NAME Math 103 Exam 1 retake 12 December 2008 100 points Instructions 1 This exam has 6 pages including this one which contain 8 problems Please check that you have all of the pages 2 Answer all of the following questions clearly and completely Justify all of your answers 3 You may not use a book or any notes for this exam 4 Give your answer to each problem completely and clearly in the space provided You may use the back of the exam pages for scratch work however if you want this work to be considered make note of it in the space provided for the problem 5 Erase or cross out work you do not wish to be graded 6 Credit partial or full will be given only if sufficient steps leading to the answers are shown 7 You have 50 minutes to complete this exam Page 1 Problem 1 8 points Find the midpoint of the line segment joining the points 2 5 and 12 3 Problem 2 14 points Solve the following inequalities a 7 points 4 3 1 x 3 b 7 points 3t 2 4 Page 2 Problem 3 21 points Solve the following equations a 7 points x 1 x 2 2 3 7 b 7 points x2 4x 1 0 c 7 points x4 10x2 25 0 Page 3 Problem 4 9 points Find the center h k and the radius r of the circle given by the equation x2 y 2 10x 2y 10 0 Problem 5 10 points Solve the following system of linear equations The equations are numbered 1 and 2 for your convenience 2x 4y 6 1 x 3y 12 2 Page 4 Problem 6 15 points a 7 points Find all intercepts of the graph of the equation 2y 8 4x b 8 points Use your answer from part a to graph the equation 2y 8 4x Be sure to describe how you know what the shape of the graph is y 5 4 3 2 1 5 4 3 2 1 1 1 2 3 4 5 Page 5 2 3 4 5 x Problem 7 8 points What is a circle Be as clear and precise as possible Problem 8 15 points An altitude of a triangle ABC is a line segment which has one endpoint at a vertex A of the triangle and the other endpoint on the side BC of the triangle opposite the vertex A and which is perpendicular to the side BC Consider the triangle whose vertices are the points 2 5 1 0 and 5 1 Find an equation for the line containing the altitude from the vertex 1 0 to the opposite side Page 6
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