Information about Exam II for Math 1823-001H

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

Information about Exam II

Exam II will be in the usual classroom on Thursday, October 26, 2006. It will cover sections 3.1-3.8.

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--- some very similar to the homework, some based on the ideas presented in class, and possibly some that require the application of our ideas in a new context. Something will be repeated that appeared on Exam I. There will be one "Challenge Problem" for you to work on after you have done all you can on the "regular" questions. 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 exam emphasizes the calculation of derivatives, especially calculations involving the chain rule. You will need to know our various definitions of the derivative, to be fluent with the derivatives of all six trigonometric functions, and to be proficient with the use of algebraic formulas and the Chain Rule in calculation. The following will definitely be covered, although the exam not necessarily restricted to these topics:

  1. Calculation of derivatives using the difference quotient (both of the standard forms).
  2. The other two definitions of derivative--- best linear approximation and “stretch factor.”
  3. Calculation of derivatives using the algebraic formulas for sums, differences, products, and quotients.
  4. The Chain Rule.
  5. Implicit differentiation.
  6. Higher derivatives. Definition, calculation, and guessing the general form based on the first few derivatives.

The following topics do not appear, at least not explicitly: trigonometric identities such as the expansion of sin(2x), verification of the Chain Rule, sin(1/x)-type examples, solving differential equations, finding polynomials given values of their derivatives at a point.

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.	Calculation of derivatives using the difference quotient (both of the standard forms).
2.	The other two definitions of derivative--- best linear approximation and “stretch factor.”
3.	Calculation of derivatives using the algebraic formulas for sums, differences, products, and quotients.
4.	The Chain Rule.
5.	Implicit differentiation.
6.	Higher derivatives. Definition, calculation, and guessing the general form based on the first few derivatives.