Special Focus: by the College Board (pdf - 129 pages) - explains the FTC and includes previous AP questions
Curriculum Module: by the College Board (pdf - 27 pages) - includes lesson plans with solutions and teacher notes
This unit basically defines integral functions and then we take the derivative of integral functions (with their applications). What allows us to take the derivative of integral functions is the Fundamental Theorem of Calculus (the antiderivative part).
Functions defined by integrals
Curriculum Module: Functions defined by Integrals - by the College Board (pdf - 19 pages) - includes handouts and worksheets
1) Definition of Integral Functions
Explanation
2) Derivative of Integral Functions
Explanation
Practice Problems:
3) Application of the Derivative of Integral Functions (Given an Explicit Integral Function Equation
Explanation:
Practice Problems:
4) Application of the Derivative Integral Functions Given the Graph of the Integrand
Explanation:
Practice Problems - Given an integral function and the graph of the integrand
2009 (Form B) Q3 - part D
5) Net change from a known value (find the value of a function given the derivative of the function and a particular solution):
Explanation:
Curriculum Module by the College Board (pdf - 30 pages)
Practice Problems:
AP Questions (remember on questions #1-3 calculators are allowed; on questions #4-6, no calculators are allowed):
2011 Q1 - Given v(t) explicitly: Khan video: part a | part b, c, and d
2010 (Form B) Q1 - Given v(t) as a graph
2009 (Form B) Q6 - Given v(t) as a table
2009 Q1 - Given v(t) as a table & equation
2008 (Form B) Q3 - Given v(t) as a graph
2008 Q1 - Given v(t) as a graph
2007 (Form B) Q2 - Given v(t) as a graph & equation
2006 (Form B) Q6 - Given v(t) and a(t) as a table
2006 Q4 - Given v(t) as a table
2005 (Form B) Q3 - Given v(t) as an equation
2005 Q5 - Given v(t) as a graph
2004 (Form B) Q3 - Given v(t) as a graph & equation
2004 Q3 - Given v(t) as an equation
2003 (Form B) Q4 -Given v(t) as an equation
2003 Q2 - Given v(t) as an equation
2002 (Form B) Q3 - Given v(t) as an equation
2002 Q3 - Given v(t) as an equation
2001 Q3 - Given a(t) as an equation
2000 Q2 - Given v(t) as a graph and as an equation
1999 Q1 - Given v(t) as an equation
1998 Q3 - Given v(t) as an equation and as a table
7) Net Change Word Problems
Explanation:
Practice Problems:
AP Questions
8) Fundamental Theorem of Calculus Review
9) Cumulative Review