The final exam will be held in the usual room on Thursday Dec. 18, 10:30 - 12:30. It will start promptly at 10:30, so make sure you're on time. The test will cover the new material since the last exam (8.3 - 8.5 and 8.8) as well as whatever was covered on the first three exams. See the information pages for the first exam, second exam, and third exam. The remarks on these pages all apply to the final exam as well.

The test will be approximately half new material, and half old material. It will have six problems, possibly with several parts each. Calculators or other mechanical assistance are not needed and are not to be used.

As with the third exam, some trig identities will be provided. From the new material, the following topics are likely to be covered, though the exam is not limited to these topics:

• performing trig substitutions, and knowing which substitutions are appropriate in which situations
• using long division to deal with rational functions that are not proper
• writing the correct form of the partial fraction expansion of a proper rational function, based on the factors of the denominator
• solving for the constants
• integrating the resulting terms, which will be (constant)/(linear) or (linear)/(quadratic)
• evaluating improper integrals (of two types) as limits
• using the comparison test to decide convergence or divergence of improper integrals

"Rationalizing substitutions" from the end of section 8.4 will not be covered on the exam.

Advice:

• Look at the "Concept Check" questions at the end of Chapters 5 - 8 to find out which conceptual areas need review.
• Learn what the "routine" problems are, and practice so that you can do them quickly and easily. Remember, they always seem harder in an exam situation, so practice and build your confidence.
• You may need to brush up on computing derivatives and integrals (eg. chain rule, substitution, etc).

When it comes time for the test itself, relax and do the best you can. Because you have studied, you know which topics you know best, and can get those problems out of the way quickly. Then you'll have time to spend on the remaining ones.