Final Exam

Final exam and Solution draft
We had a final review on Monday December 9th at 3 PM in Hall C. Solutions to the problems solved there [PDF]. The final exam took place on Friday December 13th at 2 PM. The rooms were Hall A and Hall B. (A-R in Science Center B, S-Z in SC A). Some have wondered about knowing trig identities. You can survive with the following two double angle identities
cos2(t) = (1+ cos(2t))/2 sin2(t) = (1- cos(2t))/2
This is what we usually need to integrate. Also you can get more identities from this by adding the two up, or by subtracting the two or by differentiating the first one. See the Exam Schedule PDF.

Practice I, [Solutions]

Practice II, [Solutions]

Practice III, [Solutions]

Practice IV, [Solutions]

Practice V, [Solutions]

Practice VI, [Solutions]

Second hourly

The second midterm took place November 5 at 6-7:30 PM in Hall C. We had a global review on Sunday, November 3, 6-7:30 PM in Hall C. The first midterm had an average 83 with a standard deviation 9.
Second midterm and Solution
We are heroes tonight!
Here are practice exams with solutions.


Practice 1, [Solutions]

Practice 2, [Solutions]

Practice 3, [Solutions]

If you need more practice about some topics: here are some other practice exams. Also these are adapted old exams.

Practice 4, [Solutions]

Practice 5, [Solutions]

Practice 6, [Solutions]

First hourly

The first midterm took place on Tuesday October 1, from 6-7:30 PM in Hall C. We had a global review on Sunday, September 29, 2019 from 6-7:30 PM in Hall C. The first midterm had an average 85 with a standard deviation 9.
First midterm and Solution
Here were practice exams with solutions.


Practice 1, [Solutions]

Practice 2, [Solutions]

Practice 3, [Solutions]

If you need more practice about some topics: here are some other practice exams. Also these are adapted old exams.

Practice 4, [Solutions]

Practice 5, [Solutions]

Practice 6, [Solutions]

Exam policies

"Out of sequence exams" are offered for students observing religious holidays and students who
need out of sequence exam as ordered from the accessible education office.
See student handbook.
If you have a lab conflict, it is usually possible to rearrange the lab for that exam time. 
We try to accommodate students with rehearsals, practice or regular classes, seminars or labs as     
well as possible but with a large number of requests this is not possible and would also compromise
the integrity of the exam. In case of a qualifying conflict, contact Oliver knill@math.harvard.edu.
Note that we can not offer make-up exam any other day. All requests have to arrive a week before the exam.