PRACTICE MIDTERM 1
Math 1220 sec 006
XXX
Name: |
{z
by writing my name i swear by the honor code
}
Read all of the following information before starting the exam:
• Show all work, clearly and in order, if you want to get full credit. I reserve the right to
take off points if I cannot see how you arrived at your answer (even if your final answer is
correct).
• No calculators, notes or books are allowed for this test.
• Please keep your written answers brief; be clear and to the point. I will take points off for
rambling and for incorrect or irrelevant statements.
• You have 100 minutes to work on the exam.
• The practice exam has 5 problems and the actual exam has 6 problems. Prepare accordingly.
• Remember to bring/show your ID during the actual exam.
• Good luck!
Problem (value)
1 (20 points)
2 (10 points)
3 (10 points)
4 (10 points)
5 (10 points)
Total (60 points)
Score
1.
(20 points) PRACTICE EXAM 1 Short Answer. For True/False questions you must write
’True’ or ’False’ and justify your answer.
a. (4 pts)
True or False. sinh x =
b. (4 pts)
Evaluate
c. (4 pts)
Calculate
d. (4 pts)
What is
e. (4 pts)
Prove ax ay = ax+y .
R
R
ex +e−x
2
ex
dx
1+e2x
df
dx
if f (x) = xcos(5x)
1
u du?
2.
(10 points) PRACTICE EXAM 2 At t = 0, a tank contains 100 gallons of saltwater,
holding 50 pounds of dissolved salt. Saltwater containing 3 pounds of salt per gallon is pumped
into the tank at a rate of 5 gallons per minute. Saltwater flows out of the tank at the same rate.
Assuming perfect mixing, find a function that expresses the amount of salt in the tank for t > 0.
3.
(10 points) PRACTICE
3
R EXAM2t+3
a. (5 pts)
Evaluate (t + 7)e
dt.
R
b.R (5 pts) Evaluate sec3 xdx.
(hint: sec(x)dx = ln |sec(x) + tan(x)|)
4.
(10 points) PRACTICE
4
R EXAM
1
a. (5 pts)
Evaluate x4 −16 dx
b. (5 pts)
Evaluate
R
x−7
dx
x2 −x−12
5.
(10 points) PRACTICE EXAM 5
a. (5 pts)
Find f −1 (x) if f (x) = tanh(x).
b. (5 pts)
Derive a formula for the doubling time of a bacteria population governed by
the equation P (t) = Po ekt where k > 0. (You must show all your steps to receive credit - not
just write down a formula remembered from class.)