Information about the Final Exam for Math 1823-030

Mathematics 1823-030 - Calculus I - Fall 2009

Information about the Final Exam

The final examination will be held in the usual lecture room on Tuesday, December 15 from 1:30 p. m. to 3:45 p. m. University regulations require that you take it at that time.

As you know from the syllabus, the final exam is worth 75 points--- that is, one-fourth of your grade. Actually, there will be 80 points worth of problems, giving you an opportunity to earn some extra points. I expect the score percentages to run somewhat lower that Exams II and III (but I hope not lower than Exam I!), partly because the exam is a bit more difficult than the in-class exams, and partly because most students do not perform very well on final exams. The extra difficulty will be taken into account in assigning final grades, so it will not be a factor in the final distribution of grades (which I expect to be fairly similar to the current distribution, and I hope it will be a bit higher). On the other hand, individual students can easily move up or down a letter with a good or bad performance, so put a good effort in on learning section 4.9 (antiderivatives), and do not wait until the last minute to try to prepare--- it won't work. Most importantly, do not stay up all night studying--- most of the major final exam train wrecks I've seen were from students who tried that approach. Just review the main topics as best you can, get a decent night's sleep, give the exam your best shot, and move on.

You must sit in your regularly assigned seat during the exam, and must show your OU photo ID if requested. You may leave as soon as you have completed the exam and turned it in. Of course, it is advisable to check your work as carefully as possible before turning it in. You must turn your exam in to your discussion class instructor.

No electronic devices of any kind are permitted at any time during the exam. Please turn everything off before the start of the exam.

Everything except a writing instrument will be provided. The last page of the exam will be blank scratch paper, and if you need more blank paper you may request it during the exam. In general, though, you should show all your work on the exam itself, since you can receive partial credit for partial solutions.

The final will be similar in nature and format to the in-class exams. It will emphasize certain topics, as described below, and will give extra weighting to sections 4.7, 4.8, and especially the very important section 4.9, since these sections were not covered on the three in-class examinations. The following are the most important topics, although the exam is not completely limited to them:


  1. The precise definition of limit, and its use in verifying limits of linear functions.
  2. Continuity. The definition of continuity, the Intermediate Value Theorem.
  3. The Chain Rule (of course).
  4. Implicit differentiation (one computational problem will be asked).
  5. Related rates problems (one problem).
  6. The Mean Value Theorem and its applications (one application problem).
  7. Infinite limits (not a whole lot).
  8. Optimization problems (one problem).
  9. Newton's method (not a whole lot, but understand the geometric idea).
  10. Antiderivatives. The definition of antiderivative and the nature of the set of antiderivatives of a function (that is, the most general form of an antiderivative). Several problems similar to the homework problems.

Here is an estimate of how the points on the exam are distributed among the book's sections. Of course, some problems may involve ideas from more than one section, or even a section not listed here, so this is only an approximation:

1.1	1
2.2	1
2.4	7
2.5	5
3.3	3
3.4	2
3.5	5
3.6	5
3.8	6
3.9	3
4.1	1
4.2	4
4.4	5
4.7	7
4.8	5
4.9	20
Total	80

Of course, you will need to be able to calculate derivatives using the product, quotient, and chain rules. You will need to understand the Law of Cosines, if given the formula. You should know the derivatives of all six trigonometric functions, and the antiderivatives that come from them. Of course, you should know the major theorems well, in this and in any math course you ever take.

It's not necessary to memorize formulas for areas or volumes, or trig identities, as you will be given any such formulas that you need. You will not need to do a linear approximation problem, a major graphing problem, or to be familiar with the proof of the Mean Value Theorem. There is a problem where you have to give the precise definition of a certain limit, and use it to verify the limit. There is no calculation of a derivative using the limit definition, and there are only a few problems where you need to evaluate limits.

Exams from my most recent 1823 class, in 2001, can be found at its course page, which is linked at course pages. They can be downloaded without solutions, and also you can view the solutions. Of course, that was a different class from ours, so the exams may be quite a bit different. There are also links to two Honors Calculus I classes, in 2004 and 2006, whose exams are more challenging.


1.	The precise definition of limit, and its use in verifying limits of linear functions.
2.	Continuity. The definition of continuity, the Intermediate Value Theorem.
3.	The Chain Rule (of course).
4.	Implicit differentiation (one computational problem will be asked).
5.	Related rates problems (one problem).
6.	The Mean Value Theorem and its applications (one application problem).
7.	Infinite limits (not a whole lot).
8.	Optimization problems (one problem).
9.	Newton's method (not a whole lot, but understand the geometric idea).
10.	Antiderivatives. The definition of antiderivative and the nature of the set of antiderivatives of a function (that is, the most general form of an antiderivative). Several problems similar to the homework problems.