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Calculus, Advanced Placement Standard 1: Limits and Standard 2: Differential Standard 3: Applications Standard 4: Integral Standard 5: Applications Continuity Calculus of Derivatives Calculus of Integration Students understand the Students find derivatives of Students find slopes and Students define integrals Students find velocity concept of limit, find limits of algebraic, trigonometric, tangents, maximum and using Riemann Sums, use functions and position functions at points and at logarithmic, and exponential minimum points, and points the Fundamental Theorem of functions from their infinity, decide if a function is functions. They find of inflection. They solve Calculus to find integrals, derivatives, solve separable continuous, and use derivatives of sums, optimization problems and and use basic properties of differential equations, and continuity theorems. products, and quotients, and find rates of change. integrals. They integrate by use definite integrals to find composite and inverse substitution and find areas and volumes. functions. They find approximate integrals. derivatives of higher order and use logarithmic differentiation and the Mean Value Theorem. 1. Understand the 1. Understand the concept 1. Find the slope of a 1. Use rectangle 1. Find specific concept of limit and of derivative curve at a point, approximations to find antiderivatives using estimate limits from geometrically, including points at approximate values of initial conditions, graphs and tables of numerically, and which there are integrals. including finding values. analytically, and vertical tangents and 2. Calculate the values of velocity functions from 2. Find limits by interpret the derivative no tangents. Riemann Sums over acceleration functions, substitution. as a rate of change. 2. Find a tangent line to equal subdivisions finding position 3. Find limits of sums, 2. State, understand, and a curve at a point and using left, right, and functions from velocity differences, products, apply the definition of a local linear midpoint evaluation functions, and and quotients. derivative. approximation. points. applications to motion 4. Find limits of rational 3. Find the derivatives of 3. Decide where 3. Interpret a definite along a line. functions that are functions, including functions are integral as a limit of 2. Solve separable undefined at a point. algebraic, decreasing and Riemann Sums. differential equations 5. Find one-sided limits. trigonometric, increasing. 4. Understand the and use them in 6. Find limits at infinity. logarithmic, and Understand the Fundamental Theorem modeling. 7. Decide when a limit is exponential functions. relationship between of Calculus: Interpret 3. Solve differential infinite and use limits 4. Find the derivatives of the increasing and a definite integral of equations of the form involving infinity to sums, products, and decreasing behavior of the rate of change of a y' = ky as applied to describe asymptotic quotients. f and the sign of f'. quantity over an growth and decay Calculus, Advanced Placement Standard 1: Limits and Standard 2: Differential Standard 3: Applications Standard 4: Integral Standard 5: Applications Continuity Calculus of Derivatives Calculus of Integration Students understand the Students find derivatives of Students find slopes and Students define integrals Students find velocity concept of limit, find limits of algebraic, trigonometric, tangents, maximum and using Riemann Sums, use functions and position functions at points and at logarithmic, and exponential minimum points, and points the Fundamental Theorem of functions from their infinity, decide if a function is functions. They find of inflection. They solve Calculus to find integrals, derivatives, solve separable continuous, and use derivatives of sums, optimization problems and and use basic properties of differential equations, and continuity theorems. products, and quotients, and find rates of change. integrals. They integrate by use definite integrals to find composite and inverse substitution and find areas and volumes. functions. They find approximate integrals. derivatives of higher order and use logarithmic differentiation and the Mean Value Theorem. behavior. 5. Find the derivatives of 4. Find local and absolute interval as the change problems. 8. Find special limits composite functions, maximum and of the quantity over 4. Use definite integrals sin x using the chain rule. minimum points. the interval, that is to find the area such as /x . 6. Find the derivatives of 5. Analyze curves, between a curve and 9. Understand continuity implicitly-defined including the notions the x-axis, or between in terms of limits. f'(x)dx = f(b) – functions. of monotonicity and two curves. 10.Decide if a function is f(a). 7. Find derivatives of concavity. 5. Use definite integrals continuous at a point. 5. Use the Fundamental inverse functions. 6. Find points of to find the average 11.Find the types of Theorem of Calculus 8. Find second derivatives inflection of functions. value of a function discontinuities of a to evaluate definite and derivatives of Understand the over a closed interval. function. and indefinite integrals higher order. relationship between 6. Use definite integrals 12.Understand and use and to represent 9. Find derivatives using the concavity of f and to find the volume of a the Intermediate particular logarithmic the sign of f". solid with known Value Theorem on a antiderivatives. differentiation. Understand points of cross-sectional area. function over a closed Perform analytical and 10.Understand and use inflection as places 7. Apply integration to interval. graphical analysis of the relationship where concavity model and solve 13.Understand and apply functions so defined. Calculus, Advanced Placement Standard 1: Limits and Standard 2: Differential Standard 3: Applications Standard 4: Integral Standard 5: Applications Continuity Calculus of Derivatives Calculus of Integration Students understand the Students find derivatives of Students find slopes and Students define integrals Students find velocity concept of limit, find limits of algebraic, trigonometric, tangents, maximum and using Riemann Sums, use functions and position functions at points and at logarithmic, and exponential minimum points, and points the Fundamental Theorem of functions from their infinity, decide if a function is functions. They find of inflection. They solve Calculus to find integrals, derivatives, solve separable continuous, and use derivatives of sums, optimization problems and and use basic properties of differential equations, and continuity theorems. products, and quotients, and find rates of change. integrals. They integrate by use definite integrals to find composite and inverse substitution and find areas and volumes. functions. They find approximate integrals. derivatives of higher order and use logarithmic differentiation and the Mean Value Theorem. the Extreme Value between changes. 6. Understand and use problems in physics, Theorem: If f(x) is differentiability and 7. Use first and second properties of these biology, economics, continuous over a continuity. derivatives to help definite integrals: etc., using the integral closed interval, then f 11.Understand and apply sketch graphs. as a rate of change to has a maximum and a the Mean Value Compare the give accumulated [f(x) + g(x)]dx = minimum on the Theorem. corresponding change and using the interval. characteristics of the method of setting up graphs of f, f', and f''. f(x)dx + an approximating 8. Use implicit g(x)dx Riemann Sum and differentiation to find representing its limit the derivative of an as a definite integral. inverse function. k . f(x)dx = k 9. Solve optimization f(x)dx problems. 10.Find average and f(x)dx = 0 instantaneous rates of Calculus, Advanced Placement Standard 1: Limits and Standard 2: Differential Standard 3: Applications Standard 4: Integral Standard 5: Applications Continuity Calculus of Derivatives Calculus of Integration Students understand the Students find derivatives of Students find slopes and Students define integrals Students find velocity concept of limit, find limits of algebraic, trigonometric, tangents, maximum and using Riemann Sums, use functions and position functions at points and at logarithmic, and exponential minimum points, and points the Fundamental Theorem of functions from their infinity, decide if a function is functions. They find of inflection. They solve Calculus to find integrals, derivatives, solve separable continuous, and use derivatives of sums, optimization problems and and use basic properties of differential equations, and continuity theorems. products, and quotients, and find rates of change. integrals. They integrate by use definite integrals to find composite and inverse substitution and find areas and volumes. functions. They find approximate integrals. derivatives of higher order and use logarithmic differentiation and the Mean Value Theorem. change. Understand the instantaneous rate of change as the limit f(x)dx = of the average rate of f(x)dx change. Interpret a derivative as a rate of f(x)dx + f(x)dx change in applications, including velocity, = f(x)dx speed, and If f(x) g(x) on acceleration. 11.Find the velocity and acceleration of a [a,b], then f(x)dx particle moving in a straight line. 12.Model rates of change, g(x)dx. 7. Understand and use including related rates integration by Calculus, Advanced Placement Standard 1: Limits and Standard 2: Differential Standard 3: Applications Standard 4: Integral Standard 5: Applications Continuity Calculus of Derivatives Calculus of Integration Students understand the Students find derivatives of Students find slopes and Students define integrals Students find velocity concept of limit, find limits of algebraic, trigonometric, tangents, maximum and using Riemann Sums, use functions and position functions at points and at logarithmic, and exponential minimum points, and points the Fundamental Theorem of functions from their infinity, decide if a function is functions. They find of inflection. They solve Calculus to find integrals, derivatives, solve separable continuous, and use derivatives of sums, optimization problems and and use basic properties of differential equations, and continuity theorems. products, and quotients, and find rates of change. integrals. They integrate by use definite integrals to find composite and inverse substitution and find areas and volumes. functions. They find approximate integrals. derivatives of higher order and use logarithmic differentiation and the Mean Value Theorem. problems. substitution (or change of variable) to find values of integrals. 8. Understand and use Riemann Sums, the Trapezoidal Rule, and technology to approximate definite integrals of functions represented algebraically, geometrically, and by tables of values.

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posted: | 12/1/2011 |

language: | English |

pages: | 5 |

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