Information about Exam I for Math 1823-001H

Mathematics 1823-001H - Honors Calculus I - Fall 2006

Information about Exam I

Exam I will be in the usual classroom on Tuesday, September 26, 2006. It will cover sections 1.2, 1.3, and 2.1-2.6.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with.

There will be a mix of problems--- quite a few very similar to the homework, some based on the ideas presented in class, and possibly some that require the application of ideas that we have examined in a new context. There will be one "Challenge Problem" for you to work on once you have done all you can on the "regular" questions.

The exam will be challenging (but doable), exam grades in this class usually run from 40% to 85%. Just relax and do your best. 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 emphasis of the exam is on limits. The following will definitely be covered, although the exam not necessarily limited to these topics:

  1. Limits, intuitively. Finding values of limits, including limits with infinite values, or as the variable approaches plus or minus infinity.
  2. Limits, formally. The precise definition of limit, and using it in "epsilon-delta" arguments.
  3. The limit of sin(x)/x as x -> 0. You do not need to be able to derive this limit using the Squeeze Theorem, but be familiar with it and its use to evaluate other limits.
  4. The Squeeze Theorem and its use.
  5. Right-triangle trigonomety. Given any angle and any side of a right triangle, know how to write an expression for the length of any other side using one of the six trig functions.
  6. Manipulation of graphs of functions by horizontal and vertical translation and stretching.
  7. The Intermediate Value Theorem.

Not much of the exam involves continuity, other than the Intermediate Value Theorem. For this exam, it is not necessary to know trig identities from memory. The following topics do not appear, at least not explicitly: graphs of trig functions other than sine or cosine, finding the tangent line slope by working with an expression for the secant line slope (i. e. the "long" homework problem).

Exams from previous Honors Calculus classes can be found on their course pages (links to them appear on the course pages page). Some were 50-minute classes, but most were 75-minute classes. Of course, these were different classes, so the exams may be quite a bit different.

1.	Limits, intuitively. Finding values of limits, including limits with infinite values, or as the variable approaches plus or minus infinity.
2.	Limits, formally. The precise definition of limit, and using it in "epsilon-delta" arguments.
3.	The limit of sin(x)/x as x -> 0. You do not need to be able to derive this limit using the Squeeze Theorem, but be familiar with it and its use to evaluate other limits.
4.	The Squeeze Theorem and its use.
5.	Right-triangle trigonomety. Given any angle and any side of a right triangle, know how to write an expression for the length of any other side using one of the six trig functions.
6.	Manipulation of graphs of functions by horizontal and vertical translation and stretching.
7.	The Intermediate Value Theorem.