Math 31B, Lecture 6

Final Exam Information

Time and Place

The final exam is Tuesday, March 20, from 3pm to 6pm.

It will not be held in our normal classroom, but rather in
MS 5200 (the same room as the midterms).

Don't forget!

Extra Help

I will have extra office hours Monday 2-3pm and Tuesday 10am-12noon.

Jane will hold a review session Sunday, time and place to be determined.

Exam Format

There will be 10 questions, and the exam will be worth 100 points.  Different questions will be worth different points, and there could be multiple parts per question.  The problems will vary in difficulty, but the difficulty does not necessarily correspond to the point value.  The exam covers almost all material in the course up to section 12.10, but will concentrate on chapter 12 and especially the new material since the second midterm.  Approximate Integration (8.7), Arc Length (9.1), Area of a Surface of Revolution (9.2) and material on estimating remainders in chapter 12 will not be covered on the final exam.


  1. Remember first of all that the point of this class is for you to learn the material.  The exam is a way for me to get an idea of how much you've learned, but more importantly it's a chance for you to review what we've covered so far and learn it more thoroughly.  Concentrate on things that were confusing the first time around and work on them until they are clear. Of course don't hesitate to ask Jane and myself if you have questions.  It's not possible for me to test you on everything we've covered, but my hope is that merely by reviewing the material you'll have learned it better whether you are tested on it or not.  Ideally you'll be over-prepared for the exam!
  2. Almost all test questions will be similar to homework problems.  The best way to review the material is to review your homework problems, and to work similar problems.  It is important to review the two midterms as well.  Make sure you understand the concepts, so that you can solve different problems than just ones you've already seen.  Like the second midterm, the final exam will be more focused on concepts than on computation.
  3. There will be less time pressure for the final exam than there was for the two midterms, but you should still plan to work quickly and efficiently.  Be well-prepared and well-rested.  You will need to think during the exam!
  4. On the test, show me what you know.  If you can't completely solve a problem at least show clearly what you tried, how much you understand, and how far you could get.  Don't write nonsense.  That is just a clear indication that you don't understand what you're doing.  It's better to know what you don't understand and be honest about it!
  5. You must be able to state precisely all definitions, theorems, and important results in Sections 12.1 to 12.10 of the text; that is, everything that has a red box around it.  You should also know the most fundamental integration formulas and trig identities.  If you forget something and need it to proceed, you may "buy" it for some number of points to be determined by me, just like on previous exams (I'll tell you how many points it will cost you, and you can decide whether or not you want to buy the formula or result).
    EXCEPTIONS:  You do not need to remember the following results:  2 and 3 on page 763; the Alternating Series Estimation theorem on page 774; 8 and 9 on page 799.
    You do not need to know the proofs of the theorems, except for results 3 and 4 on page 751 (you need only remember the results for the case a=1).  For result 3 on page 751, you should know both the book's proof and the proof by mathematical induction (see homework 5).
  6. You must also be able to do simple proofs at the level of the assigned homework exercises, including simple proofs by induction.  Your proofs will be graded on completeness and clarity.

Good luck!