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Mahomet-Seymour Schools

Curriculum

Mathematics - AP Calculus

 

Functions, Graphs and Limits

 

The learner will be able to (with the aid of technology) graph function.

 

The learner will be able to predict and explain local and global behavior.

 

The learner will be able to explore the interplay between the geometric and analytic information.

 

The learner will be able to gain an intuitive understanding of limits.

 

The learner will be able to estimate limits from graph or tables of data.

 

The learner will be able to describe asymptotic behavior (including limits with infinity).

 

The learner will be able to compare relative maximums and rates of change.

 

The learner will be able to analyze parametric, polar, and vector functions.

 

 

 

 

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Derivatives

 

The learner will be able to understand derivatives graphically, numerically, and analytically.

 

The learner will be able to interpret derivatives as a rate of change.

 

The learner will be able to define derivatives as a limit.

 

The learner will be able to relate differentiability and continuity.

 

The learner will be able to calculate the slope of a curve at a point (including vertical tangents).

 

The learner will be able to explain find tangent lines and approximations.

The learner will be able to use limits of the average rate of change to find instantaneous rates of change.

 

The learner will be able to approximate derivatives from graphs and tables.

 

The learner will be able to relate functions and their derivatives.

 

The learner will be able to use and interpret the Mean Value Theorem.

 

The learner will be able to use the derivative to find increasing and decreasing intervals of functions.

 

The learner will be able to use the second derivatives to explore concavity.

 

The learner will be able to apply derivatives to solving a variety of problems including related rates and optimization.

 

The learner will be able to find derivatives of sums, differences, products, and quotients and use the chain rule.

 

The learner will be able to find the derivatives of all the basic functions (including parametric, polar and vector .

 

The learner will be able to differentiate implicitly.

 

The learner will be able to use Eulerís method for approximations of differential equations

 

The learner will be able to use LíHospitalís rule to evaluate limits.

 

 

 

 

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Integrals

 

The learner will be able to calculate integrals as a limit of Riemann sums.

 

The learner will be able to interpret the integral as of a rate of change as the change in that quantity.

 

The learner will be able to use basic properties of integrals.

 

The learner will be able to apply integrals to a variety of problems including area and volume.

 

The learner will be able to use Fundamental Theorem of Calculus to evaluate integrals.

 

The learner will be able to use basic derivatives for anti-differentiation including substitution.

 

The learner will be able to solve initial value problems and other differential equations (including various growth models).

 

The learner will be able to approximation methods to evaluate integrals.

 

The learner will be able to use integration by parts and partial factions to evaluate integrals.

 

The learner will be able to evaluate improper integrals.

 

  

 

 

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Polynomial Approximation and Series

 

The Learner will be able to understand the concept of a series including the convergence or divergence of an infinite series.

 

The learner will be able to use tests to determine the interval of convergence of a series.

 

The learner will be able to develop Taylor series and approximations.

 

The learner will be able to know and use the Taylor series of all basic functions.

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