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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 problemsolving
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 xaxis , for x _>. 0.
Note: For this part, it is advisable to draw a sketch. ...
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 Three '10
 RomyArbid
 Math, Normal Distribution, Standard Deviation, ID NUMBER, stande deviation, matrix form AX=B

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