Class Information

Course Title Math 195: Precalculus with Trigonometry

Instructor Julia Williams

Website http://juliakw.net/teaching/2026/math195fall/

Email jwilliams@capecod.edu

Phone (774) 330-4260

Primary out of class contact course website or email me

Class Hours and Room Tuesdays/Thursdays 2:00–4:15, Bldg. 6 Room 121

Office Hours In-person Tuesdays/Thursdays 9:00–10:00, virtual Mondays/Wednesdays 1:00–2:00

Office Bldg. 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:

  • 10%: Homework

  • 15%: Quizzes

  • 25%: Midterm 1

  • 25%: Midterm 2

  • 25%: Final

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 Tuesday 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 one problem.

  • Rubric for completion

    • 50/50: you did all problems.

    • 30/50: you did most problems.

    • 0/50: you did only a few problems.

  • Rubric for individual problem

    • 50/50: you gave a full correct solution.

    • 40/50: you made a minor error.

    • 20/50: you were on the right track but were unable to finish or made significant errors.

    • 0/50: 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 lowest homework score 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.

Quizzes

Each class period, not including exam days and a few other exceptions, will begin with a short two question quiz about the material we covered the previous class. After the quiz we grade them together according to the following rubric for the problems.

  • 5/5: You did the problem correctly.

  • 4/5: You got all the way through to a complete solution, but you made a minor mistake along the way.

  • 2/5: You started on the problem but were unable to finish it.

  • 0/5: You didn’t make meaningful progress toward the problem. Or you didn’t show any work and got a wrong final answer.

Show your work! Like with homework, think of showing your work as communicating your process so others can follow it. Also note that, by the rubric, if you don’t show your work you cannot get partial credit.

If you miss a quiz you may take during the next in-person office hours, before the next class meeting. I will not offer any further make-up nor extension. Additionally, I will drop your lowest quiz score from consideration for your final grade.

Exams

There will be two midterm exams. Additionally, the course will conclude with a comprehensive final exam. These are in-class, written, individual exams.

I will not offer make-up exams.

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

Exam dates:

  • Midterm 1: Thursday, October 15

  • Midterm 2: Thursday, November 19

  • Final: TBA

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 quizzes. 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. If you know in advance you will have to miss a class, please email me.

Class time will be spent on a combination of quizzes, 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, both in-person and virtual, 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:

  • Submitting 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.

Calendar

  • Unit 1 (9/8–10/15): Elementary Functions

    • Week 1: Intro, Quadratic functions (3.2)

    • Week 2: Power functions, reciprocals of power functions (3.3, 3.7)

    • Week 3: Inverses, radicals (3.8)

    • Week 4: Exponential and logarithmic functions (4.1–4.4)

    • Week 5: More exponential and logarithmic functions (4.5, 4.6)

    • Week 6: Review and midterm 1

  • Unit 2 (10/20–11/19): Trigonomentry

    • Week 7: Angles and circles (5.1–5.3)

    • Week 8: Triangles (5.4, 8.1, 8.2)

    • Week 9: Waves and graphs (6.1–6.3)

    • Week 10: Identities and equations (7.1, 7.2, 7.5)

    • Week 11: Review and midterm 2

  • Unit 3 (11/24–12/10): A preview of calculus

    • Week 12: Polynomials (3.4)

    • Week 13: Rational functions (3.7)

    • Week 14: Series, review for final

Notice of Changes

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