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.

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 11:00amm 5/9/20, due noon 5/10/20

Homework Assignments

  • 4/30/20
  • 4/28/20
    • WebAssign homework.
    • Complete Task 8.15, 8.17, 8.19-8.24. Let me know if you want to present.
    • Board work
    • Video
  • 4/23/20
    • WebAssign homework.
    • Complete Task 8.12 and let me know if you want to present.
    • Board work
    • Video
  • 4/21/20
    • WebAssign homework.
    • You do not have to any tasks in the course notes.
    • Please go to WebAssign, eBook, and read Section 4.7, focus on the first two units “Inverse Sine Function” and “Other Inverse Trigonometric Functions”.
    • Board work
    • Video
  • 4/16/20
    • WebAssign homework.
    • Complete Tasks 8.2, 8.3, 8.4 and 8.6. Please let me know if you want to present.
    • Board work
    • Video
  • 4/14/20
  • 4/9/20
    • WebAssign homework.
    • Finish Task 7.16 and Task 7.20. Let me know if you want to present.
    • Board work
    • Video
  • 4/7/20
    • WebAssign homework.
    • Finihs Task 7.11 and Task 7.13. Let me know if you want to present.
    • Print a copy of this unit circle. If you have softwares that you can use to annotate pdf files, you don’t have to print it. If you don’t have either of the above, please use a letter size blank paper to draw this. You can use a bowl to help you to get the circle right. Make sure you include all the other lines in the picture as well. This table will also be needed as well.
    • Board work
    • Video
  • 4/2/20
    • WebAssign homework.
    • Finish Task 7.5 and 7.7.
    • Quiz 10. Due Friday 4/3/20 at noon.
    • Board work
    • Video
  • 3/31/20
    • WebAssign homework.
    • Finish Task 7.2 and 7.3. Let me know if you want to present.
    • Board work
    • Video
  • 3/26/20
    • WebAssign homework.
    • Finish 6.11 and send me your work if you want to present.
    • Quiz 9 is due noon (EDT) Friday, Mar 27. Please submit your solution in one PDF file to me via email.
    • Board work.
    • Video.
  • 3/24/20
    • WebAssign homework.
    • Try to complete Task 6.10 and 6.11. 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.
    • Board work. Please view the file, do not edit the file.
    • Video.
  • 3/12/20
    • WebAssign homework.
    • Attend tech training session. If you cannot make it and don’t feel comfortable about zoom, contact me.
    • Finish Task 6.5. If you want to present during the next class, please let me know by 3/23/20 and email me a picture of your work.
  • 3/10/20
    • WebAssign homework.
    • Finish your assignment for Task 6.4.
  • 3/5/20
    • WebAssign homework.
    • Stop by my office before Spring break. Bring your goal sheet so we can cross check the records.
  • 3/3/20
    • WebAssign homework.
    • Complete Task 5.14 and 5.15.
  • 2/27/20
    • WebAssign homework.
    • Complete Task 5.10 using the three principles that we found in Task 5.9.
  • 2/25/20
    • WebAssign homework.
    • Complete Task 5.7 and 5.8. Let me know if you want to present.
  • 2/20/20
    • WebAssign homework.
    • Complete Task 5.5 and let me know if you want to present.
    • 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.
    • Complete Task 5.2 and 5.3. Let me know if you want to present.
  • 2/13/20
    • WebAssign homework.
    • Complete Task 4.9. Let me know if you want to present.
  • 2/11/20
    • WebAssign homework.
    • Complete Task 4.7. Let me know if you want to present.
    • Documentary movie about Maryam Mirzakhni, Wednesday, Feb. 12, 12:30pm at Hubbard Hall 205.
  • 2/6/20
    • WebAssign homework.
    • Complete Tasks 4.2 to 4.5. Focus on your group’s priority first.
  • 2/4/20
    • WebAssign homework.
    • Complete the rest of Task 3.9 and let me know if you want to present.
  • 1/30/20
    • WebAssign homework.
    • Complete the rest of Task 3.6 and let me know if you want to present.
  • 1/28/20
    • WebAssign homework.
    • Complete Part 1, 2 and 3 of Task 3.2. Let me know if you want to present.
  • 1/23/20
    • WebAssign homework.
    • Complete Task 2.4 before Tuesday’s class. Let me know if you would like to present.
  • 1/21/20
    • Print the goal sheet if you have not already done so.
    • Check WebAssign for homework assignment. This homework assignment reminds you the concept of a slope.
    • Please complete Task 2.1. Let me know by email if you would like to present any part of the question on Thursday.

Quiz Goals

  • Quiz 1: 3L, 13F.
  • Quiz 2: 1L, 2L, 5Q, 13F.
  • Quiz 3: 4Q, 5Q, 6Q, 14F, 18F, 20F, 21F.
  • Quiz 4: 3L, 4Q, 5Q, 6Q, 14F, 18F, 20F, 21F.
  • Quiz 5: 7E, 8E, 9E, 15F, 16F, 18F, 20F.
  • Quiz 6: 7E, 8E, 9E, 15F, 16F, 17F, 18F.
  • Quiz 7: 1L, 2L, 6Q, 9E, 10E, 11E, 14F, 17F.
  • Quiz 8: 1L, 10E, 12E, 15F, 17F, 20F, 23F.
  • Quiz 9: 14F, 16F, 1F, 18F, 19F, 20F, 21F, 22F, 23F.
  • Quiz 10: 1L, 3L, 10E, 11E, 12E, 17F, 19F, 20F, 21F, 22F, 23F, 26T.
  • Quiz 11: 12E, 15F, 18F, 23F, 24T, 25T, 26T, 27T.
  • Quiz 12: 4Q, 17T, 19T, 24T, 25T, 26T, 27T.
  • Quiz 13: 21F, 23F, 24T, 25T, 27T, 28T.
  • Quiz 14: 23T, 25T, 28T, 29T, 30T.

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 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 a.m. - 11:15 a.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 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 5703 3566”. 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: 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 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.

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

  • 1L Be able to solve a linear equation.
  • 2L Be able to determine the slope and the equation of a linear function given its graph or a table of values.
  • 3L Be able to model a situation with appropriate linear functions and interpret the solution.
  • 4Q Be able to solve a quadratic equation.
  • 5Q Be able to determine the vertex and the equation of a quadratic function given its graph or a table of values.
  • 6Q Be able to model a situation with appropriate quadratic functions and interpret the solution including interpreting the vertex in context.
  • 7E Be able to solve an equation that has an unknown exponent.
  • 8E Be able to determine the equation of a function of exponential type given its graph or a table of values.
  • 9E Be able to model a situation with appropriate functions of exponential type and interpret the solution.
  • 10E Be able to solve an equation that has logarithmic expressions.
  • 11E Be able to use the definitions and properties of exponential and logarithmic functions to rewrite or simplify algebraic expressions.
  • 12E Be able to use the definitions and properties of exponential and logarithmic functions to change their bases.
  • 13F Be able to determine inputs and outputs of a function from its graph and/or a table of values.
  • 14F Be able to determine the domain and range of function given as an equation or a graph.
  • 15F Be able to perform arithmetic (sum, difference, product, quotient) on functions given in any form (graph, table, equation).
  • 16F Be able to determine a composition of functions given in any form. (graph, table, equation).
  • 17F Be able to determine the inverse of a function given in any form (graph, table, equation).
  • 18F Be able to compute the average rate of change of a given function on a given interval.
  • 19F Be able to produce a graph of a given rational function and indicating the vertical and the horizontal asymptotes.
  • 20F Be able to solve inequalities and interpret the solution.
  • 21F Be able to identify the intervals on which a given function is increasing or decreasing.
  • 22F Be able to determine an appropriate function class (linear, quadratic, exponential, trigonometric) to model a particular situation.
  • 23F Be able to determine and describe a transformation (translations, compressions, stretches, reflections) of a function given in forms of graphs or equations.
  • 24T Be able to convert degrees and radians.
  • 25T Be able to determine the length of an arc of a circle or the area of a sector of a circle.
  • 26T Be able to use the distance formula or the equation of a circle in context.
  • 27T Be able to determine an angle or its trigonometric values given other trigonometric values and the quadrant.
  • 28T Be able to determine the equation of a trigonometric function given its graph.
  • 29T Be able to simplify functions using triangles that involve trigonometric and anti-trigonometric functions.
  • 30T Be able to prove trigonometric identities.

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.


  • 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. You are allowed to use Desmos (from computer or tablet, but not cellphone) during the quizzes and the 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. You will be assigned the highest of the grades below for which you meet all criteria listed.

Letter GradeGoalsHomework PointsPresentations
Aat least 28at least 24at least 6
A-at least 27at least 22at least 5
B+at least 25at least 21at least 5
Bat least 23at least 20at least 4
B-at least 22at least 18at least 4
C+at least 20at least 16at least 3
Cat least 18at least 15at least 3
C-at least 16at least 13at least 2
D+at least 13at least 11at least 2
Dat least 10at least 10at least 1
Fless than 10less than 10less than 1

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

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.