When: October 1, in class
What Material: Sections 5.1-5.5, 5.7, 5.8, 6.2, 7.1-7.3
Procedure: The test will be closed book. You will have the entire class period for the test. Graphing calculators will be useful (no TI-89 or TI-92). One page (8 1/2 by 11 in, front and back) of notes will be allowed.
Suggested
Review: Be able to do all of the homework problems without any help
from a book
or person. Problems will be "similar" to homework and quiz problems. I
have a liberal view on how "similar" is defined. Try to understand
the concepts well enough to deal with a problem that doesn't look exactly
like one you've done before.
Overall, the
best way to study for an exam such as this is to do as many problems as
you have time for. Your calculus book contains many MANY problems
to practice with. And you can check the answers for the odd
numbered problems.
Obviously, a very good knowledge of precalculus and calculus I is required to survive this class. Make sure you know what you are doing when you take derivatives, apply algebra rules, etc. Don't rush through stuff that isn't exactly part of calc II. You still need to be able to do it.
Specific Topics:
Antiderivatives: The mother of all calc II problems. The rest of your life will revolve around these. Make sure you can do them, make sure you understand what to do, make sure you never ever make up rules, and make sure you remember your +C's. Practice Problems: 5.1, 9-44.
Antiderivative Word Problems: Given a rate of change of a function, you can use antiderivatives to find the function. You should be able to do this for any rate of change, but most specifically for acceleration/velocity/position functions. Don't forget your +C's, and how to use given information to solve for C. Also be able to answer simple questions that go beyond finding the antiderivative (such as figuring out when the truck catches up with the car). Practice Problems: 5.1, 73-93.
Riemann Sums: Yes, they are difficult. Yes, they are annoying. Yes, they will have a prominent feature on the first exam. You need to be able to do two types: ones where you are asked to get an approximate value using a certain number of rectangles (the number will be given to you), and ones where you are asked to find the exact value of the area below the curve. The second type of question can only be asked for polynomials of degree three or less. The first type can be asked about any function. Practice Problems: 5.2, 23-30 (the approximation problems), 47-62 (the limit process problems), you can also do 1-22 and 31-44 if you need practice on a certain stage of the Riemann sum process.
Integral Rules: Here you use integral rules and geometry to evaluate integrals: Practice Problems: 5.3, 41-44, 47-49.
Fundamental Theorem of Calculus: Bask in the glory which is the FTC. Make sure you know what it is (both parts) and why it is important. Also make sure you know how to use it to evaluate definite integrals. Practice Problems: 5.4, 5-22, 27-50.
u-Substitution: Be able to do it, and know how to recognize the correct choice of u. And make sure you know how to do definite integrals that involve u-sub. You will not be told to use u-sub, and you will not be told what type of u-sub to use (i.e., log or inverse trig). Practice Problems: 5.5, 7-34, 47-74, 95-110; 5.7, 1-38, 49-56; 5.8, 1-42.
Area between curves: Know the formula, and know how to find the limits of integration if they are not provided to you. Don't be afraid to graph the functions. Practice Problems: 7.1, 1-45.
Washer/Disc Method: Be able to find volumes of revolution using the washer and/or disc method. Practice Problems: 7.2, 1-10, 23-36, 47-53.
Shell Method: Be able to find volumes of revolution using the shell method. Make sure you know which method (between shell and washer) is the correct one to use. Practice Problems: 6.3, 1-20.