# 67 - Department of Mathematics Math 19000 The City College...

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Department of Mathematics The City College of New York Math 19000 Final Examination Spring 2005 Instructions: This Exam consists of two parts. In Part I you must do all 5 questions. In Part II choose any 5 complete questions. A scientific calculator is required for some questions. Graphing calculators are not permitted. Show all work. Part I. Do all 5 questions. 1. Simplify completely each of the following. Your answers should be fractions that are completely reduced. a) 2 2 4 1 44 1 x xx +− b) 22 2 232 2 12 12 yyx x yy xy x y −− ÷ 2 2. 32 43 x + −+ 1 1 3. a) 52 25 x x + b) Solve: 11 23 −= 1 4. a) 4 59 / 8 3 3 2 27 x    b) 58 2 7 2 1 2 1 37 2 7 1 8 x y 4 5 5. Solve the equation 17 4 7 x = x and check your answers. End of Part I. You should have answered all questions from this Part. Please turn the page for Part II.

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Part II. Choose any 5 complete questions (omit 2). 6. Find the center and radius of the circle whose equation is . 22 4 4 52 40 24 xy x ++=− y Solution: center (5,-3) radius 21 7. Solve for x only. 40
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67 - Department of Mathematics Math 19000 The City College...

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