Information about Exam III for Math 1823-030

Mathematics 1823-030 - Calculus I - Fall 2009

Information about Exam III

Exam III will be in the usual classroom during the usual lecture hour on Monday, November 23, 2009. It will cover sections 3.7-3.9 and 4.1-4.5. There will be 56 points possible.

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 it. 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.

Some of the exam will be similar to the homework problems, and some will be drawn from the lectures. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

The first problem on the exam is to circle the day and time of your discussion class. This problem is worth 1 point.

The following topics are the most likely to appear, although the exam is not necessarily limited to these topics:

  1. Rates of change and related rates problems. Examples of rates of change. Expect a related rates word problem.
  2. Linear approximation and differentials. Know the approximation formula and be able to use it. Know the definition of differential and be able to compute the differential of a function.
  3. Absolute and local maxima and minima. The Extreme Value Theorem. Fermat's Theorem.
  4. The Mean Value Theorem will be well covered. Statement, geometric meaning, applications. Understand at least the idea of the proof, if you can.
  5. Effect of the first and second derivative on the graph of a function. Using them to find local maxima and minima of functions. Critical numbers, inflection points.
  6. Infinite limits. Know the basic idea and the geometric meaning, and be able to calculate easy examples, but these are not a high priority for now.
  7. Finding graphs of functions using calculus and other techniques. This will be covered, but there won't be a hard example to analyze from scratch (of course, if you have learned to do some of the harder examples, you should be well prepared for any test question).

You will need to know the linear approximation formula from memory. Know the statements of the important theorems (in this and every mathematics course you take).

For this exam, you do not need to know the following (although they are all good things to know): Law of Cosines, interpretation of the differential as an infinitesimal quantity, precise definition of limits as x goes to infinity

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.	Rates of change and related rates problems. Examples of rates of change. Expect a related rates word problem.
2.	Linear approximation and differentials. Know the approximation formula and be able to use it. Know the definition of differential and be able to compute the differential of a function.
3.	Absolute and local maxima and minima. The Extreme Value Theorem. Fermat's Theorem.
4.	The Mean Value Theorem will be well covered. Statement, geometric meaning, applications. Understand at least the idea of the proof, if you can.
5.	Effect of the first and second derivative on the graph of a function. Using them to find local maxima and minima of functions. Critical numbers, inflection points.
6.	Infinite limits. Know the basic idea and the geometric meaning, and be able to calculate easy examples, but these are not a high priority for now.
7.	Finding graphs of functions using calculus and other techniques. This will be covered, but there won't be a hard example to analyze from scratch (of course, if you have learned to do some of the harder examples, you should be well prepared for any test question).