Franklin County Community School Corporation - Brookville, Indiana

Curriculum Map

Course Title: AP Calculus / Quarter: 4 / Academic Year: 2012-2013

Essential Questions for this Quarter:

1.  What calculus methods can be applied to inverse functions?
2.  How are differential equations applied to real-life situations?
3.  How can integration be applied to finding volumes of rotated solids?
4.  How can integration be used to solve applications such as work problems, arc length, and centers of mass?
5.  How can calculus be applied to solve problems involving growth and decay?
Unit/Time Frame / Standards / Content / Skills / Assessment / Resources
Chapter 5 (continued):
Logarithmic, Exponential, and Other Transcendental Functions
5.6 Inverse Trig Functions: Differentiation
5.7 Inverse Trig Functions: Integration
5.8 Hyperbolic Functions (if time)
Chapter 6:
Differential Equations
6.1 Slope Fields & Euler’s Method
6.2 Growth & Decay
6.3 Separation of Variables and the Logistic Function
6.4 1st Order Linear Differential Equations (if time)
Chapter 7:
Applications of Integration
7.1 Area Between Curves
7.2 Disk Method
7.3 Shell Method
7.4 Arc Length
7.5 Work
7.6 Moments, Centers of Mass, and Centroids
Chapter 8:
Miscellaneous Topics (if time)
8.2 Integration by Parts
8.5 Partial Fractions
8.7 L’Hopital’s Rule / State Standards
MA.C.1.7 2000
MA.C.1.8 2000
MA.C.4.4 2000
MA.C.4.5 2000
MA.C.4.6 2000
MA.C.5.1 thru 5.7 2000
Standards for Mathematical Practice
SMP 1-8 / Manipulating Inverse Functions
Solving and Applying Differential Equations
Finding Areas Between Curves
Finding Volumes of Rotated Solids
Finding Arc Length
Solving Work Problems
Using Integration by Parts and Partial Fractions to Solve Appropriate Integrals
Applying L’Hopital’s Rule to Limits in Appropriate Forms / ·  To differentiate and integrate inverse trig functions
·  To review basic differentiation formulas
·  To complete the square to integrate inverse trig functions
·  To develop properties of hyperbolic functions
·  To integrate and differentiate hyperbolic functions
·  To use initial conditions to find particular solutions to differential equations
·  To analyze slope fields to estimate solutions to differential equations
·  To use Euler’s Method to approximate differential equation solutions
·  To use separation of variables to solve simple differential equations
·  To use exponential functions to model growth and decay
·  To recognize and solve separation of variable differential equations
·  To recognize and solve homogeneous differential equations
·  To employ differential equations in applications and as they relate to the logistic function
·  To solve and apply 1st order linear differential equations
·  To use integration to find the area between curves
·  To use the disk and shell methods to find volumes of rotated solids
·  To find arc length using integration
·  To find work done by a constant and variable force
·  To apply properties of mass in 1- and 2- dimensional systems
·  To use integration by parts to find difficult integrals
·  To use partial fractions to decompose integrals
·  To apply L’Hopital’s Rule to applicable limits / Textbook Assignments
Worksheet Assignments
Notebooks
Quizzes
Tests
Oral Responses
Observations
Advanced Placement Test / Textbook
Houghton-
Mifflin
Calculus w/
Analytic Geometry,
8th Edition by Larson, Hostetler, and Edwards
Textbook
Brooks-Cole
Calculus, 6th Edition by Earl Swokowski
Texas-Instrument TI-80 series Graphing Calculators
Sample AP Question Worksheets
AP Central Website
Nettrekker© Presentations

Franklin County Community School Corporation - Brookville, Indiana

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