Calculus 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 should visit our first year student resources site to explore other options.

The test is for students who wish to enroll in calculus, Math 110 through Math 120. If you wish to start with a math course level 200+, you do not need the placement exam. For more information about choosing your first math class, please see our Guide to introductory courses.

The results are valid for two years, and students may not take the exam again within this period. If you wish to discuss the possibility of changing your placement, please attend one of our placement advising sessions. 

More detailed information, and the advising session schedule, can be found on our First Year Student Resources. page. 

Please note that students who previously enrolled in a calculus course at Yale are ineligible to take the placement exam, whether they completed the course or not. If you are in this situation and wish to consider a change of placement, please consult the DUS Miki Havlickova at math.dus@yale.edu. 

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 1100/1110, 1120, 1150, 1160, 1200, 1210) at Yale and plan to take one of these, you must take the placement exam. 
• If you have passed Math 1100 at Yale, you can take Math 1110 without the placement exam. 
• If you have passed Math 1110 or 1120 at Yale, you can take Math 1150 or 1160 without the placement exam. 
• If you have passed Math 1150 or 1160 at Yale, you can take Math 1200 or Math 1210 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 1100, 1120, 1150, 1160, 1200, 1210, nor does it give placement outside of these classes. 

In particular, it is NOT required for Math 1060, 1070, 1080, 1180, or for any course above level 2000.  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 1510). 

Math 1180 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 1110 or 1120 or Calculus AB. It does not require the placement exam, though we recommend taking it, to make sure your placement is Math 1150 or higher. 

Please note that Math 1180 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 1510, but it may be useful to take it, particularly if you are still deciding between ENAS 1510 and Math 1200. 

Please note that switching between ENAS 1510 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. They are also not necessary for placement: anyone can be placed into any calculus course, with or without AP scores. 

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 slightly 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 event schedule in the menu above.) 

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. 

If you have taken the exam in the last two years, you will not need to take it again (and will not be able to do so). 

The exam is available through Canvas, on a site called “Math placement exam [year]” where “year” is the last summer (e.g. for 2025-26, the date would be 2025).

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 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! 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. 

• 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. If the problem persists, please e-mail canvas@yale.edu for assistance. 

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. 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). 

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.

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 we can check the question and tell you whether there is an error or not.) 

Within five minutes of submitting the exam, you can access your results on the Canvas platform by selecting on the “Placement calculator” tab. 

Technical note: Viewing the placement results requires third-party cookies to be enabled in your browser. If you get an error message, you may need to change your browser settings. For information about how to do so, please visit this guide.

Some browsers are also known to give issues with Canvas in general - if the results are not loading, please try a different browser.

If none of the above resolves the issue, e-mail canvas@yale.edu for support, and cc math.dus@yale.edu so we can assist you in the meantime. 

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 event schedule 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 math.dus@yale.edu .

No. If you would like to consider having your placement changed, please see the above questions about speaking with an adviser. 

Math 1100, 1110, 1120, 1150, 1200. 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, 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, you will not receive a section assignment in any of the courses. 

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 1150 and 1160 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. The list of course directors can be found on the contact information page from the menu above. 

After that, you just need to find a section of the new course that has spots in it.

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 can be considered after add / drop ends 
2. Discuss the situation with your current instructor to see if they agree that moving to a lower level course would be productive for your learning.  
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 contact information page from the menu above. 
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 written permission of both former and new instructor).  

​The following changes  can be considered prior to Midterm. We recommend switching as soon as possible, as it becomes more difficult to join a new course later on. No changes will be considered after Midterm.  No changes by two levels are possible (e.g. from Math 1200 to Math 1100, or 1150 to 1100). 

• Math 2560 to Math 2550
• Math 2260 to Math 2250
• Math 1210 to Math 1150
• Math 1200 to Math 1150 
• Math 1160 to Math 1120
• Math 1150 to Math 1120
• Math 1120 to Math 1100 

The following changes are not permitted: 

• Math 2220 is not a part of any level sequence and no changes in or out of it are permitted past add / drop. 
• Math 1180 is outside of the regular sequence and no switches in or out of it are permitted past add / drop.  
• Math 1110 (Spring) is the second-half of a year-long sequence, and no switches into or out of it are possible. 
• ENAS 1510 is not considered a part of the calculus sequence by the Registrar; no changes are permitted between ENAS 1510 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. Note that waitlist are only active during November, April, and August registration. During add / drop, the Registrar does not operate waitlists, and you can only get into a section if there is an open spot. 

If you have not seen multivariable calculus before and need it for your major (e.g. all the combined Math majors), or for other courses you plan to take (e.g. in Economics or Physics), then you should consider taking Math 1200 as soon as you can. 

For the pure math major, you have a choice to complete either Math 1200 or 3020. Most students either complete Math 1200 in their first year (before Math 2250 and 2550), or complete Math 2250 and 2550 first and then take 3020 in their second or third year. 

Yale does not allow transfer credit for courses taken during high school, even if they were taken at a local college. That does not mean you have to repeat material you already know, however. The details depend on why you need Math 1200: 

1. If you need it as a pre-requisite for another Yale course, it should not be an issue: instructors typically accept a high school course in place of Math 1200. If you’re not able to reach the instructor, contact their program’s DUS. 
    
2. If you need it for the pure math major: You can complete the multivariable requirement with Math 3020. This option is available to all students, whether or not they have already completed a course similar to Math 1200. 
    
3. If you need it for a combined math major:  You can send your transcript (unofficial is fine) to math.dus@yale.edu , and request permission to substitute Math 3020 for Math 1200 in requirements of the relevant major (Math + CPSC / Econ / Phil / Phys). Please be sure to specify which major you are interested in. 
   
   If you would like to consider other options for substitutions (i.e. another class in the same area, such as Math 2460 or an analysis course), you can request an evaluation of the course that you have completed. For this evaluation, we would need a copy of your transcript, syllabus for the course, detailed list of topics covered, and a copy of the final exam or a sample final exam. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu .  
    
4. If you need it for another major, please contact the major’s DUS to see what options there may be, as they are in charge of all requirements and exceptions for their major. 

No (but if you passed ENAS 1510 before deciding on the math major, you can complete the multivariable calculus requirement with Math 3020). 

Yale does not allow transfer credit for courses taken during high school, even if they were taken at a local college. Beyond that, the answer and its details depend on why you need linear algebra: 

1. If you need it as a pre-requisite for another Yale course, it should not be an issue: instructors typically accept a high school course, if it is equivalent to the pre-requisite. If you’re not able to reach the instructor, contact their program’s DUS. 
    
2. If you need it for Math + Phil or Math + Phys: These majors recommend taking Math 2250 or 2260, but do not require any linear algebra, so you will not need to get permission to substitute. 
    
3. If you need it for another major, please contact the major’s DUS to see what options there may be. 
    
4. If you need it for the Pure math, Math + Econ or Math + CPSC: These three majors require Math 2250 or 2260, so substitution can only be considered if your course was fully proof-based (e.g. you learned proof techniques such as induction, and most problems on homeworks and exams explicitly asked “prove [something]”). In all three majors, students who completed linear algebra in high school typically still enroll in Math 2250 or 2260. 
   
   If your course was proof-based you can request an evaluation of it. For this evaluation, you will need to reach out to math.dus@yale.edu during the summer before your first semester at Yale. We will need a copy of your transcript, syllabus for the course, detailed list of topics covered, a copy of one or two assignments, and a copy of the final exam or a sample final exam. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu .    
   
   If the course is reasonably equivalent to Math 2250, then you may be granted permission to substitute Math 3400. We will also help you find the best starting course (likely Math 255 or 256 – or higher, if you have taken real analysis as well). Please note that this permission has to be granted by the Math DUS - obtaining permission from the Math 255 instructor to enroll will not take care of requirements of the math major. 
   
   If you know proof-based linear algebra but have not taken officially taken a course in it, or if your course is not evaluated as equivalent to Math 225, you can try placing out of Math 225 by taking an exam during the summer before your first semester at Yale.  Details are listed in a question just below. 
   
    

First, please note that the test does not award course credit or fulfill any requirements at Yale. It can only grant permission to substitute a higher level course in the same area for Math 225, in requirements of the math and joint math majors. 

The test is available to incoming first-year students who learned the material of a fully proof-based linear algebra course (such as Math 225) prior to enrolling at Yale, but the course was not evaluated as equivalent to Math 225. (See above for how to have a course evaluated.)

The test is only open to students who have had some formal training in proofs and linear algebra, including regular feedback about their work from experienced mathematicians. 

If you wish to take the test, you must first e-mail us the materials from the course you completed, at math.dus@yale.edu. This needs to be done by August 15, during the summer before you first enroll at Yale. (The exam is not available to continuing students.) 

We will offer the test in person, at the end of August, just before classes start (usually that Monday or Tuesday). We will set the time according to everyone’s availability: you will hear from us after August 15 about scheduling, if your name is on our list. 

Students who pass will receive permission to substitute a higher level course in the same area for Math 225, in requirements of the math or combined math major (Math + CPSC, Econ, Phil, Phys)  

If you need linear algebra for another major, please check in with their DUS - our process only works for math majors, we have no say in requirements of other majors (though we would be happy to assist, if the DUS wishes). 

As a rule, the answer is “no”. Courses required for the major must be completed. In rare cases where an incoming student has learned in high school the material and skills taught in a particular required course, the DUS may grant an option to substitute a higher level course in the same area. Please be sure to discuss this with the DUS prior to your first semester at Yale. 

All three courses cover linear algebra. Math 2220 focuses more on computational techniques and applications, while 2250 and 2260 emphasize mathematical proofs and a more conceptual approach.

Math 2250 (linear algebra) or 2260 (intensive linear algebra) is recommended for students who wish to take further proof-based mathematics courses. Students majoring in mathematics, Math + CPSC or Math + Econ are required to complete either Math 2250 or Math 2260. 

 In more detail: For math majors, and students who wish or need to continue with proof-based math courses, the theory and proof writing skills learned in Math 2250 or 2260 provide essential preparation for further study. That is why the math major does not accept Math 2220. 

Outside of the major: generally speaking, proofs are useful in many fields. They help one to become a better problem solver, evaluate different approaches to a question, consider options along the way, keep track of important details, check solutions for correctness, and present them in a way that is accessible to others. These skills are very helpful, in math and outside of it. 

For that reason, many students find it beneficial to take Math 2250 or 2260, even if they do not continue with further math courses. If you try the course and enjoy it, the skills you learn will not be wasted. 

If you enjoy applications more, and want to get lots of practice solving concrete problems, rather then focus on theory, then Math 2220 is a better choice. It provides great preparation on the practical side of linear algebra, and it is preferred by the majority of students in engineering, social sciences, and many other fields. 

Moving from Math 2260 to Math 2250 is permitted until Midterm. Moving from Math 2260 or 2250 to Math 222 is permitted until the end of the third week of classes (this has an earlier deadline because the courses are quite different, and it is too difficult to catch up later on). You can read more about how moving works in our Calculus FAQ. 

You can find a list and descriptions on our introductory courses and sequences page from the above menu. It includes notes about the level 1000 seminars (such as Math 1030 and 1070), all the main calculus courses (Math 1100+1110, 1120, 1150, 1160, 1180, 1200, 1210), as well as our linear algebra and other level 2000 courses. 

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. The date will be posted on our event schedule page in the menu above. If the session has already run and no other is scheduled, please contact the course director of your intended course (or any course, if you aren’t sure). You can find the list on the “contact information” page in the menu above. 
• For questions about Math 2250 and 2260, you can attend our town hall in August, it will be posted on our event schedule page by mid-July. 
• For questions about the mathematics major, and courses numbered above 2000, 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, at math.dus@yale.edu . 

A lot of questions are also answered on the math department website. You can use the menu above to access our intro courses guide, math major FAQ, and other pages that may be useful.