MAT 151 Precalculus

Undergraduate course, Mathematics Department, Utica College, 2020

Welcome to the home page of Dr. Xiao Xiao’s Precalculus 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. Note that due to the COVID-19 pandemic, this course will be entirely online for the Fall 2020 semester.

Important Dates

  • Add/Drop deadline: 8/28/20
  • Withdraw deadline: 11/2/20
  • Thanksgiving break: 11/26/20 - 11/27/20
  • SOOT: 11/27/20 - 12/4/20
  • There will be no fall break.
  • Final exam: Dec. 7 - Dec. 11

Instructor Information

  • Instructor: Prof. Xiao Xiao
  • Email:
  • Office: White Hall 255
  • Virtual Student Support Hours: book your appointment below.


  • Week 15 (Nov. 30 - Dec. 5):
    • Dec 3:
      • Quiz available on Dec. 4 (due Saturday noon Dec. 5)
      • Please complete the student survey at
      • If you would like to sign up for more presentations, please do so asap.
    • Dec. 1
      • Last WebAssign homework
  • Week 14 (Nov. 23 - Nov. 29):
    • Nov. 24
      • WebAssign homework.
      • Quiz avaiable on Nov. 27 (due Saturday noon Nov. 28)
      • Have a peaceful thanksgiving break.
  • Week 13 (Nov. 16 - Nov. 22):
    • Nov. 19
      • Quiz available on Nov. 20 (due Saturday noon Nov. 21)
      • If you would like present Task 8.7 or Task 8.9, please let me know.
    • Nov. 17
      • New WebAssign homework.
  • Week 12 (Nov. 9 - Nov. 15):
    • Nov. 12
      • Quiz available on Nov. 13 (due Saturday noon Nov. 14)
      • Complete the trig function table before Tuesday’s class.
    • Nov. 10
      • Complete Task 7.20 (the unit circle). Bring that to Thursday’s class.
      • New WebAssign homework.
  • Week 11 (Nov. 2 - Nov. 8):
    • Nov. 5
      • Quiz available on Nov. 6 (due Saturday noon Nov. 7)
      • Let me know if you would like to present Task 7.11 or 7.13.
    • Nov. 3
      • New WebAssign homework.
      • Let me know if you would like to present Task 7.5 or 7.7.
  • Week 10 (Oct. 26 - Nov. 1):
    • Oct. 29
      • Quiz available on Oct. 30 (due Saturday noon Oct. 31)
      • Let me know if you would like to present Task 7.2 or 7.3.
    • Oct. 27
      • New WebAssign homework.
      • Let me know if you would like to present Task 6.11.
      • Complete group survey Section Z1, Section Z2 by Friday night.
  • Week 9 (Oct. 19 - Oct. 25):
    • Oct. 22
      • Quiz available on Oct. 23 (due Saturday noon Oct. 24).
      • Let me know if you would like to present Task 6.10.
    • Oct. 20
      • New WebAssign homework.
      • Complete Task 6.5 and let me know if you want to present.
  • Week 8 (Oct. 12 - Oct. 18):

    • Oct. 15
      • Quiz availabe on Oct. 16 (due Saturday noon Oct. 17).
      • Complete Task 6.4 (your group assignment, eithe role of a or role of b). Let me know if you would like to present.
    • Oct. 13
      • WebAssign homework (due Saturday Oct. 17)
  • Week 7 (Oct. 5 - Oct. 11):

    • Oct. 10
      • Complete Task 5.10 and 5.11. Let me know if you want to present.
      • Quiz available on Oct. 10, due Oct. 11
    • Oct. 6
      • WebAssign homework (due Saturday Oct. 10 noon)
      • Make appointment with me to go over your goal records.
  • Week 6 (Sep. 28 - Oct. 4):
    • Oct. 1
      • Check on Engage for Quiz on Friday noon. Quiz due Saturday noon (Oct. 3)
      • Complete Task 5.7.
    • Sep. 29
      • WebAssign homework (due Saturday Oct. 3 noon)
      • Please remember to update your Zoom app.
  • Week 5 (Sep. 21 - Sep. 27):
    • Sep. 24
      • Check on Engage for Quiz on Friday noon. Quiz due Saturday noon (Sep. 26)
      • Complete Task 4.9 for more practice on expoential functions.
      • WebAssign homework due this Saturday.
    • Sep. 22
      • WebAssign homework (due Saturday Sep. 26 noon)
      • Complete Task 4.8.
  • Week 4 (Sep. 14 - Sep. 20):
    • Sep. 17
      • Check on Engage for Quiz on Friday noon. Quiz due Saturday noon (Sep. 19)
      • Complete group survey Section Z1, Section Z2 by Friday Sep. 18 night.
    • Sep. 15
      • WebAssign homework (due Saturday Sep. 19 noon)
      • Complete Task 3.9 and let me know if you would like present.
      • Complete group survey Section Z1, Section Z2 by Friday Sep. 18 night.
  • Week 3 (Sep. 7 - Sep. 13):
    • Sep. 10
      • Check on Engage for Quiz on Friday noon. Quiz due Saturday noon (Sep. 12).
      • Complete Task 3.6 and let me know if you would like to present.
      • Check your Zoom app and update it if needed.
    • Sep. 8
      • WebAssign homework (due Saturday Sep. 12 noon)
      • Complete Task 3.6 as much as possible. Please let me know if you would like to present any part of this problem.
  • Week 2 (Aug. 31 - Sep. 6):
    • Sep. 3
      • Complete the rest of Task 3.2 (Parts 3-5).
      • Weekly Quiz will be available in Engage Friday noon and is due Saturday noon.
    • Sep. 1
      • Complete Task 2.4 and please let me know if you want to present.
      • WebAssign Homework, due Saturday noon, Sep. 5. There are questions in this homework assignment that you will only be able to do after Thursday’s class.
      • Keep contributing to the norms. Especially the Zoom and discussion forum norm. Link to Section Z1 and link to Section Z2.
      • Go to Course Materials, go to Chapter 3: Quadratic Functions and their modeling, try to work on Task 3.1. We will start Thursday’s class on this problem.
  • Week 1 (Aug. 24 - Aug. 30):
    • Aug. 27
      • Complete Task 2.1 and let me know if you want to present by Friday evening.
      • WebAssign Homework, due Saturday noon, Aug. 29 (extended to Saturday noon Sep. 5)
      • Keep contributing to the norms. Link to Section Z1 and link to Section Z2.
      • Go to Course Materials, go to Chapter 2: Linear Functions and Their Modeling, try to solve Task 2.4. Feel free to ask question about it in the discussion forum in Engage.
    • Aug. 25
      • Sign up at WebAssign. The class code is: utica 9441 0560
      • Print a copy of the goal sheet. You will need that to record your learning process.
      • Sign up at Miro if you have not done so. Once you signed up, I will put you in the correct class and you will be able to finish the introduction.
      • All classroom recordings will be put in Engage so only you (and no one else) have the access to the recording. Please check in Engage.
      • Keep contributing to the norms. Link to Section Z1 and link to Section Z2.
      • Go to Course Materials, go to Chapter 2: Linear Functions and Their Modeling, try to solve Task 2.1. Feel free to ask question about it in the discussion forum in Engage.

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 151 Precalculus
  • Course credit hours: 3 credit
  • Course Prerequisite: MAT 124, or satisfactory performance in the math placement test administered by the math department, or permission of instructor.
  • Class time and location: TR 10:00 am - 11:15 am (Section A) 11:30 am - 12:45 pm (Section B) online. See above for connection information.
  • Textbook: Please see the course material link above.
  • Online homework system: We will use the WebAssign online homework system designed for Ron Larson’s Precalculus textbook. You do not need to purchase the hard copy of Ron Larson’s Precalculus 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 9781337879613. You can also purchase the access directly from the publisher at Note that it is very unlikely that any used Precalculus textbook will come with the WebAssign access.The class key you need to self-enroll in WebAssign is “utica 9441 0560”. 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 use Desmos on a computer or on a tablet. You can download Desmos at Apple or Android.
  • Course description: Precalculus covers elementary functions and their graphs including linear functions, quadratic functions, exponential functions, rational functions and trigonometric functions.
  • 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 use a pedagocial practice called 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.

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.

Intellectual Property

  • My lectures and course materials, including powerpoint presentations, tests, outlines, and similar materials, are protected by U.S. copyright law and by Utica College policy. I am the exclusive owner of the copyright in those materials I create. You may take notes and make copies of course materials for your own use. You may also share those materials with another student who is registered and enrolled in this course.
  • You may not reproduce, distribute or display (post/upload) lecture notes or recordings or course materials in any other way — whether or not a fee is charged — without my express written consent. You also may not allow others to do so. If you do so, you may be subject to student conduct proceedings under the Utica College Student Code of Conduct
  • Similarly, you own the copyright in your original work. If I am interested in posting your solution on the course web site, I will ask for your written permission.

Course Learning Goals

  1. I can model a situation with appropriate linear functions and interpret the solution.
  2. I can determine the vertex and the equation of a quadratic function given its graph or a table of values.
  3. I can model a situation with appropriate quadratic functions and interpret the solution including interpreting the vertex in context.
  4. I can model a situation with appropriate functions of exponential type and interpret the solution.
  5. I can solve an equation that has expoential or logarithmic functions.
  6. I can use the definitions and properties of exponential and logarithmic functions to rewrite or simplify algebraic expressions.
  7. I can determine the domain and range of function given as an equation or a graph.
  8. I can determine a composition of functions given in any form (graph, table, equation).
  9. I can determine the inverse of a function given in any form (graph, table, equation).
  10. I can compute the average rate of change of a given function on a given interval.
  11. I can indicate the vertical and the horizontal asymptotes of a given rational function.
  12. I can solve inequalities and interpret the solution in context.
  13. I can identify the intervals on which a given function is increasing or decreasing in context.
  14. I can determine an appropriate function class (linear, quadratic, exponential, trigonometric) to model a particular situation.
  15. I can determine and describe a transformation (translations, compressions, stretches, reflections) of a function given in forms of graphs or equations.
  16. I can determine the equation of a circle in context and find the length of an arc of a circle or the area of a sector of a circle.
  17. I can determine an angle or its trigonometric values given other trigonometric values and the quadrant.
  18. I can determine the equation of a trigonometric function given its graph.
  19. I can simplify functions using triangles that involve trigonometric and anti-trigonometric functions.
  20. I can prove trigonometric identities.

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


Homework assignments come in two formats.

  • The first kind is online homework assignment at WebAssign (Please purchase the access as soon as you can). There will be one WebAssign homework each week and they are due Saturday at noon. To earn credit, you must earn more than 90% on each WebAssign assignment. If you have made mistakes and would like more attempts, you can request extra attempts in WebAssign. Each WebAssign assignment is worth 1 point.
  • The second kind is completing tasks in the course materials assigned every week. You will be working on these assignments during the class time and discuss them with your peers. These assignments will not be collected and you will be responsible to complete them on time and ask for help if you get stuck.


  • You will spend most of the time in class solving tasks in the course materials in groups of three or four. Each group can choose their own presenter when asked. 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.
  • All presentations will be done in the virtualy format. The prensenter will record a video explaining solution of desigated tasks with the following requirements:
    • Detail work can be clearly read by the audience
    • Explantions should be clear for every single step, no matter how small the step is
    • The presenter should include a brief introduction in the beginning of the presentation to talk about the general strategy
    • In general, the presentation/recording should be less than 10 minutes. Please re-record if more than 10 minutes. If you must use more than 10 minutes because the solution is very long, contact the instructor.
  • You will earn credit for a presentation if you are able to correctly explain your solution. It is not enough to have a correct answer.
  • 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.
  • Confusions and mistakes are very common when learning new mathematics and they should be handled positively to stimulate your thinking. The audience should feel free to ask questions in the discussion forum 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 every week except for the first week. Each quiz will be posted online every Friday at noon and due Saturday at noon. There will be 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 on Thursday evenings. 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. Your final letter grade will be determined in two steps. For Step 1, you will be assigned a base letter grade based on the following criteria.

Letter GradeCriteria
Aat least 19 goals, and at least 12 homework points
Bat least 16 goals, and at least 11 homework points
Cat least 13 goals, and at least 10 homework points
Dat least 10 goals, and at least 8 homework points
Fless than 10 goals, or less than 8 homework points

For Step 2, your final letter grade will be determined based on your base letter grade from Step 1 and possible adjustment based on your presentation grade.

Final Letter GradePresentation
+more than 3
No change2-3

For example, if you score 16 goals, 12 homework points, and 4 presentations. Use the first table to determine that you letter grade is B. Then because presentation grade is 4, your final letter grade is B+.

Tentative Schedule

Chapter 2Week 1
Chapter 3Week 2-3
Chapter 4Week 4-5
Chapter 5Week 6-7
Chapter 6Week 8-9
Chapter 7Week 10-11
Chapter 8Week 12-14

Tutoring Services

There are two kinds of (free) tutoring services offered by the college.

  • The first kind is to make an appointment at the learning commons for a virtual one-on-one tutoring service.
  • The second kind is Smarthinking, which is a 24/7 online tutoring service.

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

The stuff just below is the University approved language, and is a bit… ``legalese’’. The point is, if you need accommodations to succeed in this course, talk to me and we can make sure you get what you need. And the social environment of this course is important to me, too. Let’s work together to make a welcoming and affirming space for everyone.

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.