Course Outline (taken from the College Board website)
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 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 should be able to communicate mathematics and explain solutions to problems both verbally and in written sentences.
• 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 support 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 and know the values of the trigonometric functions.
Topic Outline for Calculus AB
I. Functions, Graphs and Limits
· Analysis of graphs. Limits of functions (including one-sided limits)
· Limits of functions (including one-sided limits)
· Asymptotic and unbounded behavior
· Continuity as a property of functions
II. Derivatives
· Concept of the Derivative
· Derivative at a point
· Derivative as a function
· Application of Derivatives
· Computation of derivatives
III. Integrals
· Interpretations and properties of definate integrals
· Applications of integrals.
· Fundamental Theorem of Calculus
· Techniques of antidifferentiation
· Applications of antidifferentiation
· Numerical approximations to definite integrals.
• 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 should be able to communicate mathematics and explain solutions to problems both verbally and in written sentences.
• 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 support 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 and know the values of the trigonometric functions.
Topic Outline for Calculus AB
I. Functions, Graphs and Limits
· Analysis of graphs. Limits of functions (including one-sided limits)
· Limits of functions (including one-sided limits)
· Asymptotic and unbounded behavior
· Continuity as a property of functions
II. Derivatives
· Concept of the Derivative
· Derivative at a point
· Derivative as a function
· Application of Derivatives
· Computation of derivatives
III. Integrals
· Interpretations and properties of definate integrals
· Applications of integrals.
· Fundamental Theorem of Calculus
· Techniques of antidifferentiation
· Applications of antidifferentiation
· Numerical approximations to definite integrals.