Math 112 and 112H instructors:
Here is some information about the final exam.
1. The format will be only slightly different from last semester's
final. There will be 7 multiple choice questions worth 4 points
each and 12 problems requiring hand written solutions worth 6
points each. The instructions on the multiple choice questions will
be to circle the best answer ON the test itself. For DAYTIME
sections there will be NO bubble sheet. The EVENING sections will
take the test in the testing center and will have a bubble sheet
because it is a requirement for a test given at the testing center.
These students will be directed to circle the answer on the test
AND record it on the bubble sheet.
2. The instructions for the 12 problems requiring hand written
solutions will say "give the best answer and justify this answer
with sutiable reasons and relevant work." This is something
students should have been doing all semester, but here are some
examples you can tell your students to clarify this.
a. Answers like tan (pi/4), ln 1, e^0 would not be considered the best
answer.
b. On the other hand, because students may not use calculators on the
final, on problems such as exponential growth and decay in chapter 4,
students will have to leave answers in terms of logs since they cannot
reasonably change such answers to a decimal.
c. In solving a max-min problem, students should also justify that a
critical point is a maximum or minimum by the first derivative test,
the second derivative test, or by evaluating the function at all
critical points and endpoints.
d. If they are doing a problem by L'Hospital's rule, they should first
note that the problem is an indeterminate form, e.g., 0/0, and then
state they are using L'Hospital's rule.
e. For rules in constant use, such as the differentiation formulas,
the fundamental theorem of calculus, etc., there is no need to
specifically cite the rule they are using.
Students may check the solutions to last semester's final on the web
to see a few examples of what would be sufficient justification and
work.
3. Since last semester's final was the first given from Lynn Garner's
book, it will probably give a slightly better of indication of the
final than those of previous semesters. I recommend that students
definitely work thorough it and also a large number of the 112
review questions posted on the web. But the more previous finals
they try to work, the better. I would also advise them to work
each final before looking at the solutions. Previous finals and
the review questions may be found under Exams at
http://www.math.byu.edu/Courses/
We aren't going to say any more about content than this except
students should expect some problem using either the definition of
limit or a thorem about limits.
4. You may want to know about formulas students should know for the
test. They should know all basic differentiation and integration
formulas, power rule, product rule, quotient rule, chain rule,
basic antiderivatives at the beginning of chapter 5, all key
theorems (extreme value, intermediate value, Rolle's, mean value
theorem, fundamental theorem of calculus, etc.), the formula for
Newton's method, and rules for numerical integration. We only
thought of a few exceptions: We do not expect them to memorize
Cauchy's mean value theorem, Newton's law of cooling, the formula
for the logistic curve, or Simpson's rule as they are a little
harder to remember. We prefer not to write a comprhensive list
because we might forget something they should know, but will be
glad to answer specific questions.
5. Please emphasize that they remember to use the chain rule, to add a
constant when finding indefinite integrals, and most importantly
make sure they do not integrate when they are supposed to
differentiate and that they do not differentiate when they are
supposed to integrate.
6. Students will receive credit for any correct method for doing a
problem. For example, in the early sections of chapter 5, definite
integrals are calculated several different ways before the section
on the fundamental theorem of calculus. So there are several
integration problems that can be done in more than one way.