a.P. Calculus AB
Course Description
AP Calculus AB is an advanced level course that follows a curriculum designed to prepare students for the AP Exam, which is administered every May. Like all AP courses, AP Calculus is intended to be a collegelevel class. It is a rigorous and challenging course and a high level of effort and consistency is expected of students. Calculus can best be described as the mathematics of change. The course is organized around three big ideas. They are: 1. Functions, Graphs, & Limits, 2. Derivatives, and 3. Integrals. Prerequisite: Precalculus Advanced, minimum grade 80

AP Course Goals (from the AP Course Description)
Topic Outline for AP Calculus AB (from the AP website)
I. Functions, Graphs, and Limits
Analysis of Graphs
Limits of Functions (including onesided limits)
Asymptotic and Unbounded Behavior
Continuity as a Property of Functions
II. Derivatives
Concept of the Derivativ
Derivative at a Point
Derivative as a Function
Second Derivatives
Applications and Computation of Derivatives
III. Integrals
Interpretations and Properties of Definite Integrals
Applications of Integrals
FundamentalTheorem of Calculus
Techniques and Applications of Antidifferentiation
Numerical Approximations to Definite Integrals
Prerequisites (from the AP website)
Before studying calculus, all students should complete four years of secondary mathematics designed for collegebound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These
functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewisedefined functions. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions.
 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.
Topic Outline for AP Calculus AB (from the AP website)
I. Functions, Graphs, and Limits
Analysis of Graphs
Limits of Functions (including onesided limits)
Asymptotic and Unbounded Behavior
Continuity as a Property of Functions
II. Derivatives
Concept of the Derivativ
Derivative at a Point
Derivative as a Function
Second Derivatives
Applications and Computation of Derivatives
III. Integrals
Interpretations and Properties of Definite Integrals
Applications of Integrals
FundamentalTheorem of Calculus
Techniques and Applications of Antidifferentiation
Numerical Approximations to Definite Integrals
Prerequisites (from the AP website)
Before studying calculus, all students should complete four years of secondary mathematics designed for collegebound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These
functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewisedefined functions. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions.