Multivariable calculus: Exams and solutions

Exams #

Exams are both a necessary evil and an important part of the class. Below I have collected a variety of resources to help you prepare, as well as some administrative information, such as details about scheduling make-up exams and exams at Bowdoin’s Test Center.

Both midterm exams this semester will be administered in-class during our regular meeting times and are tentatively scheduled for the following dates:

March 3 and April 21.
Details will be announced in class. The final exam will be a three-hour affair and is currently scheduled during finals week on
May 15 at 8:30am.

How to study for a Math 1800 exam #

The exam will consist of two types of questions: those drawn from the material in the book and those that come from our labs and computational activities.

Book problems #

I encourage you to follow these three steps when preparing for exams in this course:

  1. Review your class notes. After each lecture, be able to answer the question: What was the main idea, and what type of problems can I solve with it?
  2. Go over your graded homework. Make sure that you know how to do the problems you did not answer correctly. Set up a meeting either with me or the course learning assistant to iron out any tricky problems.
  3. Finally, there is no better way to prepare for an exam that will ask you to solve a variety of problems than by solving a variety of problems. In the next section, I have assembled a collection of exercises from each section of the book. You should do as many as you can before the exam.

Labs and computational activities #

You will not be asked to use computational software during the exams. However, each exam will address the work we have done in lab. As you study, review this part of the class, asking the following questions:

  1. What was the main takeaway from this exercise?
  2. Are there circumstances where the conclusions we made might fail to hold?
  3. Are there settings to which our work can be extended?

Exam study resources #

There are many exercises in your textbook. Given infinite time, you should do them all. But since most of us are mere mortals, for each chapter, I have selected a shorter list of problems that address what I think are the most important skills you should take away from this class. The problems are all assembled from our book’s chapter reviews. The password you will need to open these files was included in the welcome email for this class. Work through a selection of the following chapter review exercises as you study:

Chapter 12 [problems]      [solutions]
Intermediate level 4, 5, 9, 10, 12, 16, 18, 19, 20
Advanced level 8, 11, 13, 21, 41
Zen level 31, 39, 40
Chapter 13 [problems]      [solutions]
Intermediate level 1, 2, 7, 8, 9, 13, 14, 15, 17, 20, 21, 24, 25, 27, 30, 31, 50, 51
Advanced level 4, 22, 23, 32, 34, 36, 48, 49, 52
Zen level 54, 55, 57
Chapter 14 [problems]      [solutions]
Intermediate level 1, 2, 4, 5, 9, 29, 32, 35, 40, 41, 42, 43, 55, 56, 76, 77, 88, 89
Advanced level 16, 36, 45, 47, 48, 49, 51, 64, 67, 69, 75, 79, 82, 84, 85, 87, 91, 94, 100
Zen level 8, 66, 86, 96
Chapter 15 [problems]      [solutions]
Intermediate level 1, 2, 3, 6, 7, 8, 9, 11, 15, 18, 22
Advanced level 26, 27, 29, 37, 38
Zen level 33, 40
Chapter 16 [problems]      [solutions]
Intermediate level 1, 2, 3, 4, 10, 11, 12, 13, 29, 30, 33, 34, 46, 47, 51, 52, 59
Advanced level 7, 14, 15, 16, 17, 24, 25, 26, 27, 36, 37, 39, 48, 60, 69
Zen level 41, 42, 43, 44, 45, 62
Chapter 17 [problems]      [solutions]
Intermediate level 1, 2, 4, 9, 19, 27, 31, 36
Advanced level 12, 25, 28, 29, 32, 41, 42, 44, 48, 56
Zen level 46, 54, 55
Chapter 18 [problems]      [solutions]
Intermediate level 1, 2, 3, 4, 5, 6, 8, 10, 15, 16, 19
Advanced level 31, 32, 34, 35, 36, 47
Zen level 40, 44, 48, 49, 50, 54

Bowdoin’s Test Center #

Make-up exams and exams that require special accomodations will be taken at Bowdoin’s Test Center. To set up an appointment for an exam, you will need to

  1. contact me first, and then
  2. schedule the time for your exam with the Test Center directly. See the website above for their contact details.

There are times of the semester when the Test Center reaches full capacity. I encourage you to schedule your test time as quickly as you can.

Exam solutions #

After each exam, I will post solutions below. The files will be password-protected. The password will be shared with you by email after each exam. Take time to review the solutions, reconcile them with your own, and please talk to me if you come up with questions.

[Exam 1 Solutions]           [Exam 2 Solutions]