Math 76O-143 Finite Mathematics
This is Paper Test # 2 [Go to web quiz 2]

Numerical answers are in our text ;
Methods will be discussed using other problems
Links to other web pages were not on original test;
CAUTION: Prof McFarland makes new tests each semester.
MATH 143
Fall 2009
TEST 2
(hour exam)
[A] Put all answers and work in blue books provided
[B] Credit given in proportion to the clarity of your WORK
[C] Enclose all matrices in brackets [ ] or parentheses ( )
[D] You need not repeat work in one problem already shown in another
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Average grade on this test : 34.21 Perfect score = 45 See future grade prospects?
[1] (a)(Pg 61 #11d)(1 pt) Find the slope m of the line with equation [ 6x + 7y + 5 = 0 ].
(b)(Pg 30 #95)(2 pts) Enter numbers below to create an equation for the line passing through
the points (500,1340) and (800,1760).
y =
 
x +
 
(enter numbers in boxes, such as ¾ or 6)
(c)(part of Pg 121 #51)(2 pts) At the right is a matrix which appears while solving (by Gauss/Jordan) a system of 3 equations in variables x and y. At the right, check whichever statement is correct.
1
0
0
-1
2
2
-7
4
4
  (a) The solution is an identity
(b) x = -5, y = 2
(c) x = -5, y = 2, z = 2
(d) There are infinitely many solutions
(e) There are no solutions
Review
these
ideas
[2]
(Pg 51 #9)(5 pts) Dolphin Sports pays $57 for each tent, and re-sells each tent for $79. This store has monthly fixed costs of $780 associated with these tents. If C is Dolphin's cost of x tents, and R is the revenue on the sale of x tents, find C, R, and Dolphin's Break-even point. Show work.

Ask me anything :
I studied this
stuff all night
Cost   C =
 
x +
 
(enter numbers in boxes, such as 3, , or 0)
Revenue   R =
 
x +
 
(enter numbers in boxes, such as 3, , or 0)
Dolphin's Break-even point occurs when   x =
 
[3]
(Pg 77 #17) Find the values of x and y satisfying both equations:
3x - 4y  = 22
2x + 5y  = 7

For each question [4][5][6] , you must state the formula you plan to use (3 pts), as well as the values of all variables occurring in the right side of that formula, such as A, P, r, R, i, m, t, n (whichever are appropriate). The left side of your formula should be a single variable whose value answers the question. After this is done, STOP: do not try to use a calculator to evaluate the right side.

Failure to practice this kind of problem accounted for
more lost points than any other problem type on this test
[4] (Pg 421 #25) To pay for repairs to his house (damaged by Garfield), Jon buys a bond today which will be worth $50,000 in five years. The bond earns interest at an annual rate of 8% compounded quarterly. How much did Jon pay for this bond? (See instructions above)
Jon doesn't like my improvements ???
[5] [Pg 412 #31](2 pts) Mrs. Fox (after much advice from son Peter) obtains a 2-year loan to buy a car. The monthly payments are $400 based upon an annual interest rate of 10% compounded monthly. How much did Mrs. Fox borrow? (See instructions above)
[6] (Pg 394 #27)(2 pts) Sam saves for a web server by depositing equal amounts at the end of every 3 months for 3 years? If the server will cost $4000 and his deposits earn 6% per year compounded quarterly, how much must Sam deposit each 3 months? (See instructions above)
[7] (a)(Pg 137 #49c)(2 pts) Write the following as a single matrix :  
3 1
-2
4
3
  - 2 0
4
2
1
   (b)(Pg 152 #41)(3 pts) Find the following matrix product :  
4
3
-2
4
1
-3
2
1
[8] Use GAUSS/JORDAN method method to solve the system below left, clearly writing all row operations BETWEEN the affected matrices, and using the format rn + k.rm = Rn or k.rn = Rn to name the row operations, where Rn is the name of the (new) row being built, and rn or rm are the name(s) of rows in the (old) existing matrix. For example, "5r2 = R2" replaces old row 2 with a new row 2 which is 5 times as big. This is the naming scheme used during class. The problem is #39 on Pg 100 with equations 1 and 3 interchanged. If your work is correct, you will see NO fractions in your matrices; each step of your work should look as below :
x + y + 2z = 9
2x + y + z = 16
2x + 4y + 2z = 6
 
old matrix
row op name
new matrix
[9] (a)(Pg 170 #9)(2 pts) Find A-1 for the matrix A below, using row operations. Name each row operation as described in [8] above. With correct work, you will encounter no fractions. Answer is given, so credit will be for correct choice and naming of row operations.
A = 
1
3
2
5
  and your answer will be
A-1
-5
3
2
-1
Remember to
check [D]
at the top
of this test
    (b)(Pg 171 #43c)(1 pt) Write the system of equations at the right as
    a a single matrix equation     A.X = B, clearly labeling A, X, and B.
  x + 2y = 3
3x + 5y = 7
  
(c) (Pg 171 #43c cont'd.) (2 pts) Find the solution to the system in [9b] above by calculating X = A-1.B
(for 1 pt), using the matrices A-1 and B from [9a] and [9b]. Separately naming the values of x and y after finding A-1.B is worth 1 pt.