Chippewa Valley High School - AP Calculus BC



Chippewa Valley High School

Advanced Placement Calculus AB Mrs. Mills

Room 230

ipospelovamills@cvs.k12.mi.us

Phone: (586)-723-2630

I. COURSE GOALS

• 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 the 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 a rate 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 should be able to communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.

• Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral.

• Students should be able to use technology to help solve problems, experiment, interpret results, and verify conclusions.

• Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

• Students should develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

• Students will work to prepare for the Calculus Advanced Placement Examination

II. COURSE CONTENT

A. Functions, Graphs and Limits

• Analysis of graphs

• Limits of functions (including one-sided limits)

• Asymptotic and unbounded behavior

• Continuity as a property of functions

• Parametric and Polar Equations

B. Derivatives

• Concept of the derivative

• Derivative at a point

• Derivative as a function

• Multiple derivatives

• Applications of derivatives

• Computation of derivatives

C. Integrals

• Interpretations and properties of definite integrals

• Applications of integrals

• Fundamental Theorem of Calculus

• Techniques of antidifferentiation

• Applications of antidifferentiation

• Numerical approximations to definite integral

D. Polynomial Approximation and Series

• Concept of Series

• Series of Constants

• Taylor Series and associated error

• Convergence Tests

III. GRADING POLICY

• All graded work will be assigned a point value.

• There will be several quizzes and one test for each chapter, also a final examination each semester.

Point will be assigned a letter grade by a straight percentage scale:

A 93-100% A- 90-92%

B+ 87-89% B 83-86%

B- 80-82% C+ 77-79%

C 73-76% C- 70-72%

D+ 67-69% D 63-66%

D- 60-62% F ................
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