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Unformatted text preview: Math 105 — First Midterm October 12, 2009 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 10 pages including this cover. There are 9 problems. Note that the problems are not of equal difficulty, so you may want to skip over and return to a problem on which you are stuck. 3. Do not separate the pages of this exam. If they do become separated, write your name on every page and point this out to your instructor when you hand in the exam. 4. Please read the instructions for each individual problem carefully. One of the skills being tested on this exam is your ability to interpret mathematical questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work (including appropriate explanation) for each problem, so that graders can see not only your answer but how you obtained it. Include units in your answer where that is appropriate. 6. You may use any calculator except a TI92 (or other calculator with a full alphanumeric keypad). However, you must show work for any calculation which we have learned how to do in this course. 7. If you use graphs or tables to find an answer, be sure to include an explanation and sketch of the graph, and to write out the entries of the table that you use. 8. Turn off all cell phones and pagers , and remove all headphones. Problem Points Score 1 8 2 11 3 12 4 6 5 14 6 18 7 6 8 16 9 9 Total 100 Math 105 / Exam 1 (October 12, 2009) page 2 1 . [8 points] For each statement below, circle TRUE if the statement is always true. Otherwise, circle FALSE. For this problem, justifications for your answers are not expected. a . [2 points] The average rate of change of f ( x ) = 10 x 2 on the interval 1 ≤ x ≤ 2 is given by the ratio (10 1 2 ) (10 2 2 ) 2 1 . True False (The order of the top terms is incorrect.) b . [2 points] In the function defined below, Q 1 (0) = 2. P 1 2 3 5 Q ( P ) 5 13 12 1 True False ( Q (2) = 0; the function is invertible as defined, so Q 1 (0) = 2.) c . [2 points] The function Q ( t ) = 9 e kt is decreasing when 0 < k < 1. True False (The function is increasing for any positive k .) d . [2 points] If f ( t ) is a linear function with a negative average rate of change, then the graph of f ( t ) is concave down. True False (Linear functions are neither concave up nor concave down.) Math 105 / Exam 1 (October 12, 2009) page 3 2 . [11 points] Suppose the University of Michigan offers the following three dining plan options for students living in dorms. The Maize Plan charges students $6 per meal. The Blue Plan charges students a $55 monthly fee in addition to $4 dollars per meal. The third plan, the Wolverine Plan, charges students $240 per month and provides an unlimited number of meals....
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 Fall '08
 Rhea
 Math, Derivative, Thomas Gross

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