AP CALCULUS AB COURSE OUTLINE
Semester I
1st Quarter
Unit P: Pre-Calculus Review (1 week)
 Linear Models and Rates of Change
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Trigonometric Functions
Functions and Their Graphs
Unit One: Limits and Their Properties (2 weeks)
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Find limits graphically and numerically
Evaluate limits analytically
Continuity and one-sided limits
Intermediate Value Theorem
Infinite limits and vertical asymptotes
Unit Two: Differentiation (3-4 weeks)
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The derivative and the tangent line problem
Differentiability and continuity concepts
Basic differentiation rules and rates of change (average and instantaneous)
Product and Quotient Rules and Higher Order derivatives
The Chain Rule
Implicit differentiation
Related Rates
Unit Three: Applications of Differentiation (4-5 weeks)
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Extrema on an interval
Rolle’s Theorem and the Mean Value Theorem
Increasing and decreasing functions
The First Derivative Test
Concavity and points of inflection
The Second Derivative Test
Limits at Infinity (horizontal asymptotes)
Summary of Curve Sketching (including monotonicity)
Optimization problems / Business problems
Newton’s Method
Differentials
Local linear approximations
2nd Quarter
Unit Four: Introduction to Integral Calculus (3 weeks)
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Antiderivatives and indefinite integration
Sigma Notation and concept of Area as the limit of a sum
Riemann sums (including left, right, and midpoint evaluation points)
Definite integrals: Properties and Solutions
The Fundamental Theorem of Calculus
The Mean Value Theorem for Integrals and Average value of a function
The Second Fundamental Theorem of Calculus
The Net Change Theorem
Integration using u-substitution
Numerical Integration and Trapezoidal Approximation
Unit Five: Transcendental Functions (4 weeks)
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The Natural Logarithmic Function and Differentiation
The Natural Logarithmic Function and Integration
Inverse Functions
Exponential Functions: Differentiation and Integration
Bases other than e and applications
Inverse trigonometric functions and Differentiation
Inverse trigonometric functions and Integration
Midterm Exam: The midterm exam includes problems from past AP exams that test the
students’ abilities to connect concepts graphically, analytically, numerically, and verbally.
Mid-Year Review: This is a time-out spent reviewing derivatives, applications of
derivatives and integrals. (1-2 weeks)
Semester II
3rd Quarter
Unit Six: Differential Equations (1.5 weeks)
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Differential equations: Slope fields
Differential equations: Growth and decay
Differential equations: Separation of variables
Unit Seven: Applications of Integration (2.5 weeks)
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Area of a region between two curves
Volume: Disk method
Volume: Washer method
Volume: Known cross-sections
Net Change and Accumulation
Position, Velocity and Acceleration Functions
Unit Eight: Integration Techniques (1 week)
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Basic Integration Rules
4th Quarter
AP Exam Preparation (5 weeks)
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Mark Howell’s Be Prepared for the AP Calculus Exam
1998, 2003 and 2008 AP Exams
2005 to 2013 Free Response Questions
Final Exam: The final exam includes problems from past AP exams that test the
students’ abilities to connect concepts graphically, analytically, numerically, and verbally.
(1 week)
Texts Required: Enhanced Web Assign with Calculus 10th Edition eBook by Ron Larson,
Bruce Edwards (2014) (available in mid-August through www.WebAssign.com for $61.25)
Enhanced Web Assign helps you develop a deeper conceptual understanding of your
subject matter and complete required online homework assignments. With Enhanced
Web Assign, you receive access to a Premium eBook along with immediate feedback and
tutorial content, which will include Watch It Videos, Animations, Practice It Questions,
Master It Tutorials, Read It Text passages, and a Personal Study Plan to aid in the mastery
of your course materials.
(Also available but not necessary) Calculus of a Single Variable 10th Edition Printed
Version by Ron Larson, Bruce Edwards (2014) ISBN13: 978-1-285-06028-6.
Be Prepared for the AP Calculus Exam Second Edition by Mark Howell and Martha
Montgomery Copyright © 2011 by Skylight Publishing ISBN 978-0-9824775-5-7. (available
through amazon.com)