The following questions about Advanced Placement (AP) credit and course choices applies to all incoming students in both Trinity College of Arts & Sciences and the Pratt School of Engineering.

###### I don't know my AP score yet, and it's time for me to select my courses for the fall. What math course should I enroll in?

If you feel good about your calculus course and your performance on the AP test, then go ahead and sign up for the course following the one for which you could get credit.

For example, if you took the AB test, then you can enroll in Math 122L(41L). If it turns out that you don't score high enough for that placement, then you can change your math course after you meet with your advisor in August.

If you took the BC test and are hoping to enroll in Math 202 or Math 212, note that the enforcement of that prerequisite will prevent you from being able to enroll in those courses. Just be sure that your score gets officially reported to Duke when it is available (see the Registrar's webpage for instructions), and if you do earn credit for Math 21 and Math 22 then you will be able to enroll in Math 202 or Math 212 in August.

###### I have credit for Math 21 Introductory Calculus (Earned through AP credit). How can I decide whether to take Math 122L Introductory Calculus II with Applications or Math 112L Laboratory Calculus II? What is the difference?

If you're going to enroll in a calculus II course in your first semester (the fall), then you should take Math 122L Laboratory Calculus II with Applications. In the fall semesters, Math 112L Laboratory Calculus II is reserved for students continuing from Math 111L Laboratory Calculus I or Math 106L Laboratory Calculus and Functions II at Duke. In the spring, however, Math 112L is the only second semester calculus class offered and is open to any student with AP credit for Math 21.

###### I have AP credit for Math 21 Introductory Calculus and would like to take Math 112L Laboratory Calculus II in the spring. I know that this course lists Math 111L as a prerequisite, and that my AB AP curriculum is not exactly the same. What are the differences that I should make sure to prepare for before entering Math 112L?

You should make sure to learn Euler's method and L'Hospital's rule, both of which are covered in Math 111L Laboratory Calculus I. You should be prepared for the fact that Math 111L covers a wider variety of applications of differential equations, and emphasizes a deeper conceptual understanding of Riemann sums, the fundamental theorem of calculus, and differential equations, than many AP AB courses. Finally, note that students who have taken Math 111L will have gained substantial experience with writing lab reports, which will be an important skill in Math 112L.

###### If I am a sophomore (or junior, or senior) at Duke who has never taken a math course at Duke, may I enroll in Math 122L Introductory Calculus II with Applications based on my AP credit?

Yes, the guidelines for your case are the same as for an entering student.

###### I have had a year (or more) of calculus, but I don't have AP credit or precollege credit for any calculus course. Should (or may) I take Math 122L or Math 112L or Math 202 or Math 212, or should I start over with Math 111L?

If your SAT score is at least 730 (700 if taken before Mar. 2016) and your ACT score is at least 32, and if your calculus background was thorough, then it would be a reasonable risk for you to enroll in Math 122L Introductory Calculus II with Applications. But it's your risk! For example, if you did not take the AP test, but you made an A in a demanding calculus course, and your SAT score is about 730 (700 if taken before Mar. 2016) or higher, then if you want to take the risk of enrolling directly in Math 122L (or a higher level course), you may do so. Or perhaps you did take the AB AP test and your score was 4 (so no advance credit) but your SAT score is over 730 (700 if taken before Mar. 2016); then enrolling in Math 122L would be a reasonable risk. Again, it's your risk!

If you have a very strong math background that includes learning Taylor polynomials and infinite series and convergence theorems, and if you want to start with multivariable calculus with no advance or precollege credit, then you should register for the Math 122L Proficiency Exam. Be sure to read all of the discussion on that registration page and prepare appropriately for the exam. If you perform strongly on that exam, then at the discretion of the Supervisor of First-Year Instruction you will be granted permission to enroll in Math 202 or Math 212, depending on your interests.

Or you might also consider taking our Math 221-222 sequence. This is a great choice for students interested in the possibility of a math major or minor. Math 222 covers multivariable calculus at a higher level than either 202 or 212, and makes powerful use of the linear algebra covered in Math 221. This sequence does not enforce its prerequisite of second semester calculus, so to start with Math 221 you should not need to take the Math 122L Proficiency Exam.

If you have had a college course in multivariable calculus and would like to be considered for the possibility of starting in a course above multivariable calculus, you should discuss your case with the Supervisor of First-Year Instruction.

On the other hand, if you took the AB AP test and scored 3 or less, then you should enroll in Math 111L Laboratory Calculus I--assuming your SAT score is at least 710 (680 if taken before Mar. 2016) and your ACT score is at least 30. If your SAT score is much less than 710 (680 if taken before Mar. 2016) or your ACT score is much less than 30, and if your AB AP score is less than 5, then you should enroll in Math 105L Laboratory Calculus and Functions I. Note that completing Math 122L Introductory Calculus II with Applications or a higher level course does NOT entitle you to credit for the "skipped" course(s). But you should be aware that if you do not have AP credit for Math 21 Introductory Calculus I (earned through AP credit), the safer academic route would be for you to enroll in Math 111L (or Math 105L if your SAT score is less than 710 (680 if taken before Mar. 2016) or your ACT score is less than 30).

There is another issue here. If you choose a major that requires Math 111L (and any other "skipped" course), then you will need to ask the Director of Undergraduate Studies in your major department to waive their requirement for the "skipped" course(s). Some departments will do this, as long as you complete the next higher math course with a C or better. Engineering students should also be aware that, in addition to needing permission to skip a required course, the total number of math courses that they are required to take will not be reduced; that is, eventually a higher level math course must be taken to replace the "missing" course(s). Furthermore, if you skip to a higher level and then make less than a C, then the Engineering School will require you to start your math over with the lowest "skipped" course.

###### May I forego my AP credit and enroll in the course for which I could have received AP credit?

Yes. For example, if you have a 5 on the AB AP test or a 4 on the BC AP test, you may choose to forego your AP credit and enroll in Math 111L Laboratory Calculus I. If you have a 5 on the BC AP test, you can forego your AP credit for Math 22 Introductory Calculus II and enroll in Math 122L Introductory Calculus II with Applications.

Your AP scores may indicate that you are sufficiently prepared to move on to the next level, and going backwards might not be worth it. On the other hand, if you are not confident in your knowledge of the material in such a course and feel it will be important to your successful completion of future courses to solidify that knowledge and hone those skills, then you are allowed to do so.

On the other hand, if you are considering taking such a course for which you already have credit "for the easy A", note that this is almost certainly not a good idea. The overwhelming majority of students in Math 111L and Math 122L have already had a full year of calculus in high school, have strong SAT scores, and many of them have waived AP credits to take the course again for the serious purpose of honing their skills further, as per the discussion above. The level of performance and competition in these courses is very high. So, while you might get an "A" (and you might not), it is unlikely that it will be "easy".

###### My AP score has not been reported to Duke, yet I made a score sufficient to earn credit and place in a higher level course. May I go ahead and enroll in the advanced course?

If you are hoping to enroll in Math 122L, then yes. But you should make sure that the score will eventually be reported to the Registrar. It would also be helpful to send an email message to the Supervisor of First-year Instruction and provide him with the information on your AP score and your placement intentions.

If you are hoping to enroll in Math 202 or Math 212, note that the system requires credit for second semester calculus to be on your Duke record, so your AP score must be officially reported, and processed by the Registrar's Office, before you will be able to enroll.

###### Does Duke administer any kind of calculus placement test whereby I can "challenge" a course for credit?

No, that is contrary to Duke's policy on course credits.

###### I did not get a 5 on the BC test, but I would like to go ahead and take Math 212 Multivariable Calculus anyway. May I get permission to do so, or may I take a placement test for Math 212?

Math 212 and Math 202 require credit for second semester calculus on your Duke record. A score of 4 or lower on the BC AP exam results in credit only for Math 21, and does not result in credit for Math 22 that would satisfy this prerequisite.

If you feel you have a much stronger background in second semester calculus than is reflected in your AP score and would like to be considered for eligibility to enroll in Math 202 or Math 212, you might consider taking the Math 122L Proficiency Exam; students who do well on this exam will be granted permission to enroll in multivariable calculus, at the discretion of the Supervisor of First-Year Instruction. This test is administered each semester shortly before the first day of classes. If you would like to take this exam, please submit the Math 122L Proficiency Exam Registration Form.

You should be aware of several issues:

- Completing Math 212 Multivariable Calculus will NOT entitle you to official credit for Math 122L Introductory Calculus II with Applications.
- If your major requires Math 122L, then you'll have to get a waiver for that requirement from the Director of Undergraduate Studies in your major department. Most Directors will grant that waiver if you make a C or better in Math 212 Multivariable Calculus (but that is up to your major department--not the Math Department); however,
*if you do not do well in Math 212*, then you should expect to have to go back and take Math 122L Introductory Calculus II with Applications (or perhaps Math 112L Laboratory Calculus II in the spring). - If you are an engineering student, then you should discuss with your academic dean before you attempt to skip Math 122L. Be aware as well that skipping Math 122L will not reduce the total number of math courses which you must take. Thus, if you "skip" Math 122L and then complete Math 212 Multivariable Calculus successfully, then you won't have to take Math 122L Introductory Calculus II with Applications but you will have to take some other (higher level) math course approved by your dean.