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112-unknown-07spex01 - MATHEMATICS 112 EXAM ONE February...

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Unformatted text preview: MATHEMATICS 112 ' EXAM ONE February 27th, 2007 Name: Instructor and section: 1. There are 8 problems on 9 pages (counting this page). 2. No graphing or programmable calculators, notes, or books are allowed. Scientific calculators are allowed but are not needed. 3. Give exact answers (fractions, square roots, etc.). Decimal approximations may not receive full credit. 4. You do not need to simplify your answers unless told to. Answers such as _ 32 \/ 25 + 6 x” 12 5. Use only the scratch paper provided. Work appearing on your scratch paper will not be graded. are okay. 6. Show your work and make your methods clear. Unjustified answers may receive no credit. 7. Put your final answer in the box provided. ._Possib1e Score 1i (5 points each) Simplify each of the following expressions as much as possible. (Answers on this page Will receive either full credit or no credit.) (a) «3 27a3b6 + 8a5b3 = Answer: (b) 6+ 1—3—1 = 22 ‘ Answer: . i 4 3 2 (‘3) $23333 : ‘ Answer: I - 2. Consider the arithmetic sequence: 9,5,1,—3,-7,—11,'... (a) (5 points) Calcuiate the 39th term in this sequence. Answer: (b) (5 points) If the sum of the let n terms in this sequence is equal to —580, find 72. Answer: (0) (5 points) A geometric sequence has lst term 1/9 and 4th term —3. .Find the 7th term. 1 Answer: , 3. ‘(a) (6 points) Find an equation for the line through (2, 3) and (10, -—7). (b) (6 points) Two lines are parallel if they have the same slope. Let Line #1 be the line through the two points (—4, —5) and (—1, —2). Find an equation for the line through (2, 3) that is parallel to Line #1. Answer: . 4. (a) (6 points) Find all real number solutions to 12x — 17 | = 35. i Answer: . l (b) (6 points) Find all real number solutions to \/$ + 5 = m — 7. Answer: 5, (a) (8 points) Find the center and radius of the circle with equation :52 —-83:+y2+6y = I 0. Answer: ' (b) (4 points) Find all intersection points of the circle 52:2 — 8:1: + y2 + 6y = O with the vertical line :3 = 8. W—‘Wfl—‘fl I Answer: 7 6. (10 points) Three years ago, Bob was twice as old as Amanda. In two years, Amanda’s age will be 3/5 of Bob’s age. How old is Bob right now? Answer: 7‘. (a) (6 points) Find all solutions to the equation t2 '— 52: = 14. Answer: . » (b) ('6 points) Find _a quadratic polynomial, written in the form (1:52 + baa + c, with roots -1 and 3, and x—coeflicient 4. ' Answer: i 8. (6 points each) Solve the following inequalities. Write your answers in interval notation. (a) (1 —- 9x2)(a: + 4) 2 0 CL‘ 1 x+2 l/\ (b) ...
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