Exam Information for Math 126

As it says on the course syllabus, there are two midterms and a final in MAT126, which count for 25%, 25%, and 35% of your grade, respectively. No Make-up exams will be given. If you miss an exam due to a documented medical or family reason, that score will be replaced by the grade on the balance of the course. If you miss more than one exam for such reasons, you should probably withdraw from the course.

First Midterm: 8:15 pm on Thursday, September 29, 2022

Bring 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 will be in one of two rooms:

Lecture 1 (R01-R06) is in ESS 001

Lecture 2 (R20-R26) is in SCGP 103

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:

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).

Old exams:
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.

Note that we have covered more material in the course so far than will be on the exam. We want you to have mastered this material before testing you on it, so only what we covered in class through and including integration by parts will be on the exam. (Most of the samples below do not include integration by parts -- their exams were earlier than ours.)

Also, here are a bunch of integration problems that you should be able to do. (And here are the solutions).

Results: Below is a graph of the score distribution on the exam. As you can see, there were a lot of people who essentially did very little correctly on the midterm (16% of the class!). If you did worse than you were expecting, it is possible to still do well in this course, but it will require effort on your part.

low score: 1 mean: 33.2 median: 33 high score: 80 possible score: 80

range letter grade 68-80 A-, A 38-59 B-, B, B+ 25-37 C, C+ 15-24 C- 8-14 D, D+ 0-7 F

If you got fewer than 25 points on this exam, you must reassess how you are approaching the class if you hope to pass. It may be appropriate for you to drop down to MAT125 or MAT131, but the deadline to do so is Friday, October 7 at 4pm; you will need to consult an advisor first. Even if you stay in the class, it is possible recover from doing badly on this exam, but it will require making changes to how you approach it.

There were three different versions of the exam, called Ziggy (solutions), TVC15 (solutions), and Jean (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 us know.

Second Midterm: 7:50 pm on Wednesday, November 2, 2022

The midterm will be in one of two rooms (which is where your lecture is held):

Lecture 1 (R01-R06) is in ESS 001

Lecture 2 (R20-R26) is in Harriman 137

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 and Trapezoid methods and how to find the right n) and improper integrals; also area between curves, volumes, and average value from from chapter 6. This list is subject to change.

Here are some more chapters from David Kahn's AP Calculus book:

Old exams:
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. Be aware that different instructors emphasize different topics more. This means that some midterms contain problems we didn't emphasize and our midterm may have few or none of these, and more of something else. None have average value, but we have done that.

Results: Below is a graph of the score distribution on the exam. Note that there are still a huge number of people who have no clue what is going on in this class. Even if you are one of those, it is still possible to pass, but serious changes will need to be made.

low score: 1 mean: 52.3 median: 52 high score: 120 possible score: 120

range letter grade 92-120 A-, A 67-91 B-, B, B+ 35-66 C, C+ 25-34 C- 10-24 D, D+ 0-9 F

There were three versions of the exam, named Drums (solutions), Space (solutions), and DarkStar (solutions).

Homeworks

Strictly 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.

Below is a graph of how people are doing on homeworks, as of Sun, 11 Dec 2022. The huge numger of people with very high homework grades came about because of the extra credit at the end of the semester. This was supposed to encourage people to actually do these extra problems as a study aid. Unfortunately, a significant number of people who were doing poorly just decided this was a good way to get free points. Since the homework counts much less than the exams or final, these "free points" didn't actually help them much, as you can see by the grades on the final exam below.

Final Exam: 2:15pm on Thursday, Dec 8, 2022

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.

Below 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 three of the samples here do polar coordinates, some cover center of mass/centroid (which we didn't do), one does complex numbers (we didn't do that), several do work (which we covered), and two cover probability (also one of our topics). A few have a question about Simpson's rule, which we did not cover; just do the problem with the trapezoid or midpoint rule instead (which you should know how to deal with. If you need the error formula, it will be provided as on the second midterm).
Also, while most of the volume roblems 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 homework Bldg and several webassign questions, as well as in class. Don't memorize formulae-- understand them!
Please work the problems before reading the solutions, or they won't do you any good.

The final this semester will include the following formula sheet. Other notes, electronic devices, books, and so on are not permitted.

Results: Below is a graph of the score distribution on the final.

low score: 1 mean: 81 median: 71 high score: 215 possible score: 224

range letter grade 160-224 A-, A 90-159 B-, B, B+ 50-89 C, C+ 40-49 C-

Overall grades in the course

Below is a chart showing the distribution of grades in the course. The median grade for MAT126 this year was C+, which is significantly lower than usual for this course. This is likely due to the exceptional number of students who did essentially no work, and barely earned any points on the exams -- this was more than 1/5 of the class.