Assign meaning to notation, accurately interpreting the notation in a given problem and across different contexts. 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 be able to deduce and interpret behavior of functions using limits. Students will know that solutions to differential equations may be subject to domain restrictions. Complete algebraic/computational processes correctly. Students will know that the derivative can be represented graphically, numerically, analytically, and verbally. 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. INCLUDES. Students will know that properties of definite integrals include the integral of a constant times a function, the integral of the sum of two functions, reversal of limits of integration, and the integral of a function over adjacent intervals. Students can access live classes and recordings on the AP YouTube Channel. Students will be able to analyze functions for intervals of continuity or points of discontinuity. Construct one representational form from another (e.g., a table from a graph or a graph from given information). Students will know that differentiation rules provide the foundation for finding antiderivatives. Students will be able to approximate a definite integral. 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. AP Calculus AB Standards and Explanations. Students will know that the chain rule provides a way to differentiate composite functions. Students will know that the derivative at a point can be estimated from information given in tables or graphs. Associate tables, graphs, and symbolic representations of functions. Title: C:\homeschool\06 - Calculus\Practice Exam\AP Calculus Practice Exam and Solutions.wpd Author: Derek Created Date: 4/16/2015 8:30:44 PM 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. ... Standard Deviation 1.40 1.40 1.38 1.36 Number of Students 316,099 308,538 300,659 AP Calculus BC Purpose. According to the College Board, Calculus BC is a full-year course in the calculus of functions of a single variable. Students will know that continuity is an essential condition for theorems such as the Intermediate Value Theorem, the Extreme Value Theorem, and the Mean Value Theorem. Learning Objective 1.1A(a) Students will be able to express limits symbolically using correct notation and (b) Interpret limits expressed symbolically. Critically interpret and accurately report information provided by technology. Students will be able to estimate limits of functions. Students will be able to estimate derivatives. Students will be able to identify the derivative of a function as the limit of a difference quotient, Students will know that the difference quotients, Students will know that the instantaneous rate of change of a function at a point can be expressed by, limit exists. Scope it out and see which topics look interesting to you! Extract and interpret mathematical content from any presentation of a function (e.g., utilize information from a table of values). Students will know that sums, differences, products, and quotients of functions can be differentiated using derivative rules. Updated May 21, 2020. Students will be able to determine limits of functions. Relate the concept of a limit to all aspects of calculus. Attend to precision graphically, numerically, analytically, and verbally and specify units of measure. The MPACs are not intended to be viewed as discrete items that can be checked off a list; rather, they are highly interrelated tools that should be utilized frequently and in diverse contexts. Mathematical Practices for AP Calculus (MPACs), 2020 AP with WE Service Scholarship Winners, AP Computer Science A Teacher and Student Resources, AP English Language and Composition Teacher and Student Resources, AP Microeconomics Teacher and Student Resources, AP Studio Art: 2-D Design Teacher and Student Resources, AP Computer Science Female Diversity Award, Learning Opportunities for AP Coordinators, Accessing and Using AP Registration and Ordering, Access and Initial Setup in AP Registration and Ordering, Homeschooled, Independent Study, and Virtual School Students and Students from Other Schools, Schools That Administer AP Exams but Donâ€™t Offer AP Courses, Transfer Students To or Out of Your School, Teacher Webinars and Other Online Sessions, Implementing AP Mentoring in Your School or District, AP Calculus AB and AP Calculus BC Course and Exam Description. If you're seeing this message, it means we're having trouble loading external resources on our website.

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