# 65 - Department of Mathematics Math 19000 Final Examination...

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Department of Mathematics The City College of New York Math 19000 Final Examination Fall 2005 Instructions: Show all work. You may use a scientific calculator. There are 4 parts. In each part choose 5 questions. Each question is worth 5 points. Part I. Choose any 5 questions from this part. 1) Find the midpoint of the line segment joining (3,- 8) and (-9,-6). 2) Find an equation of the line through point (7, 6) that is perpendicular to the line . 13 5 2 = + y x 3) Find the distance between the points and Q . ) 3 , 8 ( P ) 4 , 4 ( 4) Find the equation of the straight line through points and . ) 3 , 8 ( P ) 4 , 4 ( Q 5) Use long division to simplify the fraction 1 1 3 + + x x . 6) Rewrite 4 4 2 1 2 1 2 + + x x x as a simplified fraction. Part II. Choose any 5 questions from this part. 7) Simplify 2 1 3 3 a b b a so that only positive powers appear in your answer.

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65 - Department of Mathematics Math 19000 Final Examination...

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