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preexam1 - Answer-3-1 2 S(2 ∞ 5(10 points Find an...

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College Algebra/Analytic Geometry W1003 Section 003, Spring 2007 Exam 1, Thomas D. Peters Name: March 1, 2007 Do all problems, in any order. Show your work. An answer alone may not receive full credit. No notes, texts, or calculators may be used on this exam. Problem Possible Points Points Earned 1 10 2 10 3 10 4 10 5 10 6 15 7 15 TOTAL 80 1
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1. (10 points) Factor the expression x 5 + x 4 + 27 x 2 + 27 x completely. Answer: x ( x + 1)( x + 3)( x 2 - 3 x + 9) 2. (10 points) Simplify the expression 4 y 2 - 9 2 y 2 + 9 y - 18 2 y 2 + y - 3 y 2 + 5 y - 6 . Answer: 1 3. (10 points) Find all real solutions to the equation x - 5 + x = 5. Answer: x = 21 4. (10 points) Solve the inequality x + 2 x + 3 < x - 1 x - 2 . Express the solution using interval nota- tion and graph the solution set.
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Unformatted text preview: Answer: (-3 ,-1 2 ) S (2 , ∞ ) 5. (10 points) Find an equation of the line through (-1 , 2) which is perpendicular to the line 2 x + 5 y + 8 = 0. Answer:-5 x + 2 y-9 = 0 6. (15 points) (a) Sketch the graph of f ( x ) = 2-( x-1) 3 . (b) What is the range of f ? (c) Is f one-to-one? Why? (d) Find f-1 . Answer: b) (-∞ , ∞ ), c) yes by the horizontal line test, d) f-1 ( x ) = 1 + 3 √ 2-x 7. (15 points) What quantity of a 60% acid solution must be mixed with a 30% solution to produce 300 mL of a 50% solution? Answer: 200 mL 2...
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