AP Calculus AB
Hopkinsville High School
Brief Description of Course
Differential and Integral Calculus are the two main branches of Calculus. Differential Calculus
deals with changing quantities, while Integral Calculus deals mainly with finding sums of
infinitesimally small quantities. It is the goal of this course for all students to develop an
appreciation of Calculus and to pass the AP Calculus AB exam in the spring. To that end we will
cover all the topics that are listed on the "AP Calculus course description".
Unit Information
Unit 1: Precalculus Review (2 weeks)
Content and/or Skills Taught:
-real numbers, functions, and graphs
-linear and quadratic functins
-the basic classes of functions
-trigonometric functions
-technology: calculators and computers
Major Assignments and/or Assessments:
Rogawski’s chapter 1 review and exercises
Unit 2: Limits (3 weeks)
Content and/or Skills Taught:
-rates of change, tangent lines associated with limits
-numerical and graphical approach to limits
-basic limit laws
-limits and continuity
-evaluating limits algebraically
-trigonometric limits
-limits at infinity
-intermediate value theorem
Major Assignments and/or Assessments:
Rogawski’s chapter 2 review and exercises
Rogawski’s limit-specific AP problems
Unit 3: Differentiation (5 weeks)
Content and/or Skills Taught:
-definition of the derivative
-the derivative as a function
-product and quotient rules
-rates of change
-higher derivatives
-trigonometric functions
-the chain rule
-implicit differentiation
-related rates
Major Assignments and/or Assessments:
Rogawski’s chapter 3 review and exercises
Rogawski’s evaluating derivatives-specific AP problems
Unit 4: Applications of the Derivative (4 weeks)
Content and/or Skills Taught:
-linear approximations and applications
-extreme values
-the mean value theorem and monotonicity
-the shape of a graph
-applied optimization
-antiderivatives
Major Assignments and/or Assessments:
Rogawski’s chapter 4 review and exercises
Rogawski’s application of the derivative AP problems
Unit 5: The Integral (5 weeks)
Content and/or Skills Taught:
-approximating and computing area
-the definite integral
-fundamental theorem of calculus
-net or total change as the integral of a rate
-substitution method
-numerical integrations
Major Assignments and/or Assessments:
Rogawski’s chapter 5 review and exercises
Rogawski’s integral-specific AP problems
Unit 6: Applications of the Integral (3 weeks)
Content and/or Skills Taught:
-area between two curves
-setting u p inegrals for volume, density, and average value
-volumes of revolution
Major Assignments and/or Assessments:
Rogawski’s chapter 6 review and exercises
Rogawski’s limit application-specific AP problems
Unit 7: Exponential Functions (3 weeks)
Content and/or Skills Taught:
-derivative of f(x) = b^x and the number e
-inverse functions
-logarithms and their derivatives
-exponential growth and decay
-L’Hopital’s rule
-inverse trigonometric functions
Major Assignments and/or Assessments:
Rogawski’s chapter 7 review and exercises
Rogawski’s exponential function-specific AP problems
Unit 8: Introduction to Differential Equations (2 weeks)
Content and/or Skills Taught:
-solving differential equations
-graphical and numerical methods
Major Assignments and/or Assessments:
Rogawski’s chapter 10 review and exercises
Rogawski’s differential equation-specific AP problems
Textbook
Rogawski, Jon and Ray Cannon. Rogawski’s Calculus for AP. 2nd edition.
New York: W. H. Freeman and Company, 2012.
Other Course Materials
Material Type: Software
Description:
"Calculus in Motion" (A series of Geometer’s sketchpad presentations by Audrey Weeks,
http://www.calculusinmotin.com)
Material Type: Graphing Calculator
Description:
Graphing calculators are required. There is a classroom set of both the TI-84 and the TI-89
available.
Material Type: Other
Description:
Master Math Mentor materials (created by Stu Schwartz, www.mastermathmentor.com)
Material Type: Other
Description:
Released questions from old AP Calculus AB exams will be studied throughout the year.
Websites
URL:nmsiteachers.org
Description:
National Math and Science Institute
Additional Information
Requirement: Rule of 4
How Course Meets Requirement:
Throughout the course, students will be able to work with functions, limits, derivatives and
integrals represented graphically, numerically, analytically, or verbally. Students should
understand the connections among these representations.
Requirement: Oral explanation of solutions
How Course Meets Requirement:
Students work in groups on homework problems. Students are responsible for solving problems
on the board and explaining their thought process. Each student must present one AP-like
problem per chapter.
Requirement: Written explanations of solutions
How Course Meets Requirement:
Graded tests and homework assignments include sample free-response questions from past AP
exams where students are required to justify their solutions in well-written sentences. Students
will complete NMSI activities where they must justify their answers in complete sentences.
Students will do mathematical research on a calculus topic of their choice which is not covered
by the teacher. They will each write a report on their findings. This report will include accurate
mathematics and high quality writing.
Requirement:Graphing calculator use
How Course Meets Requirement:
Students will use graphing calculators to solve problems, experiment, interpret results and
support conclusions. Using a graphing calculator, students will be able to estimate limits,
estimate the root of a function, estimate the coordinates of the point of intersection of two
functions, perform numerical differentiation and numerical integration, determine asymptotic
behavior of a function, explore the continuity of a function, predict and find the linearization of a
function. Students will also approximate the value of an answer found analytically in order to
verify whether it seems reasonable. Students will use a graphing calculator to view the graph of a
function proposed as the answer to the problem in an appropriate viewing window and then to
check whether the answer has the desired traits.