Released Test Answer and Alignment Document
High School Math
February 2016
The following pages include the answer key for all machine-scored items, followed by the rubrics for the
hand-scored items.
− The rubrics show sample student responses. Other valid methods for solving the problem can earn
full credit unless a specific method is required by the item.
− In items where the scores are awarded for full and partial credit, the definition of partial credit will
be confirmed during range-finding (reviewing sets of real student work).
− If student make a computation error, they can still earn points for reasoning or modeling.
Answer Key
Item
Number
Evidence
Statement
Key
Course
Alignment
1.
C, E
A-SSE.3a
Algebra 1,
Math 2
2.
B, C
A-APR.1-1
Algebra 1,
Math 2
3.
Part A: A
F-BF.3-4
Algebra 1,
Math 2
A-REI.6-1
Algebra 1,
Math 1
Part B: C
4.
Part A: D
Part B: A
Part C: 0.25
Part D: 0.75
5.
see rubric
HS-D.3-3a
Algebra 1
6.
A, D
G-SRT.7-2
Geometry,
Math 2
PARCC Assessment: February 2016 High School Math Release – Answer and Alignment Document
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7.
G-SRT.6
Geometry,
Math 2
8.
A, C, E
G-CO.1
Geometry,
Math 1
9.
Part A: 42.3 or 42.4
G-Int.1
Geometry,
Math 3
G-C.2
Geometry,
Math 3
A-REI.2
Algebra 2,
Math 3
12.
F-BF.1b-1
Algebra 2,
Math 2
13.
F-BF.Int.2
Algebra 2,
Math 3
F-BF.Int.2
Algebra 2,
Math 3
HS-D.3-6
Algebra 2,
Math 3
Part B: 30
10.
Part A: 66.8 or 66.7 or 66.5
Part B: 70.5 or 70.4
11.
-2.5
Part A:
Part B:
14.
Part A: D
Part B: B
15.
Part A: see rubric
Part B: see rubric
Rubrics start on the next page.
PARCC Assessment: February 2016 High School Math Release – Answer and Alignment Document
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#5 Rubric
Score Description
3
Student response includes the following 3 elements.
o correct estimation for the average rate of change
o correct mathematical reasoning used to determine rate of
change
o correct calculations used to derive the estimation for rate
of change
Sample Student Response:
Looking at the graph, I can determine that a = 2.5 seconds.
Thus, I know h (2.5) = 34.25. Using this information and
knowing h(1) = 23 meters, I can determine that the average
34.25
11.25
− 23
7.5
=
=
rate of change from 1 to a as
2.5 − 1
1.5
meters per second. From looking at the graph, I can also
determine that a is where the maximum height will be reached
and I can also determine there is symmetry around a. The
change in height between a and b is less than the change
between 1 and a. Thus, the rate of change will be close to 7.5
(but less than 7.5) and the value will be negative. I can also
estimate that b = 3.6 seconds and h(b) = 28 meters, thus
34.25 − 28 = 6.25 = −5.68 meters per second. So, a
−1.1
2.5 − 3.6
reasonable estimation for the average rate of change between
a and b seconds is −6 meters per second.
2
Notes:
o An acceptable range for the x-value of h(b) is 3.5 to 3.75
seconds.
o An acceptable range for the y-value of h(b) is 27 to 28.5
meters.
o An acceptable range for the change in x is positive or negative
1.0 to 1.25 seconds.
o An acceptable range for the change in y is positive or negative
5.75 to 7.5 meters.
o An acceptable range for the estimate of the rate of change is 5.0 to -7.5 meters/second.
Student response includes 2 of the 3 elements.
1
Student response includes 1 of the 3 elements.
0
Student response is incorrect or irrelevant.
PARCC Assessment: February 2016 High School Math Release – Answer and Alignment Document
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#15 Rubric Part A
Score
4
Description
Student response includes the following 2 elements.
•
Modeling component = 3 points
o defining the variable
o setting up reasonable model
o correct justification
•
Computation component = 1 point
o correct number of miles: about 416,667 miles
Sample Student Response:
The traditional bus has a fuel efficiency of 5 mpg. With diesel fuel at
$4.20 per gallon, it costs about $0.84 in fuel for 1 mile of driving. The
hybrid-electric bus has a fuel efficiency of 7 mpg and costs about
$0.60 per mile of driving.
Let x represent the number of miles a bus is driven. The number of
miles at which the operating costs are the same is found as follows.
The operating cost C of a traditional bus
is C 400 , 000 + 0.84 x and
=
the operating cost C of a hybrid-electric bus
is C 500 , 00 + 0.60 x . The
=
number of miles at which the operating costs are equal is found as
follows:
400 , 000 + 0.84 x= 500 , 000 + 0.6 x
0.24 x = 100 , 000
x = 416 , 667
For x values less than 416,667, the hybrid has the greater operating
cost. For x values greater than 416,667, the hybrid has the lesser
operating cost. Therefore, after about 416,667 miles of driving, the
hybrid bus has a lower operating cost than the traditional bus.
Note:
The word “miles,” as in “416,667 miles,” should appear somewhere in
context. If not, deduct 1 point from modeling.
3
Student response includes 3 of the 4 elements.
2
Student response includes 2 of the 4 elements.
1
Student response includes 1 of the 4 elements.
0
Student response is incorrect or irrelevant.
PARCC Assessment: February 2016 High School Math Release – Answer and Alignment Document
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#15 Rubric Part B
Score
2
Description
Student response includes the following 2 elements.
Computation component = 1 point
o correct amount of time to recover the cost: 6 years
• Modeling component = 1 point
o correct justification
Sample Student Response:
•
The purchase price of 1 new hybrid-electric bus would be $100,000
greater than the purchase price of 1 new traditional bus. If the bus
runs for 6 hours a day for a year at an average speed of 32 miles per
hour, the bus can be expected to travel about 70,080 miles a year for
a fuel cost of about $42,048 per year. If a traditional bus were
purchased, the fuel cost would be about $58,867.20 per year. A
hybrid-electric bus will save about $16,879.20 in fuel costs. Therefore
it will take about
100 , 000
≈ 5.9 , or 6 years to recover the cost of
16 , 819.2
purchasing the hybrid-electric bus.
OR
If the operating costs are the same at 416,667 miles (from Part A)
and the bus drives 70,080 miles per year, it will take
41, 667
≈ 5.9 , or
70 , 080
6 years to recover the purchase price of the hybrid-electric bus.
1
Student response includes 1 of the 2 elements.
0
Student response is incorrect or irrelevant.
PARCC Assessment: February 2016 High School Math Release – Answer and Alignment Document
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