Teaching Portfolio
Brian Johnson
University of Nebraska-Lincoln
Syllabi
MATH 203–CONTEMPORARY MATH
SECTION 008, 1:30-2:20 MWF, OLDH 308
SPRING 2007
Welcome to Math 203, my name is Brian Johnson, and I will be your instructor for this course. My office is 314 Avery Hall, and my (official) office hours
this semester will be from 9:30am-10:20am Mondays and Wednesdays and 1:30pm2:20pm Tuesdays and Thursdays. If these are inconvenient, then please email me
([email protected]) or call me (Office 472-8244) and we will work something out. Another good place to find this information is on my homepage found at
http://www.math.unl.edu/∼s-bjohns67/
TEXT: We will be using A Mathematical View of Our World by H. Parks, G.
Musser, L. Trimpe, V. Maurer, and R. Maurer. ISBN: 0-495-01061-8.
COURSE OBJECTIVES: In this course we will explore the practical applications of mathematics in the real world. Where many math courses place emphasis
on mastering procedures and methods, this course focuses on developing problem
solving skills and logical thinking. Further, we will explore some of the more useful
and beautiful areas of mathematics and hopefully obtain a higher appreciation for
them. In addition, this course is intended to develop writing and communication
skills in mathematics.
EVALUATION PROCEDURES: You will be assigned a final grade for this
course based on the following:
Homework:
100 points
Quizzes(3):
75 points
Exams (2):
200 points
Journals (5): 200 points
Project:
125 points
Total:
700 points.
Your final grade will be calculated using your accumulated point total. If you get
the following scores, you will receive no less than the grades listed:
679–700: A+ 609–629: B+
651–678: A
581–608: B
630–650: A– 560–580: B–
539–559: C+ 469–489: D+ 0–419: F
511–538: C
441–468: D
490–510: C– 420–440: D–
Note: If you are taking this course Pass/No Pass, you must earn a final grade of at
least C (511 points) to receive a pass grade.
HOMEWORK: At the beginning of each week, I will assign homework problems
to be turned in at the beginning of the following week. Each homework assignment
will be a subset of (in fact, most likely all of) the problems listed in the syllabus of
assigned problems on the last page. I will usually choose to grade 3-4 of all of the
problems turned it, but will not let you know in advance which problems will be
chosen for grading. Most homework assignments turned in will be worth 10 points
each, but this will vary as each week varies in the amount of material we cover.
While some of the problems on the last page will not be collected, I advise you
to work as many of the problems as you can. If possible, do more than assigned
on the last page. Mathematics is not a spectator sport. Just as you cannot train
for a marathon by watching others run, you cannot improve your mathematical
abilities by watching someone else do problems (this will benefit you greatly when
the exams roll around).
1
QUIZZES: There will be three quizzes at the end of the semester over the last
three chapters. Two of them will be in class, and one will be a take-home quiz.
Each will be worth 25 points. Only valid (i.e., university excuses, signed doctor’s
notes, etc.) makeup quizzes will be given.
EXAMS: We will have two in-class hour exams, worth 100 points each. Only valid
(i.e., university excuses, signed doctor’s notes, etc.) makeup exams will be given.
JOURNALS: This course is designed to meet Integrated Studies requirements.
Thus, there will be five journaling assignments throughout the semester, approximately every two weeks or so. Your grade for each journal entry will not only be
based on content, but spelling and grammar as well.
PROJECT: This course involves a project worth 125 points. Details on the project
will be given at the appropriate time during the session. Expect a 4–6 page report
that will involve some sort of research and/or calculations.
ACADEMIC HONESTY: All work in this course must be completed in accordance with the Student Code of Conduct found in the University of Nebraska–
Lincoln Undergraduate Bulletin located at:
http://www.unl.edu/unlpub/undergrad/.
DISCRIMINATION POLICY: The Department of Mathematics does not tolerate discrimination or harassment based on ethnicity, gender, creed, or sexual
orientation. If you believe you were discriminated against or harassed, contact either myself or the department. If you believe your grade was assigned based on
any of the above items, then contact (in order) myself, the department chair, the
department grading appeals committee, the college grading appeals committee, and
the university grading appeals committee.
IMPORTANT DATES:
• 25 Jan 2007 Last day to drop without a “W.”
• 7 Mar 2007 Last day to change to or from Pass/No Pass.
• 11 Apr 2007 Last day to withdraw.
MISCELLANY:
• If you need to miss class, be late for class, or leave class early for any reason,
let me know ahead of time–preferably by email.
• Any students with disabilities or other special needs, who need special accommodations in the course, are invited to share those concerns or requests
with the instructor as soon as possible.
• Please make sure to check the email address associated with your Blackboard account and make sure it is one you check regularly. I will at times
be using Blackboard to make class announcements, and I want to be sure
everyone receives them.
TENTATIVE MATH 203 SCHEDULE AND ASSIGNED PROBLEMS
DATE
M 1/14
W 1/16
F 1/18
M 1/21
W 1/23
F 1/25
M 1/28
W 1/30
F 2/1
M 2/4
W 2/6
F 2/8
M 2/11
W 2/13
F 2/15
M 2/18
W 2/20
F 2/22
M 2/25
W 2/27
F 2/29
M 3/3
W 3/5
F 3/7
M 3/10
W 3/12
F 3/14
M 3/17
W 3/19
F 3/21
M 3/24
W 3/26
F 3/28
M 3/31
W 4/2
F 4/4
M 4/7
W 4/9
F 4/11
M 4/14
W 4/16
F 4/18
M 4/21
W 4/23
F 4/25
M 4/28
W 4/30
F 5/2
SECTION/HOMEWORK
Introduction Read pp.1–12; Do 1.1: 10
Chapter 1 Read pp.18-31; Do 1.1: 4,5,9,13,14,22,23,27,33,36; 1.2: 32
Chapter 1 Read pp. 37–50; Do 1.2: 2,4,5,30,21,32,33,36,37; 1.3: 26
MLK Day
Chapter 1 Read pp. 61–78; Do 1.3: 21,24,31,34,35; 2.1: 6
Chapter 2 Read pp. 86–101; Do 2.1: 4,5,14,19,25,34,36,37; 2.2: 12
Chapter 2 Read pp.112–125; Do 2.2: 3,6,11,14,16,17,21,32; 2.3: 16
Chapter 2 Read pp.339–353; Do 2.3: 4,8,9,17,19,25; 6.1: 16
Chapter 6 Read handout; Do 6.1: 6,10,11,15,20,22,26,27,29,31,32,35,40; Handout: 3b
Eulerization Handout Read pp,260–370; Do Handout: All problems; 6.2: 20
Chapter 6 Read pp.378–395; Do 6.2: 10,14,16,17,23,24,27,28,36,37; 6.3: 22
Chapter 6 Read pp.409–425 and handout; Do 6.3: 2,3,11,12,19,21,38–41; 7.1: 24
Chapter 7 Read pp.432–446; Do Worksheet Ch7a; 7.1: 11,14,18,24,29; 7.2: 22
Chapter 7 Read pp.452–465; Do 7.2: 6,14,16,19,21,25,26,30,31; 7.3: 10
Chapter 7 Do 7.3: 2,6,9,12,14,17,19,23
Catch-up/Review
Review
Exam 1 Read pp.475–489; Do 8.1: 13
Chapter 8 Read pp.503–511; Do 8.1: 3,5,12,22,33,41; 8.2: 8
Chapter 8 Read pp.527–544; Do 8.2: 4,7,10,19,27,41,44; 8.3: 17
Chapter 8 Read pp.563–573; Do 8.3: 2,9,11,14,25; 9.1: 5
Chapter 9 Read pp.578–586; Do 9.1: 1,4,8,11,13,15,17,22; Start worksheet; 9.2: 2
Chapter 9 Read pp.594–608; Do 9.2: 1,5,9,22,30ab,37–40; Worksheet; 9.3: 18
Chapter 9 Read pp.631–644; Do 9.3: 3,4,7,11,13,16abce, 27ab, 31; Finish worksheet; 10.1: 3
Chapter 10 Read pp.652–664; Do 10.1: 2,4,9,12,15,19,32,34,40,41; 10.2: 13
Chapter 10 Read pp.673–681; Do 10.2: 4,8,17,19,21,22,25,39,41,45; 10.3: 18
Chapter 10 Read pp.682–686; Do 10.3: 1,4,5,7,10,15,17,27,30,36
Spring Break
Spring Break
Spring Break
Chapter 10 Read pp.699–711; Do 10.3: 31,33–42,44,49; 11.1: 13,14
Chapter 11 Read pp.715–723; Do 11.1: 4,10,15,17,20,21,24,30,31,33,37,40,44; 11.2: 10
Chapter 11 Read pp.729–738; Do 11.2: 2,3,5,9,11,14,20,26,33; 11.3: 24
Chapter 11 Do 11.3: 1,4,7,9,17,23,30,36,39,42
Catch-up/Review
Review
Exam 2 Read pp.141–153; Do 3.1:16
Chapter 3 Read pp.163–172; Do 3.1: 2–6,8,15,18–20,25,28–40; 3.2: 22
Chapter 3 Read pp.183–192; Do 3.2: 2,3,7,11–13,17,19,20,23,25,31–33; 3.3: 26ab
Chapter 3 Read pp.205–223; Do 3.3: 6,8,13,15,17,20–22,24,28,29,34,35,38; 4.1: 24
Chapter 4 Read pp.235–249; Do 4.1: 3,6,7,12,13,25,28,32,41,44; Do 4.2: 14
Chapter 4 Read pp.256–273; Do 4.2: 1,2,9,12,14,30; Worksheet Ch4a; 4.3: 16
Chapter 4 Read pp.285–299; Do 4.3: 5,9,14,19,17,22,24,28,29,34,35,38; 5.1: 12
Catch-up/Review/Quiz
Chapter 5 Read pp.306–316; Do 5.1: 2,6,7,11,13,22,23,33,37,38; 5.2: 16
Chapter 5 Read pp.322–329; Do 5.2: 5,6,11,12,15,21–23; 5.3: 16
Chapter 5 Do 5.3: 1–3,6,7,10,11,13,18–21
Catch-up/Review/Quiz
MATH 107–CALCULUS II
SECTION 610, 9:15-10:50 MTWRF, M&N B5
2nd SUMMER SESSION 2008
Welcome to Math 107, my name is Brian Johnson, and I will be your instructor for this course.
My office is 314 Avery Hall, and my (official) office hours this semester will be from 1:30 PM-2:30 PM
Monday through Friday. If these are inconvenient, then please email me ([email protected])
or call me (Office 472-8244) and we will work something out. Another good place to find this
information is on my homepage found at
http://www.math.unl.edu/∼s-bjohns67/
TEXT: We will be using University Calculus by Hass, Weir, and Thomas, ISBN: 0-321-35014-6.
PREREQUISITES: Students who have not completed MA 106 with a grade of C or better will
be dropped from the class. If you have completed the equivalent prerequisite elsewhere, you should
contact the Mathematics Department immediately.
COURSE OBJECTIVES: We’ll cover integration techniques, some applications to physics and
other sciences with integrals, an introduction to infinite sequences and series and their convergence,
and an introduction to three dimensional calculus.
EVALUATION PROCEDURES: You will be assigned a final grade for this course based on the
following:
Quizzes:
25%
Exams (4):
40%
Gateway Exam : 10%
Final Exam:
25%
If you get the following scores, you will receive no less than the grades listed:
97%: A+
93%: A
90%: A–
87%: B+ 77%: C+ 67%: D+
83%: B
73%: C
63%: D
80%: B– 70%: C– 60%: D–
<60%: F
Note: If you are taking this course Pass/No Pass, you must earn a final grade of at least C to receive
a pass grade.
HOMEWORK: Homework will be assigned on a regular basis throughout the course. While the
homework is not collected, it is not optional. I advise you to work as many of the problems as you
can. If possible, do more than assigned on the syllabus. Mathematics is not a spectator sport. Just
as you cannot train for a marathon by watching others run, you cannot improve your mathematical
abilities by watching someone else do problems.
QUIZZES: Most quizzes will be given in recitation, but there may be unannounced quizzes in
lecture as well. The quizzes will be averaged for a significant part of your final grade.
EXAMS: We’ll have four in class exams and a final. The first four exams will be in recitation on
Fridays, and the final will be in lecture the last day of class, 14 Aug 2008. No calculators will be
allowed on the exams.
GATEWAY EXAM: This exam consists of seven questions covering techniques of integration.
You will not be allowed to use a calculator or notes. You must answer six out of the seven questions
1
completely correct to receive full credit - no partial credit is given. If you do not pass the gateway
exam when it is first given, then you can retake it online at the Mathlab (Avery 018) or the College
Testing Center (Burnett 127). A picture ID is required and you may only take the exam once per
day. The written gateway exam will be given in the last 50 minutes of recitation on 23 July 2008.
The deadline for completing the gateway exam is 4 Aug 2008.
RESOURCES: If you are having trouble, you should see me or your TA as soon as possible.
Another place you can go is the Math Resource Center (MRC). It is located in Avery 018 and is
open from 7:30 AM until 5:30 PM Monday through Friday.
ADVANCED PLACEMENT PROGRAM: If this is the first college mathematics course that
you have attempted, then you may be eligible for 5 hours of free credit for Math 106, provided you
get a grade of C, P or better in Math 107 this semester and you are a fully admitted student at UNL
(visiting students are not allowed to participate in this program). To be considered for this credit,
you should register with the Department of Mathematics, 203 Avery Hall by Friday, 25 Jul 2008.
ACADEMIC HONESTY: All work in this course must be completed in accordance with the
Student Code of Conduct found in the University of Nebraska–Lincoln Undergraduate Bulletin
located at: http://www.unl.edu/unlpub/undergrad/
DISCRIMINATION POLICY: The Department of Mathematics does not tolerate discrimination or harassment based on ethnicity, gender, creed, or sexual orientation. If you believe you were
discriminated against or harassed, contact either myself or the department. If you believe your
grade was assigned based on any of the above items, then contact (in order) myself, the department
chair, the department grading appeals committee, the college grading appeals committee, and the
university grading appeals committee.
IMPORTANT DATES:
• 18 Jul 2008 Last day to drop without a “W.”
• 29 Jul 2008 Last day to change to or from Pass/No Pass.
• 6 Aug 2008 Last day to withdraw.
MISCELLANY:
• If you need to miss class, be late for class, or leave class early for any reason, let me know
ahead of time–preferably by email.
• Any students with disabilities or other special needs, who need special accommodations in
the course, are invited to share those concerns or requests with the instructor as soon as
possible.
• Please make sure to check the email address associated with your Blackboard account and
make sure it is one you check regularly. I will at times be using Blackboard to make class
announcements, and I want to be sure everyone receives them.
SCHEDULE: This is the anticipated schedule of what I hope to cover.
July 14 M
July 15 T
July 16 W
July 17 R
July 18 F
Aug 4 M
Aug 5 T
Aug 6 W
Aug 7 R
Aug 8 F
5.4–5.6
7.1/7.2
7.3/7.4
7.5/7.7
7.6
9.1/9.2
9.3
10.1/10.2
10.3
10.4/10.5
July 21 M
July 22 T
July 23 W
July 24 R
July 25 F
Aug 11 M
Aug 12 T
Aug 13 W
Aug 14 R
6.1/6.2/6.3
(6.4?)/6.5
6.6/6.7
8.1
8.2
11.1/11.2
11.3/11.4
11.5
Final Exam
July 28 M
July 29 T
July 30 W
July 31 R
Aug 1 F
8.3/8.4
8.5/8.6
8.7
8.8/8.9
8.10
MATH 208–CALCULUS III
SECTION 601, 11:00-1:10 MTWRF, AVH 108
SECOND SUMMER SESSION 2009
Welcome to Math 208, my name is Brian Johnson, and I will be your instructor for this
course. My office is 314 Avery Hall, and my (official) office hours this semester will be from
9:30am-10:50am Monday through Friday. If these are inconvenient, then please email me
([email protected]) or call me (Office 472-8244, but don’t leave a message because I
can’t check the voicemail) and we will work something out. Another good place to find this
information is on my homepage found at
http://www.math.unl.edu/∼s-bjohns67/
TEXT: We will be using University Calculus by Hass, Weir, and Thomas. ISBN: 0-32135014-6.
PREREQUISITES: Students who have not completed Math 107 with a grade of C or
better will be dropped from the class. If you have completed the equivalent prerequisite
elsewhere, you should contact the Mathematics Department immediately.
COURSE OBJECTIVES: By the end of the course, you should understand the foundations of multivariable calculus and some applications to outside fields. Some particulars we’ll
cover will be vector functions, differentiation of multivariable functions, multiple integrals,
and vector fields.
EVALUATION PROCEDURES: You will be assigned a final grade for this course based
on the following:
Quizzes:
24%
In-class Exams (4) : 48% (i.e., 12% each)
Final Exam:
28%
If you get the following scores, you will receive no less than the grades listed:
97%: A+ 87%: B+ 77%: C+ 67%: D+ <60%: F
93%: A
83%: B
73%: C
63%: D
90%: A– 80%: B– 70%: C– 60%: D–
Note: If you are taking this course Pass/No Pass, you must earn a final grade of at least C
(73%) to receive a pass grade.
HOMEWORK: Homework is listed on the tentative schedule for the course. While the
homework is not collected, it is not optional. I advise you to work as many of the problems as
you can. If possible, do more than assigned on the schedule. Mathematics is not a spectator
sport. Just as you cannot train for a marathon by watching others run, you cannot improve
your mathematical abilities by watching others do problems.
QUIZZES: Quizzes will be a significant portion of your grade. They are not listed on the
schedule as this goes to press, but I will try to give a day or two notice when they are coming
up. Quiz problems will come directly from the homework.
1
EXAMS: We will have four in-class exams and a final exam. The final will be the last
day of lecture, 13 Aug 2009. Only valid (i.e., university excuses, signed doctor’s notes, etc.)
makeup exams will be given.
RESOURCES: If you are having trouble with the material, see me as soon as possible.
This class moves at an incredibly accelerated pace, and you cannot afford to fall behind.
Also, if possible, try to find another person in the class that you can work and check answers
with.
ADVANCED PLACEMENT PROGRAM: If this is the first college mathematics
course that you have attempted, then you may be eligible for 10 hours of free credit for
Math 106 and 107, provided you get a grade of C, P, or better in Math 208 this semester and
you are a fully admitted student at UNL (visiting students are not allowed to participate in
this program). To be considered, register with the Department of Mathematics, 203 Avery
Hall as soon as possible.
ACADEMIC HONESTY: All work in this course must be completed in accordance with
the Student Code of Conduct found in the University of Nebraska–Lincoln Undergraduate
Bulletin located at:
http://www.unl.edu/unlpub/undergrad/.
DISCRIMINATION POLICY: The Department of Mathematics does not tolerate discrimination or harassment based on ethnicity, gender, creed, or sexual orientation. If you
believe you were discriminated against or harassed, contact either myself or the department.
If you believe your grade was assigned based on any of the above items, then contact (in
order) myself, the department chair, the department grading appeals committee, the college
grading appeals committee, and the university grading appeals committee.
IMPORTANT DATES:
• 17 Jul 2009 Last day to drop without a “W.”
• 28 Jul 2009 Last day to change to or from Pass/No Pass.
• 5 Aug 2009 Last day to withdraw.
MISCELLANY:
• If you need to miss class, be late for class, or leave class early for any reason, let me
know ahead of time–preferably by email.
• Any students with disabilities or other special needs, who need special accommodations in the course, are invited to share those concerns or requests with the instructor
as soon as possible.
• Please make sure to check the email address associated with your Blackboard account
and make sure it is one you check regularly. I will at times be using Blackboard to
make class announcements, and I want to be sure everyone receives them.
TENTATIVE MATH 208 SCHEDULE AND ASSIGNED PROBLEMS
AS OF 29 JULY 2009
DATE
M 7/13
T 7/14
W 7/15
R 7/16
F 7/17
M 7/20
T 7/21
W 7/22
R 7/23
F 7/24
M 7/27
T 7/28
W 7/29
R 7/30
F 7/31
M 8/3
T 8/4
W 8/5
R 8/6
F 8/7
M 8/10
T 8/11
W 8/12
R 8/13
MATERIAL HOMEWORK
10.1-10.3
10.1: 7,17,27,37,47,49
10.2: 7,12,24,32,44,52
10.3: 3,13,29,30,33,35,43
10.4-10.5
10.4: 1,3,7,11,15,16,20,21,29,31,33,37
10.5: 3,6,9,18,19,21,22,23,25,35,43,47,59,61
10.6,11.1, Quiz 10.6: 1-12,15,20,15,20,21,23,25,27,29,31,33-44
11.1: 3,7,17,21,23,26
11.2,11.3
11.2: 2,3,4,6,7,10,11,13,17
11.3: 1,3,5,6,8,11,12
Exam, 11.4
11.4,11.5, Quiz 11.4:
11.5:
12.1,12.2
12.1: 6-9,11,13-18,21,22,29,41,42
12.2: 2,3,14,17,18,22,25,29,31,37,41,45,51,56
12.3, Quiz
12.3: 2,3,6,7,11,12,16,17,25,27,31,34,40,43,46,55,57,67,68,73,74
12.4,12.5
12.4: 3,7,10,11,15,26,29,33
12.5: 4,6,7,10,13,16,17,19,22,23,24,31,32
Exam, 12.6
12.6,12.7
12.6: 1,4,11,16,17,26,29,31,39,48,49,52
12.7: 9,17-19,23,26,28,31,34,36,39,47,51
12.8
12.8: 1,3-5,8-11,13,16,17-19,23,26-28,37
13.1,13.2, Quiz 13.1: 1,7,9,10,14,15,18,23,25,28
13.2: 1,5,8,13,15,17,19,25-27,30,35,36,39,40,45,55
13.3,13.4,13.5 13.3: 1,3,6,7,9-11,13,15,17,18,20
13.4: 3,9,12,14,16,18,19,24,28,29
13.5: 3,6,9,10,14,22,27,29,33,34,36,37,41,43,44,47
Exam, 13.5
13.6,13.7
13.6: 1,5,9,12,13,17,19,20,21,25,29
13.7: 4,10-15,18,26,27,29,32,34-38,40,49,52,59,74,77
14.1,14.2
14.1: 1-8,11-15,19-21,27,30
14.2: 3,7,10,13,14,17,18,21,22,23,27-29,35,38,41,43
14.2,14.3, Quiz 14.3: 1-6,8,9,11,14,15,18,25,31,33,36,37
14.4,14.5
14.4: 1,4,6,7,11,17-19,22,24,26,29,31,34
14.5: 2,3,5-9,12,13,15,17,20,22,23,24,27,30,38,41,47-49
Exam, 14.6
14.6,14.7
14.6: 1,3,6,7,13,15,18,20,21,27,29,33,39
14.7: 1,3,4,6,9,8-10,13,16,17,20-23,26
14.7,14.8,Quiz 14.8: 5-8,10,12,13,15,17,25
14.8, Review
Final Exam
1
Exams
MATH-101 Section 007
College Algebra
Exam #3
Name:
The majority of the credit you receive will be based on the completeness and the clarity of your
responses. Show your work, and avoid saying things that are untrue, ambiguous, or nonsensical.
This exam has 14 questions, for a total of 95 points.
1. Solve.
(5 points)
(a)
x
1
2
−
= 2
x−1 x+1
x −1
(5 points)
(b)
√
(5 points)
(c) |x − 5| − 4 = 7
(7 points)
18 − 3x = 3
2. Solve and graph (on a number line) the absolute value inequality: |2x + 3| ≤ 7
Page 1 of 5
Instructor: Brian Johnson
MATH-101 Section 007
College Algebra
Exam #3
(7 points)
3. The Addison Bank offers two checking account plans. The Smart Checking plan charges 25¢ per check
whereas the Consumer Checking plan costs $6 per month plus 10¢ per check. For what number of checks
will the Smart Checking plan cost less?
(8 points)
4. Graph f (x) = (x + 2)(x − 1)(x − 2). Be sure to include these four things: x- and y- intercepts, the end
behavior, and the intervals on which the function is positive or negative.
Page 2 of 5
Instructor: Brian Johnson
MATH-101 Section 007
College Algebra
(6 points)
(6 points)
(6 points)
Exam #3
5. Suppose f (x) = x3 + x2 + 4x − 6.
(a) Use long division to determine if x + 1 is a factor of f (x).
(b) Use synthetic division to determine if x − 2 is a factor of f (x).
6. Use any method to find the quotient and remainder for (2x4 + 7x3 + x − 12) ÷ (x + 3).
Page 3 of 5
Instructor: Brian Johnson
MATH-101 Section 007
College Algebra
Exam #3
(7 points)
7. Using the intermediate value theorem, determine, if possible, whether the function f has a real zero
between a and b: f (x) = x3 − 5x2 + 4, a = 4, b = 5.
(5 points)
8. What are the zeros and multiplicities of each of the polynomial g(x) = (x − 5)4 (x − 3)(x + 6)3 ?
(5 points)
9. Find a polynomial of degree 3 with the numbers 3, 2 −
(3 points) 10. Simplify, then write in radical notation:
√
3, 2 +
√
3 as zeros.
(2a1/3 )(5a4/3 )
Page 4 of 5
Instructor: Brian Johnson
MATH-101 Section 007
College Algebra
Exam #3
(5 points) 11. Suppose that a polynomial
function of degree 5 with rational coefficients has the numbers
√
71, −2 + 5i, 4 − 11 as zeros. Find the others.
(5 points) 12. Given that 4 is a zero of f (x) = x3 − 6x2 + 13x − 20, completely factor f (x).
(5 points) 13. Does the function h(x) =
(5 points) 14. Does the function k(x) =
x2 − 4
have any vertical asymptotes? If so, which?
x(x − 7)(x − 2)
5x2 − 4
have any horizontal asymptotes? If so, which?
+ 3x + 5
4x2
Page 5 of 5
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Exam #1
Name:
The majority of the credit you receive will be based on the completeness and the clarity of your
responses. Show your work, and avoid saying things that are untrue, ambiguous, or nonsensical.
This exam has 10 questions, for a total of 100 points.
(8 points)
1. Give a description and a sketch of the region in space bounded by the inequalities z ≤ 0 and (x + 1)2 +
(y + 2)2 + z 2 ≤ 4.
(8 points)
2. You take your pet rock out for a walk. To pull it along the ground, you must exert a force, F, of 7
pounds. The leash makes an angle of π/6 with the ground. Write F in component form.
Page 1 of 5
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Exam #1
(10 points) 3. Is the triangle determined by the points P (1, 1), Q(−1, 3), and R(2, 4) a right triangle? Explain how
you know.
v
, where θ is the angle between u and v, use the definition and
|v|
�u · v�
properties of the dot product to show that
v = projv u.
v·v
(10 points) 4. Recalling that projv u = (|u| cos θ)
(8 points)
5. Find a third vector orthogonal to the two vectors u = i − j + 2k and v = 6i + j + k.
Page 2 of 5
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Exam #1
(10 points) 6. Find parametric equations for the line through the two points (6, 2, 7) and (2, 2, 0).
(10 points) 7. Find an equation for the plane through the point A(1, −2, 1) and perpendicular to the vector from
(0, 0, 0) to A.
Page 3 of 5
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Exam #1
(16 points) 8. Below are the graphs of the four following equations. Below each graph, match the letter of the equation
corresponding to its graph.
y2
x2
(A) 4x2 + 4y 2 + z 2 = 16
(B)
−
− z2 = 1
(C) z − y 2 = 1
(D) 4x2 + 9z 2 = 9y 2
4
4
Page 4 of 5
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
(5 points)
(5 points)
Exam #1
9. A particle has a path given by r(t) = (1 − cos t)i + (sin(2t))j.
(a) Find v(t) and a(t).
(b) Are v(t) and a(t) orthogonal for all t? Justify your answer.
(10 points) 10. Find parametric equations for the tangent line to the curve r(t) = (sin 2t)i + (cos 2t)j + tk at time
t = π/4.
Page 5 of 5
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Final Exam
Name:
The majority of the credit you receive will be based on the completeness and the clarity of your
responses. Show your work, and avoid saying things that are untrue, ambiguous, or nonsensical.
This exam has 10 questions, for a total of 140 points.
(14 points) 1. Solve the following initial value problem:
Differential Equation:
Initial Conditions:
d2 r
= i + 2j + 2tk
dt2
r(0) = i + k
dr ��
= 0
�
dt t=0
Page 1 of 10
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Final Exam
(14 points) 2. Suppose r(t) = (3 cos t)i+(3 sin t)j+4tk. Find the unit tangent, principal unit normal, the unit binormal,
and curvature of r(t)
(a) unit tangent
(b) principal unit normal
(c) binormal
(d) curvature
Page 2 of 10
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
(5 points)
(9 points)
3. (a) Evaluate:
lim
(x,y)→(5,2)
Final Exam
(x5 + 4x3 y − 5xy 2 )
(b) Show the following limit does not exist:
2x2 y
(x,y)→(0,0) x4 + y 2
lim
Page 3 of 10
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Final Exam
(14 points) 4. Find and classify all local extrema and saddle points for the function
f (x, y) = x3 y + 12x2 − 8y.
Page 4 of 10
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Final Exam
(14 points) 5. Find the minimum and maximum values of f (x, y, z) = 8x − 4z subject to the constraint
x2 + 10y 2 + z 2 = 5.
Page 5 of 10
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Final Exam
(14 points) 6. Evaluate the following iterated integral, where a is a constant, by converting it first to an iterated double
integral in polar coordinates.
� a � √a2 −x2
(x2 + y 2 )3/2 dx dy
−a
0
Page 6 of 10
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
(7 points)
Final Exam
7. (a) Write an integral in cylindrical �
coordinates in the order dz dr dθ for the volume of the region
bounded below by the cone z = x2 + y 2 and above by the plane z = 2. DO NOT EVALUATE.
-2
-1
-1
0
Y
0
1
1
X
2 2
(7 points)
(b) Write an integral in spherical
coordinates in the order dρ dφ dθ for the volume of the region bounded
�
2
below by the cone z = x + y 2 and above by the upper hemisphere of the sphere x2 +y 2 +z 2 = 4z.
DO NOT EVALUATE. (Hint: You know that x2 + y 2 + z 2 = ρ2 and that z = ρ cos φ. You can use
these to find an equation for the hemisphere in terms of ρ and φ.)
-2
-1
-1
0
Y
0
1
1
X
2 2
Page 7 of 10
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
(14 points) 8. Evaluate
Final Exam
�
ey dx + 2xey dy,
C
where C is the boundary of the region enclosed by the lines x = 0, x = 1, y = 0, and y = 1.
Page 8 of 10
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Final Exam
9. Consider the portion of the plane y + 2z = 2 inside the cylinder x2 + y 2 = 1.
(7 points)
(a) Find a parametrization r(u, v) of the portion of the plane described above.
(7 points)
(b) Set up a double iterated integral to find the surface area of the portion of the plane above. DO
NOT EVALUATE.
Page 9 of 10
Instructor: Brian Johnson
MATH-208 Section 601
Calculus III
Final Exam
(14 points) 10. The upper hemisphere of radius a centered at the origin can be realized two ways. One way is as
the level surface g(x, y, z) = x2 + y 2 + z 2 − a2 = 0, where z ≥ 0. The other is the parametrization
r(φ, θ) = (a sin φ cos θ)i + (a sin φ sin θ)j + (a cos φ), where 0 ≤ φ ≤ π/2, 0 ≤ θ ≤ 2π. Use one of these to
set up a double iterated integral to find the flux of F = xi + yj + zk across the sphere in the direction
away from the origin. DO NOT EVALUATE.
Page 10 of 10
Instructor: Brian Johnson
MATH-106 Section 750
Calculus I - Fall 2011
Exam #3
Name:
The majority of the credit you receive will be based on the completeness and the clarity of your
responses. Show your work, and avoid saying things that are untrue, ambiguous, or nonsensical.
This exam has 9 questions, for a total of 100 points.
(12 points) 1. Evaluate the following limits exactly:
1 − cos x
(a) lim
x→0
x2
(b) lim
t→0
sin t
et
(10 points) 2. For the curve in the xy-plane given by the parametric equations
�
x = 2 cos t
,
0 ≤ t ≤ π,
y = 2 sin t
find the equation of the tangent line at the point corresponding to t = π/4, and sketch both the tangent
line and the curve on the same axes. Also, indicate the direction the curve is traced out.
3
2
1
-4
-3
-2
-1
0
1
2
3
-1
-2
-3
Page 1 of 5
Instructor: Brian Johnson
4
5
MATH-106 Section 750
Calculus I - Fall 2011
Exam #3
(18 points) 3. Evaluate the following integrals:
�
� �
3
3
(a)
−
4t
+
2
dt
1 + t2
(b)
� �
(c)
�
0
1
cos x +
1
+π
x
�
dx
(6z − ez ) dz (give an exact answer)
Page 2 of 5
Instructor: Brian Johnson
MATH-106 Section 750
Calculus I - Fall 2011
Exam #3
(10 points) 4. The velocity in the following table is decreasing for 0 ≤ t ≤ 8. Use n = 4 subdivisions and an upper
sum to approximate the total distance traveled.
t
v(t)
0
20
2
19
4
15
6
6
8
0
(12 points) 5. Find the area of the region contained between the two curves y = x2 − 2x − 1 and y = x − 1 (you may
want to sketch a picture).
Page 3 of 5
Instructor: Brian Johnson
MATH-106 Section 750
Calculus I - Fall 2011
Exam #3
(18 points) 6. The following graph is the graph of the function y = f (x). Define g(x) =
�
x
f (t) dt.
−1
4
3
2
y = f(x)
1
-2
-1
0
1
2
3
4
5
6
7
-1
(a) Find g(5).
(b) Find g(1).
(c) Find g � (1).
(d) Find the equation of the tangent line to the graph of g(x) when x = 1.
(e) Give the location of the local extrema (max or min) for g(x) on the interval (0, 6).
(f) Give the location of any inflection points for g(x) on the interval (0, 6).
Page 4 of 5
Instructor: Brian Johnson
MATH-106 Section 750
Calculus I - Fall 2011
(10 points) 7. Calculate
(10 points) 8. If
�
6
�
1
x2
18et sec2 (t)
dt.
t
f (x) dx = 10 and
0
(1 (bonus))
d
dx
Exam #3
�
0
4
f (x) dx = 7, find
�
4
f (x) dx.
6
9. If you choose an answer at random to this question, what is the chance you will be correct?
(a) 25%
(b) 50%
(c) 60%
(d) 25%
Page 5 of 5
Instructor: Brian Johnson
Quizzes
MATH-101 Section 007
College Algebra
Quiz #5
Name:
The majority of the credit you receive will be based on the completeness and the clarity of your
responses. Show your work, and avoid saying things that are untrue, ambiguous, or nonsensical.
This exam has 3 questions, for a total of 10 points.
(4 points)
1. Sketch a graph of the linear equation 2x − 3y = 12. Label (with their actual values) the x- and yintercepts.
(4 points)
2. Find the linear function T (x) if T (32) = 0 and T (212) = 100.
(2 points)
3. Simplify, then write in radical notation.
(4a3/5 )(6a4/5 )
Page 1 of 1
Instructor: Brian Johnson
MATH-101 Section 007
College Algebra
Quiz #6
Name:
The majority of the credit you receive will be based on the completeness and the clarity of your
responses. Show your work, and avoid saying things that are untrue, ambiguous, or nonsensical.
This exam has 3 questions, for a total of 10 points.
(4 points)
�
2,
if x ≤ 3
1. Sketch a graph of the piecewise function defined by h(x) =
x − 4, if x > 3
(4 points)
2. Draw a function that is increasing on (−10, 2), constant on (2, 4) and decreasing on (4, 10).
(2 points)
3. Simplify, then write in radical notation.
(4a3/5 )(6a4/5 )
Page 1 of 1
Instructor: Brian Johnson
MATH-106 Section 750
Calculus I
Quiz #6
Name:
The majority of the credit you receive will be based on the completeness and the clarity of your
responses. Show your work, and avoid saying things that are untrue, ambiguous, or nonsensical.
This quiz has 2 questions, for a total of 10 points.
(5 points)
1. Evaluate the following limit, if possible:
ex − 1 − x
x→0
x2
lim
(5 points)
2. For the curve in the xy-plane given by the parametric equations
�
x = 3 cos t
,
0 ≤ t ≤ π,
y = 3 sin t
find the equation of the tangent line at the point corresponding to t = π/4, and sketch both the tangent
line and the curve on the same axes.
3
2
1
-4
-3
-2
-1
0
1
2
3
4
-1
-2
-3
Page 1 of 1
Instructor: Brian Johnson
5
Math 106
Reading Quiz #5
Name:
(1) Give an example of an explicit function. That is, write down a rule that
determines y as an explicit function of x.
(2) Give an example of an implicit function. That is, write down an equation that
determines y as an implicit function of x.
Math 106
Reading Quiz #5
Name:
(1) Give an example of an explicit function. That is, write down a rule that
determines y as an explicit function of x.
(2) Give an example of an implicit function. That is, write down an equation that
determines y as an implicit function of x.
Math 106
Reading Quiz #7
Name:
(1) What are the two conditions on the first derivative of f (x) we check for when
looking for a critical point?
(2) What does it mean for a point p to be an inflection point for the graph of
f (x)?
Math 106
Reading Quiz #7
Name:
(1) What are the two conditions on the first derivative of f (x) we check for when
looking for a critical point?
(2) What does it mean for a point p to be an inflection point for the graph of
f (x)?
Reviews and Supplements
MATH 203–CONTEMPORARY MATH
JOURNAL #5
DUE 7 DEC 2007
FALL 2007
As stated in the syllabus, your journals will be graded on spelling, grammar,
punctuation, etc., as well as content. The journals should be 1-2 pages typed and
double spaced in 12 point font or smaller.
Recall the first journal assignment:
• Assignment: Introduce yourself. That is, tell me a little bit about yourself. This is a very broad assignment, but some answers I would like you
to include are: What is your mathematical background? What are some of
the things you have liked/disliked about previous math courses you have
taken? Why are you taking this class? What do you hope to get out of this
class, or what would you like to learn? Aside from those few questions, you
may take this in any direction you would like.
In reference to the first assignment, I’d like you to comment on some of the
following: How did this class, if at all, affect your mathematical thinking? What
did you like/dislike about this class? What did you get out of this class, and did
you learn what you wanted? Are there any future math classes you will be taking,
and if so, what are they? If there were specific assignments or chapters that you
liked or didn’t like, what were they and why? Also, tell me what you plan to do to
prepare for the final on Thursday, Dec. 20.
1
SYMMETRY WORKSHEET
MATH 203 FALL 2007
1. Find the image of the triangle under the reflection about the line l.
Figure 1. Triangle ABC
2. Find the symmetries (translational, rotational, reflection, glide) of the following strip pattern.
Figure 2. Strip pattern 1
1
2
SYMMETRY WORKSHEET MATH 203 FALL 2007
3. Find the symmetries (translational, rotational, reflection, glide) of the following strip pattern.
Figure 3. Strip pattern 2
4. Find the symmetries (translational, rotational, reflection, glide) of the following planar pattern.
Figure 4. Planar Escher pattern
SURVEY SAMPLING METHODS
Type of Sample
Simple random
sample
Description
Fixed Sample
Size?
Draw a sample of a given size from the entire population Yes
using a predetermined random method–similar to “drawing names from a hat.”
Independent
Select a sample so that each member of the population has No
Sample
the same predetermined chance of being selected.
1-in-k system- Order the population into groups of size k and then select Yes, if popuatic sample
the member in the same position of each group.
lation size is
known
Quota sample
Establish quotas so the sample models the population on Yes
one or more important characteristics.
Stratified ran- Divide the population into strata based on some charac- Yes
dom sample
teristic and take a simple random sample of each stratum.
Cluster sample
Divide population into clusters, select a sample of clusters, Depends
on
and measure all members of those clusters.
makeup
of
sampling units
(1) For each of the following samples, indicate which sampling technique was
used.
(a) A newspaper randomly selected 80 urban and 80 rural residents and
interviewed them about the governor’s new tax proposal
(b) A scientist surveyed every seventh person entering a fast-food restaurant about his or her sleeping habits
(c) A farmer divided a map of field corn into nonoverlapping regions. He
randomly selected six of the regions and examined all the corn plants
in each region for pest infestation.
(d) Forty percent of women who gave birth in a certain hospital had cesarean sections. An independent analyst surveyed 300 women who
recently gave birth to assess their level of satisfaction with the care
they received. Of the 300 women in the sample, the analyst randomly
selected 120 women from the group who had cesarean sections, and
180 women from the group who did not.
1
(2) Suppose the Centers for Disease Control and Prevention (CDC) want to
conduct a survey to determine health habits of children in a certain state.
For each scenario below, identify the sampling technique described and
discuss the pros and cons of using that sampling technique for the survey.
(a) The CDC randomly selects several cities in the state and interviews
all children in every school of each selected city.
(b) The CDC lists all the schools in the state, randomly selects a certain
number of schools from the list, and interviews every child in each of
the selected schools.
(c) The CDC lists every school-age child in the state, randomly selects
a certain number of children from the list, and interviews each child
selected.
(d) The CDC divides the state into urban and rural areas, randomly selects a fixed number of schools from both areas, and interviews all the
children in each selected school.
VELOCITY, DISTANCE, AND POSITION
November 4, 2011
(1) The velocity v(t) in the table given is decreasing for 2 ≤ t ≤ 10. Sketch a possible graph of
the velocity function.
t
2 4 6 8 10
v(t) 44 42 41 40 37
48
40
32
24
16
8
-1
0
1
2
3
4
5
6
7
8
9
10
(a) Using n = 2 subdivisions, find an upper and a lower estimate for the total distance
traveled. Sketch a representation of the upper sum.
48
40
32
24
16
8
-1
0
1
2
3
4
5
6
7
8
9
10
11
(b) Using n = 4 subdivisions, find an upper and a lower estimate for the total distance
traveled. Sketch a representation of the lower sum.
48
40
32
24
16
8
-1
0
1
2
3
4
5
6
7
8
9
10
11
(c) Which estimate do you think is the best estimate? Why?
11
(2) The table below gives several values of the function f (t).
t
15 17 19 21 23
f (t) 10 13 18 20 30
(a) If n = 4, what is ∆t? What are t0 , t1 , t2 , t3 , and t4 ? What are the values of f (ti ) for
i = 0, 1, 2, 3, 4?
(b) Find the left and right sums using n = 4.
(c) If n = 2, find the left and right sums.
EXAM 1 REVIEW
Math 106
Disclaimer: The review sheet is meant to provide some practice for the exam. Topics on the
real exam are not limited to those covered on this sheet. You are responsible for knowing all of the
material we have covered. I do feel the review sheet will help prepare you for the exam, but you
must be able to apply the ideas behind the problems to other problems. You should also know the
topics possibly not covered by this sheet that we have covered in class.
1. Topics you should know/study (in no particular order):
(a) Basic facts about logarithmic, exponential, trigonometric, and other functions
(b) The limit definition of continuity (from the bottom of p. 56).
(c) The limit definition of the derivative.
(d) Properties of limits and derivatives.
(e) The relationship between position, velocity, and acceleration.
(f) The difference between average rate of change and instantaneous rate of change, as well
as how to compute and interpret each.
(g) Graphic interpretations of/sketching the graph of first and second derivatives.
(h) Finding higher order derivatives.
(i) Finding equations of tangent lines.
(j) Interpretations of derivatives.
(k) What it means to be differentiable and examples of functions that are not differentiable.
(l) Techniques and rules for differentiation (power rule, exponential rule, product rule, quotient rule, trig functions, chain rule, inverse functions, implicit differentiation).
2. Are the following functions continuous on the given intervals?
(a) 2x + x−1 on [−1, 1]
1
(b)
on [−1, 1]
x−2
�
x, x ≤ 1
(c) f (x) =
x2 , x > 1
on (−∞, ∞)
3. Find k so that the following function is continuous on any interval:
�
kx, 0 ≤ x < 2
f (x) =
3x2 , 2 ≤ x
4. Exercises 2 & 3 from p. 58.
5. Evaluate the following limits, provided they exist
(a) lim
x→∞
x+3
2−x
1
x2 + 4
x→∞ x + 3
2e−x + 3
(c) lim −x
x→∞ 3e
−4
2
x + 4x + 4
(d) lim
x→−2
x+2
(b) lim
6. Find a value of k such that the following limit exists
x2 + 3x + 5
x→∞ 4x + 1 + xk
lim
7. Exercises 7–14 from p. 109.
8. Find the derivatives of the following functions using the limit definition. Then find the equation
of the tangent line at the point corresponding to the given x-value.
(a) f (x) = x2 − 1; x = 3
√
(b) g(x) = x; x = 9
(c) h(x) = 7x + 5; x = −2
9. Let f (t) be the depth, in centimeters, of water in a tank at time t, in minutes. What does the
sign of f � (t) tell us? Explain the meaning of f � (30) = 20, including units.
10. The following table gives the number of passenger cars, C = f (t) in millions, in the United
States in the year t. During the period 2002–2006, when is f � (t) positive? Negative? Estimate
f � (2003). Using units, interpret the answer.
t (year)
2002 2003 2004 2005 2006
C (cars, in millions) 135.9 135.7 136.4 136.6 135.4
11. A yam has just been taken out of the oven and is cooling off before being eaten. The temperature, T , of the yam (measured in degrees Fahrenheit) is a function of how long it has been
out of the oven, t (measured in minutes). So, T = f (t). Is f � (t) positive or negative, and why?
What are the units on f � (t)?
12. An economist is interested in how the price of a certain commodity affects its sales. Suppose
that at a price of $p, a quantity q of the commodity is sold. If q = f (p), explain in economic
terms the meaning of the statements f (10) = 240, 000 and f � (10) = −29, 000.
13. Sketch the graph of a function that satisfies all of the given conditions:
(a) f � (−1) = f � (1) = 0; f � (x) < 0 if |x| < 1; f � (x) > 0 if |x| > 1; f (−1) = 4; f (1) = 0;
f �� (x) < 0 if x < 0; and f �� (x) > 0 if x > 0.
(b) f � (−1) = 0; f � (1) does not exist; f � (x) < 0 if |x| < 1; f � (x) > 0 if |x| > 1; f (−1) = 4;
f (1) = 0; and f �� (x) < 0 if x �= 1.
(c) lim f (x) = −∞; f �� (x) < 0 if x �= 3; f � (0) = 0; f � (x) > 0 if x < 0 or x > 3; and f � (x) < 0
x→3
if 0 < x < 3.
14. Find the first derivative of the following functions:
2
(a) z = e−3y cos(3y)
cos(4x)
(b) y = 2
5x − x + 5
(c) f (u) = ln(3u5 + 5u)
t6 ln t
(d) g(t) = 3
t +3
(e) h(x) = cos(4x)esin(x)
(f) u = cos(v 5 e9v )
(g) f (v) = ln(cos(e−6 − 6v))
cos(e−5w )
(h) y =
4w4 + 6w
(i) f (z) = 5e−3z + 1 + 2 arctan(z) + 2z 4/5
15. Find
dy
if:
dx
(a) e4x + ey + x5 y 3 = 8
�
(b) 1 + x2 y 2 = 2xy
(c) x sin y + cos 2y = cos y
16. Find the fifth derivative, f (5) (x), for the function f (x) = x5/2 + x3 + 2.
17. In a test flight of the McCord Aviation’s experimental VTOL (vertical takeoff and landing)
aircraft, the altitude of the aircraft in the VTOL mode was given by the position function
s(t) =
1 4 1 3
t − t + 4t2 ,
64
2
for 0 ≤ t ≤ 16, where s(t) is in feet and t in seconds.
(a) Find the velocity function for the aircraft.
(b) At what points in the interval [0, 16] does the aircraft stop?
(c) What is the acceleration function for the aircraft?
3
MATH-106 Section 750
Calculus I - Fall 2011
Sample Exam #1
Name:
The majority of the credit you receive will be based on the completeness and the clarity of your
responses. Show your work, and avoid saying things that are untrue, ambiguous, or nonsensical.
This exam has 7 questions, for a total of 0 points.
Disclaimer: This sample exam is meant to give you a feel for the length and difficulty of our in-class
exams. The questions on it come from past in-class exams from Math 106 in previous semesters (when we
used a different book). Topics on the real exam may or may not coincide with topics on this practice exam.
1. Given the following definition for f (x), answer the questions below.


−x − 3, x ≤ −2
f (x) = 1 − x2 , −2 < x < 1 ,


x − 1,
1≤x
(a)
(b)
lim f (x) =
x→−2−
lim f (x) =
x→−2+
(c) lim f (x) =
x→0
(d) Is f (x) continuous at x = −2?
(e) Is f differentiable on the interval (−∞, 0]?
2. Find, in y = mx + b form, the equation of the tangent line to the curve y = ex+1 (x − 2) at x = −1.
Page 1 of 4
Instructor: Brian Johnson
MATH-106 Section 750
Calculus I - Fall 2011
Sample Exam #1
3. Find the first derivative of each of the following. Do not simplify your answers.
(a) y =
v 4 + e2v
ev sin v
�
�
��8
(b) f (t) = cos e−2t − t
4. Find
dx
for −2y 4 + e2x + x cos y = 8.
dy
Page 2 of 4
Instructor: Brian Johnson
MATH-106 Section 750
Calculus I - Fall 2011
Sample Exam #1
5. Suppose f and g are differentiable functions with the values shown in the following table. For each of
the following functions h, find h� (4).
(a) h(x) =
f (x)
g(x)
x
−2
−1
3
4
f (x) g(x) f � (x) g � (x)
1
2
3
4
1
3
2
1
−2
1
2
3
−1
2
3
1
(b) h(x) = f (x)(g(x))2
(c) h(x) = g(f (x))
6. A stone thrown vertically upward from the top of a 96 foot cliff with an initial velocity of 80 feet per
second eventually falls to the beach below. It reaches a height of s(t) = −16t2 + 80t + 96 feet after t
seconds.
(a) How long does it take the stone to reach its highest point?
(b) What is the maximum height of the stone?
(c) What is the acceleration of the stone when t = 2 seconds?
(d) What is the velocity of the stone upon impact?
Page 3 of 4
Instructor: Brian Johnson
MATH-106 Section 750
Calculus I - Fall 2011
Sample Exam #1
7. Using the limit definition of the derivative, find the exact value of f � (4) if f (x) =
Page 4 of 4
√
2x − 1.
Instructor: Brian Johnson
Professional Development
Student Evaluations
Math 101 - College Algebra
Spring 2009
Qualitative results have been averaged.
Questions & possible responses
Spring 2009
Do the classroom procedures and discussions seem well-planned?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.65
Are the instructor’s presentations and explanations helpful in understanding the
subject matter?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.5
Grading policies were:
0) Never mentioned 1) Never made clear 2) Perhaps stated but do not recall
3) Clear enough 4) Clearly stated
3.5
Could a student get individual help from this instructor?
0) Definitely not 1) Seldom 2) Sometimes 3) Usually 4) Yes, definitely
3.7
During lectures, does the instructor make suitable adjustments when the class
becomes lost or confused?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.65
Does the instructor seem interested in this subject and in teaching it?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes, very much
3.75
Has work done in class helped you to solve course problems on your own?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes, very much
3.55
What is your overall impression of the quality of instruction in this course?
0) Poor 1) Fair 2) Good 3) Very good 4) Excellent
3.5
Do the instructor’s way of speaking and personal mannerisms interfere with
effective teaching?
0) Nearly always 1) Frequently 2) Occasionally 3) Rarely 4) Never
3.6
How would you describe the pace of this course?
0) Very fast 1) Rather fast 2) About right 3) Slow 4) Very slow
2.05
Student Comments
•
Brian Johnson is a fantastic math instructor who excels in every area of teaching. If he weren’t
such a good teacher I would not be moving onto trig.
Math 103 - College Algebra and Trigonometry
Fall 2009
Qualitative results have been averaged.
Questions & possible responses
Fall 2009
Do the classroom procedures and discussions seem well-planned?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.76
Are the instructor’s presentations and explanations helpful in understanding the
subject matter?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.52
Grading policies were:
0) Never mentioned 1) Never made clear 2) Perhaps stated but do not recall
3) Clear enough 4) Clearly stated
3.8
Could a student get individual help from this instructor?
0) Definitely not 1) Seldom 2) Sometimes 3) Usually 4) Yes, definitely
3.92
During lectures, does the instructor make suitable adjustments when the class
becomes lost or confused?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.64
Does the instructor seem interested in this subject and in teaching it?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes, very much
3.96
Has work done in class helped you to solve course problems on your own?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes, very much
3.44
What is your overall impression of the quality of instruction in this course?
0) Poor 1) Fair 2) Good 3) Very good 4) Excellent
3.52
Do the instructor’s way of speaking and personal mannerisms interfere with
effective teaching?
0) Nearly always 1) Frequently 2) Occasionally 3) Rarely 4) Never
3.72
How would you describe the pace of this course?
0) Very fast 1) Rather fast 2) About right 3) Slow 4) Very slow
1.84
Student Comments
•
•
Brian is very clear in his explanations. He will tell you why a problem is worked a certain way
rather than just hammering through examples, this helps us understand much better. Brian
is also very helpful our of class and is almost always available.
I have two things to say: One is that the Gateway Exam needs some work, too many problems.
As for the (unreadable), my teacher Mr. Johnson is good at his job.
•
very good teacher!
•
Hire Brian Johnson as a teacher. Very good at what he does.
Math 106/198 - Calculus I Excel Recitation
Fall 2010
Qualitative results have been averaged.
Questions & possible responses
Fall 2010
Do the classroom procedures and discussions seem well-planned?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.24
Are the instructor’s presentations and explanations helpful in understanding the subject matter?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.48
Grading policies were:
0) Never mentioned 1) Never made clear 2) Perhaps stated but do not recall
3) Clear enough 4) Clearly stated
3.52
Could a student get individual help from this instructor?
0) Definitely not 1) Seldom 2) Sometimes 3) Usually 4) Yes, definitely
3.71
During lectures, does the instructor make suitable adjustments when the class becomes lost or confused?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.48
Does the instructor seem interested in this subject and in teaching it?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes, very much
3.71
Has work done in class helped you to solve course problems on your own?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes, very much
3.24
What is your overall impression of the quality of instruction in this course?
0) Poor 1) Fair 2) Good 3) Very good 4) Excellent
3.43
Do the instructor’s way of speaking and personal mannerisms interfere with effective
teaching?
0) Nearly always 1) Frequently 2) Occasionally 3) Rarely 4) Never
3.62
How would you describe the pace of this course?
0) Very fast 1) Rather fast 2) About right 3) Slow 4) Very slow
1.76
Was the recitation instructor well prepared?
0) Almost never 1) Seldom 2) Frequently 3) Usually 4) Nearly always
3.48
Was the recitation instructor effective in answering questions?
0) Almost never 1) Seldom 2) Frequently 3) Usually 4) Nearly always
3.33
Did the recitation instructor seem to be interested in helping you?
0) Almost never 1) Seldom 2) Frequently 3) Usually 4) Nearly always
3.76
What is your overall impression of how your recitation instructor met his responsibilities?
0) Poor 1) Fair 2) Good 3) Very good 4) Excellent
3.62
Did the recitation instructor’s manner of speaking interfere with effective teaching?
0) Nearly always 1) Frequently 2) Occasionally 3) Rarely 4) Never
3.76
Student Comments
•
•
Yay Math!
I ♥ Calculus!
2
Math 107 - Calculus II Recitations
Fall 2006 (2 sections)
Qualitative results have been averaged.
Questions & possible responses
Fall 2006
Fall 2006
Was the recitation instructor well prepared?
0) Almost never 1) Seldom 2) Frequently 3) Usually 4) Nearly always
3.63
3.47
Was the recitation instructor effective in answering questions?
0) Almost never 1) Seldom 2) Frequently 3) Usually 4) Nearly always
3.75
3.8
Did the recitation instructor seem to be interested in helping you?
0) Almost never 1) Seldom 2) Frequently 3) Usually 4) Nearly always
4
3.73
What is your overall impression of how your recitation instructor met
his responsibilities?
0) Poor 1) Fair 2) Good 3) Very good 4) Excellent
3.81
3.67
Did the recitation instructor’s manner of speaking interfere with effective teaching?
0) Nearly always 1) Frequently 2) Occasionally 3) Rarely 4) Never
3.88
3.8
Math 203 - Contemporary Math
Fall 2007 (2 sections), Spring 2008, Fall 2008 (2 sections)
Qualitative results have been averaged.
Questions & possible responses
Fall
2007
Fall
2007
Spring
2008
Fall
2008
Fall
2008
Do the classroom procedures and discussions seem wellplanned?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.22
3.59
3.62
3.87
3.65
Are the instructor’s presentations and explanations helpful in
understanding the subject matter?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
2.85
3.35
3.62
3.7
3.52
Grading policies were:
0) Never mentioned 1) Never made clear 2) Perhaps stated but
do not recall 3) Clear enough 4) Clearly stated
3.81
4
3.95
3.87
3.87
Could a student get individual help from this instructor?
0) Definitely not 1) Seldom 2) Sometimes 3) Usually 4) Yes,
definitely
3.96
4
3.86
3.87
3.78
During lectures, does the instructor make suitable adjustments
when the class becomes lost or confused?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
2.85
3.65
3.62
3.83
3.65
Does the instructor seem interested in this subject and in teaching it?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes,
very much
3.44
3.88
3.71
3.87
3.87
Has work done in class helped you to solve course problems on
your own?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes,
very much
2.81
3.47
3.62
3.52
3.43
What is your overall impression of the quality of instruction in
this course?
0) Poor 1) Fair 2) Good 3) Very good 4) Excellent
2.74
3.65
3.71
3.65
3.48
Do the instructor’s way of speaking and personal mannerisms
interfere with effective teaching?
0) Nearly always 1) Frequently 2) Occasionally 3) Rarely 4)
Never
3.41
3.71
3.65
3.78
3.43
How would you describe the pace of this course?
0) Very fast 1) Rather fast 2) About right 3) Slow 4) Very slow
2
2.24
2.14
2.13
2
Student Comments
•
•
•
This instructor was good because he knew he was capable of error and understood we were not all
math majors.
Just a suggestion, making homework mandatory (needs to be turned in) would be more encouraging
to do it. �
He is a great teacher. His lectures weren’t boring and math was pleasant thanks to him. I have
gone to his office numerous times for help and always has time. Even if he’s eating lunch he helps
me. He graded very fairly and always help me if I needed it. He was the best math teacher I ever
had. NO LIE. I’d take another class with him if I could. And I love his math jokes.
•
•
Great teacher. My favorite yet!
Brian was a great teacher. If I was ever lost, he was always willing to help. He took a lame subject
(sorry!) and made it almost fun to come to.
•
Great job!
•
Instructor, methods, content, pace, etc. was perfect!
•
Brian Johnson is Awesome!
•
F*** yeah, Brian!
•
•
No concerns �
My only suggestion is for him to tell students to be quiet while he is teaching.
2
Math 208 - Multivariable Calculus
Spring 2011
Qualitative results have been averaged.
Questions & possible responses
Spring 2011
Do the classroom procedures and discussions seem well-planned?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.67
Are the instructor’s presentations and explanations helpful in understanding the
subject matter?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.56
Grading policies were:
0) Never mentioned 1) Never made clear 2) Perhaps stated but do not recall
3) Clear enough 4) Clearly stated
3.81
Could a student get individual help from this instructor?
0) Definitely not 1) Seldom 2) Sometimes 3) Usually 4) Yes, definitely
3.85
During lectures, does the instructor make suitable adjustments when the class
becomes lost or confused?
0) Never 1) Seldom 2) Sometimes 3) Often 4) Always
3.56
Does the instructor seem interested in this subject and in teaching it?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes, very much
3.85
Has work done in class helped you to solve course problems on your own?
0) Not at all 1) Not much 2) Hard to tell 3) Yes, usually 4) Yes, very much
3.44
What is your overall impression of the quality of instruction in this course?
0) Poor 1) Fair 2) Good 3) Very good 4) Excellent
3.59
Do the instructor’s way of speaking and personal mannerisms interfere with
effective teaching?
0) Nearly always 1) Frequently 2) Occasionally 3) Rarely 4) Never
3.74
How would you describe the pace of this course?
0) Very fast 1) Rather fast 2) About right 3) Slow 4) Very slow
1.7
Student Comments
•
•
I feel the exams are extremely well written and test what we have learned in class fairly.
I loved this class and Brian Johnson. He is the best teacher I’ve had in my time at UNL! I
hope I can take higher level courses from him.
•
great teacher, much better than my last one
•
Good class! Enjoyed it a lot!
•
I think this class would benefit greatly from a little focus on why we are learning what we are
learning. Application is always nice.