – June ’23 [19] [OVER]

36 On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose the

palm tree population is decreasing at an annual rate of 3% per year and the flamingo population

is growing at a continuous rate of 2% per year.

Write two functions, P(x) and F(x), that represent the number of palm trees and flamingos on this

island, respectively, x years from now.

State the solution to the equation P(x) 5 F(x), rounded to the nearest year. Interpret the meaning

of this value within the given context.

Score 4: The student gave a complete and correct response.

Question 36

Algebra II – June ’23 [77]

Algebra II – June ’23 [19] [OVER]

36 On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose the

palm tree population is decreasing at an annual rate of 3% per year and the flamingo population

is growing at a continuous rate of 2% per year.

Write two functions, P(x) and F(x), that represent the number of palm trees and flamingos on this

island, respectively, x years from now.

State the solution to the equation P(x) 5 F(x), rounded to the nearest year. Interpret the meaning

of this value within the given context.

Score 4: The student gave a complete and correct response.

Question 36

Algebra II – June ’23 [78]

Algebra II – June ’23 [19] [OVER]

36 On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose the

palm tree population is decreasing at an annual rate of 3% per year and the flamingo population

is growing at a continuous rate of 2% per year.

Write two functions, P(x) and F(x), that represent the number of palm trees and flamingos on this

island, respectively, x years from now.

State the solution to the equation P(x) 5 F(x), rounded to the nearest year. Interpret the meaning

of this value within the given context.

Score 3: The student created an incorrect equation for F(x).

Question 36

Algebra II – June ’23 [79]

Score 3: The student did not interpret the meaning of 18 years.

Algebra II – June ’23 [19] [OVER]

36 On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose the

palm tree population is decreasing at an annual rate of 3% per year and the flamingo population

is growing at a continuous rate of 2% per year.

Write two functions, P(x) and F(x), that represent the number of palm trees and flamingos on this

island, respectively, x years from now.

State the solution to the equation P(x) 5 F(x), rounded to the nearest year. Interpret the meaning

of this value within the given context.

Question 36

Algebra II – June ’23 [80]

Algebra II – June ’23 [19] [OVER]

36 On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose the

palm tree population is decreasing at an annual rate of 3% per year and the flamingo population

is growing at a continuous rate of 2% per year.

Write two functions, P(x) and F(x), that represent the number of palm trees and flamingos on this

island, respectively, x years from now.

State the solution to the equation P(x) 5 F(x), rounded to the nearest year. Interpret the meaning

of this value within the given context.

Score 2: The student wrote an incorrect equation for P(x) and rounded the solution to P(x) 5 F(x)

incorrectly.

Question 36

Algebra II – June ’23 [81]

Algebra II – June ’23 [19] [OVER]

36 On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose the

palm tree population is decreasing at an annual rate of 3% per year and the flamingo population

is growing at a continuous rate of 2% per year.

Write two functions, P(x) and F(x), that represent the number of palm trees and flamingos on this

island, respectively, x years from now.

State the solution to the equation P(x) 5 F(x), rounded to the nearest year. Interpret the meaning

of this value within the given context.

Score 1: The student received one credit for correctly writing P(x).

Question 36

Algebra II – June ’23 [82]

Algebra II – June ’23 [19] [OVER]

36 On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose the

palm tree population is decreasing at an annual rate of 3% per year and the flamingo population

is growing at a continuous rate of 2% per year.

Write two functions, P(x) and F(x), that represent the number of palm trees and flamingos on this

island, respectively, x years from now.

State the solution to the equation P(x) 5 F(x), rounded to the nearest year. Interpret the meaning

of this value within the given context.

Score 0: The student did not show enough correct work to receive any credit.

Question 37

Algebra II – June ’23 [83]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 6: The student gave a complete and correct response.

Question 37

Algebra II – June ’23 [84]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [85]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 6: The student gave a complete and correct response.

Question 37

Algebra II – June ’23 [86]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [87]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 5: The student incorrectly found the value for B.

Question 37

Algebra II – June ’23 [88]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [89]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 5: The student did not nd all the intersections within the 5 second interval.

Question 37

Algebra II – June ’23 [90]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [91]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 5: The student made a notation error.

Question 37

Algebra II – June ’23 [92]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [93]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 4: The student did not nd the correct value for B and did not graph the correct period.

Question 37

Algebra II – June ’23 [94]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [95]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 4: The student did not write an equation and did not graph the correct period for E(t).

Question 37

Algebra II – June ’23 [96]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [97]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 3: The student did not nd the correct value for B, and made two graphing errors.

Question 37

Algebra II – June ’23 [98]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [99]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 3: The student did not graph the correct amplitude or period and made a notation error.

Question 37

Algebra II – June ’23 [100]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [101]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 3: The student did not nd the correct values of B and C for N(t) and did not graph the

correct midline for E(t).

Question 37

Algebra II – June ’23 [102]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [103]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 2: The student earned one point for the N(t) equation and one point for the number of

intersections.

Question 37

Algebra II – June ’23 [104]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [105]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 1: The student found the correct number of intersections based on their graph.

Question 37

Algebra II – June ’23 [106]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [107]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 1: The student found the correct number of intersections based on their graph.

Question 37

Algebra II – June ’23 [108]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued

Question 37

Algebra II – June ’23 [109]

Algebra II – June ’23 [20]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

Utilize the information provided to determine your answer. Note that diagrams are not

necessarily drawn to scale. A correct numerical answer with no work shown will receive

only 1 credit. The answer should be written in pen. [

Algebra II – June ’23 [20] [OVER]

37 The volume of air in an average lung during breathing can be modeled by the graph below.

0 1 2 3 4 5

1000

2000

N(t)

3000

4000

5000

6000

Seconds

Volume (mL)

Using the graph, write an equation for N(t), in the form N(t) 5 A sin (Bt) 1 C.

Question 37 is continued on the next page.

Score 0: The student did not show enough correct work to receive any credit.

Question 37

Algebra II – June ’23 [110]

Algebra II – June ’23 [21]

That same lung, when engaged in exercise, has a volume that can be modeled by

E(t) 5 2000 sin(pt) 1 3200, where E(t) is volume in mL and t is time in seconds.

Graph at least one cycle of E(t) on the same grid as N(t).

How many times during the 5-second interval will N(t) 5 E(t)?

Question 37 continued