Course Syllabus

Precalculus (Math 12) Fall 2021

Section 3314

Please click on each tab to read the entire syllabus.

I am here to help, and I look forward to hearing from you! Here are several ways you can contact me. Monday through Thursday I will get back to you within 24 hours (during regular hours), while Friday through Sunday it might take up to 48 hours.

  • The Canvas Inbox is the best way to contact me every day of the week. It is located on the global navigation grey bar on the left of the page.
  • Zoom Virtual Office is the best place to get help with math questions. This ARE NOT MANDATORY meetings. You could attend this meetings if you have questions or you need help or guidance. 
    • Mondays 5:00 - 6:30PM and
    • Thursdays 5:00 - 6:30PM 
  • Email me at iradu@collegeofthedesert.edu
  • Reply to an Announcement in Canvas
  • Post a question in our Cyber Café discussion board
  • Post a question in our "Q and A" discussion of the week

Instructor-to-Student Communication

I want to make sure you know that you're not alone in the course. I care about you, I care about the challenges you face, and I care about supporting your learning. You can expect that I will reach out to you a few times each week, via one or more of the following methods:

  • Announcements
  • Assignment Comments
  • Rubric Feedback
  • Canvas Inbox
  • Class FAQ
  • Take Notes 

 

Announcements

I will post important information at least twice a week. Please check announcements regularly, or set Canvas Notifications to email you when a new announcement is posted.

  • I will send an overview announcement for every module before the new week starts (Sunday evenings). These announcements will include heads up about assignments to help you plan your time. As needed, I will send announcements to give timely feedback, answer questions, and provide resources and updates. You will be able to reply to announcements to ask questions.
  • You can find a record of all announcements on the Announcement Index page. Click on Announcements in the course navigation menu bar to see them all. The current Announcements will be found at the top of the Home page.

 

Assignment Comments

  • You can add a comment to assignments. This is a great way to remind me of a previous conversation we had or add needed information about your submission.
  • You can also ask questions. When you're reviewing your work in Grades, you can click on an assignment, quiz, or discussion and add a quick question or comment right there.
  • If your question is timely, I will answer it Monday-Friday, except holidays, within 48 hours. Otherwise, I will reply when I grade your work.
  • NOTE: In addition to written comments, I might also annotate your work or leave a verbal comment. This feedback will help you revise and improve your work, so be sure you review all the feedback I offer for your work on the rubrics, in comments, with annotations, and with audio/video messages.

 

Rubric Feedback

  • Almost every assignment will have a feedback rubric with grading criteria. These rubrics explain how well you completed the assignment, discussion, and essay. You can depend on these rubrics to offer you helpful feedback.
  • In Grades, once you click on an assignment, you can then click on the “Show Rubric” to see the feedback on the rubric.
  • Read these rubrics carefully; my feedback will help in multiples ways:
    1. show your strengths
    2. direct you to where to review
    3. give advice on Mastery improvement for the next assignment
    4. direct you to how to revise and resubmit.

 

Messaging in Canvas Inbox

  • I will occasionally reach out via the Inbox to check in with you, and nudge you if you have missed an assignment.

 

Cyber Café Discussions

  • I have created a discussion board that will be open all semester. This discussion is a place for you to ask & answer questions about using technology and other general problems you have in class.
  • If you have a question about tech skills or assignments, check the Q&A first; the answer you’re looking for might be there already. If you found the answer helpful, you can "like" it to show other students that you found it helpful.
  • You can also informally chat with the whole class (50ish people) here as opposed to just your Group. Think of this as a place for those “before and after class” type of discussions.
  • I will only skim these discussions to make sure that there aren’t any questions I need to answer. Otherwise, feel free to chat with your classmates, but keep the Netiquette [See Netiquette syllabus section on Canvas for infographic rules in mind.

 

Module Q&A for Exercises

      • As mentioned earlier, our class Cyber Café (on Canvas) is a place for you to ask & answer questions about technology and other general problems. However there will be another Q and A space for exercises.
      • There is a Module  "Q and A" discussion type where you can ask and find answers for exercises done. This Module is organized on Chapters. 
      • You can ask questions and you can answer your classmate's questions. For your answer you can get some credit points (between 1 and 3) depending on how well done and helpful your answer is!!  This points will be added to "Group Work Projects" assignments. 

 

Take Notes

  • I have written for every section in the course a summarize Handout that you have to complete. Each Handout has contains the maid definitions and "How to Do" explanations from the textbook. It is also contains referrals to what examples you have to read from the textbook and what exercises you have to do. You will complete and submit this "Take Notes" Handouts using the online submission. I encourage you to treat the take notes like face-to-face lectures by taking notes, engaging with additional content, asking questions, and applying course skills to our essays.

 

Student-to-Student Interactions

Just like in a face-to-face class, you will have formal and informal opportunities to interact with your classmates. Online classes are not intended to be solitaire endeavors. Your classmates may not be in the next desk over, but they are striving to complete this online class just like you. And just like you, they are balancing work and family obligations. You can be a support network for each other. I encourage you to find classmates to be friends with. Just like with face-to-face classes, you are more likely to “come to class” if you are looking forward to chatting with your friends. *:)*

You will have multiple opportunities to communicate with each other. I encourage you to use these communication ways to connect with your classmates and build a community to help you succeed.

  • Small Group Discussions
  • Canvas Inbox. You can use Canvas Inbox to message your classmates. Instead of putting my name in the “To” line, you can search for your classmates’ names to message them.
  • Chat
  • Class Q&A

 

Course Details and Meeting Times

Note: Some students register for an online class thinking it will be easier than a traditional class.​ Unfortunately, this is not true. In​ fact, many students find that online classes are more difficult than traditional classes because there is no set time you must be in class so you have to be very​ self-disciplined to make sure that you get your work done every week. To be successful in this class you have to work at least 12 hours/week. This time will be used for reading the material, watching videos, making handout notes, completing the assignments.   

Course Title/section number:

Precalculus

Math 12/ Section number - 3314

Units:

5.0 units

Term

Fall 2021

Class Days/Times: asynchronous class. No meetings.  

08/30/2021 - 12/17/2021 

Class Location: online


Course Catalog Description:

This course is the second in a two semester sequence preparing students for Calculus. In this course, students will extend the concept of a function to polynomial, rational, exponential and logarithmic functions as well as studying analytic trigonometry. Topics include recognizing, graphing and solving equations and word problems involving polynomial, rational, exponential and logarithmic functions, trigonometric identities, inverse trigonometric functions, and solving trigonometric equations.

Course Pre-requisites, co-requisites or advisories:

  • MATH 005 

Course Objectives

Upon successful completion of the course, students should be able to demonstrate the following activities:

    1. a. Analyze functions and graphs that are described either parametrically, using polar coordinates, or using rectangular coordinates. Demonstrate an understanding of the relationship between different coordinate systems.
      b. Apply the properties of equality to solve equations in one variable involving polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric expressions which may involve parameters.
      c. Apply the properties of the real numbers to solve inequalities in one variable involving polynomial, rational, root, exponential and trigonometric, and absolute value expressions.
      d. Perform arithmetic with the complex numbers and use the complex numbers to completely solve a quadratic equation. Represent complex numbers in both rectangular and polar form and use DeMoivre's theorem to calculate powers and roots of complex numbers.
      e. Analyze polynomial functions in one variable using methods such as end behavior analysis, the factor theorem, the remainder theorem, the theorem on rational zeros, Descartes' rule of signs, the intermediate value theorem, division algorithms, conjugate zeros and the fundamental theorem of algebra.
      f. Analyze rational functions in one variable by analyzing the polynomials in the numerator and denominator and interpreting these to find domain, range, intercepts, and asymptotes and visualizing these through the construction of a graph.
      g. Analyze exponential and logarithmic functions by finding an exponential expression based on essential characteristics such as the growth factor and in terms of domain, concavity, intercepts, asymptotes, transformations, and by visualizing these in the construction of a graph for the function.
      h. Demonstrate an understanding of a rich variety of trigonometric identities including the Pythagorean identities, addition identities, the double angle identities, the half angle identities, sum to product and product to sum identities by proof and through the application of these identities to solve trigonometric equations and simplify trigonometric expressions.
      i. Analyze trigonometric and inverse trigonometric functions in terms of their domain, range, asymptotes, and periodicity, and how these relate to chords, secants and arcs on the unit circle. Demonstrate an understanding of these circular functions by constructing graphs and solving equations.
      j. Use Polya's problem solving strategies to solve problems, with an emphasis on the algebraic method with appropriate applications of polynomial, rational, root, exponential, logarithmic, trigonometric and inverse trigonometric expressions.
      k. Communicate mathematics effectively using proper terminology in both verbal and written expressions.
      l. Apply the properties of equality and the real numbers to solve systems of equations and inequalities. Represent a system of equations using matrix notation and demonstrate an understanding of the arithmetic of matrices.

Student Learning Outcomes

  1. Demonstrate improved mastery of fundamental skills and knowledge from arithmetic, algebra, and geometry introduced in prerequisite courses.

    3. Create, analyze, and interpret graphs of algebraic and trigonometric functions, especially in relation to their real-world analogs.
    4. Develop an appreciation for the use of deductive reasoning skills in mathematics, in the context of  algebra and trigonometry. 
  2. Demonstrate problem solving skills in application problems in the areas of algebra, geometry, and trigonometry, with an emphasis on the concept of function.

Course Content:

  1. POLYNOMIAL AND RATIONAL FUNCTIONS.

    Complex zeros and the Fundamental Theorem of Algebra. Rational functions. Modeling: Fitting polynomials to data.
    2. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
    Exponential functions. Exponential growth and decay. Logarithmic functions. Graphs of exponential and
    logarithmic functions. Properties of logarithms. Exponential and logarithmic equations. Modeling with
    exponential and logarithmic functions. Fitting exponential and power curves to data.
    3. ANALYTIC TRIGONOMETRY.
    Proofs of trigonometric identities. Addition and subtraction formulas. double-angle, half-angle, and
    sum-product identities. Inverse trigonometric functions. Solutions of trigonometric equations. Simplifying
    trigonometric expressions.
    4. POLAR COORDINATES.
    Polar coordinates. Graphs of polar equations. Polar form of complex numbers; DeMoivre's theorem.
    Parametric equations.
    5. SYSTEMS OF EQUATIONS AND INEQUALITIES.
    Systems of equations. Systems of linear equations in several variables. Best fit versus exact fit with
    matrices. Arithmetic of matrices. 

Polynomial functions and their graphs. Dividing polynomials. Rational and irrational zeros of polynomials.

 

Course Materials

    1. We will be using the OpenStax book Precalculus by Jay Abramson, which is freely available as a pdf and as a website (Links to an external site.). It is also available for purchase as a physical book if you would like.

Precalculus

 

  1. Some of our precalculus problems can be completed with just a scientific calculator; others will require a graphing calculator. I will be providing tutorials for using DESMOS (Links to an external site.), a free online graphing calculator. You are also welcome to use a physical calculator if you have one.
  2. Graph paper (Links to an external site.)may be required for some assignments, and can be printed as needed.
  3. You will need to keep all notes and work in an organized notebook, labeled with section and page/video number and time/problem as appropriate. An organized notebook is extremely important for this course since all of your assignments will be submitted online and you won’t be able to refer to your work easily when you go to study for the final. In addition, if there are any computer glitches, you can show me your notebook as verification of the exercises you completed. Finally, I will be grading your written work on some problems, so you will need to scan your paper and upload it to Canvas. (I will provide a tutorial for using CamScanner (Links to an external site.).)

The notebook should be divided into the following sections:

    • Reading/Video Lessons: You will be taking notes while reading sections in the book and/or watching videos for each section. You can expect to read about 10-20 pages or watch about 6 videos per section, with each video around 10 minutes or less.
    • Take Notes Assignments: While you are taking notes for each section, you will also be working on some Try-It questions to make sure that you understand the basic content from that section. See below for more information.
    • Practice Assignments: After completing the Reading/Video Assignments, you will answer a series of questions, usually between 10-20, about the section. Even though you will be submitting your answers online, it is important to write down the question and to show your work for the problem on paper.
    • Quizzes/Tests: Similarly to the Practice Assignments, you will submit most of your Quiz/Test answers online, but it is important to write down the question and to show your work for the problem on paper.

Graded Components

  • Homework: Homework will be assigned for each week and it will be accessed in Canvas. Homework will worth 15% of the total grade. Late homework will have penalty. You have one grace period: you can ask for 2 days extension for one homework without penalty. The homework will be graded based on accuracy, completeness, and presentation. Most of these problems will be auto-graded by the software. You will have multiple attempts on each homework problem, and many problems have a help video attached. Any problems I need to grade by hand will be graded within a week.

 

  • Video Assignments: Video Assignments: objective-level videos that cover the content of each section plus a basic exercise following each video for the student to demonstrate that they have a basic understanding of that objective.  Many of them are also part of the Video Lessons. Video Assignments worth 5% of your grade.

 

  • Exams: There will be 6 online exams worth a total of 35% of the overall grade. Tests will be conducted online, and I will give you directions for showing your work. You have to take the tests during the window time on the announced days.

 

  • Projects/Discussions: During the semester you'll have some group-work activities using Collaborations tool, and Discussions. This will be 15% from your grade.

 

  • Take  Notes: This part represents 15% from your grade. For each section you have to submit a filled out Handout which is provided. 

 

  • Final: The final exam is comprehensive and worth 15%. This exam has a few assignments (beside the Final Exam) that have to be completed in the final week.

Grade Weights or Point System:

  • Homework: 15%
  • Exams: 35%
  • Group Work Projects: 15%
  • Take Notes: 15%
  • Video Assignments: 5% 
  • Final: 15%

Letter Grade

Grading: The grade will be calculated based on the following percentages. You'll get an A, B, C, D, or F based on these overall percentages:

  • 90-100%: A
  • 80-89%: B
  • 70-79%: C
  • 60-69%: D
  • 0-59%: F

Late Policy on Tests

Every student gets one emergency extension to use on a a test, but it must be used within 2 days because I grade and give feedback right away, typically within a week.

Viewing Grades in Canvas

Points you receive for graded activities will be posted to the Canvas Grade Book. Select the Grades link in the Course Navigation menu to view your points. I will update the online grades each time a grading session has been completed, typically at the end of each week.


Academic Integrity

In accordance with Moreno Valley's Student Code of Conduct cheating and plagiarism with not be tolerated. Incidents of cheating and/or plagiarism will result in a failing grade on the work and a report filed with the Office of Student Life.

As in all healthy relationships, honesty and respect form the foundation of class interaction. I hold myself to this standard as well as all students. Academic dishonesty includes, but is not limited to, copying from another student’s homework, quiz, or test, allowing another student to copy your work, or using unauthorized resources during a test. See the Student Handbook for details. At the very least, cheating on a test will result in a zero for that assessment, and that score will not be dropped.

Classroom Conduct:

  • Be respectful of other class members.
  • All assignments must be appropriate for the entire class.
  • All assignments should be the original work of the student.
  • No assignment should be recycled from other classes.

 

 

Drop Policy

A student may be dropped from the class if, without directly notifying the instructor in advance, they:

  • Fail to post in the Discussion Forum "Introduce yourself” and complete the Quiz "Syllabus check" before Wednesday Sep 1st. If you fail to do this, you will be dropped as "no-show".
  • Lack of participation:
    • Miss an exam
    • Miss to submit Homework and Video assignments for two weeks
    • Miss to submit Take Notes for two weeks

Note: Students who choose not to continue the course are responsible for turning in a drop card to the admissions office. 


Disabled Students Programs and Services

College of the Desert views disability as an important aspect of diversity, and is committed to providing equitable access to learning opportunities for all students.  Disabled Students Programs and Services (DSPS) is the office that collaborates with students with disabilities to provide reasonable accommodations.  Please contact the DSPS office at (760) 773-2534, email DSPS (dspsinfo@collegeofthedesert.edu), or visit CSSC Room 101 for more information.  Once registered with DSPS, students will be provided with a DSPS Faculty Notification Letter that can be shared with faculty.

Veteran Students 

Welcome Veterans!  If you have any special circumstances (e.g., VA appointment, upcoming deployments, drill requirements, or disabilities), you are welcome and encouraged to communicate these, in advance if possible, to the instructor.

 

Additional Student Resources


 

 

weekly schedule

Week

 

 

0

 

 

1

Aug 30-Sep4

1.1     Functions and Function Notation

1.2     Domain and Range

1.3     Rates of Change and Behavior of Graphs

 

 

2

Sep 6 - 11

1.4 Composition of Functions

1.5 Transformations of Functions

1.7 Inverse Functions

 

Test 1

3

Sep 13 - 18

3.1 Complex Numbers

3.2 Quadratic Functions

3.3 Power Functions and Polynomial Functions

3.4 Graphs of Polynomial Functions

 

 

4

Sep 20 - 25

3.5 Dividing Polynomials

3.6 Zeros of Polynomial Functions

3.7 Rational Functions

3.8 Inverses and Radical Functions

 

Test 2

5

Sep 27 – Oct 2

4.1 Exponential Functions

4.2 Graphs of Exponential Functions

4.3 Logarithmic Functions

4.4 Graphs of Logarithmic Functions

 

 

6

Oct 4 - 9

4.5 Logarithmic Properties

4.6 Exponential and Logarithmic Equations

4.7 Exponential and Logarithmic Models

 

Test 3

7

Oct 11 - 16

5.1 Angles

5.2 Unit Circle: Sine and Cosine Functions

5.3 The Other Trigonometric Functions

5.4 Right Triangle Trigonometry

 

 

8

Oct 18 - 23

7.2 Sum and Difference Identities

7.3 Double-Angle, Half-Angle, and Reduction Formulas

7.5 Solving Trigonometric Equations

 

9

Oct 25 - 30

6.1 Graphs of the Sine and Cosine Functions

6.2 Graphs of the Other Trigonometric Functions

6.3 Inverse Trigonometric Functions

 

Test 4

10

Nov 1 - 6

8.3 Polar Coordinates

8.4 Polar Coordinates: Graphs

8.5 Polar Form of Complex Numbers

 

 

11

Nov 8 - 13

8.6 Parametric Equations

8.7 Parametric Equations: Graphs

8.8 Vectors

12

Nov 15 - 20

9.1 Systems of Linear Equations: Two Variables

9.2 Systems of Linear Equations: Three Variables

 

Test 5

13

Nov 22 - 27

9.3 Systems of Nonlinear Equations and Inequalities: Two Variables

9.4 Partial Fractions

 

 

14

Nov 29 – Dec 4

9.5 Matrices and Matrix Operations

9.6 Solving Systems with Gaussian Elimination

 

15  Dec 6 - 10

Review

Test 6

16  Dec 11 - 17

 

 

This syllabus is intended to give the student guidance about this course and will be followed as closely as possible. However, the professor reserves the right to modify this syllabus as course needs arise.