# Math 21b - Exams

Course preceptor: Yu-Wen Hsu (yuwenhsu@g.harvard.edu)

## Final Exam

### What to Expect

The exam will cover the entire semester, but there will be a slight emphasis on the material since the last midterm (the material on Problem Sets 28 - 35).

Books, calculators, and notes will not be permitted on the exam.

### How to Study

As this recent article highlights, two of the best study strategies are testing yourself (with flashcards, practice problems, and so on) and spacing your studying over a period of time. So, we encourage you to start your studying early: use these review questions to help you recall the key skills and concepts we've learned this semester, and go back to your notes, worksheets, and homework to help you fill in details you've forgotten. Make a list of important ideas and strategies, and think about how different ideas connect. Do some practice problems on each topic. Here is some material to help you with this process:

As always, we strongly encourage you to complete several practice exams without looking at the solutions or using extra aids. After you've finished a practice exam, go to office hours with any questions you have!

### Review Sessions and Office Hours

A full schedule is posted here.

• We have asked for the review sessions to be taped. Videos of the review sessions will be posted here as soon they're available.

## Exam 2

Exam 2 will be Tuesday 11/14, 5:30 - 7:30 pm in Science Center C. If you have a valid conflict (see the top of this page), please fill out this exam conflict form by Wednesday 11/8 to arrange an earlier exam time. Please note that most sections and labs can be rearranged to accomodate an exam, and we expect you to contact your section organizers right away to arrange to attend a different section if your section conflicts with the 21b exam.

### What to Expect

The exam will focus on the material on Problem Sets 12 - 27, but it is cumulative in the sense that this material relies on the ideas and techniques from Problem Sets 0 - 11, so you will still need to be comfortable with those. Remember that Math 21b emphasizes deep and flexible understanding of the material. As such, you should expect the exam to include problems you haven't previously encountered, so that you can demonstrate your ability to apply the fundamental concepts to new problems.

Books, calculators, and notes will not be permitted on the exam.

### How to Study

We encourage you to start studying early by reviewing your notes, worksheets, and homework to help you recall the key definitions, skills, and concepts we've covered so far. Make a list of important definitions, ideas, and strategies for yourself, and explain to yourself why the strategies work. Here is some material that may help you with this review:

The single best thing you can do after this is to complete a few practice exams without looking at the solutions or using extra aids. (It is very tempting to peek at the solutions when you get stuck, but we have found repeatedly that this is not a useful study strategy. Recent research backs this up!) After you've finished a practice exam, don't look at the solutions yet! Instead, go back to any problems you weren't able to do, and try them again, using any source you like except the solutions (so, for example, look for related problems from the worksheets and homework). Finally, after you've done that, look at the solutions and grade your work, and go to office hours with any questions you have!

• Practice Exam Reflection: To get the most out of a practice exam, you don't want to just do it; you also want to use it to figure out what to study next, as well as what errors you tend to make and how to avoid those errors in the future. This practice exam reflection is meant to help you do that; do it right after you've taken a practice exam (before looking at the solutions).
• Practice Exam 1 - solutions
This practice exam only covers the material through Problem Set 23, so it's a good one to do if you're starting your studying early.
• Practice Exam 2 - solutions
• Practice Exam 3 - solutions
• Practice Exam 4 - solutions
• Updated 11/12 to fix a typo in #7(a) (the last entry in the given vector should be -5); thanks, Alexandra!
• Practice Exam 5 - solutions
• Fall 2009 exam - solutions
This exam only covers the material on Problem Sets 15 - 24, so it's another good one to do if you're starting your studying early.
• Solution updated 11/8 to fix an arrow in the phase plane analysis on pg. 17. (Thanks, Sofia!)
• Recommended practice problems by topic (mostly from Bretscher) - includes lots of true-false questions!

### Review Session

There will be a course-wide review session Thursday 11/9, 2:45 - 4:15 pm in Science Center E. We've asked for the review session to be taped.

### Exam Solutions

Here are the solutions to your exam.

## Exam 1

Exam 1 will be Wednesday 10/4, 5:30 - 7:30 pm in Science Center B. If you have a valid conflict (see the top of this page), please fill out this exam conflict form by Wednesday 9/27 to arrange an earlier exam time. Please note that most section meetings and lab sections can be rearranged to accomodate an exam, and we expect you to contact your section organizers right away to arrange to attend a different section if your section conflicts with the 21b exam.

### What to Expect

The exam will cover the material on Problem Sets 0 - 11. Remember that Math 21b emphasizes deep and flexible understanding of the material. As such, you should expect the exam to include problems you haven't previously encountered, so that you can demonstrate your ability to apply the fundamental concepts to new problems.

Books, calculators, and notes will not be permitted on the exam.

### How to Study

We encourage you to start by reviewing your notes, worksheets, and homework to help you recall the key definitions, skills, and concepts we've covered so far. Make a list of important definitions, ideas, and strategies for yourself, and talk over your list with other students.

The single best thing you can do after this is to complete a few practice exams without looking at the solutions or using extra aids. (It is very tempting to peek at the solutions when you get stuck, but we have found repeatedly that this is not a useful study strategy. Recent research backs this up!) After you've finished a practice exam, don't look at the solutions yet! Instead, go back to any problems you weren't able to do, and try them again, using any source you like except the solutions (so, for example, look for related problems from the worksheets and homework). Finally, after you've done that, look at the solutions and grade your work, and go to office hours with any questions you have!

Here is review material; the 4 practice exams are formatted in the same style as your exam will be, but the past exams are also excellent sources of problems.

### Review Session

There will be a course-wide review session Friday 9/29, 2:30 - 4 pm in Science Center A. We have asked for the review session to be taped.
• Here are the review session problems. Full solutions will not be posted, but you are welcome to discuss them with a TF in office hours.
• Video of the review session will be posted here as soon as it is available..

### Exam Solutions

Here are solutions to your exam.