November 24, 2003

When: Wednesday, December 10, 11:00-12:50, in our normal classroom

What Material: Cumulative, with an emphasis on the material not covered.

Procedure: The test will be closed book. You will be allowed one page (8 ½ - 11 in) of notes, front and back. You may put anything you want on this page of notes. Calculators will be necessary for some of the problems.

Suggested Review: First study the material from the first two tests. To make this material easier, I guarantee that any question based on previous material will be similar (though not exactly the same) as a question from the previous exams. For the new material, the advice is always the same: practice. Do all the problems listed below. Make sure you can do them in a test-type situation (mixed, no help from the book, no checking answers immediately after doing the problems, with a page of notes). If you read this, draw a smiley on the front of your exam. This will make me happy. You should also review material that is a prerequisite for the new stuff (exponent rules, domain, range, long division, etc). Keep in mind, having a cheat sheet does not guarantee you a better grade. Do not slack off on the studying just because you are allowed a bit of help.

Thoughts on the cheat sheet: I have a couple reasons for allowing the sheet of notes. First, there is a lot of information on the final exam, including several long procedures from the last few sections, and I feel it is ok if you don’t commit all of it to memory. Second, it keeps people from cheating. Not that any of you are cheating, but some people are known to put formulas in their graphing calculators or write answers on their hands, stuff like that. Now everyone is on a level playing field.

DO NOT THINK THE CHEAT SHEET WILL HELP YOU!!!! Many students actually do worse on this exam because of the cheat sheet. People tend to study less, because they think all of the answers will be with them, so practice isn’t necessary. This is just plain wrong. Treat this exam as if you wouldn’t have any help. Study and practice as if the cheat sheet wasn’t going to be there. Then use the cheat sheet when you get stuck. Writing up a cheat sheet is NOT the same thing as studying. You have been warned.

Second Guessing the Prof: Many people wonder what I would put on the exam from the old material. As a general rule, profs like me like to retest the students on problems they did poorly on. This is so the students will study the material again and hopefully get it right the second time around. The problems that this class did worse on are as follows:

Exam 2, #2 - Average grade: 38%

Exam 2, #3 - Average grade: 42%

Exam 1, #6 - Average grade: 51%

Exam 1, #3 - Average grade: 59%

Exam 1, #5 - Average grade: 66%

Exam 2, #5 - Average grade: 67%

Exam 2, #7 - Average grade: 68%

This is not to say I wouldn't put on material other than these seven questions, and this is not to say that I will put all seven of these questions on the exam. They are just more likely to show up. Also keep in mind that much of the new material relies on old material. So even if there is no long division problem, it would still likely show up in an oblique asymptote problem.

Specific Topics from New Material:

Graphing Functions: You should know the graphs of the identity function, square function, cube function, absolute value function, exponential function and logarithm function. Then you should know how to translate it, reflect it, and scale it. You should also be able to recognize symmetries, either from the graph of the function or from the equation itself. Practice Problems: 3.6, 1-40.
Quadratic Functions: Given a quadratic function, you should be able to find the vertex, x-intercepts, y-intercept, vertex, domain, range, whether it opens up or down, and you should be able to graph it. Practice Problems: 4.1, 1-26.
Polynomials: Given a polynomial function, you need to find its x-intercepts, its y-intercept, any symmetries, and its ending behavior. Using all this, you should be able to sketch a rough graph of the polynomial. Also, you should be able to use the techniques from Section 3.6 to graph certain polynomials. Practice Problems: 4.4, 1-18, 21-28.
Rational Functions: Be able to find horizontal, vertical, and oblique asymptotes for any rational function (along with x-intercepts, y-intercepts, domains, ranges, etc). Practice Problems: 4.5, 1-40.
Inverse Functions: Be able to use the horizontal line test to tell if a function is one-to-one. Also, given a function or the graph of a function, be able to figure out its inverse. Practice Problems: 13-26, 35-56, 61-68.
Exponential Functions: You should be able to evaluate exponential functions, both with and without a calculator, you should be able to graph exponential functions, and you should be able to solve exponential equations. Practice Problems: 5.1, 1-12, 19-28, 31-38, 49-61.
Logarithmic Functions, Logarithmic Equations, and Exponential Equations: Lots of material here, and lots of things you need to be able to do. You should be able to evaluate a logarithm (with or without a calculator), rewrite a logarithm in its exponential form (and vice versa), split up a logarithm using the logarithm rules, write an expression as one logarithm using the logarithm rules. You should also be able to solve equations involving exponential and involving logarithms. Practice this stuff, it ain't easy! Practice Problems: 5.3, 1-16, 19-30, 57-74; 5.4, 11-22, 35-42, 49-52; 5.5, 5-34.