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AP Calculus
AB Correlations
BC Correlations
5th Six Weeks Assignment
Calculus AB
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All of the following came from Collegeboard's Course Discription of
AP Calculus
Topic Outline for Calculus AB
I. Functions, Graphs, and Limits
Analysis of Graphs
Limits of Functions (Including onesided limits)
An intuitive understanding of the limiting process
Calculating limits using algebra
Estimating limits from graphs or tables of data
Asymptotic and unbounded behavior
Understanding asymptotes in terms of graphical behavior
Describing asymptotic behavior in terms of limits involving infinity
Comparing relative magnitudes of functions and their rates of change
Continuity as a property of functions
An intuitive understanding of continuity.
Understanding continuity in terms of limits
Geometric understanding of graphs of continuous functions
II. Derivatives
Concept of the derivative
Derivative presented graphically, numerically, and analytically
Derivative interpreted as an instantaneous rate of change
Derivative defined as the limit of the difference quotient
Relationship between differentiability and continuity
Derivative at a point
Slope of a curve at a point.
Tangent line to a curve at a point and local linear approximation
Instantaneous rate of change as the limit of average rate of change
Approximate rate of change from graphs and tables of values
Derivative as a function
Corresponding characteristics of graphs of f and f'
Relationship between the increasing and decreasing behavior of f and the sign of f'
The Mean Value Theorem and its geometric consequences
Equations involving derviatives. Verbal descriptins are translated into equations involving derivatives and vice versa.
Second derivatives
Corresponding characteristics of the graphs of f, f', and f''
Relationship between the concavity of f and the sign of f''
Points of inflection as places where concavity changes
Applications of derivatives
Analysis of curves, including the notions of monotonicity and concavity
Optimization, both absolute and relative extrema
Modeling rates of change, including related rates problems
Use of implicit differentiation to find the derivative of an inverse function
Interpretation of the derivative as a rate of change in varied applied contexts
Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations.
Computation of derivatives
Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions
Basic rules for the derivative of sums, products, and quotients of functions
Chain rule and implicit differentiation
III. Integrals
Interpretations and properties of definite integrals
Defined integral as a limit of Riemann sums
Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval
Basic properties of definite integrals
Applications of integrals
Fundamental Theorem of Calculus
Use of the Fundamental Theorem to evaluate difinite integrals
Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined
Techniques of antidifferentiation
Antiderivatives following directly from derivatives of basic functions
Antiderivatives by substitution of variables
Applications of antidifferentiation
Finding specific antiderivatives using initial conditions, including applications to motion along a line
Solving separable differential equations and using them in modeling
Numerical approximations to definite integrals
Riemann Sums(using left, right, and midpoint evaluation points)
Trapezoidal sums
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Topic Outline for Calculus AB
I. Functions, Graphs, and Limits
Analysis of Graphs
Limits of Functions (Including onesided limits)
 An intuitive understanding of the limiting process
 Calculating limits using algebra
 Estimating limits from graphs or tables of data
Asymptotic and unbounded behavior Understanding asymptotes in terms of graphical behavior
 Describing asymptotic behavior in terms of limits involving infinity
 Comparing relative magnitudes of functions and their rates of change
Continuity as a property of functionsII. Derivatives
Concept of the derivative
 Derivative presented graphically, numerically, and analytically
 Derivative interpreted as an instantaneous rate of change
 Derivative defined as the limit of the difference quotient
 Relationship between differentiability and continuity
Derivative at a point Slope of a curve at a point.
 Tangent line to a curve at a point and local linear approximation
 Instantaneous rate of change as the limit of average rate of change
 Approximate rate of change from graphs and tables of values
Derivative as a function Corresponding characteristics of graphs of f and f'
 Relationship between the increasing and decreasing behavior of f and the sign of f'
 The Mean Value Theorem and its geometric consequences
 Equations involving derviatives. Verbal descriptins are translated into equations involving derivatives and vice versa.
Second derivatives Corresponding characteristics of the graphs of f, f', and f''
 Relationship between the concavity of f and the sign of f''
 Points of inflection as places where concavity changes
Applications of derivatives Analysis of curves, including the notions of monotonicity and concavity
 Optimization, both absolute and relative extrema
 Modeling rates of change, including related rates problems
 Use of implicit differentiation to find the derivative of an inverse function
 Interpretation of the derivative as a rate of change in varied applied contexts
 Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations.
Computation of derivativesIII. Integrals
Interpretations and properties of definite integrals
 Defined integral as a limit of Riemann sums
 Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval
 Basic properties of definite integrals
Applications of integralsFundamental Theorem of Calculus
 Use of the Fundamental Theorem to evaluate difinite integrals
 Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined
Techniques of antidifferentiation Antiderivatives following directly from derivatives of basic functions
 Antiderivatives by substitution of variables
Applications of antidifferentiation Finding specific antiderivatives using initial conditions, including applications to motion along a line
 Solving separable differential equations and using them in modeling
Numerical approximations to definite integrals