First Midterm: 8:30 pm on Thursday, September 29, 2016Bring a photo ID. No calculators will be allowed. Bring a pen to the exam: while you may do the midterm in pencil (or crayon), you can only contest grading of problems done in non-erasable ink. Sorry. The midterm focuses on material in the first half of Chapter 5 of the text (through 5.6); that is, you should understand the definite integral as a limit of Riemann sums, as well as be able to evaluate them using the Fundamental Theorem of Calculus, be familiar with using the technique of substitution, and be able to do a simple integration by parts.
Doing all of the homework problems prior to the exam is a very good idea. Doing additional problems from the text can be helpful.
You should make sure that you know the antiderivatives of all the basic functions that you learned in first-semester calculus. You should know all the antiderivatives on this table of integrals (and, of course, how to use them).
You should be able to do the problems on the exams from previous semesters that you see below. The coverage varies somewhat, since the exam falls at different places in different semesters. Note that our exam will have different problems, in possibly different formats, from any of these old exams. Still, they should give you an idea of the range and difficulty to expect. Note that our exam is a few days later in the semester than any of the sample exams below; this means we have covered integration by parts, but the sample exams have not. You are responsible for integration by parts, but it won't be a major emphasis on the exam.
Results: Below is a graph of the score distribution on the exam. While this was not a terribly difficult exam (easier than most of the homework problems), a lot of people got grades of C- or lower.
If you got less than 30 on the exam, you really need to reconsider your approach to this course. If you haven't already taken MAT125, you should seriously consider moving down to it; this can be done with this form.
There were three different versions of the exam, called Clotho (solutions), Atropos (solutions), and Lachesis (solutions). You get to figure out why they have these names. If you see any typos in the solutions, please let me know.
Second Midterm: 8:30 pm on Thursday, November 3, 2016
The second midterm will cover all the material we have covered since the first exam: the rest of Chapter 5 (on various techniques of integration, as well as numerical integration (ie, Midpoint, Trapezoid, and Simpson's rules) and improper integrals; also area between curves and volumes from chapter 6.
In order to help you review and prepare, David Kahn has kindly allowed us to use some chapters from his AP Calculus book:
- Chapter 13: Antiderivatives (solutions to problems)
- Chapter 14: Area Under A Curve (solutions to problems)
- Chapter 14: Derivatives of Integrals (solutions to problems)
- Chapter 21: Substitution (solutions to problems)
- Chapter 18: Integration by Parts (solutions to problems)
- Chapter 19: Integrals of Powers of Trig Functions (solutions to problems)
- Chapter 20: Partial Fractions (solutions to problems)
- Chapter 16: The Area Between Two Curves (solutions to problems)
- Chapter 17: The Volume of a Solid of Revolution (solutions to problems)
You can watch a video of a review session from spring 2016. This doesn't include all the material we've done, but will probably be helpful anyway.
Here are some old exams (or sample problems) from previous semesters to help
you prepare. Some of these occured a bit earlier in the semester than ours
did, so some of the later material may be missing. In other cases, some of
the earlier material may be missing.
- Spring 2000 midterm 2 (solutions)
- Spring 2007 practice problems (solutions)
- Fall 2009 practice problems (solutions)
- Spring 2010 midterm 2 (solutions)
- Fall 2012 practice problems (solutions )
- Fall 2015 integral practice (solutions)
- Fall 2015 midterm 2 (solutions)
- Spring 2016 practice problems (solutions)
- Spring 2016 midterm 2 (solutions)
Results: Below is a graph of the score distribution on the exam.
HomeworksStrictly speaking, homeworks don't belong here, but I don't know where else to put this information.
A small part of your grade corresponds to the paper homeworks and webassign scores. However, there is a strong correspondence between homework grades and how people do on the midterms and the final, although it only goes one way. Very few people who do well on the midterms are doing poorly on the homeworks, but quite a few people do well on the homeworks but not on the midterms. Most people, however, do about the same on both.
Here is a graph of how people are doing on homeworks, as of Thu, 8 Dec 2016. From this, you can see that there is a group of people who just don't do homework much. Not surprisingly, these correspond closely to the group that is getting terrible grades on the exams. (However, there are also lot more grades of A on homework than people getting an A in the class.)
Final Exam: 2:15pm on Wednesday, Dec 14, 2016
The final will be cumulative, covering everything that we have done in the class.
Here are a few more chapters from David Kahn's AP Calculus book, in case you want to use them.
Here are some finals (or sample finals) from previous years to help you
study. Be aware that some of the applications of integration covered in
MAT126 differ from semester to semester. For example, only one of the
samples here does polar coordinates and complex numbers, some cover center
of mass/centroid (which we didn't do), and only one does probability.
Also, while most of the volume problems are for surfaces of revolution, note
that you (should) know how to compute volume if you know a formula for the
area of a cross-section, as in the paper homeworks
and problem 4 of the second midterm. Don't
memorize formulae-- understand them!
Please work the problems before reading the solutions, or they won't do you any good.
The finalwill be in a variety of rooms, depending on which recitation you are in. Note that some rooms have changed yet again! Check carefully!
|Earth&Space 001||Thomas Rico
(R02, R30), |
Mariangela Ferraro (R03, R33),
| Scott Sutherland
Lec 01 (R02, R03 only), |
Zhiqiang Li Lec 03 (R30, R33 only)
|Frey 102||Rayne Goldberg
Gaurish Telang (R04, R05)
| Scott Sutherland
Lec 01 (R04, R05 only), |
Zhiqiang Li Lec 03 (R32 only)
|Harriman 137||Alaa Abd-El-Hafez
(R20, R21) |
Frederik Benirschke (R22,R23)
|Jozef Bodnár Lec 02 (all sections)|
|Javits 103||John Sheridan
Aleksei Golota (R34)
|Zhiqiang Li Lec 03 (R31, R32 only)|