HSPA Math Macro 2b: Applying
principles of congruence, similarity, transformations, and coordinate
geometry in problem-solving situations
Sample Open-ended
Item #2
Sample Item
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A car starts at point A, travels 8 miles east, and
then turns and travels 10 miles south to reach point B.
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Using graph paper, make a scale drawing using
vectors to show the cars movement, starting from point
A.
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Draw a vector that would show the direct
path from point A to point B. What would be the
approximate number of miles the car could have traveled
along this path?
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Approximately how many
degrees from north would this path be? Explain
how you arrived at this answer.
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Item Introduction
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this item by clicking on one of the links below:
Sample Responses
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responses and scorer comments to this sample test item:
"0" Response | "1" Response | "2" Response | "3" Response | Top
"0" Response
This response scored a "0"
because it does not present or correct answer, and it does not
show any knowledge of the Pythagorean Theorem.
"0" Response | "1" Response | "2" Response | "3" Response | Top
"1" Response
This response scored a "1"
because it shows no work and no answer, even though the diagram
is set up correctly.
"0" Response | "1" Response | "2" Response | "3" Response | Top
"2" Response
This response scored a "2"
because it presents the correct use of the Pythagorean Theorem
and estimation. The response to the angle is reasonable, but incorrect.
"0" Response | "1" Response | "2" Response | "3" Response | Top
"3" Response
This sample shows a complete
understanding of Pythagorean theorem, angles, and calculation,
and answers all parts of the question correctly.
"0" Response | "1" Response | "2" Response | "3" Response | Top
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