Franklin County Community School Corporation - Brookville, Indiana
Curriculum Map
Course Title: AP Calculus
Quarter: 1
Academic Year: 2012-2013
Essential Questions for this Quarter:
1.
2.
3.
4.
5.
What Pre-Calculus skills are required to be successful in this course?
How does solving limits relate to graphic behavior of functions?
How do limits provide the groundwork for differentiation?
How can the use of a graphing calculator clarify and expedite solutions to limits and derivatives at a point?
How can differentiation be used to model real world situations?
Unit/Time Frame
Chapter 1:
Limits & Their
Properties
P.3 Functions &
Graphs
1.1 Intuitive
Groundwork for
Calculus
1.2 Finding Limits
Numerically and
Graphically
1.3 Finding Limits
Analytically
1.4 Continuity & 1sided Limits
1.5 Infinite Limits
Chapter 2:
Differentiation
2.1 Tangents &
Derivatives
2.2 Basic
Differentiation Rules &
Rates of Change
2.3 Product & Quotient
Rules, Plus Higher
Derivatives
2.4 The Chain Rule
Standards
State
Standards
MA.C.1.1 thru
1.13 2000
MA.C.2.1 thru 2.6
2000
MA.C.2.8 2000
MA.C.2.10 2000
MA.C.3.1 2000
Standards for
Mathematical
Practice
SMP 1-8
Content
Definitions of Limits &
Derivatives
Skills


Finding Limits
Finding Derivatives
Continuity & Graphing of
Functions
Related Rates









To find domains and ranges of
functions
To establish relationship
between calculus and other
areas of math
To establish & apply the
definition of a limit
To find limits graphically,
analytically, and numerically
To find limits with special
functions such as absolute
value, greatest integer, and trig
functions
To recognize and find various
types of discontinuities
To assimilate asymptotes with
infinite limits
To define a derivative in terms
of a limit
To associate the derivative
with its primary applications of
slope of a tangent and rate of
change
To apply rules of differentiation
and algebraically simplify
results
To use product & quotient
Assessment
Textbook
Assignments
Worksheet
Assignments
Notebooks
Quizzes
Tests
Oral Responses
Observations
Resources
Textbook
HoughtonMifflin
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
Franklin County Community School Corporation - Brookville, Indiana
Curriculum Map
Course Title: AP Calculus
Quarter: 1
Academic Year: 2012-2013
Essential Questions for this Quarter:
1.
2.
3.
4.
5.
What Pre-Calculus skills are required to be successful in this course?
How does solving limits relate to graphic behavior of functions?
How do limits provide the groundwork for differentiation?
How can the use of a graphing calculator clarify and expedite solutions to limits and derivatives at a point?
How can differentiation be used to model real world situations?
Unit/Time Frame
2.5 Implicit
Differentiation
2.6 Related Rates
Standards
Content
Skills









rules to solve derivatives
To manually calculate higher
order derivatives
To apply the chain rule to
solving difficult derivatives
To recognize the difference
between explicit & implicit
differentiation
To calculate derivatives in an
implicit manner
To use the graphing calculator
to examine behaviors of
functions and their derivatives
To use the graphing calculator
to find a derivative at a specific
point
To determine the slope and
equation of a tangent line at a
point
To determine the velocity
using derivatives
To use implicit differentiation to
solve related rates problems
Assessment
Resources
Nettrekker©
Presentations
Franklin County Community School Corporation - Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS