Calculus and placement exam FAQ

We want calculus students to have a good experience with their first math 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.

Please note that the test is for calculus only - it does not give placement above Math 120. If you have already completed multivariable calculus, you can visit our first year student resources site to explore other options.

• 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.
• If you have already completed multivariable calculus, you can visit our first year student resources site to explore other options.

The placement exam is not required to take any Math class other than Math 110, 112, 115, 116, 120, 121, nor does it give placement outside of these classes. 

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). 

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. 

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 past shopping period (for more information, see the section below on changing courses). 

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

The results expire every year during the summer. If you take the exam during the summer of (say) 2022, you can use the result for Fall 2022, Spring 2023, Summer 2023, as well as during April registration for Fall 2023. 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. 

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 math.dus@yale.edu .

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!

• 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. 

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. 

• Questions about the mechanics of taking the exam should be directed to canvas@yale.edu . 
• All other questions about taking the exam should be directed to math.dus@yale.edu .
• 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. 

Write to math.dus@yale.edu .

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.

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.

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 math.dus@yale.edu . (Please note that we 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.) 

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 canvas@yale.edu for assistance. 

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 e-mail math.dus@yale.edu .

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. 

Math 110, 111, 112, 115, 116, 120. Note that we only use preference selection during August and December registration. During April registration, continuing students can simply register for any section they wish, provided they have placement in the course. 

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.

This is 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. 

The result will be displayed on the preference selection site within a few days after the lottery runs.

After preference selection runs, all calculus courses will have open registration - that is to say, you can register for any section that has spots in it (provided that you have placement in the course). If a section does not have a spot, you can enter the waitlist through YCS. Note that you can only register for one section at a time. If you are already registered for one, the system will not allow you to register for another until you give up your existing seat. 

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 just need to find a section of the new course that has spots in it, or use YCS to enter a waitlist for a section that you want. 

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
• 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 permitted until the end of the third week of classes: 

• Math 226 to Math 222
• Math 225 to Math 222

(The deadline is earlier because the courses are quite different, and after more than three weeks, it is too difficult to catch up in Math 222.) 

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. 

No. If there is room in the section, you can simply register for it. If there is not, you have to enter the YCS waitlist. The waitlist is automated, and the instructor has no control over it. 

This should be possible, as we keep waitlists relatively short. (Please note that attending does not guarantee that you will be able to register for the section. )

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

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. 

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. 

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.

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

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. 

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 write to math.dus@yale.edu .
• 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.