First Midterm: 8:30 pm on Thursday, October 11, 2018Bring 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 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.
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)
David Kahn held a review session on Sunday, Sept 30 at 2pm in Earth and Space 001. While this was recorded (here is a link to the video), there are some issues with quality. Cave videntium!)
There are also one and a half review sessions a previous semseter that you can watch on video: Substitution and review and More review. Although this was a while ago, the material covered is pretty much the same (but it doesn't include integration by parts).
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 date of the midterm 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. Some are easier overall than our exam will be, others are harder.
This semester, our exam is significantly later in the semester than any of the sample exams below; this means we have covered more material. Not everything we have covered will be on the exam, because that would be too much. The material we covered in the class through and including integration by parts will be on the exam. (Most of the samples below do not include integration by parts.)
- Spring 2007 (solutions).
- Fall 2007 (solutions).
- Spring 2008 (solutions).
- Spring 2010 (solutions).
- Spring 2014 (solutions).
- Spring 2015 (solutions).
- Fall 2015 (solutions).
- Spring 2016 (solutions).
- Fall 2016 (solutions).
- Spring 2018 (this one is kinda hard!) (solutions).
Results: Below is a graph of the score distribution on the exam. As you can see, there were quite a few grades of A and A- (with A- being the most common score-- this is unusual for this class), but sadly also a lot of grades below C (about 15% of the class!).
If you got less than 40 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; while the deadline to do so has passed, contact Prof. Sutherland or Kahn right away if you want to do this. We might be able to help, but it needs to be done no later than Oct 18.
There were three different versions of the exam, called Bird (solutions), Diz (solutions), and Max (solutions). There were a couple of typos on the exam, which have been fixed in the version here. If you see any typos in the solutions, please let me know.
Second Midterm: 8:30 pm on Thursday, November 1, 2018
The second midterm will cover all the material we have covered that wasn't on 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. This list is subject to change.
Here are some more chapters from David Kahn's AP Calculus book:
- Chapter 20: Partial Fractions (solutions to problems)
- Chapter 19: Integrals of Powers of Trig Functions (solutions to problems)
- Chapter 20: Improper Integrals (solutions to problems)
- Chapter 16: The Area Between Two Curves (solutions to problems)
Review Sessions: 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.
David Kahn held a review session in Earth and Space 001 on Sunday, October 28 at 2 pm; you can watch it here. All three lectures will also be doing review in class during the week of the exam (Oct. 29-Nov. 1).
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, and some later material may be added (in this case, I marked the question(s) that use material we have not covered).
- Fall 2009 midterm 2 (solutions)
- Spring 2010 midterm 2 (solutions)
- Fall 2015 integral practice (solutions)
- Fall 2015 midterm 2 (solutions) -
- Spring 2016 practice problems (solutions)
- Spring 2016 midterm 2 (solutions)
- Fall 2016 midterm 2 (solutions)
- Spring 2017 midterm 2 (solutions)
- Fall 2017 midterm 2 (solutions)
- Spring 2018 midterm 2 (solutions)
Results: Below is a graph of the score distribution on the exam.
This time there were two versions of the exam: Tweedledum (solutions) and Tweedledee (solutions).
Final Exam: 2:15pm on Thursday, Dec 13, 2018
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.
- Chapter 17: The Volume of a Solid of Revolution (solutions to problems)
- Chapter 20: Arc Length (solutions to problems)
- Chapter 20: Calculus of Polar Curves (solutions to problems)
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 two of the
samples here does polar coordinates and complex numbers, some cover center
of mass/centroid (which we didn't do), several do work (we also didn't do
that), 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
memorize formulae-- understand them!
Please work the problems before reading the solutions, or they won't do you any good.
- All lectures will be doing some review in class. You can find the ones for the Tuesday/Thursday classes on Echo360, and here are the ones for the MWF lectures: 5 Dec 2018, 7 Dec 2018, and 10 Dec 2019.
- Videos from previous semesters (which cover much of the same material) are here: 2 May 2016 and 4 May 2016
- There will be a review session on the reading day, Dec 11 2018 in ESS001 from noon to 2pm. Here is a video of it in case you missed it, or just want to relive the experience.
- Remember that there are videos of all the material for the class on the class schedule page, as well as on Echo.
The final will be in a variety of rooms, depending on which recitation you are in. Note that some rooms have changed yet again! Check carefully!
|Frey 100||Aleksander Doan
Holly Chen (R20, R31)
Yuhan Sun (R22, R33)
| Scott Sutherland
Lec 01/03(R02, R31,
R33 only), |
David Kahn Lec 02 (R20, R22 only)
|Engineering 145||Stephanie Salvator
Jin-Cheng Guu (R04, R05),
Yao Xiao (R32)
|Scott Sutherland Lec 01/03 (R03, R04, R05, R32 only)|
|Engineering 143||Jiahao Hu
(R01, R21) |
Paul Sweeney (R30)
| David Kahn
Lec 02 (R21 only)
Scott Sutherland Lec 03 (R01, R30 only)
Results: Below is a graph of the score distribution on the final.