Students will know that the chain rule provides a way to differentiate composite functions. Attend to precision graphically, numerically, analytically, and verbally and specify units of measure. Students should know, the algebraic properties of limits and techniques for finding limits of indeterminate, forms, and they should be able to apply limits to understand the behavior of a, function near a point. If the limit exists and is a real number, then the common notation is. Students will be able to determine limits of functions. Sign in|Recent Site Activity|Report Abuse|Print Page|Powered By Google Sites, AP Calculus AB Standards and Explanations, Students will be able to express limits symbolically using correct notation and, ). Students will be able to analyze functions for intervals of continuity or points of discontinuity. Students will know that the definite integral of the rate of change of a quantity over an interval gives the net change of that quantity over that interval. There are 38 courses in total: Research; Seminar; Art and Design (formerly Studio Art): 2 … Use definitions and theorems to build arguments, to justify conclusions or answers, and to prove results. AP Calculus AB Standards and Explanations. Students will know that an antiderivative of a function. AP Calculus AB and Calculus BC Course and Exam Description, Revised Edition, Effective Fall 2016 Author: The College Board Subject: AP Calculus AB and Calculus BC Course and Exam Description, Revised Edition, Effective Fall 2016 Keywords Students will know that types of discontinuities include removable discontinuities, jump discontinuities, and discontinuities due to vertical asymptotes. Students will know that the chain rule is the basis for implicit differentiation. Identify how mathematical characteristics of functions are related in different representations. AP Calculus AB covers basic introductions to limits, derivatives, and integrals. then the consequences of a limiting case. Therefore, the idea of limits is essential, for discovering and developing important ideas, definitions, formulas, and theorems, in calculus. Critically interpret and accurately report information provided by technology. Students will know that a function defined as an integral represents an accumulation of a rate of change. Embedding these practices in the study of calculus enables students to establish mathematical lines of reasoning and use them to apply mathematical concepts and tools to solve problems. Students will know that the definition of the definite integral may be extended to functions with removable or jump discontinuities. Associate tables, graphs, and symbolic representations of functions. Students will be able to determine higher order derivatives, Students will be able to use derivatives to analyze properties of a function, Students will know that first and second derivatives of a function can provide information about the function and its graph including intervals of increase or decrease, local (relative) and global (absolute) extrema, intervals of upward or downward concavity, and points of inflection, Students will know that key features of functions and their derivatives can be identified and related to their graphical, numerical, and analytical representations, Students will know that key features of the graphs of, Students will be able to recognize the connection between differentiability and continuity, Students will know that a continuous function may fail to be differentiable at a point in its domain, Students will know that if a function is differentiable at a point, then it is continuous at that point, Students will be able to interpret the meaning of a derivative within a problem, Students will know that the derivative of a function can be interpreted as the instantaneous rate of change with respect to its independent variable, Students will be able to solve problems involving the slope of a tangent line, Students will know that the derivative at a point is the slope of the line tangent to a graph at that point on the graph, Students will know that the tangent line is the graph of a locally linear approximation of the function near the point of tangency, Students will be able to solve problems involving related rates, optimization, and rectilinear motion, Students will know that the derivative can be used to solve rectilinear motion problems involving position, speed, velocity, and acceleration, Students will know that the derivative can be used to solve related rates problems, that is, finding a rate at which one quantity is changing by relating it to other quantities whose rates of change are known, Students will know that the derivative can be used to solve optimization problems, that is, finding a maximum or minimum value of a function over a given interval, Students will be able to solve problems involving rates of change in applied contexts, Students will know that the derivative can be used to express information about rates of change in applied contexts, Students will be able to verify solutions to differential equations, Students will know that solutions to differential equations are functions or families of functions, Students will know that derivatives can be used to verify that a function is a solution to a given differential equation, Students will be able to estimate solutions to differential equations, Students will know that slope fields provide visual clues to the behavior of solutions to first order differential equations, Students will be able to apply the Mean Value Theorem to describe the behavior of a function over an interval. That is. Consider multiple representations (graphical, numerical, analytical, and verbal) of a function to select or construct a useful representation for solving a problem. Select appropriate mathematical strategies. Students will be able to interpret the definite integral as the limit of a Riemann sum and, express the limit of a Riemann sum in integral notation, Students will know that a Riemann sum, which requires the partition of an interval. Updated May 21, 2020. For instance, if more than half of the schools on your list require a general education math course, and they allow a 3 or above on the AP Calculus BC exam to fulfill that requirement, you might be inclined to take the AP Calculus BC course. Produce examples and counterexamples to clarify understanding of definitions, to investigate whether converses of theorems are true or false, or to test conjectures. Full curriculum of exercises and videos. Students will know that definite integrals can be approximated for functions that are represented graphically, numerically, algebraically, and verbally. Students will know that the derivative at a point can be estimated from information given in tables or graphs. recognize antiderivatives of basic functions. Students will know that sums, differences, products, and quotients of functions can be differentiated using derivative rules. Big Idea 1: Limits . Use the connection between concepts (e.g., rate of change and accumulation) or processes (e.g., differentiation and its inverse process, antidifferentiation) to solve problems. Students will know that in some cases, a definite integral can be evaluated by using geometry and the connection between the definite integral and area. Construct one representational form from another (e.g., a table from a graph or a graph from given information). ... Standard Deviation 1.40 1.40 1.38 1.36 Number of Students 316,099 308,538 300,659 AP Calculus BC Purpose. Before we delve into popularity and difficulty, this basic list can be really helpful.

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