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 Spring 2008 TEST 2 (hour exam) |
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[A] Put all answers and work in blue books provided |
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[B] Credit given in proportion to the clarity of your WORK |
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[C] Enclose all matrices in brackets [ ] or parentheses ( ) |
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[D] You need not repeat work in one problem already shown in another |
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_________________ PRINT name above |
_________________ grade on this test |
_________________ web test credit |
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| [1] |
(a)(Pg 28 #13)(1 pt) Find the slope m of the line
with equation [ x - 3y + 6 = 0 ]. |
(b)(Pg 62 #39)(2 pts) Enter numbers below to create an equation for the line passing
through the points (0,22000) and (5,3000). |
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y = |
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x + |
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(enter numbers in boxes, such as 231 or -46) |
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(c)(part of Pg 121 #57)(2 pts) At the right is an intermediate matrix
when solving (by Gauss/Jordan) a system of 3 equations
in variables x and y. What can be said of the set of solutions
to that original system from which this matrix came? (Hint: Finish Gauss/Jordan) |
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| [2] |
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(part of Pg 53 #49) Marge Simpson's Perfect Body health club exactly breaks even
when it has x = 260 members whose fees produce revenue of $3120. When the club
had only x = 200 members, it lost $330. What were Perfect Body's
costs (in dollars) when it had only 200 members? Show work. Look at the figure (i.e., graph) at the right as you think |
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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. |
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Failure to practice this kind of problem accounted for
more lost points than any other problem type on this test |
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| [4] |
(Pg 394 #29) Uncle Ebenezer deposits $5000 at the end of each year into a trust
for his nephew Tiny Tim. This trust earns 7% compunded annually. If Uncle Ebenezer
dies an hour after making the ninth deposit, how much will Tiny Tim's trust contain
when Uncle Ebenezer dies? (See instructions above) |
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How'd you like to look at my annuities this Friday night? |
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| [5] |
(Pg 412 #43) Courtney borrows $9700 to buy a Toyota Prius. She plans to repay the
loan in monthly payments over the next 5 years. If the bank charges an annual
interest rate of 9% compounded monthly, how much will Courtney pay each month?
(See instructions above) |
| [6] |
(Pg 380 #23 rephrased) Abbey bought a bond 15 years ago which has earned 6%
annual interest rate compounded semiannually and is worth $25000 today. How
much money did Abbey originally invest? (See instructions above) |
| [7] |
(a)(Pg 137 part of #49d)(2 pts) Write the following as a single matrix : |
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| [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 #41 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 : |
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+ |
2y |
- |
z |
= |
-1 |
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y |
+ |
4z |
= |
-7 |
| 2x |
- |
3y |
+ |
2z |
= |
15 |
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Pssst.... Osama will be angry if you ignore this! |
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| [9] |
(a)(Pg 170 #11)(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. |
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A = |
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3 4 |
2 3 |
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and your answer will be |
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A-1 = |
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3 -4 |
-2 3 |
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Remember to check [D] at the top of this test |
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(b)(Pg 170 #11a, on syllabus)(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. |
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| (c) |
(Pg 170 #11a 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. |
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