Exam_1_Solns precalc - MATH 105 FIRST MIDTERM EXAM...

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MATH 105 — FIRST MIDTERM EXAM Solutions Febuary 05, 2008 NAME: INSTRUCTOR: SECTION NO: 1. Do not open this exam until you are told to begin. 2. This exam has 9 pages including this cover. There are 9 questions. 3. Do not separate the pages of the exam. If any pages do become separated, write your name on them and point them out to your instructor when you turn in the exam. 4. Please read the instructions for each individual exercise carefully. One of the skills being tested on this exam is your ability to interpret questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work for each exercise so that the graders can see not only the answer but also how you obtained it. Include units in your answers where appropriate. 6. You may use your calculator, but all work must be shown. 7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of the graph to make clear how you arrived at your solution. 8. Please turn off all cell phones and other sound devices, and remove all headphones. PROBLEM POINTS SCORE 1 8 2 13 3 8 4 9 5 15 6 15 7 12 8 8 9 12 TOTAL 100
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2 1. (2 points each) For each question, circle either increasing or decreasing. Also, circle either linear, concave down, or concave up. You should circle only one item per row. (a) Jared runs cross country. At the beginning of a race, he has a lot of energy. As the race starts off he loses energy slowly, but as the race goes on, he loses energy more and more rapidly. Is Jared’s energy an increasing or decreasing function of time, and is it linear, concave up, or concave down? increasing decreasing linear concave up concave down (b) An aircraft is ascending at a smaller and smaller rate. Is the aircraft’s altitude as a function of time increasing or decreasing, and is it linear, concave up, or concave down? increasing decreasing linear concave up concave down (c) In a certain country, people are being born at a greater rate than they are dying. However, both the birth and the death rates are constant. Is the population of that country increasing or decreasing, and is it linear, concave up, or concave down? increasing decreasing linear concave up concave down (d) A function is given by x 0 2 4 6 f ( x ) -15 -12 - 8 -3 Based on the data, do you expect this function is increasing or decreasing, and do you expect it is linear, concave up, or concave down? increasing decreasing linear concave up concave down
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3 2. The graph below depicts four linear functions, P , Q , R , and S . The functions y 1 , y 2 , y 3 , and y 4 are the equations of the four lines, and the constants a, b, c > 0 are all positive.
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