MATH 142 Midterm: MATH142 South Carolina 18se1Solution
Spring 2018 Exam 1
MARK BOX
problem points
0 10
1-13 65=13x5
14 5
15 10
16 10
%100
HAND IN PART
NAME: Solutions
PIN: 17
INSTRUCTIONS
•This exam comes in two parts.
(1) HAND IN PART. Hand in only this part.
(2) STATEMENT OF MULTIPLE CHOICE PROBLEMS. Do not hand in this part. You can take this part
home to learn from and to check your answers once the solutions are posted.
•This exam has 3 types of problems: Problem 0, Multiple Choice, and Show All Your Work.
– On Problem 0, fill in the blanks. As you know, if you do not make at least half of the points on Problem 0,
then your score for the entire exam will be whatever you made on Problem 0.
– For Multiple Choice problems, circle your answer(s) on the provided chart. No need to show work. The
statement of multiple choice problems will not be collected.
– For the Show All Your Work problems, to receive credit you MUST:
(1) work in a logical fashion, show all your work, indicate your reasoning;no credit will be
given for an answer that just appears; such explanations help with partial credit
(2) if a line/box is provided, then:
— show you work BELOW the line/box
— put your answer on/in the line/box
(3) if no such line/box is provided, then box your answer.
•The mark box above indicates the problems along with their points.
Check that your copy of the exam has all of the problems.
•Upon request, you will be given as much (blank) scratch paper as you need.
•During the exam, the use of unauthorized materials is prohibited. Unauthorized materials include: books, electronic
devices, any device with which you can connect to the internet, and personal notes. Unauthorized materials
(including ✿✿✿
cell✿✿✿✿✿✿
phones, ✿
as
✿✿✿✿
well✿✿
as
✿✿✿✿✿
your ✿✿✿✿✿
watch) must be in a secured (e.g. zipped up, snapped closed) bag placed
completely under your desk or, if you did not bring such a bag, given to Prof. Girardi to hold for you during the
exam (and they will be returned when you leave the exam). This means no electronic devices (such as cell phones)
allowed in your pockets. At a student’s request, I will project my watch upon the projector screen.
•Cheating is grounds for a F in the course.
•During this exam, do not leave your seat unless you have permission. If you have a question, raise your hand.
When you finish: turn your exam over, put your pencil down and ✿✿✿
raise
✿✿✿✿✿
your ✿✿✿✿
hand.
•This exam covers (from Calculus by Thomas, 13th ed., ET): §8.1-8.5, 8.7, 8.8 .
Honor Code Statement
I understand that it is the responsibility of every member of the Carolina community to uphold and maintain the University of South
Carolina’s Honor Code.
As a Carolinian, I certify that I have neither given nor received unauthorized aid on this exam.
I understand that if it is determined that I used any unauthorized assistance or otherwise violated the University’s Honor Code then
I will receive a failing grade for this course and be referred to the academic Dean and the Office of Academic Integrity for additional
disciplinary actions.
Furthermore, I have not only read but will also follow the instructions on the exam.
Signature :
Prof. Girardi Page 1 of 15 Math 142
Spring 2018 Exam 1
0. Fill-in the blanks.
0.1. arcsin( -1
2) = -π
6(Your answers should be an angle in RADIANS.)
0.2. Double-angle Formula. Your answer should involve trig functions of θ, and not of 2θ.
sin(2θ) = 2 sin θcos θ
0.3. Rdu
u
u6=0
= ln |u|+ C
0.4. Rundu n6=−1
=un+1
n+1 +C
0.5. Reudu =eu+C
0.6. Rsec2u du = tan u+C
0.7. Rsec u du = ln |sec u+ tan u|or
=-ln |sec u−tan u|+C
0.8. R1
a2+u2du a>0
=1
atan-1 u
a+C
0.9. Trig sub.: if the integrand involves u2−a2, then one makes the substitution u=asec θ
0.10. Integration by parts formula: Ru dv =uv −Rvdu
Prof. Girardi Page 2 of 15 Math 142
Spring 2018 Exam 1
MULTIPLE CHOICE PROBLEMS
•Indicate (by circling) directly in the table below your solution to the multiple choice problems.
•You may choice up to 2answers for each multiple choice problem. The scoring is as follows.
∗For a problem with precisely one answer marked and the answer is correct, 5 points.
∗For a problem with precisely two answers marked, one of which is correct, 2 points.
∗All other cases, 0 points.
•Fill in the “number of solutions circled” column. (Worth a total of 1 point of extra credit.)
Table for Your Muliple Choice Solutions Do Not Write Below
problem
number of
solutions
circled
1 2 B x
11a
1b 1c 1d 1e
22a
2b 2c 2d 2e
3 3a 3b 3c 3d
3e
4 4a 4b
4c 4d 4e
55a
5b 5c 5d 5e
6 6a 6b
6c 6d 6e
7 7a 7b 7c 7d
7e
8 8a 8b
8c 8d 8e
9 9a 9b 9c
9d 9e
10 10a 10b 10c 10d 10e
11 11a 11b 11c 11d
11e
12 12a 12b 12c
12d 12e
13 13a 13b 13c 13d
13e
5 2 0 0
Extra Credit:
Prof. Girardi Page 3 of 15 Math 142
Document Summary
Instructions: this exam comes in two parts. (1) hand in part. Hand in only this part. (2) statement of multiple choice problems. You can take this part home to learn from and to check your answers once the solutions are posted: this exam has 3 types of problems: problem 0, multiple choice, and show all your work. On problem 0, ll in the blanks. As you know, if you do not make at least half of the points on problem 0, then your score for the entire exam will be whatever you made on problem 0. For multiple choice problems, circle your answer(s) on the provided chart. The statement of multiple choice problems will not be collected. Put your answer on/in the line/box (3) if no such line/box is provided, then box your answer: the mark box above indicates the problems along with their points.
