M17 LE2 Sem2 09-10 - Mathematics 17 Second Semester AY...

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Unformatted text preview: Mathematics 17 Second Semester AY 2009-2010 Second Long Exam WORK INDEPENDENTLY. SHOW ALL NECESSARY SOLUTIONS. 1. Modified True or False. Write TRUE if the statement is always true. Otherwise, change the underlined phrase/expression to make the statement always true. Show your computations. 1.5 pts each (a) The solution set of the inequality ax 2 + bx + c > 0 is R if a > 0 and b 2- 4 ac < . (b) The general equation of a circle whose diameter has endpoints (1 , 4) and (- 1 , 0) is x 2 + y 2- 4 y + 24 = 0 . (c) The range of the function f ( x ) = √ 9- x 2 is [- 3 , 3] . (d) The graph of the function f ( x ) = x 3- x | x 3 | + 1 is symmetric with respect to the origin . (e) The points (2 , √ 2), ( √ 2 , 2- √ 2), and (0 , √ 2) are collinear . 2. Find the solution set of the following. (a) 2 x 2- | 5 x- 2 | = 0 4 pts (b) r 20 + x x- r 20- x x = √ 6 4 pts (c) | x 2- 5 | x | + 4 | ≥ | 2 x 2- 3 | x | + 1 | 5 pts 3. Find all values of m such that the system 2 mx + y = 6 m 2- 5 m + 1...
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