MAT 201 Calculus 1

Undergraduate course, Mathematics Department, Utica College, 2020

Welcome to the home page of Dr. Xiao Xiao’s Calculus 1 course at Utica College. You can find all the information and documents for this course on this page. Please check this page frequently for announcements and assignments.

Important Dates

  • Add/Drop deadline: 1/24/20
  • Spring break: 3/16/20 - 3/20/20
  • Withdraw deadline: 3/30/20
  • SOOT: 4/27/20 - 5/4/20
  • Final exam: Will be posted at noon 5/7/20, due noon 5/8/20

Homework Assignments

  • 4/30/20
    • Finish your last Perusall Assignment and WebAssign homework.
    • Board work
    • Video
  • 4/28/20
    • WebAssign homework.
    • New Perusall Assignment.
    • Complete Activities 3.4.2, 3.4.3 and 3.4.5.
    • Board work
    • Video did record correctly. Sorry!
  • 4/23/20
    • WebAssign homework.
    • Complete Activity 3.3.3.
    • Board work (Note: Please see the last page of the board work for an arithmetic error/correction)
    • Video
  • 4/21/20
    • WebAssign homework.
    • New Perusall Assignment.
    • Complete Activity 3.1.3 and let me know if you want to present.
    • Board work
    • Video
  • 4/16/20
    • WebAssign homework.
    • Complete Activity 3.1.2 and let me know if you want to present.
    • Board work
    • Video
  • 4/14/20
    • WebAssign homework.
    • Complete Activity 3.1.1 and let me know if you want to present.
    • There is a new reading assignment in Perusall.
    • Board work
    • Video
  • 4/9/20
  • 4/7/20
    • WebAssign homework.
    • Complete Activity 3.5.2. Please volunteer as a team as this activity is quite long for one individual to present.
    • New Perusall assignment.
    • Board work
    • Video
  • 4/2/20
  • 3/31/20
    • WebAssign homework.
    • New Perusall Assignment.
    • Complete Activity 2.6.4 and let me know if you want to present.
    • There will be no derivative proficency test for this semester. This has been approved by the math department.
    • Board work
    • Video
  • 3/26/20
    • WebAssign homework.
    • Quiz 9 is due noon (EDT) Friday, Mar 27. Please submit your solution in one PDF file to me via email.
    • New Perusall Assignment.
    • Complete Activity 2.6.2 and Activity 2.6.4 (b) and (e). Send me your work if you want to present.
    • Board work
    • Video1 Video2
  • 3/24/20
    • WebAssign homework.
    • Complete Activity 2.5.2 and 2.5.3. Re-Connect with your teammates if you can between classes to work on these problems. Send me email if you need help/hints for these problems. Send me an email with your work if you would like to present on Thursday.
    • Perusall reading assignment for the chain rule unit.
    • Board work. Please view the file, do not edit the file.
    • Video.
  • 3/12/20
    • WebAssign homework.
    • New Perusall Assignment.
    • Attend tech training session. If you cannot make it and don’t feel comfortable about zoom, contact me.
    • We won’t be presenting the rest of the rest of Activity 2.4.4 on 3/24/20. We will start unit 2.5 immediately.
  • 3/10/20
    • WebAssign homework.
    • There is a new reading assignment in Perusall.
    • Complete Task 2.3.4 Part (d) and (e).
    • Complete your assignment of finding the derivatives of various trig functions.
  • 3/5/20
    • WebAssign homework.
    • There is a new reading assignment in Perusall.
    • Complete Activity 2.3.2. Read the quotient rule and try to do Activity 2.3.3.
    • Stop by my office before Spring break. Bring your goal sheet so we can cross check the records.
    • Starting Quiz 8, no forms of calculators (including but not limited, four function calculators, TI-XX, Desmos) will not be allowed during the quiz and the exam.
  • 3/3/20
    • WebAssign homework.
    • Complete Activity 2.2.4.
    • There is a new reading assignment in Perusall.
  • 2/27/20
    • WebAssign homework.
    • Complete Activity 2.1.3. Each group will have a presenter to be ready for Tuesday.
    • There is a new reading assignment in Perusall.
    • Do Questions 1 to 9 at the end of section [Section 2.1]{} for practice.
  • 2/25/20
    • WebAssign homework.
    • Complete Activity 1.8.3. Let me know if you want to present.
    • Do Questions 1 to 4 at the end of section [Section 1.8]{}.
  • 2/20/20
    • WebAssign homework.
    • Complete Activity 1.8.1 if you have not done so.
    • We will switch seats on Tuesday 2/25/20. Fill out [this]{} survey by Saturday 2/22/20 if there is anything you would like me to know.
  • 2/18/20
    • WebAssign homework.
    • There is a new reading assignment in Perusall.
    • Complete Activity 1.7.2. Let me know if you want to present.
    • Questions 1 to 4 at the end of [Section 1.7]{} are good practices.
  • 2/13/20
    • WebAssign homework.
    • There is a new reading assignment in Perusall.
    • Questions 1,2,4,5 at the end of [Section 1.6]{} are good practices.
  • 2/11/20
    • WebAssign homework.
    • Complete Preview Activity 1.6.1. Finish sketching the graphs!
    • Documentary movie about Maryam Mirzakhni, Wednesday, Feb. 12, 12:30pm at Hubbard Hall 205.
  • 2/6/20
    • WebAssign homework.
    • There is a new reading assignment in Perusall.
    • Complete your assignment for Activity 1.4.3. Make sure you look at the other ones once you complete your priority.
    • Questions 1 to 5 at the end of [Section 1.4]{} are good practices.
  • 2/4/20
    • WebAssign homework.
    • Complete your assignment for Activity 1.4.2. Work with your teammates if you can. At the beginning of Thursday’s class, each group should have one representative to put up your work on the board. If you would like to have more practices of sketching derivative graph, go to [Sketch]{}. You can check the accuracy after you complete sketching. You can click reset the graph to do a new one.
    • There is a new reading assignment in Perusall.
  • 1/30/20
    • WebAssign homework.
    • Complete Activity 1.3.3 and let me know if you would like to present.
    • If you want more practices for finding derivatives, Questions 1 to 5 at the end of [Section 1.3]{} are helpful.
  • 1/28/20
    • WebAssign homework.
    • Complete Activity 1.2.3. Hint: The process is very similar to Activity 1.1.4. Make sure you use limit notation when appropriate.
    • There is a new reading assignment in Perusall.
    • If you want more practices for finding limits, Questions 1 to 4 at the end of [Section 1.2]{} are helpful.
  • 1/23/20
    • WebAssign homework. This homework is very short. It will get longer next week.
    • There is a new Perusall reading assignment. Make sure you read Section 1.2 The Notation of Limits, from the beginning to Example 1.2.3. You are strongly encouraged to work on Preview Activity 1.2.1 and discuss that in Perusall before coming to class on Tuesday.
    • Please complete Activity 1.1.4. Let me know if you want to present that on Tuesday.
    • Go to Section 1.1, complete Exercises 1 and 2 in 1.1.4 Exercises Section.
  • 1/21/20
    • Please print the goal sheet if you have not already done so.
    • Check Perusall for reading assignments. You are strongly encouraged to start working on Activities 1.1.2, 1.1.3 and 1.1.4 to get prepared for Thursday. You can discuss how to solve them in Perusall.
    • There are no WebAssign homework for today.
    • Go to Section 1.1, scroll all the way down, complete Exercises 3 and 4 in 1.1.4 Exercises Section. Note that you can check your answers by clicking “Check Answers”. Do not click solutions unless you absolutely need help on the problem. If you need some hint(s) on how to solve these problems, feel free to send me emails.

Quiz Goals

  • Quiz 1: 1
  • Quiz 2: 1, 2, 3, 4
  • Quiz 3: 2, 3, 4, 5
  • Quiz 4: 2, 3, 5, 6
  • Quiz 5: 2, 5, 6, 7, 8, 9, 10
  • Quiz 6: 6, 7, 8, 9, 10, 11, 12
  • Quiz 7: 4, 10, 11, 12, 13, 14, 16
  • Quiz 8: 7, 11, 12, 13, 14, 16, 18, 19
  • Quiz 9: 8, 11, 12, 14, 16, 18, 19, 20
  • Quiz 10: 1, 2, 15, 17, 18, 19, 20, 21
  • Quiz 11: 15, 17, 21, 22
  • Quiz 12: 12, 21, 22, 25
  • Quiz 13: 22, 23, 24, 25
  • Quiz 14: 23, 24, 25, 26

Instructor Information

  • Instructor: Dr. Xiao Xiao
  • Email:
  • Office: White Hall 255
  • Office hour: TR 1:00 p.m. - 2:30 p.m. or by appointment.

An Important Course Policy

I pride myself on having a good environment for working and learning. It is very important to me that we all treat each other with care and respect, in equal measure. I know that I ask students to take risks in class almost every day, and this can be challenging for many. I ask that you help me keep our classroom a supportive place for each of the people in it. Each of us deserves the space to bring our full, authentic selves to class and be comfortable.

General Course Information and Policies

  • Course name: MAT 201 Calculus 1
  • Course credit hours: 3 credit
  • Course Prerequisite: MAT 151, or satisfactory performance in the math placement test administered by the math department, or permission of instructor.
  • Class time and location: TR 11:30 a.m. - 12:45 p.m. at Hubbard Hall 210.
  • Textbook: Please see the course material link above.
  • Online homework system: We will use the WebAssign online homework system designed for Ron Larson’s Calculus textbook. You do not need to purchase the hard copy of Ron Larson’s Calculus textbook. If you want to have that textbook as a reference, you will have the access to an electronic version of it after you have purchase the WebAssign access. The ISBN for the WebAssign standalone access card is 9781337631853. You can also purchase the access directly from the publisher at Note that it is very unlikely that any used Calculus textbook will come with the WebAssign access. The class key you need to self-enroll in WebAssign is “utica 3873 1993”. Please use your Utica College official name and email address to register at WebAssign. Do not use nickname or your private email address. If you have not purchased the access card or have purchased it but have not received it, please still go ahead and register as soon as possible as the WebAssign website will have a grace period and you can start to work on homework problems immediately.
  • Calculator: We will be using a free graphing calculator app called Desmos. You can use Desmos directly by going to their website at You are strongly encouraged to bring a laptop or a tablet (with a minimum 7” screen) to class in order to use Desmos effectively. You can download Desmos at Apple or Android
  • Course description: We will discuss the concepts of limits and derivatives, how to compute them, and how to apply them to solve real world problems.
  • Class organization: This course will likely be different from any other math course you have taken before. As an instructor, I will not be lecturing most of the time although I love lecturing very much. Scientific research shows that most people do not learn mathematics by listening, instead, they learn by doing it! I am sure you have said to yourself before “It looked so easy when the professor was doing it, but now I am confused when I have to do it by myself.” Why? Because the knowledge belongs to your professor and does not belong to you. You do not learn the knowledge simply by hearing it once or twice from somebody else. In order for you to have a more thorough understanding of the knowledge, we will incorporate ideas from an educational philosophy called the Moore method (after R. L. Moore). More precisely, we will use inquiry-based learning. Most of the time during the class, students will be working in groups and presenting solutions that they have produced by themselves and not by other people or textbooks.
  • Attendance is mandatory. Attending class meetings will have a direct impact on your learning as well as your grade. If you miss class for any reason, you are responsible for getting the information from a classmate, and checking the course web page for any handouts and assignments. You will not be able to make up the quiz for the day if you were not in class unless you have met the makeup policy below.
  • Makeup policy: You can only make up a quiz or an exam if all three conditions are met:
    • You have a legitimate reason (as determined by me) with documented proof. Visit of emergency rooms due to urgent health conditions is an example of legitimate reason. Attending non-academic events, such as someone’s wedding is an example of non-legitimate reason.
    • You have informed me well in advanced.
    • You can only make up the quiz or the exam after the scheduled date.
  • Course learning objectives: Upon successful completion of this course, students will be able to:
    • formulate and solve mathematical problems using the differential calculus of Newton and Leibniz.
    • understand necessary differential calculus content for license for teachers in the State of New York.
    • communicate mathematics orally and in written form.

Your Role and My Role

  • Professor Xiao’s role: I want you to succeed and I am here to help you succeed, but I cannot succeed for you! I have designed the structure of the course to help you learn. The class format will challenge you but it will be exhilarating and even fun at times. I will do what I think is the best to help you understand the material in the course. I hold office hours to provide you the opportunity to get additional help, and I check and respond to email frequently.
  • Student’s Role:
    • You are responsible for making sense of the concepts and processes in this course. Success in mathematics is less about “ability” and more about willingness to think and to work hard to make sense of things.
    • Attend every class meeting, participate, present whenever you can and work on the assignments outside of class.
    • Please respect the ideas and opinions of others.
    • If you are having trouble, please come to office hours or make an appointment to visit me.
    • Cell phones should be off or set to vibrate. Do not place a call or send a text during class, and do not answer a phone call without first leaving the room.

Course Learning Goals

  • 1: Be able to calculate average rates of change algebraically.
  • 2: Be able to compute instantaneous rate of change by using average rates of change.
  • 3: Be able to evaluate limits of basic functions algebraically.
  • 4: Be able to evaluate limits of basic functions geometrically.
  • 5: Be able to use the limit definition to find derivatives.
  • 6: Be able to use first derivative to describe the monotonicity of a function.
  • 7: Be able to use second derivative to describe concavity of a function.
  • 8: Be able to determine whether a function has a limit at a point.
  • 9: Be able to determine whether a function is continuous at a point.
  • 10: Be able to determine whether a function is differentiable at a point.
  • 11: Be able to find the algebraic equation of tangent lines to a differentiable function.
  • 12: Be able to use the tangent line of a function to approximate function values.
  • 13: Be able to compute derivatives of polynomials.
  • 14: Be able to compute derivatives of exponential functions.
  • 15: Be able to compute derivatives of logarithmic functions.
  • 16: Be able to compute derivatives of trigonometric functions.
  • 17: Be able to compute derivatives of anti-trigonometric functions.
  • 18: Be able to compute derivatives using product rule.
  • 19: Be able to compute derivatives using quotient rule.
  • 20: Be able to compute derivatives using the chain rule.
  • 21: Be able to find derivatives of inverse functions.
  • 22: Be able to find derivatives using implicit differentiation.
  • 23: Be able to use derivatives to find local extreme values.
  • 24: Be able to use derivatives to find global extreme values.
  • 25: Be able to solve related rates problem.
  • 26: Be able to solve optimization problem.

You are strongly encouraged to download and print a copy of the learning goals to record your grade.


  • Homework assignment may come in two formats. Most frequently, you will get a online homework assignment at WebAssign (Please purchase the access as soon as you can). But you may also be asked to complete problems from the course notes distributed in class. Please check this page for homework assignment daily. WebAssign assignment are always due on the day of the next class unless explicitly said otherwise. The hand written assignment are due after the class. Each homework assignment is worth 1 point. To earn credit for a homework, you must earn more than 90% on WebAssign homework.

  • Another type of homework assignment is reading assignment. For a reading assignment, you will log in to Perusall and complete the assignment. For the first time user, please sign up using your legal name and Utica College email. Then go to the “Enter an Access Code” on the top right and enter XIAO-RUB4W. Each reading assignment is due at 11:00 p.m. of the day before the next class meeting. You need to make annotations on the course notes to show your understanding of the materials. Your annotations can be questions, comments or responses to other people’s questions. Perusall will analyze your annotations and determine the level of your understanding. For example, if you just post “I don’t understand this sentence”, that is basically no credit. If you post “I don’t understand the concept A because concept B says C”, that is some partial credit. If you respond to the previous comment as “I think concept A says D because concept B also says D in this manner”, then you will be getting significant credit. If you want to know more about the rubrics, you can check out this file. Note that if your comments are clustered, you will not get full credit. If your comments are past deadline, you also will not get credit. Each reading assignment is graded in 0-3 scale.


  • You will spend most of the time in class solving problems in groups of three or four and present their solutions.
  • Each group can choose their own presenter. If there are more than one group member that wants to present, the one with fewest goals achieved at that time has the first dibs. The instructor reserves the right to choose any member from a group that he deemed necessary.
  • You will earn credit for a presentation if you are able to correctly explain your solution in front of the class. It is not enough to have a correct answer.
  • Fellow students and the instructor are allowed to ask questions at any point and it is the responsibility of the presenter to answer those questions to the best of his or her ability. The group members of the presenter may also help answering the questions.
  • In order to make presentations go smoothly, presenters need to write out the solution in detail and go over the major ideas and transitions, so that he or she can make the solution clear to others.
  • The purpose of presentations is not to prove to me that the presenter or their group has done the problem. It is to make the ideas of the solution clear to the other students.
  • Since the presentation is directed at the students, the presenter should frequently make eye contact with the students in order to address questions when they arise and also be able to see how well the other students are following the presentation.
  • Confusions and mistakes are very common when learning new mathematics and they should be handled positively to stimulate your thinking. Feel free to ask questions at any time but please respect the ideas and opinions of others. For example, instead of using the phrase “You should change XYZ.”, start your sentence like “Do we want to change … ?”
  • Though the atmosphere in this class should be informal and friendly, what we do in the class is serious business. In particular, the presentations made by students are to be taken very seriously since they spearhead the work of the class.

Quizzes and Examinations

There will be a quiz on each Thursday and one cumulative final exam.


In this class, we will use a system known as standards-based grading. You will have multiple opportunities to demonstrate that you have met a goal. A goal is met if a student has successfully demonstrated it twice in either (a) quizzes, or (b) on one quiz and one other (final exam or a presentation). There is no partial credit. Once you have score a goal from a quiz or a presentation, you should put a note in one of the boxes before the relevant goal on this print out. You should use clear labeling to indicate when you score that goal, for example, Q2 stands for Quiz 2, or 3/2(P) stands for presentation on March 2. If you are unsuccessful on a quiz problem, prepare yourself to do better on the next quiz. Feel free to stop by my office and ask for practice problems. Quizzes are scheduled on Fridays. The goals that will be tested on a quiz will be posted at this page at least 24 hours ahead of time. Presenting problems and participating discussion in class, doing homework and exercises are all ways to help you prepare for the next quiz. All of goals appear on multiple quizzes so you have multiple chance to demonstrate that you have met the goals.

Letter GradeGoalsHomework PointsPresentationsPerusall Grade
Aat least 24at least 24at least 6at least 2.6
A-at least 22at least 22at least 5at least 2.4
B+at least 21at least 21at least 5at least 2.2
Bat least 20at least 20at least 4at least 2.0
B-at least 18at least 18at least 4at least 1.8
C+at least 16at least 16at least 3at least 1.6
Cat least 15at least 15at least 3at least 1.4
C-at least 13at least 13at least 2at least 1.2
D+at least 11at least 11at least 2at least 1.0
Dat least 10at least 10at least 1at least 0.5
Fless than 10less than 10less than 1less than 0.3

A new grading guideline for Perusall Grade. Your final letter grade will be determined by two steps:

  • Determine your letter grade based on the numbers goals, homework points and presentations number. Note that one must satisfy all three columns.
  • Determine your final letter grade according to the following rule based on your Perusall Grade.
Final Letter GradePerusall Grade
Up 1/3at least 2.70
No change1.70 - 2.69
Down 1/30.70 - 1.69
Down 2/30.69 or lower

For example, if you score 19 goals, 23 homework points, 5 presentations, and 1.6 Perusall scores. Use the first table to determine that you letter grade is B-. Then because Perusall grade is 1.6, your final letter grade is down by 1/3 so final letter grade will be C+.

Tentative Schedule

Chapter 1Week 01-05
Chapter 2Week 06-10
Chapter 3Week 11-14

Academic Integrity

I have zero tolerance on dishonesty. Any forms of dishonesty such as copying homework or cheating on quizzes and examinations, will result in zero credit for that particular assignment, and will be reported to the Academic Standards Committee. The highest penalty a student can receive is “F for cheating” for the course. There might be additional sanctions by the Academic Standards Committee such as dismissal from the college. See Utica College official page for Academic Honesty for more details.

Special Accommodation

Any student who has need of special accommodations in this class due to a documented disability should speak with me as soon as possible, preferably within the first two weeks of class. You should also contact Judy Borner, Director of Learning Services in the Academic Support Services Center (315-792-3032 or ) in order to determine eligibility for services and to receive an accommodation letter. We will work with you to help you in your efforts to master the course content in an effective and appropriate way. See Utica College official page for Office of Learning Services.


It is the students’ responsibility to keep informed of all announcements, syllabus adjustments, or policy changes during the semester via this web page or via school emails. The author of this syllabus reserves the right to change it with notice at any time during the semester.