\\
/.
Math 1090.003 Midterm 02
Spriiig 2016
Stucleilt ID #:
Class ID
#:_
Instruct ions:
o
Remove headphones and hats during the exam.
given where appropriate. If no work is shown, there
o Show all work, as partial credit will be
niav be
110
credit givell.
• All final answers should be written in the space provided on the exam and in snnplified
form. When needed give your answer as an exact amount, i.e. a fraction or symbolic
expression, except for dollar amounts which should be rounded to the nearest cent.
• You may ask for scratch paper You may use only the scratch paper provided. Please
transfer all finished work onto the proper page in the test. \Ve will ot grade the work
on the scratch paper. Box your final answer to each problem and write it on the
lines in the right—hand corner, if provided!
• Scientific calculators are allowed on this exam. Absolutely no graphing calcu
lators. No other electronics arc allowed.
• If your phone is out during the exam it will be considered a cheating offense
put your phone away!
PLEASE DO NOT WRITE BELOW. THE TABLE IS TO BE USED FOR GRADING.
Problem
1
2
3
4
5
6
Bonus
Total
1
Score
-
Midterm 02
]\Iatli 1090.003
1. Given
E—3 —3 —31
A=I0
answer the following
why it’s not possible.
questions.
—2
2
If the
—2L
n=[i 2 5],
0]
computation is impossible, state
that and tile reason
BA.
(a) Find
1c3
[10 points]
3
3
A
Inr
-1]
IvCz
c proed
_3
2
-;-4t0
J
0
L
(ii)
Find ATB
[10 points]
rx3
3’
o
/Có(rt
1
cJo
=
A
B
T
-f
OLS
r
fvix
tta
2
Math 1090.003
Miclterin 02
2. For the function y = —3x
2 + iSa; 25, find the vertex, x-intercepts (if there are any), and
determine if the parabola is concave up or (lowli, and sketch the graph
—
[15 points]
—
vertex:
5
C
(3)
3
I (3)
-
5
xi11te1ccpt()
-+54-5
(a))
S4-5c
-
1
z
Concave up
&
-
Concave down
(circle one)
C. D.
0
3
.
Ivlidterni 02
Math 1090.003
Label your lines and axes. I will be grading for accuracy of lines and points.
r
2-
j
-
2
—2
—2
-4
4
6
K
C)1
I
C
I
•%ç
6h
I I
>
-c
I
1_0
—
—
3
1
0
t:J
,.:
0
€
-
i
I
_d°
—‘Jl-0
-
OrJ
o0
±
-7V
I
—
—c-’
60
o
1
I(J
—
-
LA;
U
.c-
(jJ
0
—
0
—
—
0
0
—
,
ltI
rO
—
I
0
H
—
0
—
—,
ill’
cj
0
—
V
Ii
—
0
C
—
cI
-J
C
c)
—
I’
I’
I’
C)
p
-J
çz
Midterm 02
Math 1090.003
4. Given the revenue and cost functions below:
where
R(w)
=
2 + 1600w,
—w
0(w)
=
1500w + 1600
w is the quantity of units produced and sold.
(a) What is the maximum profit?
P()=R()—C(
[15 points]
—/O
- LAJ
-i <
\I,r X
. O1-tó
Cov€1-
-
=)
-
0
D
-
/ OD]
CD.
(a)
kWkXI rr U\ YVX
o
-o
%tAC
=—[oQ
j(Z_io,
-
)00
-
0
(°°() —1oo
SOoSO0O-
oo
0O
(b) How many units must be sold to obtain this maximum
profit?
[5 points]
(b)
6
Math 1090.003
Midterm 02
5. Following the steps below, solve this system of equations using Gauss—Jordan elimination
19.1: + 5y + 3z
3 + 2y + z
2T +
+
2
=
=
=
1
1
1
[20 points]
(a) Begin by writing the system in
çfl
)\f
Matrix
orm.
1
(b) Write the Augmented Matrix.
r9f3
21
I.
\
a:
953
(c) Use Gauss-Jordan elimination to solve for
y
1
2
1-1-2
—
3
J
I
z=
ri
1
1
—3
—
1
-t
0
-ii
—(-3
L°
-t —to
o
(
I
o
ftJ
1)
-I
I
1
I
Jo
-
1
-4
-3
-1D
)
U
I
—.
t—o
—i
-3
L-f
—0
I
o oH
fl
QiD
o
—
1
Midterm 02
Math 1090.002
(Continue work from (c) if needed.)
[
0
(
(2
C
0
J
3
0
H
(d) Check your work
C
0
0
using
Matrix Multiplication to show that your solution is correct.
SHOW YOUR WORK.
—1
1
r
/
V
LA
8
Midterm 02
Math 1090.003
6.
(a) Suppose you are given the equation ax
2 + bx + c
finding the solutions to tins equation.
0. Write the ciuadratic formula for
[15 points]
x
(b) Solve the following quadratic equation for x
using
any method: 3x
2
—
16x + 5
=
b- l.:2
C
x
£
(
(- (bY— 4( )_5
-
0.
Midterm 02
Math 1090.003
Bonus: For the polynomial fmniction below, find the following:
1i(r)
3
a
—
372
—
(a) Its degree.
3
(b) All the zeros (or roots)
—1D
A
(
C
2
x— /Q
)+ )
(e) The v-intercept.
(Uo)
(d) The x-intercept(s).
(uD)
S
(so)
(-1)0)
10