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Advanced
Placement
Calculus
Standard
1: Understands various strategies and processes used to
solve problems and to communicate mathematical ideas
+ Uses and applies the derivative to solve real-world
problems
+ Uses and applies the definite integral to solve real-world
problems
Standard
2: Understands the concepts of numbers, numeration, and
number theory
Not assessed at this level
Standard
3: Understands number operations and the processes of
computation
+ Uses and applies numerical integration techniques to
find the area under a curve
Standard
4: Understands the concepts of measurement
Not assessed at this level
Standard 5: Understands the concepts of geometry and
spatial sense
+ Uses and applies derivatives to determine the shape
of a graph
Standard
6: Understands the concepts of statistics, data analysis,
and probability
Not assessed at this level
Standard
7: Understands the properties of patterns and functions
and the concepts of algebra
+ Uses and applies the properties of elementary functions,
including algebraic, trigonometric, exponential and composite
functions, and graphs these functions using a graphics
calculator
+ Uses and applies the properties of limits of functions
+ Uses the definition of continuity to determine whether
a function is continuous or discontinuous
+ Understands and uses the definition of the derivative
+ Uses and applies formulas to find the derivatives of
algebraic, trigonometric, exponential, and logarithmic
functions
+ Uses and applies formulas to find higher order derivatives
+ Knows how to find the indefinite integral of a function
+ Understands the properties of the definite integral
+ Knows how to apply differential and integration techniques
to inverse functions
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