Semester 1
P. Preparation for Calculus (.5 weeks)
 Inverse Functions
 Exponential and Logarithmic Functions
I. Limits and Their Properties (2 weeks)
 An intuitive understanding of the limiting process
 Find limits graphically and numerically
 Evaluate limits analytically
 An intuitive understanding of continuity
 Continuity and onesided limits
 Intermediate Value Theorem
 Infinite limits and vertical asymptotes
 Limits at Infinity and horizontal asymptotes
II. Differentiation (23 weeks)
 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
 Derivatives of Inverse Functions
 Implicit differentiation
 Related Rates
 Newton's Method
III. Applications of Differentiation (3 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 and business problems
 Differentials
 Linear (or tangent line) approximations
2nd Quarter
IV. Introduction to Integral Calculus (3 weeks)
 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 usubstitution
 Numerical Integration and Trapezoidal Approximation
 The natural logarithmic Function: Integration
 Inverse Trigonometric Functions: Integration
V. Differential Equations (2 weeks)
 Differential equations: Slope fields and Euler’s Method
 Differential equations: Growth and decay
 Differential equations: Separation of variables
 The Logistic Equation
VI. Applications of Integration (2 weeks)
 Position, Velocity and Acceleration Functions
 Net Change and Accumulation
 Area of a region between two curves
 Volume: Disk method
 Volume: Washer method
 Volume: Known crosssections
 Arc Length
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
VII. Integration Techniques (23 weeks)
 Basic integration techniques
 Integration by parts
 Partial fractions
 Indeterminate forms and L’Hôpital’s Rule
 Improper integrals
VIII. Infinite Series (5 weeks)
 Sequences
 Series and convergence
 The Integral Test and pSeries
 Comparison of series
 Alternating series
 The Ratio and Root Tests
 Taylor Polynomials and Approximations
 Power series
 Representation of functions by power series
 Taylor and Maclaurin Series
 Lagrange Error Bound
IX. Parametric Equations, Polar Coordinates and Vectors (3 weeks)
 Plane curves and parametric equations
 Parametric equations and calculus
 Polar coordinates and polar graphs
 Area and Arc Length in polar coordinates
 Vectors in a plane
 Vectorvalued functions
 Differentiation and integration of vectorvalued functions
 Velocity and acceleration
4th Quarter
X. AP Exam Preparation (3 weeks)
 Mark Howell’s Be Prepared for the AP Calculus Exam
 1997, 1998, 2003, 2008 and 2012 Released AP Exams
 2013 to 2017 Audit AP Practice 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, 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) 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.
