The Advanced Placement Calculus BC course is equivalent to a first and second semester college calculus course devoted to topics in differential and integral calculus including parametrically defined curves, polar curves, and vector-valued functions; develops additional integration techniques and applications; and introduces the topics of sequences and series. The rigor of this course is consistent with colleagues and universities and will prepare students for the Advanced Placement exam in May. Upon successful completion of the exam, students may receive college credit and will be well-prepared for advanced calculus coursework. Additional details on each course from the College Board can be found here: AP Calculus BC.

In this course, students will explore three big ideas:

**(1) Change:** Using derivatives to describe rates of change of one variable with respect to another or using definite integrals to describe the net change in one variable over an interval of another allows students to understand change in a variety of contexts.

**(2) Limits:** Beginning with a discrete model and then considering the consequences of a limiting case allows us to model real-world behavior and to discover and understand important ideas, definitions, formulas, and theorems in calculus.

**(3) Analysis of Functions:** Calculus allows us to analyze the behaviors of functions by relating limits to differentiation, integration, and infinite series and relating each of these concepts to the others.

This course incorporates a variety of textbook and multimedia resources including an adaptive problem set platform that provides various feedback on student assessments. Students will also connect concepts in calculus to real-world applications, in order to develop a deeper understanding of calculus in today’s world.

Students will be expected to enroll in My AP Classroom through their VHS Learning AP course and will be guided to complete review work in My AP Classroom throughout the course. My AP Classroom resources include AP Daily Videos and unit-based Personal Progress Checks, which include AP-style multiple choice and free response questions.

Students enrolled in VHS Learning Advanced Placement courses with a passing grade are expected to take the AP Exam. Students register for AP exams through their local school or testing site as “Exam Only” students. AP exam scores will be reported to VHS Learning through My AP Classroom; exam results will not affect the student’s VHS Learning grade or future enrollment in VHS Learning courses.

**About the Self-Paced Course Model**

Self-Paced courses are comprehensive and designed for students who need or desire more flexibility in their academic schedule. VHS Learning teachers will regularly interact with students in asynchronous discussions, will host weekly office hours, and will invite students to monthly 1-on-1 progress meetings. Teachers will support students, answer questions, and provide feedback on work. Students will work independently on course activities; the course does not include class discussion assignments or other collaborative work.

Students may start this course on any Monday from September through the first Monday in December. Students must maintain enrollment for a minimum of **20 weeks** and have until **mid-June** to complete all assignments in the course. It is expected that students will work for approximately 330 hours to complete this course, though the amount of time may vary depending on a student’s work habits and comfort with the material.

**Course Essential Questions:**

- How can we describe rate of change and net change using calculus?
- How is the concept of the limit the foundation of calculus?
- How does calculus allow us to analyze the behaviors of functions?

**Course Objectives:**

- Work with functions represented in multiple ways: graphical, numerical, analytical, or verbal.
- Explain the meaning of the derivative in terms of a rate of change and local linear approximation as well as use derivatives to solve problems.
- Explain the meaning of the definite integral as a limit of Riemann sums and as the net accumulation of change as well as use integrals to solve problems.
- Describe the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
- Communicate mathematics and explain solutions to problems verbally and in writing.
- Model a written description of a physical situation with a function, a differential equation, or an integral.
- Use technology to solve problems, experiment, interpret results, and support conclusions.
- Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.