Math 165 - Calculus I, Final

Grading

After a lot of agonizing, I used the following cutoffs, lower than those at the midterm. They mean 'if you scored x or more, then your Grade is y or better'. If your score seems to be incorrect or you have any complaint about grading, email me. A few people have scores very close to the next better grade. Be assured that I looked hard at your individual records. With 150+ people, this was bound to happen somewhere, and in your case I just could not find good reasons to lower the cutoff even more. If your final score is missing or definitely incorrect, tell me ASAP! ask to see your final exam - arrange a meeting via email.

Score	540+	504+	480+	438+	409+	373+	314+	280+	249+
	A	A-	B+	B	B-	C+	C	C-	D	F

Time, Place

The time is 7-9 pm on Tuesday, May 3rd. The exam will be in Gilman 1002 for the 10-11 class and in Gerdin 1148 for the 11-12 class. Please make sure you know where that is before the exam. If you are not taking the exam because you feel ill (and don't take chances!), then get a doctor's note to show me later. If you know beforehand that you will not be able to take it, email me ASAP and/or come forward after the lecture on Friday.

Format

Like the midterm, there will be a paper-and-pencil part without calculators (30 min) and a part with calculators (90 min). Bring your own scratch paper, but there will be enough space provided for all your work on the exam. I recommend to bring a watch (I will announce the time occasionally). One error: between questions 3 and 4 there is another question without a number. Make that question 7.

Standards

'Show all work' means in particular that I want to see the intermediate function u(x) when you evaluate an integral using the method of substitution. In max-min problems, I would like to see the domain of the objective function and the list of critical points. If you are doing the First Derivative Test, the sign pattern of the derivative is required.

Material covered

See the departmental calculus page for the syllabus, sections covered and objectives of this course. This has the list of topics/skills/keywords that will be covered in the Final. The Final is comprehensive, but we stress the topics that were not examined in the midterm. This allows me to modify the list of topics - cut out chapters 2, 3 and much of 4. On the other hand, I can make it more detailed for those topics that are most relevant.

evaluating integrals using ALL the methods that we did. That includes
- Riemann sums (memorize those sums of 1, of i, of i^2 from i=1 to n)!
- Fundamental Theorem of Calc
- Method of substitution (the most important one)
- Symmetry
applications of the integral to area under curve, to word problems
general inverse functions
- when do they exist?
- what is their derivative?
general exponential functions, inverse trig functions, their derivatives
properties of ln and exp, inverse trig functions (asymptotes, symmetry etc)
applications to exponential growth/decay

Less relevant, because much of it already covered in midterm:

optimization, but still on the Final for one of the new functions to be maximized!
curve discussion (max/min, local extrema, CONCAVITY, asymptotes ...)
limits (but there are some limits for new functions)
approximation by differentials

Cut out section 11.3 (Newton/bisection method).

Derivatives, antiderivatives to memorize

You are expected to know the derivatives of trig functions, their inverses, general exponentials and logarithms as well as the basic Rules of Differentiation, so that you can differentiate about any function we throw at you without a calculator.

More stuff to memorize

For integration, you are expected to know from memory the items 2-13,16,17,19 from the 'Table of Integrals' at the back of the textbook, but items 16,17,19 only for a=1. Furthermore, you are expected to use these when performing the Substitution Method with simple substitutions. You should memorize the special sums of 1, of i and of i^2 for i from 1 to n and be able to apply these to working with Riemann sums.

Practice for the exam

Look at homework problems, not just the hand-in problems.
Look at the relevant section of the textbook and the worked examples there.
If that still leaves questions, see or email your TA. Or go to SI, or the Math Help Room, or see me (if you cannot make regular consulting hour, make an appointment by email).
The departmental calculus page has a couple of old Finals. We can go over parts of them in lecture, and I will put a model solution for at least one of them on WebCT.
Attend review lectures, recitation, SI, come to consulting hour ...
... and SIT DOWN AT HOME AND DO SOME WORK BY YOURSELF. Working with a group of friends can be very useful as long as you are actively participating.

Old exams are not a good way of learning the material - but they are good for practicing the exam situation, and for getting a feel for what real exam questions look like.