Review Sheet, Exam 3
April 18, 2011
Wednesday, April 27, 9:00-10:50
, in our usual classroom (note the time is wrong on the syllabus)
Cumulative, with an emphasis on new material (2.4-2.8, 3.1, 3.5, 4.1-4.5).
The test will be closed book. You will
be allowed one page (8 1/2 - 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.
No TI-89's or TI-92's.
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.
Note that the questions that got cut from the first exam are fair game. 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, no help from MyMathLab, 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).
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.
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
I will set up a MyMathLab assignment that contains practice problems
for old material that is likely to show up on the final exam.
This assignment will be optional, but it will probably be really really
Specific Topics from New Material:
- Linear Functions: You
should be able to plot a line, and you should be able to figure out the
equation of a line or the slope of a line based on different
information. Practice Problems: 2.4, 7-24, 35-42, 45-50, 53-58; 2.5, 5-26, 31-39, 47-56.
- Piecewise Functions: You should be able to graph a piecewise function. Practice Problems: 2.6, 17-34.
- Graphing Techniques: Given
a function, you need to know the transformations that perform
reflections, translations, and stretches. You should also be able
to determine if a function is even or odd, and if it is symmetric about
the y-axis or symmetric about the origin. Practice Problems: 2.7, 3-14, 23-57.
- Function Operations: Given
two functions, be able to add, subtract, multiply, divide, and compose
them. Make sure you understand how the domain is affected by
these operations. Practice Problems: 2.8, 1-14, 23-30, 33-54, 57-72, 77-80.
- Quadratic Functions: Given
a quadratic function, be able to find its vertex, whether it is open up
or down, its y-intercept, its x-intercepts (if they exist), its domain
and range. Then be able to graph it. Practice Problems: 3.1, 13-26.
- Rational Functions: Given
a rational function, be able to find its asymptotes, intercepts, and
graph it. Make sure you can figure out what types of asymptotes
exist from the degree of the polynomials in the numerator and
denominator. Practice Problems: 3.1, 61-96.
- Inverse Functions: Given
the graph of a function, determine if it is one-to-one (horizontal line
test). Given a one-to-one function, find its inverse.
Verify two functions are inverses of each other. Draw the graph
of the inverse of a function. Practice Problems: 4.1, 3-17, 41-50, 55-76.
- Exponential Functions: Evaluate them (either exactly or approximately with a calculator), and solve exponential equations. Practice Problems: 4.2, 1-12, 49-69.
- Logarithmic Functions: Evaluate them (either exactly or approximately with a calculator), and then manimpulate them using log rules. Practice Problems: 4.3, 3-30, 59-88; 4.4, 11-26, 61-72.
- Exponential and Log Equations: Use exponential and log rules to solve equations. Practice Problems: 4.5, 5-56.