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