Pocatello/Chubbuck School District
INSTRUCTIONAL BIG IDEAS OF ESSENTIAL LEARNING
ADVANCED PLACEMENT CALCULUS
The Big Ideas of Essential Learning were identified to guide the content of common assessments and the work
of PLCs.
1. Derivative as a function
 Relationship between the increasing and decreasing behavior of f and the sign of f’
 The MVT and its geometric consequences
2. Second Derivatives
 Corresponding characteristics of graphs of f, f’, f”
 Points of inflection
 Relationship of the concavity of f and the sign of f”
 POI as places where concavity Changes
3. Applications of the derivative
 Analysis of curves, including the notions of monotonicity and concavity
 Optimization, both absolute and relative extrema
 Modeling rates of change, including related rates problems
4. Interpretations and properties of definite integrals
o Definite integral as a limit of Riemann sums
o Definite integral of the rate of change of a quantity over an interval interpreted as the change of the
quantity over the closed interval of [a,b]
o Basic properties of definite integrals
o Use of Riemann sums and trapezoidal sums to approximate definite integrals of functions
5. Fundamental Theorem of Calculus
o Use of FTC to evaluate integrals
o Use of FTC to represent a particular antiderivative analytically and graphically (slope fields)
6. Applications of integrals
o Area, Volume, infinite sums, distance, speed, velocity, business properties
o Finding specific antiderivatives using intial conditions including applications to motion along a line
o Solving separable differentiable equations and using them to model exponential growth and decay
o Solving logistic differential equations
7. Techniques of antidifferentiation
o Antiderivatives following directly from derivative rules
o Antiderivatives by substitution
o Antiderivatives by parts
Revised December 2008
1
Pocatello/Chubbuck School District
Math Instructional Calendar
Advanced Placement Calculus – Standards correlated with the Acorn Book*
1st Trimester
Textbook Resource: Calculus: Graphical, Numerical, Algebraic
by Finney Demana Waits and Kennedy 3rd Edition
STANDARD
Derivative as a function
Second Derivatives
CURRICULUM OBJECTIVES
*The student will: understand the relationship between
the f and the sign of f  , understand the MVT and its
geometric consequences
The student will: understand the corresponding
characteristics of the graphs of f , f , f  , find the
POI, understand the relationship of concavity to
RESOURCES/ACORN BOOK
4.1, 4.2
4.3
f 
Applications of the Derivative
The student will: understand the notion of monotonicity
and concavity, be able to optimize a function, model
rates of change (including relative rates of change)
4.1-4.6
Interpretations and properties of
definite integrals
The student will: find the definite integral a a limit of
Riemann sums, understand the integral over a specific
interval, understand the basic properties of integrals, use
Riemann sums and Trapezoidal sums to approximate
definite integrals
5.1-5.3, 5.5
Advanced Placement Calculus – Standards correlated with the Acorn Book*
2nd Trimester
STANDARD
Fundamental Theorem of Calculus
Applications of Integrals
Techniques of antidifferentiation
CURRICULUM OBJECTIVES
*The student will: use the FTC to evaluate integrals, use
the FTC to represent a particular antiderivative
analytically and graphically
The student will: calculate area, volume, infinite sums,
distance, speed, velocity, business properties, Find
specific antiderivatives using initial conditions including
applications to motion along a line, solve separable
differentiable equations and use them to model
exponential growth, solve logistic differential equations
The student will: be able to find the antiderivative
directly from derivative rules, substitution and parts
RESOURCES/ACORN BOOK
5.4, 6.1
6.4, 6.5, 7.1-7.3
6.2, 6.3
Advanced Placement Calculus – Standards correlated with the Acorn Book*
3rd Trimester
STANDARD
AP Exam Prep
CURRICULUM OBJECTIVES
*The student will: successfully prepare for all topics
included in the previous two trimesters
Revised December 2008
RESOURCES/ACORN BOOK
D&S practice exams and APcentral.com
2