The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA I (Common Core)
Tuesday, June 13, 2017 — 1:15 to 4:15 p.m.
MODEL RESPONSE SET
Table of Contents
Question 25 . . . . . . . . . . . . . . . . . . . 2
Question 26 . . . . . . . . . . . . . . . . . . . 5
Question 27 . . . . . . . . . . . . . . . . . . . 9
Question 28 . . . . . . . . . . . . . . . . . . 14
Question 29 . . . . . . . . . . . . . . . . . . 18
Question 30 . . . . . . . . . . . . . . . . . . 21
Question 31 . . . . . . . . . . . . . . . . . . 24
Question 32 . . . . . . . . . . . . . . . . . . 30
Question 33 . . . . . . . . . . . . . . . . . . 35
Question 34 . . . . . . . . . . . . . . . . . . 43
Question 35 . . . . . . . . . . . . . . . . . . 57
Question 36 . . . . . . . . . . . . . . . . . . 63
Question 37 . . . . . . . . . . . . . . . . . . 70
Question 25
25 Express in simplest form: (3x
2
⫹ 4x ⫺ 8) ⫺ (⫺2x
2
⫹ 4x ⫹ 2)
Score 2: The student gave a complete and correct response.
Algebra I (Common Core) – June ’17 [2]
Question 25
25 Express in simplest form: (3x
2
⫹ 4x ⫺ 8) ⫺ (⫺2x
2
⫹ 4x ⫹ 2)
Score 1: The student did not add 3x
2
and 2x
2
.
Algebra I (Common Core) – June ’17 [3]
Question 25
25 Express in simplest form: (3x
2
⫹ 4x ⫺ 8) ⫺ (⫺2x
2
⫹ 4x ⫹ 2)
Score 0: The student wrote the problem as addition and combined the constant terms incorrectly.
Algebra I (Common Core) – June ’17 [4]
Algebra I (Common Core) – June ’17 [5]
Question 26
Score 2: The student gave a complete and correct response.
26 Graph the function f(x) ⫽ ⫺x
2
⫺ 6x on the set of axes below.
f(x)
f(x)
x
State the coordinates of the vertex of the graph.
Algebra I (Common Core) – June ’17 [6]
Question 26
Score 1: The student only graphed f(x) over the interval ⫺6 to 0.
26 Graph the function f(x) ⫽ ⫺x
2
⫺ 6x on the set of axes below.
f(x)
f(x)
x
State the coordinates of the vertex of the graph.
Algebra I (Common Core) – June ’17 [7]
Question 26
Score 1: The student graphed f(x) incorrectly, but stated an appropriate vertex.
26 Graph the function f(x) ⫽ ⫺x
2
⫺ 6x on the set of axes below.
f(x)
f(x)
x
State the coordinates of the vertex of the graph.
Algebra I (Common Core) – June ’17 [8]
Question 26
Score 0: The student drew an incorrect graph and did not state a vertex.
26 Graph the function f(x) ⫽ ⫺x
2
⫺ 6x on the set of axes below.
f(x)
f(x)
x
State the coordinates of the vertex of the graph.
Algebra I (Common Core) – June ’17 [9]
Question 27
Score 2: The student gave a complete and correct response.
27 State whether 7 ⫺
3
––
2 is rational or irrational. Explain your answer.
Algebra I (Common Core) – June ’17 [10]
Question 27
Score 2: The student gave a complete and correct response.
27 State whether 7 ⫺
3
––
2 is rational or irrational. Explain your answer.
Algebra I (Common Core) – June ’17 [11]
Question 27
Score 1: The student made an error in describing an irrational number.
27 State whether 7 ⫺
3
––
2 is rational or irrational. Explain your answer.
Algebra I (Common Core) – June ’17 [12]
Question 27
Score 1: The student only explained why is irrational. The student did not address the
difference.
2
27 State whether 7 ⫺
3
––
2 is rational or irrational. Explain your answer.
Algebra I (Common Core) – June ’17 [13]
Question 27
Score 0: The student did not write the full display of the calculator and wrote an incorrect
explanation.
27 State whether 7 ⫺
3
––
2 is rational or irrational. Explain your answer.
Algebra I (Common Core) – June ’17 [14]
Question 28
Score 2: The student gave a complete and correct response.
28 The value, v(t), of a car depreciates according to the function v(t) ⫽ P(.85)
t
, where P is the purchase
price of the car and t is the time, in years, since the car was purchased. State the percent that the
value of the car decreases by each year. Justify your answer.
Algebra I (Common Core) – June ’17 [15]
Question 28
Score 2: The student gave a complete and correct response.
28 The value, v(t), of a car depreciates according to the function v(t) ⫽ P(.85)
t
, where P is the purchase
price of the car and t is the time, in years, since the car was purchased. State the percent that the
value of the car decreases by each year. Justify your answer.
Algebra I (Common Core) – June ’17 [16]
Question 28
Score 1: The student wrote an appropriate justification, but did not state the percent of decrease.
28 The value, v(t), of a car depreciates according to the function v(t) ⫽ P(.85)
t
, where P is the purchase
price of the car and t is the time, in years, since the car was purchased. State the percent that the
value of the car decreases by each year. Justify your answer.
Algebra I (Common Core) – June ’17 [17]
Question 28
Score 0: The student wrote a completely incorrect response.
28 The value, v(t), of a car depreciates according to the function v(t) ⫽ P(.85)
t
, where P is the purchase
price of the car and t is the time, in years, since the car was purchased. State the percent that the
value of the car decreases by each year. Justify your answer.
Algebra I (Common Core) – June ’17 [18]
Question 29
Score 2: The student gave a complete and correct response.
29 A survey of 100 students was taken. It was found that 60 students watched sports, and 34 of these
students did not like pop music. Of the students who did not watch sports, 70% liked pop music.
Complete the two-way frequency table.
Watch Sports Don’t Watch Sports Total
Like Pop
Don’t Like Pop
Total
Algebra I (Common Core) – June ’17 [19]
Question 29
Score 1: The student made an error when calculating 70% of 40, but then completed the table
appropriately.
29 A survey of 100 students was taken. It was found that 60 students watched sports, and 34 of these
students did not like pop music. Of the students who did not watch sports, 70% liked pop music.
Complete the two-way frequency table.
Watch Sports Don’t Watch Sports Total
Like Pop
Don’t Like Pop
Total
Algebra I (Common Core) – June ’17 [20]
Question 29
Score 0: The student made multiple errors.
29 A survey of 100 students was taken. It was found that 60 students watched sports, and 34 of these
students did not like pop music. Of the students who did not watch sports, 70% liked pop music.
Complete the two-way frequency table.
Watch Sports Don’t Watch Sports Total
Like Pop
Don’t Like Pop
Total
Algebra I (Common Core) – June ’17 [21]
Question 30
Score 2: The student gave a complete and correct response.
30 Graph the inequality y ⫹ 4 ⬍ ⫺2(x ⫺ 4) on the set of axes below.
y
x
Algebra I (Common Core) – June ’17 [22]
Question 30
Score 1: The student graphed the dotted line correctly, but did not shade the inequality.
30 Graph the inequality y ⫹ 4 ⬍ ⫺2(x ⫺ 4) on the set of axes below.
y
x
Algebra I (Common Core) – June ’17 [23]
Question 30
Score 0: The student made two graphing errors by drawing a solid line and not shading.
30 Graph the inequality y ⫹ 4 ⬍ ⫺2(x ⫺ 4) on the set of axes below.
y
x
Algebra I (Common Core) – June ’17 [24]
Question 31
Score 2: The student gave a complete and correct response.
31 If f(x) ⫽ x
2
and g(x) ⫽ x, determine the value(s) of x that satisfy the equation f(x) ⫽ g(x).
Algebra I (Common Core) – June ’17 [25]
Question 31
Score 2: The student gave a complete and correct response.
31 If f(x) ⫽ x
2
and g(x) ⫽ x, determine the value(s) of x that satisfy the equation f(x) ⫽ g(x).
Algebra I (Common Core) – June ’17 [26]
Question 31
Score 2: The student gave a complete and correct response.
31 If f(x) ⫽ x
2
and g(x) ⫽ x, determine the value(s) of x that satisfy the equation f(x) ⫽ g(x).
Algebra I (Common Core) – June ’17 [27]
Question 31
Score 1: The student wrote the solutions to f(x) ⫽ g(x) as coordinates.
31 If f(x) ⫽ x
2
and g(x) ⫽ x, determine the value(s) of x that satisfy the equation f(x) ⫽ g(x).
Algebra I (Common Core) – June ’17 [28]
Question 31
Score 1: The student found one correct solution.
31 If f(x) ⫽ x
2
and g(x) ⫽ x, determine the value(s) of x that satisfy the equation f(x) ⫽ g(x).
Algebra I (Common Core) – June ’17 [29]
Question 31
Score 0: The student showed appropriate work, but did not state either solution.
31 If f(x) ⫽ x
2
and g(x) ⫽ x, determine the value(s) of x that satisfy the equation f(x) ⫽ g(x).
Algebra I (Common Core) – June ’17 [30]
Question 32
Score 2: The student gave a complete and correct response.
32 Describe the effect that each transformation below has on the function f(x) ⫽
|
x
|
, where a ⬎ 0.
g(x) ⫽
|
x ⫺ a
|
h(x) ⫽
|
x
|
⫺ a
Algebra I (Common Core) – June ’17 [31]
Question 32
Score 2: The student gave a complete and correct response.
32 Describe the effect that each transformation below has on the function f(x) ⫽
|
x
|
, where a ⬎ 0.
g(x) ⫽
|
x ⫺ a
|
h(x) ⫽
|
x
|
⫺ a
Algebra I (Common Core) – June ’17 [32]
Question 32
Score 1: The student reversed the horizontal and vertical shifts.
32 Describe the effect that each transformation below has on the function f(x) ⫽
|
x
|
, where a ⬎ 0.
g(x) ⫽
|
x ⫺ a
|
h(x) ⫽
|
x
|
⫺ a
Algebra I (Common Core) – June ’17 [33]
Question 32
Score 1: The student only stated one shift correctly.
32 Describe the effect that each transformation below has on the function f(x) ⫽
|
x
|
, where a ⬎ 0.
g(x) ⫽
|
x ⫺ a
|
h(x) ⫽
|
x
|
⫺ a
Algebra I (Common Core) – June ’17 [34]
Question 32
Score 0: The student wrote two incorrect responses.
32 Describe the effect that each transformation below has on the function f(x) ⫽
|
x
|
, where a ⬎ 0.
g(x) ⫽
|
x ⫺ a
|
h(x) ⫽
|
x
|
⫺ a
Algebra I (Common Core) – June ’17 [35]
Question 33
Score 4: The student gave a complete and correct response.
33 The function r(x) is defi ned by the expression x
2
⫹ 3x ⫺ 18. Use factoring to determine the zeros
of r(x).
Explain what the zeros represent on the graph of r(x).
Algebra I (Common Core) – June ’17 [36]
Question 33
Score 4: The student gave a complete and correct response.
33 The function r(x) is defi ned by the expression x
2
⫹ 3x ⫺ 18. Use factoring to determine the zeros
of r(x).
Explain what the zeros represent on the graph of r(x).
Algebra I (Common Core) – June ’17 [37]
Question 33
Score 3: The student wrote an incomplete explanation by referencing points and not the x-values
at which the parabola crosses the x-axis.
33 The function r(x) is defi ned by the expression x
2
⫹ 3x ⫺ 18. Use factoring to determine the zeros
of r(x).
Explain what the zeros represent on the graph of r(x).
Algebra I (Common Core) – June ’17 [38]
Question 33
Score 2: The student used a method other than factoring to find the zeros of r(x) and wrote
an incomplete explanation.
33 The function r(x) is defi ned by the expression x
2
⫹ 3x ⫺ 18. Use factoring to determine the zeros
of r(x).
Explain what the zeros represent on the graph of r(x).
Algebra I (Common Core) – June ’17 [39]
Question 33
Score 2: The student showed no work to find the zeros and wrote an incomplete explanation.
33 The function r(x) is defi ned by the expression x
2
⫹ 3x ⫺ 18. Use factoring to determine the zeros
of r(x).
Explain what the zeros represent on the graph of r(x).
Algebra I (Common Core) – June ’17 [40]
Question 33
Score 1: The student made a factoring error and wrote an incorrect explanation.
33 The function r(x) is defi ned by the expression x
2
⫹ 3x ⫺ 18. Use factoring to determine the zeros
of r(x).
Explain what the zeros represent on the graph of r(x).
Algebra I (Common Core) – June ’17 [41]
Question 33
Score 1: The student wrote a correctly factored equation.
33 The function r(x) is defi ned by the expression x
2
⫹ 3x ⫺ 18. Use factoring to determine the zeros
of r(x).
Explain what the zeros represent on the graph of r(x).
Algebra I (Common Core) – June ’17 [42]
Question 33
Score 0: The student did not show enough work to receive any credit.
33 The function r(x) is defi ned by the expression x
2
⫹ 3x ⫺ 18. Use factoring to determine the zeros
of r(x).
Explain what the zeros represent on the graph of r(x).
Algebra I (Common Core) – June ’17 [43]
Question 34
34 The graph below models Craig’s trip to visit his friend in another state. In the course of his travels,
he encountered both highway and city driving.
20
0
1 2 3 4 5 6 7
40
60
80
100
120
140
160
180
200
220
240
260
BC
D
E
A
Hours
Miles Traveled
Based on the graph, during which interval did Craig most likely drive in the city? Explain your
reasoning.
Question 34 is continued on the next page.
Algebra I (Common Core) – June ’17 [44]
Question 34
Score 4: The student gave a complete and correct response.
Explain what might have happened in the interval between B and C.
Determine Craig’s average speed, to the nearest tenth of a mile per hour, for his entire trip.
Question 34 continued.
Algebra I (Common Core) – June ’17 [45]
Question 34
34 The graph below models Craig’s trip to visit his friend in another state. In the course of his travels,
he encountered both highway and city driving.
20
0
1 2 3 4 5 6 7
40
60
80
100
120
140
160
180
200
220
240
260
BC
D
E
A
Hours
Miles Traveled
Based on the graph, during which interval did Craig most likely drive in the city? Explain your
reasoning.
Question 34 is continued on the next page.
Algebra I (Common Core) – June ’17 [46]
Question 34
Score 4: The student gave a complete and correct response.
Explain what might have happened in the interval between B and C.
Determine Craig’s average speed, to the nearest tenth of a mile per hour, for his entire trip.
Question 34 continued.
Algebra I (Common Core) – June ’17 [47]
Question 34
34 The graph below models Craig’s trip to visit his friend in another state. In the course of his travels,
he encountered both highway and city driving.
20
0
1 2 3 4 5 6 7
40
60
80
100
120
140
160
180
200
220
240
260
BC
D
E
A
Hours
Miles Traveled
Based on the graph, during which interval did Craig most likely drive in the city? Explain your
reasoning.
Question 34 is continued on the next page.
Algebra I (Common Core) – June ’17 [48]
Question 34
Score 3: The student calculated the average speed incorrectly.
Explain what might have happened in the interval between B and C.
Determine Craig’s average speed, to the nearest tenth of a mile per hour, for his entire trip.
Question 34 continued.
Algebra I (Common Core) – June ’17 [49]
Question 34
34 The graph below models Craig’s trip to visit his friend in another state. In the course of his travels,
he encountered both highway and city driving.
20
0
1 2 3 4 5 6 7
40
60
80
100
120
140
160
180
200
220
240
260
BC
D
E
A
Hours
Miles Traveled
Based on the graph, during which interval did Craig most likely drive in the city? Explain your
reasoning.
Question 34 is continued on the next page.
Algebra I (Common Core) – June ’17 [50]
Question 34
Score 3: The student made an error in calculating the average speed of the entire trip.
Explain what might have happened in the interval between B and C.
Determine Craig’s average speed, to the nearest tenth of a mile per hour, for his entire trip.
Question 34 continued.
Algebra I (Common Core) – June ’17 [51]
Question 34
34 The graph below models Craig’s trip to visit his friend in another state. In the course of his travels,
he encountered both highway and city driving.
20
0
1 2 3 4 5 6 7
40
60
80
100
120
140
160
180
200
220
240
260
BC
D
E
A
Hours
Miles Traveled
Based on the graph, during which interval did Craig most likely drive in the city? Explain your
reasoning.
Question 34 is continued on the next page.
Algebra I (Common Core) – June ’17 [52]
Question 34
Score 2: The student wrote a correct interval, but with an incomplete explanation, and made a
rounding error.
Explain what might have happened in the interval between B and C.
Determine Craig’s average speed, to the nearest tenth of a mile per hour, for his entire trip.
Question 34 continued.
Algebra I (Common Core) – June ’17 [53]
Question 34
34 The graph below models Craig’s trip to visit his friend in another state. In the course of his travels,
he encountered both highway and city driving.
20
0
1 2 3 4 5 6 7
40
60
80
100
120
140
160
180
200
220
240
260
BC
D
E
A
Hours
Miles Traveled
Based on the graph, during which interval did Craig most likely drive in the city? Explain your
reasoning.
Question 34 is continued on the next page.
Algebra I (Common Core) – June ’17 [54]
Question 34
Score 1: The student calculated the average speed correctly.
Explain what might have happened in the interval between B and C.
Determine Craig’s average speed, to the nearest tenth of a mile per hour, for his entire trip.
Question 34 continued.
Algebra I (Common Core) – June ’17 [55]
Question 34
34 The graph below models Craig’s trip to visit his friend in another state. In the course of his travels,
he encountered both highway and city driving.
20
0
1 2 3 4 5 6 7
40
60
80
100
120
140
160
180
200
220
240
260
BC
D
E
A
Hours
Miles Traveled
Based on the graph, during which interval did Craig most likely drive in the city? Explain your
reasoning.
Question 34 is continued on the next page.
Algebra I (Common Core) – June ’17 [56]
Question 34
Score 0: The student wrote a completely incorrect response.
Explain what might have happened in the interval between B and C.
Determine Craig’s average speed, to the nearest tenth of a mile per hour, for his entire trip.
Question 34 continued.
Algebra I (Common Core) – June ’17 [57]
Question 35
Score 4: The student gave a complete and correct response.
35 Given:
g(x) ⫽ 2x
2
⫹ 3x ⫹ 10
k(x) ⫽ 2x ⫹ 16
Solve the equation g(x) ⫽ 2k(x) algebraically for x, to the nearest tenth.
Explain why you chose the method used to solve this quadratic equation.
Algebra I (Common Core) – June ’17 [58]
Question 35
Score 3: The student did not distribute 2 to both 2x and 16.
35 Given:
g(x) ⫽ 2x
2
⫹ 3x ⫹ 10
k(x) ⫽ 2x ⫹ 16
Solve the equation g(x) ⫽ 2k(x) algebraically for x, to the nearest tenth.
Explain why you chose the method used to solve this quadratic equation.
Algebra I (Common Core) – June ’17 [59]
Question 35
Score 2: The student made a correct substitution into the quadratic formula and wrote a correct
explanation.
35 Given:
g(x) ⫽ 2x
2
⫹ 3x ⫹ 10
k(x) ⫽ 2x ⫹ 16
Solve the equation g(x) ⫽ 2k(x) algebraically for x, to the nearest tenth.
Explain why you chose the method used to solve this quadratic equation.
Algebra I (Common Core) – June ’17 [60]
Question 35
Score 2: The student made a rounding error and did not write an explanation.
35 Given:
g(x) ⫽ 2x
2
⫹ 3x ⫹ 10
k(x) ⫽ 2x ⫹ 16
Solve the equation g(x) ⫽ 2k(x) algebraically for x, to the nearest tenth.
Explain why you chose the method used to solve this quadratic equation.
Algebra I (Common Core) – June ’17 [61]
Question 35
Score 1: The student wrote an appropriate explanation, but a method other than algebraic was
used, and only one correct solution was stated.
35 Given:
g(x) ⫽ 2x
2
⫹ 3x ⫹ 10
k(x) ⫽ 2x ⫹ 16
Solve the equation g(x) ⫽ 2k(x) algebraically for x, to the nearest tenth.
Explain why you chose the method used to solve this quadratic equation.
Algebra I (Common Core) – June ’17 [62]
Question 35
Score 0: The student did not show enough work to receive any credit.
35 Given:
g(x) ⫽ 2x
2
⫹ 3x ⫹ 10
k(x) ⫽ 2x ⫹ 16
Solve the equation g(x) ⫽ 2k(x) algebraically for x, to the nearest tenth.
Explain why you chose the method used to solve this quadratic equation.
Algebra I (Common Core) – June ’17 [63]
Question 36
Score 4: The student gave a complete and correct response.
36 Michael has $10 in his savings account. Option 1 will add $100 to his account each week.
Option 2 will double the amount in his account at the end of each week.
Write a function in terms of x to model each option of saving.
Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike.
Determine which option(s) will enable him to reach his goal. Justify your answer.
Algebra I (Common Core) – June ’17 [64]
Question 36
Score 4: The student gave a complete and correct response.
36 Michael has $10 in his savings account. Option 1 will add $100 to his account each week.
Option 2 will double the amount in his account at the end of each week.
Write a function in terms of x to model each option of saving.
Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike.
Determine which option(s) will enable him to reach his goal. Justify your answer.
Algebra I (Common Core) – June ’17 [65]
Question 36
Score 3: The student wrote an incorrect function for option 2, but gave an appropriate determination
and justification.
36 Michael has $10 in his savings account. Option 1 will add $100 to his account each week.
Option 2 will double the amount in his account at the end of each week.
Write a function in terms of x to model each option of saving.
Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike.
Determine which option(s) will enable him to reach his goal. Justify your answer.
Algebra I (Common Core) – June ’17 [66]
Question 36
Score 3: The student did not write two correct functions, but wrote two appropriate inequalities
that they used to justify their answer.
36 Michael has $10 in his savings account. Option 1 will add $100 to his account each week.
Option 2 will double the amount in his account at the end of each week.
Write a function in terms of x to model each option of saving.
Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike.
Determine which option(s) will enable him to reach his goal. Justify your answer.
Algebra I (Common Core) – June ’17 [67]
Question 36
Score 2: The student made a correct determination, but did not write either function using
proper notation.
36 Michael has $10 in his savings account. Option 1 will add $100 to his account each week.
Option 2 will double the amount in his account at the end of each week.
Write a function in terms of x to model each option of saving.
Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike.
Determine which option(s) will enable him to reach his goal. Justify your answer.
Algebra I (Common Core) – June ’17 [68]
Question 36
Score 1: The student stated both options will work.
36 Michael has $10 in his savings account. Option 1 will add $100 to his account each week.
Option 2 will double the amount in his account at the end of each week.
Write a function in terms of x to model each option of saving.
Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike.
Determine which option(s) will enable him to reach his goal. Justify your answer.
Algebra I (Common Core) – June ’17 [69]
Question 36
Score 0: The student wrote only one appropriate expression.
36 Michael has $10 in his savings account. Option 1 will add $100 to his account each week.
Option 2 will double the amount in his account at the end of each week.
Write a function in terms of x to model each option of saving.
Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike.
Determine which option(s) will enable him to reach his goal. Justify your answer.
Algebra I (Common Core) – June ’17 [70]
Question 37
37 Central High School had fi ve members on their swim team in 2010. Over the next several years,
the team increased by an average of 10 members per year. The same school had 35 members in
their chorus in 2010. The chorus saw an increase of 5 members per year.
Write a system of equations to model this situation, where x represents the number of years since
2010.
Question 37 is continued on the next page.
Algebra I (Common Core) –June ’17 [71]
Question 37
Question 37 continued.
Graph this system of equations on the set of axes below.
x
y
Explain in detail what each coordinate of the point of intersection of these equations means in the
context of this problem.
Score 6: The student gave a complete and correct response.
Algebra I (Common Core) – June ’17 [72]
Question 37
37 Central High School had fi ve members on their swim team in 2010. Over the next several years,
the team increased by an average of 10 members per year. The same school had 35 members in
their chorus in 2010. The chorus saw an increase of 5 members per year.
Write a system of equations to model this situation, where x represents the number of years since
2010.
Question 37 is continued on the next page.
Algebra I (Common Core) –June ’17 [73]
Question 37
Question 37 continued.
Graph this system of equations on the set of axes below.
x
y
Explain in detail what each coordinate of the point of intersection of these equations means in the
context of this problem.
Score 5: The student wrote an incomplete explanation.
Algebra I (Common Core) – June ’17 [74]
Question 37
37 Central High School had fi ve members on their swim team in 2010. Over the next several years,
the team increased by an average of 10 members per year. The same school had 35 members in
their chorus in 2010. The chorus saw an increase of 5 members per year.
Write a system of equations to model this situation, where x represents the number of years since
2010.
Question 37 is continued on the next page.
Algebra I (Common Core) –June ’17 [75]
Question 37
Question 37 continued.
Graph this system of equations on the set of axes below.
x
y
Explain in detail what each coordinate of the point of intersection of these equations means in the
context of this problem.
Score 4: The student wrote a correct system of equations. Both lines are graphed correctly, but
neither one is labeled. An incomplete explanation was written.
Algebra I (Common Core) – June ’17 [76]
Question 37
37 Central High School had fi ve members on their swim team in 2010. Over the next several years,
the team increased by an average of 10 members per year. The same school had 35 members in
their chorus in 2010. The chorus saw an increase of 5 members per year.
Write a system of equations to model this situation, where x represents the number of years since
2010.
Question 37 is continued on the next page.
Algebra I (Common Core) –June ’17 [77]
Question 37
Question 37 continued.
Graph this system of equations on the set of axes below.
x
y
Explain in detail what each coordinate of the point of intersection of these equations means in the
context of this problem.
Score 4: The student wrote a correct system of equations and explained both coordinates in
the context of the problem.
Algebra I (Common Core) – June ’17 [78]
Question 37
37 Central High School had fi ve members on their swim team in 2010. Over the next several years,
the team increased by an average of 10 members per year. The same school had 35 members in
their chorus in 2010. The chorus saw an increase of 5 members per year.
Write a system of equations to model this situation, where x represents the number of years since
2010.
Question 37 is continued on the next page.
Algebra I (Common Core) –June ’17 [79]
Question 37
Question 37 continued.
Graph this system of equations on the set of axes below.
x
y
Explain in detail what each coordinate of the point of intersection of these equations means in the
context of this problem.
Score 3: The student wrote a correct system of equations, but did not graph them correctly. An
incomplete explanation was written.
Algebra I (Common Core) – June ’17 [80]
Question 37
37 Central High School had fi ve members on their swim team in 2010. Over the next several years,
the team increased by an average of 10 members per year. The same school had 35 members in
their chorus in 2010. The chorus saw an increase of 5 members per year.
Write a system of equations to model this situation, where x represents the number of years since
2010.
Question 37 is continued on the next page.
Algebra I (Common Core) –June ’17 [81]
Question 37
Question 37 continued.
Graph this system of equations on the set of axes below.
x
y
Explain in detail what each coordinate of the point of intersection of these equations means in the
context of this problem.
Score 2: The student wrote an appropriate explanation based on their graph.
Algebra I (Common Core) – June ’17 [82]
Question 37
37 Central High School had fi ve members on their swim team in 2010. Over the next several years,
the team increased by an average of 10 members per year. The same school had 35 members in
their chorus in 2010. The chorus saw an increase of 5 members per year.
Write a system of equations to model this situation, where x represents the number of years since
2010.
Question 37 is continued on the next page.
Algebra I (Common Core) –June ’17 [83]
Question 37
Question 37 continued.
Graph this system of equations on the set of axes below.
x
y
Explain in detail what each coordinate of the point of intersection of these equations means in the
context of this problem.
Score 1: The student wrote two appropriate expressions.
Algebra I (Common Core) – June ’17 [84]
Question 37
37 Central High School had fi ve members on their swim team in 2010. Over the next several years,
the team increased by an average of 10 members per year. The same school had 35 members in
their chorus in 2010. The chorus saw an increase of 5 members per year.
Write a system of equations to model this situation, where x represents the number of years since
2010.
Question 37 is continued on the next page.
Algebra I (Common Core) –June ’17 [85]
Question 37
Question 37 continued.
Graph this system of equations on the set of axes below.
x
y
Explain in detail what each coordinate of the point of intersection of these equations means in the
context of this problem.
Score 0: The student did not show enough correct work to receive any credit.
