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

If you have a question that is not answered here, e-mail Miki.


Information about the exam.

Taking the exam

 Exam results, changing placement 

Pre-registration / waitlist / switching sections / switching courses

Other questions about introductory classes 

Information about the exam. 

Where can I find information about the test? 

The following site has up to date information about the test: .

How do I access the placement exam? 

When the test opens, a self-enroll link will be posted on the placement exam information site

Which classes require the placement exam? 

  • If you have not taken a calculus class (Math 110/111, 112, 115, 116, 120) 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 doing the placement exam. 
  • If you have passed Math 111 or 112 at Yale, you can take Math 115 or 116 without doing the placement exam. 
  • If you have passed Math 115 or 116 at Yale, you can take Math 120 without doing the placement exam. 
  • The placement exam is not required to take any Math class other than those listed above. 

Is the placement exam required for Math 110? 


Is the placement exam required for Math 118? 

No. It is recommended to take the test anyway, partly to assess your current knowledge, partly in case you later decide to take one of the other calculus courses instead. 

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. 

Is the placement exam required for Math 222, 225, or 230? 

No. The test does not even go that high: it only tests topics through Math 115, and the highest placement it is capable of returning is Math 120. It may be a good idea to take it anyway, partly to see if you do get the highest possible placement, partly in case you later decide to enroll in Math 120 after all. 

Is the placement exam required for ENAS 151? 

No. It may be useful to take the test: if you are ready for ENAS 151, the placement should say Math 120. 

Please note that switching between ENAS 151 and a calculus course in the math department is not permitted past shopping period (see the section on changing courses 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 do not end up taking a calculus class during the year, and want to take one the following year or later, you will have to retake the exam. 

Taking the exam 

What is on the exam? 

  • The first two questions are about AP exam scores. Note that AP exams are not necessary for placement, and they alone are not sufficient either. 
  • 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? 

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

Write to Brett Smith ( and Miki Havlickova ( 

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 (usually around the middle of August). 

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 Brett Smith ( and Miki Havlickova ( (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. 

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 (see for information about the session).  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 pre-registration deadline, so you will have time to enter section lottery afterwards. 

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 were placed into, or the class you would like to join.  The course directors are listed on the placement exam information site

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. 

Pre-registration / waitlist / switching sections during shopping period 

Which Math courses require pre-registration? 

Math 110, 111, 112, 115, 120. 

What is the deadline for pre-registering? 

The deadline is common to most pre-registration courses at Yale. Typically, in the Fall it is 5pm on Monday before classes start, and in the Spring it is 5pm on Wednesday or Thursday of the week before classes start. For current dates, please see the placement exam information site . 

Can I pre-register for a course even if I do not have the placement for it? 

The pre-registration website will not stop you from pre-registering without placement, but your section assignment will not be honored if you do not have placement in the course. Please see the FAQ in the “placement exam results” section for what to do if you would like to change your placement. 

Where do I find results of section lottery? 

The result will be displayed on the pre-registration site, after the lottery runs. Please note that due to the way calculus classes are structured, there is no way to “push” the assignments to OCS. It is your responsibility to look back on the lottery site for you assigned section, add the correct section to your schedule, and remove any section(s) that you may have put in there before that. 

I missed pre-registration, what can I do? 

All math courses requiring pre-registration have a waitlist, and there is a link to it on the main course site on Canvas. (if you cannot find the link e-mail an instructor of the course and they will share the link with you). Entering the waitlist is the only way to get a spot in a section past pre-registration. 

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 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 will be permitted after Midterm): 

  • Math 230/231 to Math 120 (If you have taken multivariable calculus, you can also change to Math 222. Please note that if you do this and have not taken Math 120 at Yale, you will not have credit for multivariable calculus, and should consult with the DUS of your intended major first.) 
  • 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 flexibility as to which one they can attend. 

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 equal 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 very difficult for instructors to answer individual messages from all the 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. The course directors are very skilled teachers, but so are many other instructors, and your chances of doing well in the course do not depend on getting one particular teacher. You may well find that another instructor’s style suits you better, and so 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 every section 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, or stop by the section and see if there is room. If there is not, we ask that you give seating priority to students who are registered for the section. 

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 even before classes start, and more invitations after the first class takes place (depending on how many of the assigned students attended). 
  • Instructors of all sections continue to monitor their roster and send out invitations throughout shopping period. 
  • Every student on the waitlist should receive either an invitation or a message with an update within one week of the first day of classes. 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. You can find more information about it on the placement exam information site.   If the session has already run, you can contact one of the calculus directors (if you are not sure who they are, ask any calculus instructor and they will tell you). 
  • For questions about the mathematics major, and courses numbered 222 or above, the best place is the Academic Fair, which typically takes place at the end of 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, 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 120 and Math 250? 

120 is “multivariable calculus” and 250 is “vector calculus”. What is the difference? 120 focuses on situations where “multi” really means 2 or 3 – that means it leans heavily on geometric intuition, and is strongly grounded in geometric applications in engineering and the sciences. Math 250 generalizes this to the setting of n dimensions, or variables, where n can be 3, 10, or 450,000. In order to do this, linear algebra must be brought in as a tool to manage the computations and to clarify what is conceptually going on – that’s why 222 or 225 is a prerequisite to 250. The theorems of Green, Gauss and Stokes, the beautiful integral equalities that are the capstone of 120, are generalized in 250 to a single master theorem (still called Stokes’ theorem) which applies in any dimension. Don’t think that 450,000 dimensions means the subject is not practical: any large system, such as the economy or the weather, can easily involve that many variables. Note that Math 250 requires both Math 120 and Math 222/225.

What is the difference between Math 222 and Math 225? 

Both courses cover linear algebra, but 222 focuses more on computational techniques and applications, while 225 emphasizes mathematical proofs and a more conceptual approach. Math 225 is recommended for students who wish to take further proof-based mathematics courses. 

What is the difference between Math 230 and Math 250? 

230-231 is a two term course with an integrated treatment of linear algebra and vector calculus. This is a demanding but rewarding course for students with a very strong interest and background. 250 is the third semester of the sequence 120-225-250 (or 120-222-250), and covers just the vector calculus. 

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, these are the two most common options: 

1. If you are interested in taking proof-based math courses, you may consider taking Math 230+231, as an alternative to calculus and linear algebra. Most students benefit from taking this sequence, even if they have already seen multivariable calculus

2. You can enroll directly in a higher level course, such as linear algebra (Math 222 or 225). 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). 

Can I take linear algebra before finishing the calculus sequence? 

We recommend completing Math 120 before enrolling in linear algebra. However, Math 222 may be taken after 115, and Math 225 requires Math 120 only concurrently, so it is possible.