AP Calculus AB focus on students’ understanding of calculus concepts and provide experience with methods andapplications. Through the use of big ideas of calculus (e.g., modeling change, approximation and limits, andanalysis of functions), each course becomes a cohesive whole, rather than a collection of unrelated topics. Bothcourses require students to use definitions and theorems to build arguments and justify conclusions. The coursesfeature a multi-representational approach to calculus, with concepts, results, and problems expressed graphically,numerically, analytically, and verbally. Exploring connections among these representations builds understandingof how calculus applies limits to develop important ideas, definitions, formulas, and theorems. A sustainedemphasis on clear communication of methods, reasoning, justifications, and conclusions is essential. Teachersand 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 indifferential and integral calculus. Before studying calculus, all students should complete the equivalent of fouryears of secondary mathematics designed for college-bound students: courses that should prepare them with astrong foundation in reasoning with algebraic symbols and working with algebraic structures. Prospective calculusstudents should take courses in which they study algebra, geometry, trigonometry, analytic geometry, andelementary functions. These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric,inverse trigonometric, and piecewise-defined functions. In particular, before studying calculus, students must befamiliar with the properties of functions, the composition of functions, the algebra of functions, and the graphs offunctions. 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 howthe sine and cosine functions are defined from the unit circle and know the values of the trigonometric functions atthe numbers 0, pi over 6, pi over 4, pi over 3, pi over 2 and their multiples.
