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203-exam_1_solutions - Exam#1 Solutions Math 203 Spring...

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Exam #1 Solutions Math 203 — Spring 2011 Fred Bourgoin 1. Translate English phrase or sentence into an algebraic expression or equation. (12 points) (a) 5 more than twice a number Solution. 2 x + 5 (b) The difference between a number and 3 is 9. Solution. x - 3 = 9 (c) Fifteen times the sum of a number and twice another number Solution. 15( x + 2 y ) 2. Calculate. (8 points) (5 - 6) 2 - 4 | 5 - 9 | 135 - 3 · 5 2 Solution. Follow the order of operations. (5 - 6) 2 - 4 | 5 - 9 | 135 - 3 · 5 2 = ( - 1) 2 - 4 | - 4 | 135 - 3 · 5 2 = 1 - 4(4) 135 - 3 · 25 = 1 - 16 135 - 75 = - 15 60 = - 1 4 . 3. Plot each of the points (1 , 2), ( - 2 , 5 2 ), and (3 , 0). (This problem worth 6 pts) y x 1 2 3 - 1 - 2 - 3 - 3 - 2 - 1 1 2 3 0 (1 , 2) (3 , 0) ( - 2 , 5 2 ) 1
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4. Using the graph below, find the slope, the y -intercept, and an equation for the line. (8 points) y x 1 2 3 - 3 - 2 - 1 1 2 3 0 (0 , 2) (3 , 0) Solution. From (0 , 2) to (3 , 0), we have m = rise run = - 2 3 = - 2 3 . The y -intercept is (0 , 2). The equation, then, is y = - 2 3 x + 2 . 5. (12 points) (a) Evaluate the given expression if a = - 2 and b = 3: 2 ab 2 - ( a 3 - 3 b ) Solution. Plug in carefully: 2( - 2)(3) 2 - (( - 2) 3 - 3(3)) = 2( - 2)(9) - ( - 8 - 3(3)) = - 36 - ( - 8 - 9) = - 36 - ( - 17) = - 36 + 17 = - 19 .
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