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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