109 MA -- College Algebra EXAM 2
Spring 2009 03/11/2009
Name:
Sec.:
Do not remove this answer page -- you will turn in the entire exam. You have two hours to do this exam. No books or notes may be used. You may use a graphing calculator during the exam, but NO calculator with a Computer Algebra System (CAS) or a QWERTY keyboard is permitted. Absolutely no cell phone use during the exam is allowed. The exam consists of multiple choice and short answer questions. Record your answers on this page. For each multiple choice question, you will need to fill in the box corresponding to the correct answer. For example, if (a) is correct, you must write a b c d e
Do not circle answers on this page, but please do circle the letter of each correct response in the body of the exam. It is your responsibility to make it CLEAR which response has been chosen. You will not get credit unless the correct answer has been marked on both this page and in the body of the exam. GOOD LUCK! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. a a a a a a a a a a a b b b b b b b b b b b c c c c c c c c c c c d d d d d d d d d d d e e e e e e e e e e e For grading use: Total (out of 110 pts) 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. a a a a a b b b b b c c c c c d d d d d e e e e e
2 y - 73 = - 7 (x - 77) 5 y = 6 x + 12
9/11 x = -1, y = -13/3 3/2 -7
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Multiple Choice Questions Show all your work on the page where the question appears. Clearly mark your answer both on the cover page on this exam and in the corresponding questions that follow.
1. Let f (x) = x2 - 10x + 24. Find the x-intercept(s) of the graph of f (x). Possibilities: (a) Both (0, 6) and (0, 4) (b) Only (0, 24) (c) Both (6, 0) and (4, 0) (d) Only (0, -24) (e) Both (-6, 0) and (-4, 0)
2. A circle has a diameter with endpoints (13,0) and (1,-6). Find an equation for the circle. Possibilities: (a) (x - 7)2 + (y + 3)2 = 3 5
(d) (x - 7)2 + (y + 3)2 = 45
(b) (x + 7)2 - (y - 3)2 = 45 (c) (x - 6)2 + (y - 3)2 = 3 5 (e) (x - 6)2 + (y - 3)2 = 45
3. A graph contains the point (5, -9). If the graph is symmetric with respect to the origin, then the graph must also contain the point(s): Possibilities: (a) Both (-5, 9) and (-5, -9) (c) (5, 9)
(b) Both (-5, -9) and (5, 9) (d) (-5, 9) (e) (-5, -9)
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4. Which of the following are equations for the line through the points P (-10, 4) and Q(3, 7)? 3 (I) y - 7 = (x - 3) 13 3 (III) y = (x + 10) + 4 13 Possibilities: (a) Only (I). (b) Only (II) and (IV). (c) Only (IV). (d) Only (II). (e) Only (I) and (III). 3 x - 14 13 3 (IV) y + 4 = (x - 10) 13 (II) y =
5. Suppose you need to solve a system of equations in which one equation is y = x2 and the other equation represents a line. How many solutions could your system have? Be sure to included ALL that are possible. Possibilities: (a) The system could only have 0 or 2 solutions. (b) The system could only have 0, 1, or 2 solutions. (c) The system could only have 1 or 2 solutions. (d) The system could only have 0, 1, or infinitely many solutions. (e) The system will never have any solutions because the graph of y = x2 is not a line.
6. A chemist has two large containers of hydrochloric acid (HCl) solution. The concentration of the acid is different in the two containers. She blends 150 mL of the first solution with 50 mL of the second solution to obtain a solution that is 13.750% acid. She blends 50 mL of the first solution with 350 mL of the second solution to obtain a solution that is 8.125% acid. What are the concentrations of hydrochloric acid in the original containers? Possibilities: (a) The first solution is 5% acid, and the second solution 18% is acid. (b) The first solution is 18% acid, and the second solution is 5% acid. (c) The first solution is 7% acid, and the second solution is 16% acid. (d) The first solution is 16% acid, and the second solution is 7% acid. (e) The first solution is 14% acid, and the second solution is 9% acid.
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7. Let f (x) = x2 + 3x - 6. Find f (u + v). Possibilities: (a) u2 + 3u - 12 + v 2 + 3v (c) u2 + 2uv + v 2 + 3u + 3v - 6
(b) u2 + 3u - 6 + v 2 + 3v
(d) u2 + 2uv + v 2 + 3u + 3v - 12 (e) (x2 + 3x - 6) (u + v)
8. A rectangle has an area of 45 square feet and a perimeter of 56 feet. Which system of equations would you solve to find the length l and width w of the rectangle? Possibilities: (a) (b) (c) (d) (e) 2lw = 45 l + w = 56 lw = 45 2l + 2w = 56 lw = 45 l + w = 56 lw = 56 l + w = 45 lw = 56 2l + 2w = 45
9. Which of the following equations are linear equations? (I) y = Possibilities: (a) All of the equations are linear. (b) Only equations (I) and (II) are linear (c) None of the equations are linear. (d) Only equations (II) and (III) are linear (e) Only equation (II) is linear. 7 x+2 (II) y - 3 = 9(x - 2) (III) y = x - 2
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10. Let f (x) =
1 . Find the domain of f (x). x2 - 2x - 15
Possibilities: (a) (-, -3) (-3, 5) (5, ) (c) (-3, 5)
(b) (-, -15) (-15, )
(d) (-, -5) (-5, 3) (3, ) (e) (-, 15) (15, )
11. In the picture below, the graph of y = f (x) is the solid graph, and the graph of y = g(x) is the dashed graph. Find the true statement. y5
4 3
Possibilities: (a) f (2) < g(2) (b) f (4) = 1 (c) f (-3) < g(-3) (d) f (-1) > g(-1) (e) f (-1) = 2
-5 -4 -3 -2
2 1 0 -1 0 -1 -2 -3 -4 -5 1 2 3 4 5
x
12. Let f (x) = 7 - 3x2 . Find Possibilities: 14 - 6x2 - 6xh - 3h2 h 7 (c) - 3h h -6x2 - 6xh - 3h2 (d) h (e) 6x + 3h (b) (a) -6x - 3h
f (x + h) - f (x) . h
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13. The graph of y = f (x) is shown below. Find the maximal interval on which f is increasing. y5
4 3
Possibilities: (a) [-3, 2] (b) [-4, -2] (c) [-2, 4] (d) [-4, 4] (e) Never Increasing
-5 -4 -3 -2
2 1 0 -1 0 -1 -2 -3 -4 -5 1 2 3 4 5
x
14. A child kicks a soccer ball that is on the ground straight up in the air. Two seconds later, the ball lands on a b...