Semester 1
Unit P: Preparation for Calculus (2 weeks)
 Graphs and models
 Linear models and rates of change
 Review of trigonometric functions
 Functions and their graphs
 Inverse functions
 Exponential and logarithmic functions
Unit One: Limits and Their Properties (2.5 weeks)
 Find limits graphically and numerically
 Evaluate limits analytically
 Continuity and onesided limits
 Intermediate Value Theorem
 Infinite limits and vertical asymptotes
 Limits at Infinity (horizontal asymptotes)
Unit Two: Differentiation (34 weeks)
 The derivative and the tangent line problem
 Differentiability and continuity
 Basic differentiation rules and rates of change (average and instantaneous)
 Product and Quotient Rules and higher order derivatives
 The Chain Rule
 Implicit differentiation
 Derivatives of inverse functions
 Related Rates
 Newton's Method
2nd Quarter
Unit Three: Applications of Differentiation (45 weeks)
 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
 Summary of curve sketching (including monotonicity)
 Optimization problems / business problems
 Differentials
 Local linear approximations
Unit Four: Introduction to Integral Calculus (3.5 weeks)
 Antiderivatives and indefinite integration
 Differential equations
 Position, velocity, acceleration problems
 Riemann sums (including left, right, and midpoint evaluation points)
 Definite integrals solved using geometric formulas
 Properties of definite integrals
 Trapezoidal Rule
 The Fundamental Theorem of Calculus
 Average value of a function
 Second Fundamental Theorem of Calculus
 Integration using usubstitution
 Displacement and definite integrals
 The natural logarithmic function: Integration
 Inverse trigonometric functions: 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.
Semester 2
MidYear Review: This is a timeout spent reviewing derivatives, applications of derivatives and integrals. (2 weeks)
Unit Five: Differential Equations (2 weeks)
 Differential equations: slope fields
 Differential equations: growth and decay
 Differential equations: separation of variables
Unit Six: Applications of Integration (23 weeks)
 Area of a region between two curves
 Volume: disk method
 Volume: washer method
 Volume: known crosssections
 Position, velocity, and acceleration
 Net accumulation
Unit Seven: Integration Techniques (1 week)
 Basic integration rules
 L'Hopital's Rule
4th Quarter
AP Exam Preparation (5 to 6 weeks)
 Mark Howell’s Be Prepared for the AP Calculus Exam
 1998, 2003 and 2008 Released AP Exams
 2013 to 2018 Audit Practice AP Exams
Final Exam: The final exam is in the form of a past AP exam that tests the students’ abilities to connect concepts graphically, analytically, numerically, and verbally. (1 week)
Texts Required: Enhanced Web Assign with Calculus for AP 1st Edition eBook by Ron Larson, Paul Battaglia (2017) (available in midAugust through www.WebAssign.com for $35.00)
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, 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) Calculu for AP 1st Edition Printed Version by Ron Larson, Paul Battaglia (2017) ISBN13: 9781305674912.
Be Prepared for the AP Calculus Exam Third Edition by Mark Howell and Martha Montgomery Copyright © May, 2016 by Skylight Publishing ISBN 9780997252859.
