10TH GRADE
PATTERNS, FUNCTIONS AND ALGEBRA ANSWERS
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Question 31
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When a diver goes underwater, the weight of the water exerts pressure on the diver. The
table below shows how the water pressure on the diver increases as the diver's depth
increases.
Water Pressure on a Diver
Diver's Depth
Water Pressure
(in feet)
(in pounds per square inch)
10
4.4
20
8.8
30
13.2
40
17.6
50
22.0
a. Based on the table above, what will be the water pressure on a diver at a depth of
60 feet? Show your work or explain how you obtained your answer.
b. Based on the table above, what will be the water pressure on a diver at a depth of
100 feet? Show your work or explain how you obtained your answer.
c. Write an equation that describes the relationship between the depth, D, and the
pressure, P, based on the pattern shown in the table.
d. Use your equation from part c to determine the depth of the diver, assuming the
water pressure on the diver is 46.2 pounds per square inch. Show your work or
explain how you obtained your answer.
Scoring Guide
Score
Description
4
The student response demonstrates an exemplary understanding of the algebraic
and patterning concepts underlying the task.
3
The student response demonstrates good understanding of the algebraic and
patterning concepts underlying the task Although there is significant evidence
that the student was able to work with the concepts involved, some aspect of the
response is flawed. As a result the response does not merit a top score.
2
The student response contains fair evidence of understanding some of the
algebraic and patterning concepts and skills underlying the task. While some
aspects of the task are completed correctly, others are not. The mixed evidence
provided merits no more than 2 points.
1
The student response contains only minimal evidence of understanding the
algebraic and patterning concepts/skills underlying the task.
0
The student response contains insufficient evidence of understanding the
algebraic and patterning concepts underlying the task to merit any points.
5
Blank No Response.
2002 MCAS
Grade 10 Mathematics
Question # 31 - Score Point 4
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Question 42
The diagram shown below represents the path of a ball that is dropped from a height of
18 feet. On its first bounce, the ball rebounds to a height of 12 feet; on its second bounce,
it rebounds to a height of 8 feet.
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a. Show that the ratio of the height of Bounce 1 to the starting height is equal to the
ratio of the height of Bounce 2 to the height of Bounce 1. Show your work or
explain how you obtained your answer.
b. Create a table like the one shown below in your Student Answer Booklet.
Bounce, b
Height, h
(in feet)
0 (Starting height)
18
1
12
2
8
3
4
5
c.
If the pattern in the table continues, complete your table to show the height of
bounces 3, 4, and 5.
d. Based on the pattern shown in the table, if h is the height of a certain bounce,
write an expression that represents the height of the next bounce in terms of h.
e. Based on the pattern shown in the table, write an equation that represents the
relationship between height, h, and bounce, b.
Scoring Guide
Score
4
Description
The student response demonstrates an exemplary understanding of the algebraic
and patterning concepts underlying the task.
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3
The student response demonstrates good understanding of the algebraic and
patterning concepts underlying the task Although there is significant evidence
that the student was able to work with the concepts involved, some aspect of the
response is flawed. As a result the response does not merit a top score.
2
The student response contains fair evidence of understanding some of the
algebraic and patterning concepts and skills underlying the task. While some
aspects of the task are completed correctly, others are not. The mixed evidence
provided merits no more than 2 points.
1
The student response contains only minimal evidence of understanding the
algebraic and patterning concepts/skills underlying the task.
0
The student response contains insufficient evidence of understanding the
algebraic and patterning concepts underlying the task to merit any points.
Blank No response.
2002 MCAS
Grade 10 Mathematics
Question # 42 - Score Point 4
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Open Response Question 13
Use the figure below to answer question 13.
In the figures below, math tiles were used to build rectangular arrays to represent each
of the quadratic expressions.
1. Show how to build rectangular arrays, if possible, for each of the following
expressions using the three math tiles.
2x 2 + 3x + 1
3x 2 + 2x
3x 2 + 6x + 5
2. How can you determine if a rectangular array can be built for an expression?
Scoring Guide
Score
4
Description
The response demonstrates a thorough understanding of and facility with
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factoring polynomial expressions.
3
The response demonstrates a general understanding of and facility with factoring
polynomial expressions.
2
The response demonstrates a partial understanding of factoring polynomial
expressions.
1
The response demonstrates a minimal understanding of factoring polynomial
expressions.
0
The response is incorrect or contains some correct work that is irrelevant to the
skill or concept being measured.
Blank No response.
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Open Response Question 16
When Elena works on Saturdays, she buys a salad and juice for lunch. There are two
take-out restaurants near where she works. The prices in the two restaurants are given
below.
Hector's To Go
Juice
$2.00 per bottle
Salad bar 25¢ per ounce
Tammy's Take-Out
Juice
$1.00 per bottle
Salad bar 50¢ per ounce
a. How many ounces of salad, together with a bottle of juice, can Elena buy at
Hector’s To-Go for $4.50?
b. Write an equation that shows the cost, C, of Elena’s lunch at Hector’s To-Go if she
buys a bottle of juice and n ounces of salad.
c. On the grid in your Student Answer Booklet, graph the equation you wrote in part
b.
 Use the horizontal axis for the number of ounces, with each increment
representing one ounce.
 Use the vertical axis for cost, with each increment representing 50¢.
d. What are the different amounts of salad that Elena can buy so her complete lunch
is less expensive at Tammy’s Take-Out than at Hector’s To-Go?
Remember that Elena always buys a bottle of juice with her salad. Show or
explain how you found your answer.
Scoring Guide
Score
4
Description
Response shows comprehensive understanding of systems of linear equations in
two variables by correctly analyzing linear situations algebraically and
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graphically, and by using and explaining correct methods for comparing such
relationships.
3
Response shows general understanding of systems of linear equations by
analyzing situations algebraically or graphically, and by using and/or explaining
correct methods for comparing such relationships.
2
Response shows basic understanding of how to analyze linear relationships
algebraically or graphically.
1
Response shows minimal understanding linear relationships.
0
Response is incorrect or contains some correct work that is irrelevant to the skill
or concept being measured.
Blank No response.
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Open Response Question 41
Use the chart below to answer question 41.
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Mr. Chrostowski is choosing one of the billing plans shown above for his cellular phone.
He estimates that he will use the phone less than 50 minutes per month.
a. If he chooses Plan 1 and uses the phone exactly 50 minutes in one month, what
will his bill be for that month?
b. Suppose that he chooses Plan 1 and uses the phone m minutes in one month.
Write an equation for his total bill, B, for that month.
c. On the grid in your Student Answer Booklet, construct a graph that shows the
monthly bills for Plan 1 for between 0 and 50 minutes of calls.
d. Using your equation or graph, find the number of minutes of phone use for which
the two plans cost the same. Show or explain how you found your answer.
Scoring Guide
Score
Description
4
Response demonstrates a thorough understanding of a real-life linear
relationship by describing and analyzing it algebraically and graphically.
3
Response demonstrates a general understanding of a real-life linear relationship
by describing and analyzing it algebraically and/or graphically, with possible
minor errors.
2
Response demonstrates a basic understanding of describing a real-life linear
relationship algebraically and/or graphically.
1
Response demonstrates a minimal understanding of a real-life linear
relationship.
0
Response is incorrect or contains some correct work that is irrelevant to the skill
or concept being measured.
Blank No response.
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Answer: (1)
Answer: (2)
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Answer: (4)
Answer: (1)
Answer: (2)
Answer: (1)
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Answer: (2)
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Answer: 4
Answer: 4
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Answer: 2
Answer: 3
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Answer: 3
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Answer:
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Answer: 3
Answer: 1
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Answer: 4
Answer: 3
Answer: 3
Answer: 3
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Answer: 2
Answer:
Answer:
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Answer:
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ANSWER: B
ANSWER: C
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ANSWER: A
ANSWER: C
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ANSWER: B
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