MCAS 2002, 10th Grade Math, Questions 41 to 42
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Question #41 (Open-Response Question)
Cube A is a 1-inch solid cube. Figure B shows a 1-inch solid cube after a
cylindrical hole has been drilled through its center. The diameter of the
cylindrical hole is 1/2 inch, and its height is perpendicular to two opposite
faces of the original cube, as shown in the diagram.
a. What is the total surface area of Cube A?
b. What is the total surface area of Figure B? Show your work or explain how
you obtained your answer.
Question #42 (Open-Response Question)
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.
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.
If the pattern in the table continues, complete your table to show the height
of bounces 3, 4, and 5.
c. 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.
d. Based on the pattern shown in the table, write an equation that represents
the relationship between height, h, and bounce, b.
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