Final-Fall-2005-06-Muna-Jurdak

Final-Fall-2005-06-Muna-Jurdak - Name: ID number: Time: 2...

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Unformatted text preview: Name: ID number: Time: 2 hours MATH 204 21/01/06 FINAL EXAM First Semester 05/06 Instructor: Mrs. Muna Jurdak Section 9 Tues. 3:30 Section 10 Tues 2:00 Section 11 Tues. 12:30 Section 12 Tues 11:00 1. Mt; your name and ID number clearly where indicated. 2. Circle your section number above, according to the time of the problem-solving session in which you are enrolled. 3. Solve the problems on this= the white guestion sheet. Use the colored sheets for scratch work only. You may use the back of a white sheet to complete the solution of a problem. a — 2 6 (6%) 2. The value of the determinant b 4 —1 = 7. Find the value of the c l 3 5a 0 — 2 determinant 5b 11 4 . Give reasons for your answer. 5c 6 1 (6%) 3. The solution to a system of equations, written in the matrix form AX=B, can be changed to the form *8 ill—il- a) What was the original system of equations? b) What is the solution set for this system? (16%) 4. Perform the following operations: a) Find y = f(x) if g = (x2+ 3)e("+9‘) and 110) = 2 4x b —————dx )£(1+15x2)% (“I 3x+4 x2(x+2)dx 2 (8%) 5. Find all second order partial derivatives (all 4 of them) for f(x,y) =. W 1 x + (9%) 6.Given the function f(x,y) = x2— 4x — 3 + y4 - 2y2. Locate and determine the nature of all critical points of this function. (6%) 7. Approximate the integral J: \lx3 +1dx , using: a) The rectangle rule b) Simpson’s rule Use n = 4 in both (a) and (b). (9%) 8. A graduating class consists of 60% females and 40%males. Of the females, 25% are business majors. Of the males 30% are business majors. If a graduate is selected at random from this class, what is the probability that: a) The student is a male business major. b) The student is a female who isn’t a business major. (7%) 9. A box contains 5 blue socks and 6 white socks. Find the number of ways that two socks can be drawn from the box in the following cases: a) There are no restrictions. b) The 2 socks are of different colors. c) The 2 socks are of the same color. (7%) 10. A normally distributed set of values has mean ,u = 200 and stande deviation 0' =20. Find the values x1, x2 , and x3 , that will divide this set into 4 equal parts. Show your work. (8%) 11. The scores on a quiz for a class of 50 students have a mean of 70 and standard deviation of 10. If the teacher decides to raise each student’s grade by 3 grades, a) What will be the mean of the new raised grades? Justify your answer. b) What will be the new stande deviation? Justify your answer. (11%) 12. Determine the combination of integrals that give the value of each area: Do not evaluate the integrals. a) The area bounded by f(x) = x3 and g(x) = - x2 + 6x. . b) The area bounded by f(x) = 81 - x2, g(x) = 8x2 and the x-axis , for x _>. 0. Note: For this part, it is advisable to draw a sketch. ...
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This note was uploaded on 01/02/2011 for the course MATH 204 taught by Professor Romyarbid during the Three '10 term at Notre Dame AU.

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Final-Fall-2005-06-Muna-Jurdak - Name: ID number: Time: 2...

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