ARS Mathematica Online                                                    AP Calculus AB
                                            AP Calculus AB Course Outline



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 one-sided limits
  • Intermediate Value Theorem
  • Infinite limits and vertical asymptotes
  • Limits at Infinity (horizontal asymptotes)

Unit Two:  Differentiation (3-4 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 (4-5 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 u-substitution
  • 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

Mid-Year Review: This is a time-out 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 (2-3 weeks)

  • Area of a region between two curves
  • Volume:  disk method
  • Volume:  washer method
  • Volume:  known cross-sections
  • 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 mid-August through 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) ISBN-13: 9781305674912.

Be Prepared for the AP Calculus Exam Third Edition by Mark Howell and Martha Montgomery Copyright © May, 2016 by Skylight Publishing ISBN 978-0-9972528-5-9.


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