**For Approved STEM Advanced Placement Access Expansion Enrollments (SAPAO)**

The Advanced Placement Calculus BC course is equivalent to a first and second semester college calculus courses 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 colleges 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 this course from 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.

Students will investigate topics such as limits and continuity, differentiation – definition and fundamental properties, differentiation – composite, implicit, and inverse functions, contextual applications of differentiation, analytical applications of differentiation, integration and accumulation of change, differential equations, applications of integrations, parametric equations, polar coordinates, and vector-valued functions, and infinite sequences and series.

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 engage in collaborative activities, including discussions, and 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 year. 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.

This AP course has a required summer assignment. The summer assignment is a review of prerequisite content and critical concepts students must be comfortable with before beginning the course. Students are expected to complete their summer assignment before the course begins and submit their work by the end of Week 1. Students who register on or after September 1 will receive an extension to complete the summer assignment by the end of Week 3.

**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.