# AP Calculus AB Online

AP Calculus AB focus on students’ understanding of calculus concepts and provide experience with methods and

applications. Through the use of big ideas of calculus (e.g., modeling change, approximation and limits, and

analysis of functions), each course becomes a cohesive whole, rather than a collection of unrelated topics. Both

courses require students to use definitions and theorems to build arguments and justify conclusions. The courses

feature a multi-representational approach to calculus, with concepts, results, and problems expressed graphically,

numerically, analytically, and verbally. Exploring connections among these representations builds understanding

of how calculus applies limits to develop important ideas, definitions, formulas, and theorems. A sustained

emphasis on clear communication of methods, reasoning, justifications, and conclusions is essential. Teachers

and students should regularly use technology to reinforce relationships among functions, to confirm written work,

to implement experimentation, and to assist in interpreting results.

AP Calculus AB is designed to be the equivalent of a first semester college calculus course devoted to topics in

differential and integral calculus. Before studying calculus, all students should complete the equivalent of four

years of secondary mathematics designed for college-bound students: courses that should prepare them with a

strong foundation in reasoning with algebraic symbols and working with algebraic structures. Prospective calculus

students should take 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 piecewise-defined functions. In particular, before studying calculus, students must be

familiar with the properties of functions, the composition 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 descriptors such as increasing and decreasing). Students should also know how

the sine and cosine functions are defined from the unit circle and know the values of the trigonometric functions at

the numbers 0, pi over 6, pi over 4, pi over 3, pi over 2 and their multiples.

Semester 1

Unit 1: Precalculus Review

Unit 2: Bridge to Calculus

Unit 3: Limits and Continuity

Unit 4: Derivatives

Unit 5: Rates of Change

Semester 2

Unit 6: The Integral and the Fundamental Theorem of Calculus

Unit 7: Application of the Integral

Unit 8: Inverse and Transcendental Functions

Unit 9: Separable Differential Equations

Unit 10: AP Exam Review and Final Exam