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

What is the goal of the exam? 

We want everyone to find the right “first class” at Yale, and our calculus placement exam is intended to identify the best starting point for you. This choice may be clear for some students - for example, those who did well in AP Calculus AB in high school often continue with Math 115, and students who mastered the topics and skills in AP Calculus BC often enroll in Math 120. For others, seeing similar topics again at the college level can be useful - and many students are coming from a different curriculum where the course sequence is not as clear. To be safe, we ask all students to take the calculus placement exam before enrolling in a 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 the placement exam contact listed on our first year resources site

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 question is answered or an existing 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 taking the exam should be directed to the placement exam contact listed on our first year resources site.  
  • If you have questions about results of the test, please attend our placement advising session in August. 
  • 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, or if results of the test are not loading in the “placement calculator” tab), switching a browser might help. 

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

Write to the placement exam contact listed on our first year resources site

Is the exam timed? 

No. The site does have a timer running, but you can take as much time as you need to complete the test, provided you submit it before the final deadline.

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

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 most questions have been 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 have found a mistake, please e-mail the placement exam contact listed on our first year resources site. . (Please note that they will not be able to give you any feedback about your answer before you submit the test, but they can check the question and tell you whether 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? 

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. 

If you have questions about your placement and missed the August advising session, please contact the course director of the class you were placed into. The course directors are listed on our first year student resources 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. 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? 

This is not permitted. It is technically possible, because 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.

Can I enter preference selection for more than one math course in the same semester? 

This is technically possible, but not allowed. If you enter preference selection for more than one math course in the same semester, we will not be able to give you any section assignments. 

Our calculus courses are typically very full, and we are not able to hold spots for one student in two or more courses. It is essential that you complete the placement exam (and seek assistance with your placement, if needed) before preference selection opens, so that you can sign up for the course that is best for you. 

There is one exception to this rule: Math 115 and 116 are at the same level, and while we encourage you to make your choice in advance, you may enter preference selection for both courses if you wish. 

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.  In particular, e-mailing the instructors will not increase your chances of getting into a section. 

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. We recommend switching as soon as possible, as it becomes more difficult to join a new course later on. No changes are permitted after Midterm.  

  • Math 256 to Math 255
  • Math 226 to Math 225 or 222
  • Math 225 to Math 222
  • Math 121 to Math 115
  • Math 120 to Math 115 
  • Math 116 to Math 112
  • Math 115 to Math 112 
  • Math 112 to Math 110 

The following changes are not permitted: 

  • Math 118 is outside of the regular sequence and no switches in or out of it 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 in 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 messages 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 teaching 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) it is unlikely that you will get in. Usually no more than five invitations are sent from those sections, to replace students who left, and the waitlist can easily be 100 students or more.  
  • 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 attend). 
  • 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 

Is there a math course that fulfills the QR requirement even if I haven’t taken any calculus? 

We offer several options - you can find a list and descriptions on our first year student resources site.

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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 other calculus or 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?  

Please see the corresponding question in our Math major and advanced course FAQ. 

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. 

I have other questions, where can I got to get them answered? 

We have several events to assist you: 

  • 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 calculus placement advising session in August. If the session has already run, you can contact one of the calculus directors. They are listed our the first year resources site
  • For information about individual calculus courses, we encourage you to attend the course town hall. These typically run in August. 
  • For questions about the mathematics major, and courses numbered above 200, the best place is the Academic Fair, which is scheduled by the university (usually in August).  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. 

A lot of questions are also answered on the math department website. You can use the menu on the left side of this page to access our first year student resources site, our math major and advanced courses FAQ, and other pages that may be useful.