Calculus and placement exam FAQ

Questions about courses other than calculus, and information for math majors, can be found in our math major and advanced courses FAQ


Information about the exam.

Taking the exam

 Exam results, changing placement 

Preference selection / waitlist / switching sections / switching courses

Other questions about introductory classes 

Information about the exam. 

What is the placement exam? 

The mathematics placement exam has been designed for students who wish to take a calculus course at Yale: one of Math 110, 112, 115, 116, 120, and 121. The test takes into accounts AP exam scores, and asks multiple choice questions from pre-calculus, differential calculus, and integral calculus, in order to determine the best possible placement for the student. The test is required of every student before their first Yale calculus course. 

Which classes require the placement exam? 

  • If you have not taken a calculus class (Math 110/111, 112, 115, 116, 120, 121) at Yale and plan to take one of these, you must take the placement exam. 
  • If you have passed Math 110 at Yale, you can take Math 111 without the placement exam. 
  • If you have passed Math 111 or 112 at Yale, you can take Math 115 or 116 without the placement exam. 
  • If you have passed Math 115 or 116 at Yale, you can take Math 120 without the placement exam.

Which classes do NOT require the placement exam? 

The placement exam is not required to take any Math class other than Math 110, 112, 115, 116, 120, 121.

In particular, it is NOT required for Math 106, 107, 108, 118, or for any course above level 200.  It is also not required for any course outside of the math depatment (in particular, you do not need the exam to enroll in ENAS 151). 

What about Math 118? 

Math 118 is a combination of linear algebra and multivariable calculus, designed for social science majors, particularly economics. Knowledge of integral calculus is recommended, but not required: it can be taken after Math 111 or 112 or Calculus AB. 

Please note that Math 118 is a terminal course, there is no convenient way to continue from it into further calculus / linear algebra classes. If you are considering the possibility of taking further math courses, we strongly encourage you to stay with the regular calculus sequence, followed by linear algebra. 

What about ENAS 151? 

The placement exam is not required for ENAS 151, particularly if you are still deciding between ENAS 151 and Math 120. 

Please note that switching between ENAS 151 and a calculus course in the math department is not permitted by the Registrar past shopping period (see the section on changing courses below for more information). 

Do I have to take the exam even if I have taken the AP Calculus exam AB or BC? 

Yes. The placement exam will ask about your AP scores – they are taken into account, but not sufficient for placement. 

How long do placement results remain valid? 

The results expire every year in August. If you take the exam during the summer of (say) 2021, you can use the result for Fall 2021, Spring 2022, Summer 2022, as well as during April pre-registration for Fall 2022. If you do not take any calculus course during that time, and wish to enroll after that, you would need to take the new placement exam. 

Taking the exam 

How do I access the placement exam? 

Starting in July 2021: Incoming first-year students will automatically be enrolled on a Canvas site called “Math placement exam [current year]”, where the test lives. Continuing students need to request access by e-mailing .

Spring 2021, continuing students: with upcoming pre-registration in May 2021, if you need to take the test, you need to self-enroll on the site, using the following link: . Once you are on the site, e-mail to have a session of the exam opened for you. The deadline for completing the test will be May 31. 

What are the exam rules? 

The purpose of the exam is to help you determine which calculus course at Yale is the most suited to your current mathematical background. You are not in competition with anyone, and do not need to be worried about scoring as high as possible. To ensure that the placement is accurate, it important that you follow these rules: 

  • Do not use notes, books, calculators, internet resources, or any other aid. 
  • Answer each question as best you can, but do not guess.
  • If you do not know how to solve a problem, select the answer I don’t know how to do this problem. This is a perfectly valid answer!

What is on the exam? 

  • The first two questions are about AP exam scores. Note that AP exams are not necessary for placement, but they are taken into account if you have them. 
  • The next 10 questions are pre-calculus. 
  • The next 5 questions are differential calculus. 
  • The next 5 questions are integral calculus. 

If you have not taken one or more of the courses that are being tested, you can simply click “I do not know how to answer the question” for problems in that category. 

How often should I save my answers? 

You do not need to save the quiz, it is saved automatically. You can leave the test any time and finish it later. If you close the page, it will give a warning about possibility of losing progress. You can disregard the warning, the test is saved every time a new answer is submitted or an answer changed. To be extra safe, you can check on the bottom of the page the last time your progress was saved, or you can look in the upper right hand corner where checkmarks are displayed next to question numbers that have been already saved. 

Whom do I contact with questions about the exam? 

  • Questions about the mechanics of taking the exam should be directed to 
  • All other questions about the exam should be directed to both Brett Smith ( and Miki Havlickova ( 
  • Extra note: Canvas sometimes gives issues to certain browsers. If the test does not seem to be working right (for example, if you cannot see equations or graphs that the questions refer to), switching a browser might help. 

I accidentally submitted the exam before I solved all the questions, what can I do? 

Write to both and .

Is the exam timed? 

No. The site does have a timer running, but it does not matter at all how long it takes you to complete the test, provided you submit it before the deadline.

What should I do if I need special accommodations on the test? 

Please note that the test is not timed, so there is nothing you need to do for extra time accommodations: you can take as much time as you need, within a window of several weeks. If you need other accommodations, please refer to the following information from Student Accessibility Services:

Students with documented disabilities may request accommodations for placement testing through the Student Accessibility Services office. Please contact them through the online registration form to submit your request at least one week before they plan to begin the placement test. 
Please note that these requests for accommodations apply to the placement testing period alone. To register for ongoing accessibility arrangements, students should submit a request and meet with SAS before the start of the semester.
More information for first-years seeking accommodations is available on the Student Accessibility Services website.

I think I found an error on the test, what should I do? 

We would first encourage you to take a close look at the question again. While errors are possible, the test has been checked by many people and taken by thousands of students in the past few years. It is not likely that there is an error at this point. It is possible, of course, and if you believe that you found a mistake, please e-mail both and (Please note that we will not be able to give you any feedback about your answer before you submit the test, but we can check the question and tell you whether we agree that there is an error or not.) 

Exam results, changing placement 

Where can I find the placement exam results? 

Immediately after submitting the test, you can click on the “Placement calculator” tab on the left, and your course placement will be displayed. 

If the page is not loading, we recommend switching browsers. (Some browsers have a difficult time with the placement calculator tab.)  If it is still not displaying, please e-mail for assistance. 

I have questions about my placement / I think I was placed too high / too low, what can I do? (during the summer, before Fall term starts) 

If you have any questions your placement, we encourage you to attend our placement advising session in August.  Advisers at the session can answers your questions and/or tell you more about our calculus classes.  In particular, if you both feel that another placement is more suitable, they can override your existing placement.  The advising session takes place before preference selection deadline, so you will have time to enter section lottery afterwards. 

Please note that in order to discuss your placement with an adviser, you must first complete the placement exam - without the test, and adviser cannot issue placement for you. 

I have questions about my placement / I think I was placed too high / too low, what can I do? (after Fall term starts, or in the Spring) 

Please contact one of the calculus instructors to discuss your placement.  The best choice is the course director of the class you would like to join. If you are not sure which class that might be, feel free to write to any one of them.  The course directors are listed on [updated link for Summer 2021 will be provided here]. 

Is it possible to get a second try with the placement test?

It is not possible to take the exam twice in the same academic year. If you would like to consider having your placement changed, please see the above questions about speaking with an adviser. 

Preference selection / waitlist / switching sections during shopping period 

Which Math courses require preference selection? 

Math 110, 111, 112, 115, 116, 120. 

Can I enter preference selection for a course if I do not have placement for it? 

Preference selection does not know about placements, and any Yale student can enter it - but your section assignment will not be honored if you do not have placement in the course. Please be sure to take the placement exam, and see the “placement exam results” section for what to do if you would like to change your placement. 

Where do I find results of preference selection? 

The result will be displayed on the preference selection site after the lottery runs. 

I missed preference selection, what can I do? 

All math courses requiring preference selection have a waitlist, and there is a link to it on the main course site on Canvas. You can reach the main course site through the syllabus link on Yale Course Search. If you cannot find the link, e-mail an instructor of the course and they will assist you.

Entering the waitlist is the only way to get a spot in a section after preference selection has finished.   

How can I switch sections within the same course during shopping period? 

If you wish to switch sections, you can enter the online waitlist – a link to the waitlist is posted on the main course site on Canvas. 

How can I switch into a different calculus course during shopping period? 

First, you will need to discuss your placement with new course director. If they agree that the new course is more suitable, they can override your existing placement. 

After that, you will need to find a section of the new course, by entering the online waitlist, linked from the main course site on canvas. If you have some flexibility as to which section you can attend, it is likely that a spot can be found for you. 

Are changes of course permitted after shopping period ends? How does it work? 

If you feel that a lower level course would be more suitable, these are the steps you will need to take: 

  1. Check whether the switch you are considering is permitted (see below for the list of allowed changes).
  2. Discuss the situation with your current instructor to see if they agree that it is a good idea. 
  3. Meet with the course director / instructor of the new course, get their permission to join, find out how the transition will work (how your grade will be calculated, any work you will have to make up etc.), and get assistance finding a section of the course. 
  4. Meet with your College Dean to discuss the situation. 
  5. Provided everyone agrees, you will need to submit a form to your Dean, dropping the old course and adding the new one (it requires signatures of both former and new instructor).  

The following changes are permitted before Midterm (no changes are permitted after Midterm): 

  • Math 226 to Math 225 or 222
  • Math 225 to Math 222
  • Math 120 to Math 115 
  • Math 115 to Math 112 
  • Math 112 to Math 110 

The following changes are not permitted: 

  • Math 116 and 118 are outside of the regular sequence and no switches in or out of these classes are permitted past shopping period. 
  • Math 111 (Spring) is the second-half of a year-long sequence, and no switches into or out of it are possible. 
  • ENAS 151 is not considered a part of the calculus sequence by the Registrar; no changes are permitted between ENAS 151 and any math course past shopping period. 

I am on the waitlist, is there anything I can do to increase my chances of getting in? 

To increase your chances of getting into the course, we encourage you to list as many sections as you can when you are entering the waitlist. We are usually able to find a section for every student who has some flexibilityin their schedule. 

Will e-mailing the instructor increase my chances of getting into a particular section? 

No. One of the reasons for the online waitlist is to give the same chances to every student; no one can jump to the front of the list by sending a message to the instructor. 

Another reason for the online waitlist is that we have sections with long waitlist (easily over 100 entries), and it is difficult for instructors to answer individual messages from so many students. 

I only wish to take a section with instructor [name]. What should I do? 

If you did not get your desired section in the lottery, you can enter the waitlist. Please note that some sections are very much oversubscribed (with waitlists over 100 entries long), and chances of getting in after the lottery runs are very small. 

We very much encourage you to try other sections - we have many skilled teachers whose style might suit you, as might a smaller section. 

I am on the waitlist, can I attend the waitlisted section in the meantime? 

As a rule, the answer is “no”, because we have sections with more than 100 entries on the waitlist, and it is not possible for every student on the waitlist to attend the (already full) section. This typically includes sections taught by the course director. 

For sections that are less oversubscribed, it may be possible for you to attend while on the waitlist. You can e-mail the instructor and ask, thought please expect that some instructors may not be able to answer right away, if they are getting dozens or hundreds of messages (if you don’t hear back, then you should assume there is no room for students on the waitlist to attend). 

How long does it take to hear back about my waitlisted sections? 

That depends a lot on your entry, and how many options you gave. Generally speaking: 

  • If you only listed the most oversubscribed sections (eg. those taught by the course director, easily with over 100 students on the waitlist) it is unlikely that you will get in. Usually no more than five invitations are sent from those sections, to replace students who left. 
  • Sections with room usually send some invitations before classes start, and more invitations after the first class takes place (depending on how many of the assigned students attended). 
  • Every student on the waitlist should receive either an invitation or a message with an update by the middle of shopping period. If you do not hear by then, feel free to e-mail an instructor and inquire about your status. 

Other questions about introductory classes 

Where can I go to get my questions answered? 

  • A lot of questions are answered on the math department website, there is a section about all the introductory courses, about calculus and the placement exam, and an extensive FAQ (this part is about calculus and the placement exam, another part talks about the major, and other classes). 
  • If you have further questions about the calculus sequence or if you seek advice about your placement, the best place to ask them is the advising session. If the session has already run, you can contact one of the calculus directors. [Link to 2021 list of directors will be provided here in May.]
  • For questions about the mathematics major, and courses numbered above 200, the best place is the Academic Fair, which typically takes place during the summer.  If the Academic Fair has already run, you can get in touch with the instructor of the class you are interested in, or with the DUS. 

What is the difference between Math 115 and Math 116? 

Both courses cover integral calculus. Math 116 places emphasis on application to biology, and it is particularly suitable for biology and pre-medical students. Both can be used as pre-requisite for any course that requires Math 115. 

What is the difference between Math 118 and Math 120? 

Math 120 is a multivariable calculus course, covering differential and integral multivariable calculus, and integration theorems (Green, Gauss, and Stokes). 

Math 118 is a combination of linear algebra and differential multivariable calculus, designed for social science majors, particularly economics. In other words, it teaches a part of Math 120 and a part of Math 222, with focus on optimization. Math 118 can be taken directly after Math 112, though Math 115 is recommended as a pre-requisite (for more practice with calculus and math in general, as Math 118 is a relatively sophisticated course). 

Please note that Math 118 is a terminal course, there is no convenient way to continue from it into further calculus / linear algebra classes. If you are considering the possibility of taking further math courses, we strongly encourage you to stay with the regular calculus sequence, followed by linear algebra. 

What is the difference between Math 222, Math 225, and Math 226? 

All three courses cover linear algebra, but 222 focuses more on computational techniques and applications, while 225 and 226 emphasize mathematical proofs and a more conceptual approach. Math 225 (linear algebra) or 226 (intensive linear algebra) is recommended for students who wish to take further proof-based mathematics courses. Math majors are required to complete either Math 225 or Math 226. More information about these courses can be found in the math major FAQ.

I took multivariable calculus in high school, can I skip Math 120?  

Yale does not allow transfer credit for courses taken in high school, even if they were taken at a local college. If your course covered all of Math 120, then you may be able to enroll directly in courses above 200 level, such as linear algebra (Math 222 or 225 or 226). 

If your intended major requires Math 120, then you should speak with the major’s DUS ahead of time, to see if they would permit an alternative arrangement (for example, substituting a higher level course). Mathematics majors can fulfill their multivariable requirement by completing Math 302 instead of Math 120 at Yale. 

Can I take linear algebra before finishing the calculus sequence? 

We recommend completing Math 120 before enrolling in linear algebra. However, Math 222, 225 and 226 can be taken directly after integral calculus (such as AP Calculus BC, or Math 115). 

Math 225 or 226 is a part of the introductory sequence into the mathematics major. Prospective math majors, and students interested in abstract mathematics, may consider enrolling in Math 225 or 226 directly after Math 115.