MAC6130T: AP Calculus BC (2012-2013)
CURRICULUM PROGRAM: Virtual School Program
COURSE TITLE: AP Calculus BC
CALENDAR YEAR: 2012-2013
GRADE LEVEL: 11-12
COURSE LENGTH: 36 weeks
SUGGESTED PREPARATION: Algebra I, Algebra II, Geometry, Math Analysis
About the Program:
AP Calculus BC provides a deeper understanding of the fundamental concepts and methods of single-variable calculus developed in AP Calculus AB. There is a continued emphasis on calculus applications and techniques, with the use of multiple representations including graphic, numeric, analytic, algebraic, and verbal and written responses. Technology is an integral part of the course and includes the use of graphing calculators, computers, and data analysis software. The College Board requires the use of graphing calculators for this course. Though our system has an open enrollment policy, students should understand that this course is designed to be a fourth-year mathematics course, and the equivalent of a year-long, college-level course in single variable calculus. The course requires a solid foundation of topics in advanced algebra, geometry, trigonometry, analytic geometry, and elementary functions. AP Calculus BC is an extension of AP Calculus AB, and provides the equivalent of a second course in a college calculus sequence. Teaching strategies include collaborative small-group work, pairs engaged in data analysis, whole-group presentations, peer-to-peer discussions, and an integration of technology when appropriate. All aspects of progress in the course are measured using multiple methods such as authentic, performance, observational, and assessment for learning (formative); group and individual projects, student presentations, and assessment of learning (summative). Students are expected to take the AP Calculus BC Exam at the end of this course.
Major Concepts/Content: AP Calculus BC is a college-level course which differs from a high school calculus course in terms of depth of coverage and time commitments for study. The content is organized to emphasize major topics which include the following: (1) functions, graphs, and limits; (2) derivatives, (3) integrals, and (4) polynomial approximations and series. These topics are detailed in the AP Calculus BC course description, which is available at AP Central.
- Develop an in-depth understanding of major topics of calculus including functions, limits, derivatives, integrals, and polynomial approximations and series.
- Incorporate multiple representations of functions using graphic, numeric, analytic, algebraic, and verbal and written responses, and understand the connections among these representations.
- Construct an understanding of derivatives as an instantaneous rate of change, applications of derivatives as functions, and use various techniques to solve problems including local linear approximations.
- Understand definite integrals as a limit of Riemann sums, and as the net accumulation of sums, and use them to solve a variety of problems.
- Develop an understanding of the Fundamental Theorem of Calculus as a relationship between derivatives and definite integrals.
- Understand the concept of a series as a sequence of partial sums, and use the Power series and Taylor polynomial approximations and series.
- Analyze parametric, polar, and vector functions through the use of parametric equations, polar coordinates, and derivatives and applications of these functions.
- Use graphing calculators to problem solve, experiment with ‘what if’ hypotheses, display and interpret results, and justify conclusions.
- Make sense of and determine the reasonableness of solutions including units of measurement.
- Develop an appreciation for an historical perspective of calculus.
Course Philosophy: Understanding change is the basis of this course. The study of the concept of the derivative in calculus is the formal study of mathematical change. A key component of the course is fluency in the use of multiple representations that include graphic, numeric, analytic, algebraic, and verbal and written responses. The course is more than a collection of topics; it is a coherent focused curriculum that develops a broad range of calculus concepts and a variety of methods and real-world applications. These include practical applications of integrals to model biological, physical, and economic situations. Although the development of techniques and fluency with algebraic symbolism to represent problems is important, it is not a primary focus of the course. Rather, the course emphasizes differential and integral calculus for functions of a single variable through the Fundamental Theorem of Calculus.