The Unversity of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA I
Wednesday, January 25, 2023 — 1:15 to 4:15 p.m.,
MODEL RESPONSE SET
Table of Contents
Question 25 . . . . . . . . . . . . . . . . . . . 2
Question 26 . . . . . . . . . . . . . . . . . . . 6
Question 27 . . . . . . . . . . . . . . . . . . 10
Question 28 . . . . . . . . . . . . . . . . . . 16
Question 29 . . . . . . . . . . . . . . . . . . 20
Question 30 . . . . . . . . . . . . . . . . . . 25
Question 31 . . . . . . . . . . . . . . . . . . 31
Question 32 . . . . . . . . . . . . . . . . . . 35
Question 33 . . . . . . . . . . . . . . . . . . 41
Question 34 . . . . . . . . . . . . . . . . . . 48
Question 35 . . . . . . . . . . . . . . . . . . 55
Question 36 . . . . . . . . . . . . . . . . . . 63
Question 37 . . . . . . . . . . . . . . . . . . 71
Question 25
Algebra I – Jan. ’23 [2]
25 Graph the function g(x) ⫽
x
3
⫹
on the set of axes below.
g
(
x
)
x
Score 2: The student gave a complete and correct response.
Question 25
Algebra I – Jan. ’23 [3]
25 Graph the function g(x) ⫽
x
3
⫹
on the set of axes below.
g
(
x
)
x
Score 1: The student graphed the equation over the interval 23 # x # 6.
Question 25
Algebra I – Jan. ’23 [4]
25 Graph the function g(x) ⫽
x
3
⫹
on the set of axes below.
g
(
x
)
x
Score 1: The student only graphed two points correctly.
Question 25
Algebra I – Jan. ’23 [5]
25 Graph the function g(x) ⫽
x
3
⫹
on the set of axes below.
g
(
x
)
x
Score 0: The student attempted to graph g(x) 5
x
1 3, but made graphing errors.
Question 26
Algebra I – Jan. ’23 [6]
26 The sixth-grade classes at West Road Elementary School were asked to vote on the location of
their class trip. The results are shown in the table below.
Playland Splashdown Fun Central
Boys 38 53 25
Girls 39 46 37
Determine, to the nearest percent, the percentage of girls who voted for Splashdown.
Score 2: The student gave a complete and correct response.
Question 26
Algebra I – Jan. ’23 [7]
26 The sixth-grade classes at West Road Elementary School were asked to vote on the location of
their class trip. The results are shown in the table below.
Playland Splashdown Fun Central
Boys 38 53 25
Girls 39 46 37
Determine, to the nearest percent, the percentage of girls who voted for Splashdown.
Score 1: The student expressed the answer as a fraction instead of a percentage.
Question 26
Algebra I – Jan. ’23 [8]
26 The sixth-grade classes at West Road Elementary School were asked to vote on the location of
their class trip. The results are shown in the table below.
Playland Splashdown Fun Central
Boys 38 53 25
Girls 39 46 37
Determine, to the nearest percent, the percentage of girls who voted for Splashdown.
Score 1: The student gave a percent for girls who chose Splashdown over the total number of
students.
Question 26
Algebra I – Jan. ’23 [9]
26 The sixth-grade classes at West Road Elementary School were asked to vote on the location of
their class trip. The results are shown in the table below.
Playland Splashdown Fun Central
Boys 38 53 25
Girls 39 46 37
Determine, to the nearest percent, the percentage of girls who voted for Splashdown.
Score 0: The student used the wrong denominator and made a rounding error.
Question 27
Algebra I – Jan. ’23 [10]
27 Solve the inequality ⫺
2
3
x ⫹ 6 ⬎ ⫺12 algebraically for x.
Score 2: The student gave a complete and correct response.
Question 27
Algebra I – Jan. ’23 [11]
27 Solve the inequality ⫺
2
3
x ⫹ 6 ⬎ ⫺12 algebraically for x.
Score 1: The student did not use the correct inequality symbol.
Question 27
Algebra I – Jan. ’23 [12]
27 Solve the inequality ⫺
2
3
x ⫹ 6 ⬎ ⫺12 algebraically for x.
Score 1: The student made one computational error.
Question 27
Algebra I – Jan. ’23 [13]
27 Solve the inequality ⫺
2
3
x ⫹ 6 ⬎ ⫺12 algebraically for x.
Score 1: The student divided by 20.67 instead of 2
2
3
.
Question 27
Algebra I – Jan. ’23 [14]
27 Solve the inequality ⫺
2
3
x ⫹ 6 ⬎ ⫺12 algebraically for x.
Score 0: The student did not multiply both sides of the inequality by 3 and did not have the correct
inequality symbol.
Question 27
Algebra I – Jan. ’23 [15]
27 Solve the inequality ⫺
2
3
x ⫹ 6 ⬎ ⫺12 algebraically for x.
Score 0: The student made multiple errors.
Question 28
Algebra I – Jan. ’23 [16]
28 Determine the common difference of the arithmetic sequence in which a
1
⫽ 3 and a
4
⫽ 15.
Score 2: The student gave a complete and correct response.
Question 28
Algebra I – Jan. ’23 [17]
28 Determine the common difference of the arithmetic sequence in which a
1
⫽ 3 and a
4
⫽ 15.
Score 2: The student gave a complete and correct response.
Question 28
Algebra I – Jan. ’23 [18]
28 Determine the common difference of the arithmetic sequence in which a
1
⫽ 3 and a
4
⫽ 15.
Score 1: The student stated 4, but did not show work.
Question 28
Algebra I – Jan. ’23 [19]
28 Determine the common difference of the arithmetic sequence in which a
1
⫽ 3 and a
4
⫽ 15.
Score 0: The student did not show enough correct work to receive any credit.
Question 29
Algebra I – Jan. ’23 [20]
29 Given: A ⫽
363
and B ⫽
27
Explain why A ⫹ B is irrational.
Explain why A
• B is rational.
Score 2: The student gave a complete and correct response.
Question 29
Algebra I – Jan. ’23 [21]
29 Given: A ⫽
363
and B ⫽
27
Explain why A ⫹ B is irrational.
Explain why A
• B is rational.
Score 2: The student gave a complete and correct response.
Question 29
Algebra I – Jan. ’23 [22]
29 Given: A ⫽
363
and B ⫽
27
Explain why A ⫹ B is irrational.
Explain why A
• B is rational.
Score 1: The student gave only one correct explanation.
Question 29
Algebra I – Jan. ’23 [23]
29 Given: A ⫽
363
and B ⫽
27
Explain why A ⫹ B is irrational.
Explain why A
• B is rational.
Score 1: The student gave a correct explanation for A • B and an incomplete explanation for A 1 B.
Question 29
Algebra I – Jan. ’23 [24]
29 Given: A ⫽
363
and B ⫽
27
Explain why A ⫹ B is irrational.
Explain why A
• B is rational.
Score 0: The student did not write correct explanations.
Question 30
Algebra I – Jan. ’23 [25]
30 Use the quadratic formula to solve x
2
⫺ 4x ⫹ 1 ⫽ 0 for x.
Round the solutions to the nearest hundredth.
Score 2: The student gave a complete and correct response.
Question 30
Algebra I – Jan. ’23 [26]
30 Use the quadratic formula to solve x
2
⫺ 4x ⫹ 1 ⫽ 0 for x.
Round the solutions to the nearest hundredth.
Score 2: The student gave a complete and correct response.
Question 30
Algebra I – Jan. ’23 [27]
30 Use the quadratic formula to solve x
2
⫺ 4x ⫹ 1 ⫽ 0 for x.
Round the solutions to the nearest hundredth.
Score 1: The student made one computational error.
R
ou
n
d
t
he
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ol
ut
io
ns
t
o
th
e
ne
ar
es
t
hund
re
dt
h
.
Question 30
Algebra I – Jan. ’23 [28]
30 Use the quadratic formula to solve x
2
⫺ 4x ⫹ 1 ⫽ 0 for x.
Round the solutions to the nearest hundredth.
Score 1: The student found
2
12
4
, but no further correct work was shown.
Question 30
Algebra I – Jan. ’23 [29]
30 Use the quadratic formula to solve x
2
4x 1 0 for x.
Round the solutions to the nearest hundredth.
Score 0: The student did not use the quadratic formula and did not write the solutions as decimals.
Question 30
Algebra I – Jan. ’23 [30]
30 Use the quadratic formula to solve x
2
4x 1 0 for x.
Round the solutions to the nearest hundredth.
Score 0: The student did not show enough correct work to receive any credit.
Question 31
Algebra I – Jan. ’23 [31]
31 Factor completely:
4x
3
49x
Score 2: The student gave a complete and correct response.
Question 31
Algebra I – Jan. ’23 [32]
31 Factor completely:
4x
3
49x
Score 1: The student did not factor the expression completely.
Question 31
Algebra I – Jan. ’23 [33]
31 Factor completely:
4x
3
49x
Score 1: The student found x(4x
2
2 49), but no further correct work was shown.
Question 31
Algebra I – Jan. ’23 [34]
31 Factor completely:
4x
3
49x
Score 0: The student gave an incorrect response.
Question 32
Algebra I – Jan. ’23 [35]
32 The function g is defined as
x 2
2 x 2
|x 3|,
g(x)
{
x
2
1,
On the set of axes below, graph g(x).
g
(
x
)
x
Score 2: The student gave a complete and correct response.
Question 32
Algebra I – Jan. ’23 [36]
32 The function g is defined as
x 2
2 x 2
|x 3|,
g(x)
{
x
2
1,
On the set of axes below, graph g(x).
g
(
x
)
x
Score 1: The student graphed both equations, but did not use the given domains.
Question 32
Algebra I – Jan. ’23 [37]
32 The function g is defined as
x 2
2 x 2
|x 3|,
g(x)
{
x
2
1,
On the set of axes below, graph g(x).
g
(
x
)
x
Score 1: The student made one graphing error.
Question 32
Algebra I – Jan. ’23 [38]
32 The function g is defined as
x 2
2 x 2
|x 3|,
g(x)
{
x
2
1,
On the set of axes below, graph g(x).
g
(
x
)
x
Score 1: The student graphed g(x) 5 x
2
1 1 over its given domain, but no further correct work was
shown.
Question 32
Algebra I – Jan. ’23 [39]
32 The function g is defined as
x 2
2 x 2
|x 3|,
g(x)
{
x
2
1,
On the set of axes below, graph g(x).
g
(
x
)
x
Score 1: The student graphed the end points of both functions incorrectly.
Question 32
Algebra I – Jan. ’23 [40]
32 The function g is defined as
x 2
2 x 2
|x 3|,
g(x)
{
x
2
1,
On the set of axes below, graph g(x).
g
(
x
)
x
Score 0: The student made multiple graphing errors.
Question 33
Algebra I – Jan. ’23 [41]
33 Anessa is studying the changes in population in a town. The graph below shows the population
over 50 years.
10 20 30
2
4
6
8
10
Years
Population (in thousands)
0
40 50
State the entire interval during which the population remained constant.
State the maximum population of the town over the 50-year period.
Determine the average rate of change from year 30 to year 40.
Explain what your average rate of change means from year 30 to year 40 in the context of
the problem.
Score 4: The student gave a complete and correct response.
Question 33
Algebra I – Jan. ’23 [42]
33 Anessa is studying the changes in population in a town. The graph below shows the population
over 50 years.
10 20 30
2
4
6
8
10
Years
Population (in thousands)
0
40 50
State the entire interval during which the population remained constant.
State the maximum population of the town over the 50-year period.
Determine the average rate of change from year 30 to year 40.
Explain what your average rate of change means from year 30 to year 40 in the context of
the problem.
Score 3: The student wrote an incomplete explanation.
Question 33
Algebra I – Jan. ’23 [43]
33 Anessa is studying the changes in population in a town. The graph below shows the population
over 50 years.
10 20 30
2
4
6
8
10
Years
Population (in thousands)
0
40 50
State the entire interval during which the population remained constant.
State the maximum population of the town over the 50-year period.
Determine the average rate of change from year 30 to year 40.
Explain what your average rate of change means from year 30 to year 40 in the context of
the problem.
Score 3: The student found an incorrect rate of change.
Question 33
Algebra I – Jan. ’23 [44]
33 Anessa is studying the changes in population in a town. The graph below shows the population
over 50 years.
10 20 30
2
4
6
8
10
Years
Population (in thousands)
0
40 50
State the entire interval during which the population remained constant.
State the maximum population of the town over the 50-year period.
Determine the average rate of change from year 30 to year 40.
Explain what your average rate of change means from year 30 to year 40 in the context of
the problem.
Score 2: The student stated the correct interval and maximum population, but no further correct
work was shown.
Question 33
Algebra I – Jan. ’23 [45]
33 Anessa is studying the changes in population in a town. The graph below shows the population
over 50 years.
10 20 30
2
4
6
8
10
Years
Population (in thousands)
0
40 50
State the entire interval during which the population remained constant.
State the maximum population of the town over the 50-year period.
Determine the average rate of change from year 30 to year 40.
Explain what your average rate of change means from year 30 to year 40 in the context of
the problem.
Score 2: The student stated the correct interval and maximum population, but no further correct
work was shown.
Question 33
Algebra I – Jan. ’23 [46]
33 Anessa is studying the changes in population in a town. The graph below shows the population
over 50 years.
10 20 30
2
4
6
8
10
Years
Population (in thousands)
0
40 50
State the entire interval during which the population remained constant.
State the maximum population of the town over the 50-year period.
Determine the average rate of change from year 30 to year 40.
Explain what your average rate of change means from year 30 to year 40 in the context of
the problem.
Score 1: The student stated the correct interval, but no further correct work was shown.
Question 33
Algebra I – Jan. ’23 [47]
33 Anessa is studying the changes in population in a town. The graph below shows the population
over 50 years.
10 20 30
2
4
6
8
10
Years
Population (in thousands)
0
40 50
State the entire interval during which the population remained constant.
State the maximum population of the town over the 50-year period.
Determine the average rate of change from year 30 to year 40.
Explain what your average rate of change means from year 30 to year 40 in the context of
the problem.
Score 0: The student did not show enough correct work to receive any credit.
Question 34
Algebra I – Jan. ’23 [48]
34 The table below shows the number of math classes missed during a school year for nine students,
and their final exam scores.
Number of Classes
Missed (x)
2 10 3 22 15 2 20 18 9
Final Exam Score (y) 99 72 90 35 60 80 40 43 75
Write the linear regression equation for this data set. Round all values to the nearest hundredth.
State the correlation coefficient for your linear regression. Round your answer to the nearest
hundredth.
State what the correlation coefficient indicates about the linear fit of the data.
Score 4: The student gave a complete and correct response.
Question 34
Algebra I – Jan. ’23 [49]
34 The table below shows the number of math classes missed during a school year for nine students,
and their final exam scores.
Number of Classes
Missed (x)
2 10 3 22 15 2 20 18 9
Final Exam Score (y) 99 72 90 35 60 80 40 43 75
Write the linear regression equation for this data set. Round all values to the nearest hundredth.
State the correlation coefficient for your linear regression. Round your answer to the nearest
hundredth.
State what the correlation coefficient indicates about the linear fit of the data.
Score 3: The student wrote an expression instead of an equation.
Question 34
Algebra I – Jan. ’23 [50]
34 The table below shows the number of math classes missed during a school year for nine students,
and their final exam scores.
Number of Classes
Missed (x)
2 10 3 22 15 2 20 18 9
Final Exam Score (y) 99 72 90 35 60 80 40 43 75
Write the linear regression equation for this data set. Round all values to the nearest hundredth.
State the correlation coefficient for your linear regression. Round your answer to the nearest
hundredth.
State what the correlation coefficient indicates about the linear fit of the data.
Score 3: The student made a data entry error, but showed the full display of the calculator and gave
an appropriate response based on the display.
Question 34
Algebra I – Jan. ’23 [51]
34 The table below shows the number of math classes missed during a school year for nine students,
and their final exam scores.
Number of Classes
Missed (x)
2 10 3 22 15 2 20 18 9
Final Exam Score (y) 99 72 90 35 60 80 40 43 75
Write the linear regression equation for this data set. Round all values to the nearest hundredth.
State the correlation coefficient for your linear regression. Round your answer to the nearest
hundredth.
State what the correlation coefficient indicates about the linear fit of the data.
Score 2: The student did not write x in the equation and did not state strong.
Question 34
Algebra I – Jan. ’23 [52]
34 The table below shows the number of math classes missed during a school year for nine students,
and their final exam scores.
Number of Classes
Missed (x)
2 10 3 22 15 2 20 18 9
Final Exam Score (y) 99 72 90 35 60 80 40 43 75
Write the linear regression equation for this data set. Round all values to the nearest hundredth.
State the correlation coefficient for your linear regression. Round your answer to the nearest
hundredth.
State what the correlation coefficient indicates about the linear fit of the data.
Score 1: The student made a rounding error in the regression equation, and no further correct work
was shown.
Question 34
Algebra I – Jan. ’23 [53]
34 The table below shows the number of math classes missed during a school year for nine students,
and their final exam scores.
Number of Classes
Missed (x)
2 10 3 22 15 2 20 18 9
Final Exam Score (y) 99 72 90 35 60 80 40 43 75
Write the linear regression equation for this data set. Round all values to the nearest hundredth.
State the correlation coefficient for your linear regression. Round your answer to the nearest
hundredth.
State what the correlation coefficient indicates about the linear fit of the data.
Score 1: The student wrote an appropriate indication based an incorrect correlation coef cient.
Question 34
Algebra I – Jan. ’23 [54]
34 The table below shows the number of math classes missed during a school year for nine students,
and their final exam scores.
Number of Classes
Missed (x)
2 10 3 22 15 2 20 18 9
Final Exam Score (y) 99 72 90 35 60 80 40 43 75
Write the linear regression equation for this data set. Round all values to the nearest hundredth.
State the correlation coefficient for your linear regression. Round your answer to the nearest
hundredth.
State what the correlation coefficient indicates about the linear fit of the data.
Score 0: The student did not show enough correct work to receive any credit.
Question 35
Algebra I – Jan. ’23 [55]
35 A fence was installed around the edge of a rectangular garden. The length, l, of the fence was
5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.
Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Score 4: The student gave a complete and correct response.
Question 35
Algebra I – Jan. ’23 [56]
35 A fence was installed around the edge of a rectangular garden. The length, l, of the fence was
5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.
Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Score 4: The student gave a complete and correct response.
Question 35
Algebra I – Jan. ’23 [57]
35 A fence was installed around the edge of a rectangular garden. The length, l, of the fence was
5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.
Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Score 4: The student gave a complete and correct response.
Question 35
Algebra I – Jan. ’23 [58]
35 A fence was installed around the edge of a rectangular garden. The length, l, of the fence was
5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.
Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Score 3: The student wrote only one equation in the system correctly, but solved the system
appropriately.
Question 35
Algebra I – Jan. ’23 [59]
35 A fence was installed around the edge of a rectangular garden. The length, l, of the fence was
5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.
Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Score 3: The student made one computational error.
Question 35
Algebra I – Jan. ’23 [60]
35 A fence was installed around the edge of a rectangular garden. The length, l, of the fence was
5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.
Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Score 2: The student wrote only one equation correctly and solved the system appropriately, but
found only one dimension.
Question 35
Algebra I – Jan. ’23 [61]
35 A fence was installed around the edge of a rectangular garden. The length, l, of the fence was
5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.
Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Score 1: The student wrote only one equation correctly.
Question 35
Algebra I – Jan. ’23 [62]
35 A fence was installed around the edge of a rectangular garden. The length, l, of the fence was
5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.
Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Score 0: The student did not show enough correct work to receive any credit.
Question 36
Algebra I – Jan. ’23 [63]
36 Given: 3y 9 12
y
2x 4
Graph the system of inequalities on the set of axes below.
Score 4: The student gave a complete and correct response.
State the coordinates of a point that satisfies both inequalities. Justify your answer.
Question 36
Algebra I – Jan. ’23 [64]
36 Given: 3y 9 12
y
2x 4
Graph the system of inequalities on the set of axes below.
State the coordinates of a point that satisfies both inequalities. Justify your answer.
Score 4: The student gave a complete and correct response.
Question 36
Algebra I – Jan. ’23 [65]
36 Given: 3y 9 12
y
2x 4
Graph the system of inequalities on the set of axes below.
State the coordinates of a point that satisfies both inequalities. Justify your answer.
Score 3: The student did not label one of the inequalities.
he
coordinates
of
a
point
that
satisfies
both
inequalities
.
Justify
your
answer
.
Question 36
Algebra I – Jan. ’23 [66]
36 Given: 3y 9 12
y
2x 4
Graph the system of inequalities on the set of axes below.
State the coordinates of a point that satisfies both inequalities. Justify your answer.
Score 2: The student only graphed one inequality correctly and did not write a complete
justi cation.
Question 36
Algebra I – Jan. ’23 [67]
36 Given: 3y 9 12
y
2x 4
Graph the system of inequalities on the set of axes below.
State the coordinates of a point that satisfies both inequalities. Justify your answer.
Score 2: The student graphed both inequalities correctly, but no further correct work was shown.
Question 36
Algebra I – Jan. ’23 [68]
36 Given: 3y 9 12
y
2x 4
Graph the system of inequalities on the set of axes below.
State the coordinates of a point that satisfies both inequalities. Justify your answer.
Score 1: The student made the same shading error in both inequalities, and no further correct work
was shown.
Question 36
Algebra I – Jan. ’23 [69]
36 Given: 3y 9 12
y
2x 4
Graph the system of inequalities on the set of axes below.
State the coordinates of a point that satisfies both inequalities. Justify your answer.
Score 1: The student graphed and labeled one inequality correctly, but no further correct work was
shown.
Question 36
Algebra I – Jan. ’23 [70]
36 Given: 3y 9 12
y
2x 4
Graph the system of inequalities on the set of axes below.
State the coordinates of a point that satisfies both inequalities. Justify your answer.
Score 0: The student did not show enough correct work to receive any credit.
3
y
9
12
y
2
x
4
h
e s
y
stem o
f
ine
q
ua
l
ities on t
h
e set o
f
axes
b
e
l
ow.
Question 37
Algebra I – Jan. ’23 [71]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
Question 37 is continued on the next page.
Score 6: The student gave a complete and correct response.
Question 37
Algebra I – Jan. ’23 [72]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
y
x
0
50
100
Fe
et
150
51
0
15
nswer.
x
Question 37
Algebra I – Jan. ’23 [73]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
Question 37 is continued on the next page.
Score 5: The student did not label at least one of the lines.
Question 37
Algebra I – Jan. ’23 [74]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
y
x
0
50
100
Feet
150
510
Seco
n
ds
15
Question 37
Algebra I – Jan. ’23 [75]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
Question 37 is continued on the next page.
Score 5: The student wrote two correct equations but graphed one incorrectly. They found an
appropriate point of intersection and justi ed their answer.
Question 37
Algebra I – Jan. ’23 [76]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
Question 37
Algebra I – Jan. ’23 [77]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
Question 37 is continued on the next page.
Score 4: The student did not label at least one of the lines and did not give a justi cation.
Question 37
Algebra I – Jan. ’23 [78]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
Question 37
Algebra I – Jan. ’23 [79]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
Question 37 is continued on the next page.
Score 4: The student did not graph the equations.
Question 37
Algebra I – Jan. ’23 [80]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
Question 37
Algebra I – Jan. ’23 [81]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
Question 37 is continued on the next page.
Score 4: The student wrote two correct equations and justi ed 7.5.
Question 37
Algebra I – Jan. ’23 [82]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
Question 37
Algebra I – Jan. ’23 [83]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
Question 37 is continued on the next page.
Score 3: The student wrote two correct equations and stated the correct number of seconds.
Question 37
Algebra I – Jan. ’23 [84]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
Question 37
Algebra I – Jan. ’23 [85]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
Question 37 is continued on the next page.
Score 2: The student wrote the correct equations for Aidan and Ella.
Question 37
Algebra I – Jan. ’23 [86]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
Question 37
Algebra I – Jan. ’23 [87]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
Question 37 is continued on the next page.
Score 1: The student only wrote the correct equation for Ella.
Question 37
Algebra I – Jan. ’23 [88]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
Question 37
Algebra I – Jan. ’23 [89]
37 Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs
at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of
the starting line.
Let y represent the distance from the starting line and x represent the time elapsed, in seconds.
Write an equation to model the distance Aiden traveled.
Write an equation to model the distance Ella traveled.
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 I – Jan. ’23 [90]
On the set of axes below, graph your equations.
y
x
0
50
100
Feet
150
510
Seconds
15
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.
Question 37 continued
