Course Title: | AP® Calculus BC Section MW |
Course Code: | apcalcmw |
MA NCES Code: | 02125 |
Discipline: | Mathematics |
Grade Level: | 10, 11, 12 |
Level: | Advanced Placement |
Offering: | Full Year (Fall: 25 Seats; Spring: 25 Seats; )
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Duration: | 33 weeks |
Prerequisites: | Four courses of secondary mathematics designed for the college bound student: courses covering algebra, geometry, trigonometry, analytic geometry, elementary functions and their notations. Students should have graphing calculators, access to a scanner and access to MS PowerPoint or a PowerPoint Viewer. |
Additional Requirements: | |
Accredited by: | Certified by NCAA for initial-eligibility (VHS School Code: 221356); Middle States Commission on Secondary Schools; Northwest Accreditation Commission |
Course Requires a Media Kit to be Shipped to Students:
No |
Course Requires a Media Kit to be Purchased by Course Sponsor
(see additional details below):
Yes |
Description:
The VHS AP Calculus BC course is a full academic-year course. It is a challenging course designed for high school students who have completed four years of secondary mathematics courses such as Algebra, Geometry, Advanced Algebra, Trigonometry/Pre-Calculus (which includes some Analytic Geometry and elementary functions). Work is comparable to that required in most college and university Calculus courses. Students should plan on taking the AP Calculus BC exam offered in May. Successful completion of the AP Exam may provide students with the opportunity to receive college credit.
The AP Calculus BC course covers all topics in the AP Calculus AB course plus the following additional topics:
Parametric, polar and vector functions
Slope Fields
Euler's method
L'Hopital's Rule
Improper Integrals
Logistic differential equations
Polynomial approximations and Series
Taylor Series
Emphasis is on conceptual understanding. However, facility with manipulation and computational skills are important outcomes. Students should expect the course as well as the AP Exam to truly push the depth of their understanding of mathematics generally and calculus specifically. Areas of emphasis From the College Board’s online resourse for AP Calculus at http://apcentral.collegeboard.com/repository/ap03_cd_calculus_0405_4313.pdf
-Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations.
-Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems.
-Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.
-Students should understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
Students will be expected to complete daily/weekly assignments and regular quizzes and exams. Each student will need a graphing calculator such as the TI-83 or equivalent and knowledge on how to work with their calculator. As in most online courses the student will be required to do a significant amount of independent learning. Individual responsibility, good work habits, discipline and organization will be important attributes for success.
Students enrolled in Advanced Placement VHS courses are required to take the AP exam, and are required to report their AP examination scores to VHS (note: students who are failing their AP class are not required to take the exam). Upon receipt of the student's exam score, each score will be recorded by VHS and assigned an anonymous tracking number to ensure student anonymity and confidentiality. By enrolling in an AP VHS class, the student authorizes their school site coordinator and school administration to report AP examination scores to VHS. Exam results will not affect the student's VHS grade or future enrollment in VHS courses.
**Please Note: This course may not be appropriate for students with specific accessibility limitations as written. Please refer to the VHS Handbook policy on Special Education/Equity for more information on possible modifications. If you need additional assistance, please let us know at service.goVHS.org. |
MediaKit Contents:
Calculus: Concepts and Applications
The Complete Idiot's Guide to Calculus
Syllabus:
Chapter 1: Limits, Derivatives, Integrals, and Integrals
Overview and introduction of the “four” basic concepts of Calculus
Chapter 2: Properties of Limits
Looking more in-depth at Limits, Continuity and The Intermediate Value Theorem
Chapter 3: Derivatives and Indefinite Integrals
A close look at Derivatives, numerically, graphically and algebraically. Then a look at Indefinite Integrals.
Chapter 4: Products, Quotients, and Parametric Functions
Further development of algebraic differentiation techniques.
Foci are working with combinations of two functions and trigonometric functions.
Chapter 5: Definite and Indefinite Integrals
Learn about the formal definition of definite integral, Riemann sums and the fundamental theorem of calculus.
Chapter 6: The Calculus of Exponential and Logarithmic Functions
Applying previous calculus concepts, especially finding derivatives, to exponential and logarithmic functions.
Learn about l’Hospital’s rule.
Chapter 7: The Calculus of Growth and Decay
Application of calculus is extended from the previous chapter to specific cases of exponential growth and decay problems.
Chapter 8: The Calculus of Plane and Solid Figures
A wonderfully visual chapter with solids of revolution at the core.
Area of plane regions is also an important application here.
Chapter 9: Algebraic Techniques for the Elementary Functions
Study the remaining algebraic techniques needed to differentiate and integrate each of the elementary transcendental functions.
Chapter 10: The Calculus of Motion—Averages, Extremes, and Vectors
Return to problems involving motion, emphasizing average value of a function, related rates, and max-min problems.
By the end of the chapter you will also explore vector functions.
Chapter 11: The Calculus of Variable-Factor Products
A very short chapter applying integration in variable force problems.
Chapter 12: The Calculus of Functions Defined by Power Series
Learn to generate the power series for a given function by equating derivatives.
Interval of convergence and ratio “technique” are also presented.
Course Objectives:
· Understand the Topics.
· Use the Topics appropriately.
· Apply the Topics correctly.
· Demonstrate knowledge of the Topics.
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