Class Information

Course Title Math 195: Precalculus with Trigonometry

Instructor Julia Williams

Website http://juliakw.net/teaching/2026/math195/

Email jwilliams@capecod.edu

Phone (774) 330-4260

Primary out of class contact course website or email me

Class Hours and Room MW 11:00–1:15, Building 4 Room 106

Office Hours MW 10:00–11:00, TR 1:00–2:00, Building 6 Room 119

Textbook Precalculus 2e, Openstax. (Available freely online)

Course Description Targeting students in Mathematics, Engineering, and Physical Sciences, this course provides the foundation necessary for a rigorous study of calculus. It covers non-linear inequalities, functions, and graphs. The primary focus is on polynomial, rational, exponential, logarithmic, and trigonometric functions. Applications are also discussed extensively. Additional topics may include analytic geometry with an emphasis on the conic sections, Gibbs notation vector algebra, polar coordinates, sequences, series, and mathematical induction.

Prerequisite A grade of C- or higher in MAT175 (College Algebra) or satisfactory basic skills assessment score

Departmental Syllabus (with formal learning outcomes) https://www.capecod.edu/media/capecodedu/content-assets/documents/syllabi/mat195.pdf

Informal Learning Outcomes

Upon completion of this class you will be adept at working with functions of continuous quantities. You will understand how to approach them from both an algebraic and geometric perspective. You will understand how they model covariation and how to determine both global and pointwise behavior. This class prepares you for the calculus sequence.

Grading Policy

Your learning outcomes for this class will be assessed with exams, homework, and in-class writing exercises. The breakdown for your grade is as follows:

  • 20%: Homework

  • 25%: Midterm 1

  • 25%: Midterm 2

  • 25%: Oral Final

  • 5%: In-Class Writing Exercises

Grades will be assigned on the standard A through F scale, with +’s or –’s for borderline cases. I reserve the right to make adjustments for individual circumstance.

Homework

Homework will be assigned weekly, due in-class the Monday of the following week.

Show your work on homework! You do not need to show every minor algebraic step, but I need to be able to follow your thought process. More important than arriving at a correct final answer is being able to explain how you obtained it. Think of showing your work as communicating your process so others can follow it.

Homework grades are based on completion and my selection of two problems.

  • Rubric for completion

    • 20/20: you did all problems.

    • 10/20: you did most problems.

    • 0/20: you did only a few problems.

  • Rubric for individual problems

    • 40/40: you gave a full correct solution.

    • 35/40: you made a minor error.

    • 15/40: you were on the right track but were unable to finish or made significant errors.

    • 0/40: you didn’t make meaningful progress toward a correct solution.

You are encouraged to work together on homework, but the work you turn in is expected to be your own. If you do collaborate with classmates, please say so and give their names with your submitted work.

I will not accept late work. Instead, I will drop your two lowest homework scores from consideration for your final grade.

For this class you should expect to spend roughly two hours out of class for each hour of in-class time, for a total of six hours. Homework is due weekly to give you flexibility in when to fit in those six hours. That said, I strongly encourage you to start your homework as soon as possible. Material from later in the week will build on earlier ideas.

Exams

There will be two midterm exams. These are in-class, written, individual exams.

No calculators nor notes are allowed for midterm exams, unless otherwise stated.

Additionally, the course will conclude with an oral final. These will be individually scheduled, one-on-one sessions in my office. You will demonstrate how you work through a few problems, and we will discuss how the class went overall.

I will provide a problem list before the sessions. You will be asked to present one problem of your choice with me choosing the remainder.

Exam dates:

  • Midterm 1: Wednesday, February 25th

  • Midterm 2: Wednesday, April 15th

  • Oral Final: Week of May 4th

In-Class Writing Exercises

Every class period will begin with a 5 minute focused free write. You will write in response to a prompt, and turn it in at the end of the class. These writing exercises will be used as a basis for class discussions.

The writing exercises are graded based on completion, and no late submissions will be accepted.

Textbook Information

We will use Precalculus 2e, Openstax (Available freely online) for our textbook. It will be a reference for you as well as a source of homework problems. While the book is freely available online in multiple formats, if you prefer a paper copy you may purchase one.

Attendance and Class Participation Guidelines

You are expected to attend class sessions, and this is factored into your grade via the in-class writing exercises. Like most math classes the material in this class builds upon itself. If you skip class and fall behind it is difficult to get back on track. If you miss a class, it is your responsibility to ensure you make up the missed lesson. The schedule on the course website gives the textbook sections we will cover each week, and any worksheets or handouts will be posted on the course website. If you know in advance you will have to miss a class, please email me.

Class time will be spent on a combination of in-class writing exercises, lecture, and group work/discussion.

You are expected to participate in all parts of class sessions. For lecture you should be actively listening, taking notes, and asking questions as appropriate. For group work/discussion you should engage in the work, sharing ideas with your classmates.

Mathematics has a reputation for being removed from social concerns and identities. Whether or not this is true for the content of mathematics, it is certainly false for the process of learning mathematics. Our classroom is to be a welcoming one, where everyone feels able to participate and learn regardless of their background or identity. As learners it is your obligation to treat others with respect and generosity, and be willing to exchange ideas with others.

Communication Policy and Office Hours

Announcements and homework will be posted to the course website.

The best way to contact me outside of class is by email. Please put “math 195” in the subject line of your email. If I do not respond by the end of the next weekday, please send me a follow up reminder message.

Office hours are held multiple times in the week, to give you an opportunity to ask questions and receive help in-person outside of class time. If you prefer to meet at a different time, please contact me to arrange that.

Accessibility

Students with disabilities are legally entitled to reasonable accommodations to ensure equal access to education. I am committed to providing you with equal access to this class, and am happy to work with you to ensure reasonable accommodations. Because the accommodations offered are usually forward-looking modifications, it is important to get them set up as soon as possible.

Anyone who feels they may need accommodation based on the impact of a disability should contact the O’Neill Center for Student Access and Support (774-330-4453; oneillcenter@capecod.edu)

The Americans with Disabilities Act defines a disability as a medical condition that substantially limits one or more major life activities—including things like walking, sleeping, taking care of yourself, learning, and regulating your emotions—or major bodily functions. If you have a medical condition—including mental health conditions—that significantly interferes with your schoolwork, you probably qualify. You do not need to disclose your condition to your instructors to receive accommodations.

Academic Honesty and AI Policy

You are expected to know and uphold the college’s policies on academic honesty as described in the Student Handbook. Mathematics classes form part of the core base of skills you need to succeed in many later classes, and you are harming yourself if you try to avoid learning the material for this class.

The point of this class is to learn fundamental skills to serve you later in your education and career. AI tools interfere with this goal. For that reason, the use of ChatGPT or other AI tools to produce or help produce material you turn in for a grade is prohibited. Submitted work using these tools will receive a zero, with no chance for making up the lost points. I reserve the right to escalate the consequences for repeated violations.

The following are examples of prohibited AI use:

  • Submitted work entirely generated by an LLM.

  • Asking Claude to solve a homework problem for you, then writing up its solution.

  • Using ChatGPT to draft a paper.

Outside of work you submit for a grade I am not interested in policing your use of AI. If you want to use AI tools to help you take notes, generate extra practice problems before an exam, or similar then that is none of my business.

You are encouraged to collaborate with classmates for homework, but the work you submit is expected to be your own. If you do work with others, please say so and give their names with your submitted homework.

Notice of Changes

This syllabus is subject to change. If this happens, you will be informed.