Calculus AB / Mr. Hansen 12/9/2003

Name: ________________________

Study Guide for Chapter 5 Test

Note
         Please understand that I will not normally provide this much information in advance about the content of a test. However, I wish to make the testing environment as fair and equal as possible, especially for this test, in which some people may be taking the test more than once. (Recall, however, that if you take the test twice, you must make the decision at the end of the first test regarding which test you wish to be graded.)

Part I.	Multiple Choice (8 questions, 6 points each).
	Wrong answers are –1½ points each to discourage guessing. Omitted problems count as 0. Problems will be taken from the Barron’s AP review book and other similar sources. It goes without saying that any problems involving FTC1 would be without calculator.
Part II.	Essay (8 points).
	State FTC1 accurately and give an example that shows that you understand it.
	or
	State the rule for odd functions evaluated over symmetric intervals. Provide a diagram and a worked example to show that you understand the rule.
	or
	State the rule for even functions evaluated over symmetric intervals. Provide a diagram and a worked example to show that you understand the rule.
	or
	State the definition of definite integral in terms of Riemann sums, and give a three-phase example to show that you understand how the Riemann sums become a better and better estimate as the mesh size decreases.
	or
	You will be asked to state either the IVT or the MVT. Then, you will be told to violate one of the conditions in a specific way and to explain, using words and/or diagrams, why the theorem would then become false. For example, you might be asked to show why the MVT is false if the continuity condition does not apply to one of the endpoints.
Part III.	Investigation (20 points).
	Given a continuous function on a closed interval, estimate the definite integral three ways: (1) using the midpoint rule with 4 subintervals, M4, (2) using the trapezoid rule with 4 subintervals, T4, and (3) using Simpson’s rule with 8 subintervals, S8. Then show algebraically that (2M4 + T4)/3 = S8. Although you will be allowed to use your calculator in this section, you must show your work in order to earn credit. The answers, by themselves, are worth little. (Using calculator programs to help you is permitted and does not constitute an honor violation. As with the AP exam, anything stored in your calculator’s memory is acceptable, and memories are not cleared before the start of the test.)
Part IV.	Proof Completion (8 points).
	Given a proof of FTC1 Þ FTC2, or of the converse, furnish reasons for 4 designated steps in the proof.
Part V.	What It All Means (16 points).
	You will be given a variable-factor product word problem. You must not only compute the answer but also explain why your method is necessary and suitable.