MATH 115 — FIRST MIDTERM EXAM
October 8, 2003
NAME:
SOLUTION KEY
INSTRUCTOR:
SECTION NO:
1. Do not open this exam until you are told to begin.
2. This exam has 9 pages including this cover. There are 10 questions.
3. Do not separate the pages of the exam. If any pages do become separated, write your name on them
and point them out to your instructor when you turn in the exam.
4. Please read the instructions for each individual exercise carefully. One of the skills being tested on
this exam is your ability to interpret questions, so instructors will not answer questions about exam
problems during the exam.
5. Show an appropriate amount of work for each exercise so that the graders can see not only the answer
but also how you obtained it. Include units in your answers where appropriate.
6. You may use your calculator. You are also allowed 2 sides of a 3 by 5 notecard.
7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of
the graph to make clear how you arrived at your solution.
8. Please turn
oﬀ
all cell phones.
PROBLEM
POINTS
SCORE
1
16
2
5
3
6
4
11
5
12
6
6
7
8
8
10
9
14
10
12
TOTAL
100
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The questions on this page are multiple choice. They do not require an explanation. For each
question, circle your choice for the correct answer(s). (4 points each part. No partial credit.)
(1A.) Let
V
(
t
) represent the number of thousands of gallons of water in a tank
t
hours after midnight
on a ﬁxed day. Circle the pair of equations below that expresses the following statement:
“At 3PM there were 9000 gallons of water in the tank, and the amount of water in the tank was
decreasing at the rate of 200 gallons per hour.”
(a)
V
(3) = 9000,
V
0
(3) =

200
(b)
V
(3) = 9,
V
0
(3) = 200
(c)
V
(15) = 9000,
V
0
(15) =

200
(d)
V
(15) = 9,
V
0
(15) =

0
.
2
(e)
V
(15) = 9,
V
0
(15) = 0
.
2
(1B.) As
x
→ ∞
, the function
f
(
x
) =
x
3
+3
x
+5
2
x
3

7
x
+6
approaches
(a)
y
= 0
(b)
y
=
1
2
(c)
y
=
5
6
(d)
y
= 1
(e)
∞
(1C.) If the product
f
(
x
0
)
·
f
0
(
x
0
)
·
f
00
(
x
0
)
>
0, then which of the following is possible? Circle any
answer(s) which could be true:
(a) The graph is above the
x
axis, and is decreasing and concave up.
(b) The graph is above the
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 Fall '08
 BLAKELOCK
 Math, Calculus, Derivative, candy corn, cell phone subscribers

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