© Scarborough
Math 141
Exam 1
Spring 2012
Scarborough
FORM: SNOW
Spring 2012
Math 141
Exam I
NEATLY PRINT NAME: _______________________________________________
STUDENT ID: ____________________________
DATE: February 8, 2012
SECTION: 502/503 (3pm) 510 (11:30am)
SEAT ROW NUMBER: _____________
"On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work."
____________________________________
Signature of student
Academic Integrity Task Force, 2004
http://www.tamu.edu/aggiehonor/FinalTaskForceReport.pdf
This is a 15-question multiple-choice exam; there is no partial credit. Each problem is worth 7 points, for
a total of 105 points. There will be a 20-point deduction if your phone rings or vibrates, or if you have
your phone on your person during the exam. There will be a 5-point deduction if you have other
transgressions. Other transgressions include not having the correct Scantron form 882E, not filling out
your Scantron form correctly, having a folded or mutilated Scantron, not clearing your calculator before
and after the exam, having any electronic device on you during the exam, not having your TAMU student
ID, not following directions, not turning in your exam and Scantron on time (you must be finished filling
in your Scantron and exam cover before time is called), not filling out this exam cover sheet correctly.
You must put your first name and last name, as officially known by TAMU, on this exam cover as well as
on your Scantron; no nicknames or middle names, without your first and last name. The Scantron will not
be returned so also mark all your answers on this test paper. Your exam grade will be posted in WebAssign.
ALL CELL PHONES MUST BE TURNED OFF AND PLACED IN YOUR BACKPACK!
CALCULATORS MUST BE RESET BEFORE AND AFTER THE EXAM!
SCANTRON: Please double check to make sure you have completed your Scantron correctly, as shown
below.
Name: print your legal name neatly (NO NICKNAMES)
Subject: Math 141
Test No.: SNOW
Date: February 2012
Period: your section number
Clear your calculator BEFORE and AFTER your exam. MEM (2nd +), Reset, ALL, Reset
To turn on the correlation coefficient: Catalog (2nd 0), DiagnosticOn, Enter, Enter
Once a mathematician named Dix
Gardened his lot, just for kicks.
And, as everything grows
In columns and rows,
He cheerfully weeded matrix.
-
Jan Gullberg
© Scarborough, Spring 2012, Math 141, Exam 1
2
1. A piece of office equipment, originally worth $6576.41, is worth $5706.92 after 3 years. If the
equipment depreciates linearly, what is its rate of depreciation?
a.
b.
c.
d.
e.
$0.00345 per year
– $289.83 per year
$6576.41 per year
– $6576.41 per year
$289.83 per year
2. Which is a possible solution for X for the matrix equation 2X  B  CX  D ?
Assume all dimensions are compatible and all matrix algebra is defined.
a.
X   B  D  2I  C 
b.
X  2  C 
1
1
 B  D
BD
2I  C
1
d. X   B  D  2  C 
c.
X
e.
X   2I  C 
1
 B  D
3. Assume a is a fixed real number constant. Which of the following is a particular solution to the system
x  y  4z  4  0
of equations?
2 x  3 y  8z  7  0
a.
b.
c.
d.
e.
 8a  5,1, 2a 
 2a,1, 8a  5
 8a  5,1, 2a 
 8a  5, 2a,1
 8a  5,0, 2a 
4. Agco will not market any gadgets if the price drops to $23.50 per gadget. It will supply 1200 gadgets if
it can get $30.25 per gadget. Assuming a linear supply equation, at a price of $55, how many gadgets
will be marketed?
a.
b.
c.
d.
e.
2182
24
6500
5600
991,378
© Scarborough, Spring 2012, Math 141, Exam 1
3
5. The table below gives the dimensions and characteristics of five matrices.
Which one of the following matrix operations is defined?
Matrix
A, singular
B
C
D, non- singular
E
a.
Dimensions
33
43
53
44
34
AB  C 1
b. D1DBT  E
c.
 EE 
T T
A1
d. DET  D
e. D1  E T  B 
6. Matrix A shows the pounds of nails, screws, and bolts needed to build a cottage, townhome, and villa.
Matrix B shows the number of cottages, townhomes, and villas that will be built in the subdivisions of
Aggie, Maroon, and White. Which product matrix has meaning; interpret its meaning?
nails
cottage 100
A  townhome  220
villa 180
screws
bolts
80
200
90 
240 
190 
150
Aggie Maroon White
cottage  60
B  townhome 120
villa  70
70
180
90
80 
140 
130 
a. AT B yields the number of pounds of nails, screws and bolts needed to build in each subdivision
b. B 1 A yields the number of pounds of nails, screws and bolts needed to build each cottage,
townhome and villa
c. ABT yields the number of pounds of nails, screws and bolts needed to build each subdivision
d. BAT yields the number of pounds of nails, screws and bolts needed to build each cottage,
townhome and villa
e. A1B yields the number of cottages, townhomes and villas in each subdivision
© Scarborough, Spring 2012, Math 141, Exam 1
4
7. A toy company has monthly fixed production costs of $18,600 and its costs $15.50 to produce one more
toy. If a toy sells for $25.50, find and interpret the break-even point.
a. To break even, the toy company should produce and sell 1860 gadgets monthly for $47,430 in
revenue.
b. To break even, the toy company should produce and sell 1860 gadgets monthly for $69,192,000
in revenue.
c. To break even, the toy company should spend $18,600 monthly to have no profit or loss.
d. To break even, the toy company should produce and sell 19,250 gadgets monthly to have no
profit or loss.
e. To break even, the toy company should spend $18,615.50 monthly to have no profit or loss.
8. When 6400 items are produced and sold at a price of $200 each, both producers and consumers are
satisfied. No items can be sold when the selling price is $250. What is the price if 9984 items are
demanded by consumers?
a.
b.
c.
d.
e.
$172
$364
$200
$160
$250
9. The data below gives a company’s sales of soccer balls (in thousands of dollars) for certain years. Using
the line of best fit, what would you predict the dollar sale to be in 2014 and in what year would you
predict the sales to be $102,500, respectively?
Year
$K in sales
a.
b.
c.
d.
e.
$96,655.74
$96.66
$2621.25
$2621.25
$96,655.74
2000
80
2003
82
2005
84
2008
90
2011
93
year 2019
year 2018
year 2019
year 2018
year 2018
10. It costs a company $391,620 to make 1050 electronic readers and $729,820 to make 2000 electronic
readers. If there is a loss of $1670 when 50 electronic readers are produced and sold, what is the revenue
if 350 electronic readers are sold?
a.
b.
c.
d.
e.
$3953.40
$237,650
$1,383,690
None of these
$679
© Scarborough, Spring 2012, Math 141, Exam 1
5
11. A plant nursery sells 3 sizes of potted plant arrangements: small, medium, and large. A small potted
plant arrangement contains 3 plants, 5 units of soil, and 1 yard of ribbon. A medium potted plant
arrangement contains 5 plants, 6 units of soil, and 2 yards of ribbon. A large potted plant contains 7
plants, 8 units of soil, and 3 yards of ribbon. The nursery has 526 plants, 662 units of soil, and 212 yards
of ribbon. If the nursery has plenty of pots and wants to use all of the plants, units of soil, and ribbon,
find the number of each type of plant arrangements that should be created. What is the sum of the
number of small and medium plant arrangements?
a.
b.
c.
d.
e.
34
102
68
76
60
12. What are the next 2 best Gauss-Jordan operations in the process to convert this matrix to reduced row1 0 2 4 


echelon form? 0 2 6 8  ?
0 4 5 7 
a.
b.
c.
d.
e.
1
R2  R2 ,  4 R2  R3  R3
2
1
2 R2  R3  R3 , R3  R3
5
1
R1  R1 ,  6 R1  R2  R2
2
1
R2  R2 ,  4 R3  R2  R3
2
3R1  R2  R2 ,  5R1  R3  R23
13. Find the sum of the coordinates of the solution point(s) of the system of equations. That is, if  p, q  is
the solution, what is the value of p  q ?
a. 6
4
b.
3
c. No solution
7
d.
3
11
e.
3
2x  y  5
10 x  y  39
14 x  5 y  63
© Scarborough, Spring 2012, Math 141, Exam 1
6
5 4  2 a 1
14. If C  

 , what is the value of c2,1  c 21  ?
2 1   b 0 3 
a.
b.
c.
d.
e.
Not defined
b
5a – 4
–4 + b
5a
15. In the given system of equations, identify a coefficient matrix and a solution matrix, respectively.
ax  4 y  10
9 x  by  12
1
a 4 
a. 
,
 9 b 
10  a
b.   , 
12  9
10  a 4 
12  9 b 
 

4  10
b  12
a 4 
c. 
,
 9 b 
10  a
d.   , 
12  9
a 4 
e. 
,
 9 b 
 a 4  10
 9 b  12

  
1
4  10
b  12
 a 4  10
 9 b  12

 
1