Calculus and placement exam FAQ

For information about introductory calculus and math major courses, and help navigating your first set of math courses at Yale, please visit the first year student resources site

Detailed information for continuing 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 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 should visit our first year student resources site to explore other options.

Which classes require the placement exam? 

Summary: Your first calculus course at Yale will require the placement exam (even if you plan to enroll at the lowest level). No other math class requires the test. In more detail: 

  • 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 or Math 121 without the placement exam.
  • If you have already completed multivariable calculus, you can visit our first year student resources site to explore other options.

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, 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). 

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

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. They are also not necessary for placement: anyone can be placed into any calculus course, with or without AP scores. 

How does another curriculum fit in, for example IB?  

Many Yale students have gone to schools that have a different curriculum from AP courses, so do not worry - you are not alone! The calculus placement procedure is the same, regardless of previous math courses taken; but it can be especially useful to speak with an adviser afterward. The IP curriculum, for example, covers some portion of two or three of our calculus courses (among other things), while leaving out other portions. This can lead to a choice, where the students could take a slighly higher calculus course (if they’re prepared to study a few of the missing topics on their own), or a slightly lower calculus course (where some topics will be a review for them, and some will be new), depending on their preference and the time they want to dedicate to the class. After you complete the placement exam, stop by one of our August advising sessions, and our advisers will be happy to assist you. (You can find the schedule in our guide to introductory math courses.) 

How long do placement results remain valid? 

We accept results of the exam for two years.  If you plan to enroll in calculus during your first two years at Yale (academic year or summer), you should take the exam during the summer before your first year, so you can have the results ready, and take advantage of our August advising sessions. If you do not end up taking calculus in the two years following, you will need to take a new placement test in order to enroll in calculus. 

Taking the exam

How do I access the placement exam? 

The exam is available through Canvas, on a site called “Math placement exam [current year]”. The link to Canvas is

Incoming first-year students will automatically be enrolled on the site at the end of June. Continuing students need to request access by e-mailing .

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! Indeed, many students will not have seen some portion of the topics covered on the exam, and we look forward to covering those with you in our calculus classes. 

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 .
  • 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. If the problem persists, please e-mail for assistance. 

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

Write to .

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. Note that if your exam has been started when the final deadline arrives, the test will get auto-submitted. That being so, you should only start the test if you plan to complete it within the current open window (otherwise your placement will be calculated and recorded based on an incomplete test). 

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 days or 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 . (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 there is an error or not.) 

Exam results, changing placement 

Where can I find the placement exam results? 

Within five minutes 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, and cc

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. Information about the sessions will be posted on our first-year student resources site by mid-July. 

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 .

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 add / drop period 

Which Math courses require preference selection? 

Math 110, 111, 112, 115, 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. 

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 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 within a few days after the lottery runs.

I missed preference selection / I need to switch sections before the end of add drop period, what can I do? 

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. 

How can I switch into a different calculus course during add/drop 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. The list of course directors can be found in the “contact information” section of the first-year student resources site .

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. 

Are changes of course permitted after add/drop 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 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. The list of course directors can be found on the first-year student resources site .
  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. 

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

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. 

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

This should be possible, as we keep waitlists relatively short. (Note that attending does not guarantee that you will be able to register for the section. )   Please do not attend a section for which you are not registered or on the waitlist. 

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 on the first-year student resources site . 

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. 

For more advice about how to choose between Math 120 and linear algebra, please see the first-year student resources site . 

I have other questions, where can I go 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 write to .
  • For information about individual calculus courses, we encourage you to look for course-specific information on the first-year student resources site. The videos will be posted at the beginning of 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.