AP Calculus BC Syllabus 
       Course Overview 
        
       AP Calculus BC is the study of the topics covered in college-level Calculus I and Calculus II. This 
       course includes instruction and student assignments on all of the topics as listed in the AP 
       Course Description: “Topic Outline for Calculus AB”. AP Calculus BC is primarily concerned with 
       developing the students’ understanding of the concepts of Calculus and providing experience 
       with its methods and applications. The course is to help students see and interpret the world 
       through the lens of integral and differential calculus. To that end, a focus is placed on providing 
       a strong conceptual foundation including the concepts of a limit, a derivative and an integral. 
       With  a  strong  foundation  and  extensive  practice  with  applications  and  problems,  students 
       become prepared for the AP Calculus Exam as well as additional coursework in Calculus. 
        
       Rule of Four 
        
       The course emphasizes an approach to Calculus, with concepts, results, and problems being 
       expressed  geometrically,  numerically,  analytically,  and  verbally.  This  course  gives  equal 
       emphasis to all four methods of representing functions and their rates of change.  Students are 
       encouraged to be open-minded when approaching problems and to keep the “Rule of Four” in 
       mind.  Whenever  possible,  concepts  are  developed  and  applied  using  all  of  these 
       representations.  Additionally,  emphasis  is  placed  upon  the  connections  among  the 
       representations. Technology is used regularly by students to reinforce the relationships among 
       the  multiple  representations  of  functions,  to  confirm  written  work,  to  implement 
       experimentation, and to assist in interpreting results. Through the use of the unifying themes of 
       derivatives,  integrals,  limits,  approximations  and  applications  and  modeling,  the  course 
       becomes a cohesive whole, rather than a collection of unrelated topics. 
        
       Assessment 
        
       With each lesson, problems and exercises are assigned from WebWork (homework system) as 
       well as the textbook. Released AP questions are used throughout the course as assessment 
       items, homework and launching points for discussion. Students solve both calculator active and 
       non-calculator problems, and they are required to provide appropriate written presentation of 
       solutions, similar to the requirements of the Free Response section of the AP Calculus Exam. 
       Written justification of calculator solutions are taught and learned so that there is a clear and 
       logical link leading from the mathematics to the technology and then supporting the result. 
       Explaining the  “why” is  stressed  as much as the “how.”  Examinations are designed to be 
       experiences  that  allow  students  to  make  connections  beyond  merely  learning  procedures. 
       Students are required to maintain a Calculus notebook to summarize their learning and provide 
       a valuable resource for preparing for the AP exam. 
        
       AP Calculus BC Syllabus                 Page 1 
        
       Calculus Classroom Team 
        
       In order to facilitate student learning and ownership of content, the students are placed into 
       teams. The typical class begins each day with students articulating previously covered topics 
       and  discussing  homework  assignments  within  their  respective  team  and  in  whole-class 
       discussion.    Homework  assignments  are  designed  to  reinforce  new  topics  covered.    The 
       emphasis for the class is discussion among team partners and fellow teams as opposed to a 
       more traditional direct-lesson approach.  Students are expected to take an active part in daily 
       discussions and activities. 
        
       Technology 
        
       Instruction will be given using primarily the TI-83/84. This graphing calculator will be used daily 
       in the class. The chapter tests are divided in two parts: one without the use of any calculator 
       and the other part requiring the use of a graphing calculator. The graphing calculator allows the 
       student to support their work graphically, and to make conjectures regarding the behavior of 
       functions, limits, and other topics. This allows students to view problems in a variety of ways. 
       The most basic skills on the calculator: graphing a function with an appropriate window, finding 
       roots  and  points  of  intersection,  finding  numerical  derivatives  and  approximating  definite 
       integrals, are mastered by all students. Students have their own calculator and programs, such 
       as Riemann sums, slope fields, and Newton’s method, to name a few. The homework delivery 
       system of WebWork will provide a bulk of the practice and grading of the daily exercises. This 
       system  provides  instant  feedback  on  correctness.  Key  Curriculum’s  SketchPad  program 
       “Calculus in Motion”, web based “Visual Calculus”, and “Winplot” graphing utility (for student 
       presentations) are also incorporated.   
        
       Principle Classroom Text 
        
       Ron Larson & Bruce Edwards; Calculus with Early Transcendental Functions 6E.  Cengage 
       Learning 
       AP Calculus BC Syllabus                 Page 2 
        
                 Course Outline  
                  
                                                              st
                                                            1  Semester 
                    Unit 1                     •   Functions as models of change 
                    A Library of                       o  Representing functions using the “Rule of Four” 
                    Functions                          o  Domain & range, increasing & decreasing, even & odd, 
                    (13 days)                              concavity of graphs, zeros, end behavior, asymptotic 
                                                           behavior graphically and in terms of limits involving 
                    (Unit tests for all                    infinity 
                    units are included         •   Linear functions 
                    in days indicated.)                o  Slope as a rate of change 
                                               •   Exponential functions 
                                                       o  Applications 
                                               •   Logarithmic functions 
                                               •   Trigonometric functions 
                                               •   Power functions, polynomials and rational functions 
                                               •   Transformation of functions (calculator activity) 
                                                       o  Inverse functions 
                                                       o  Composition of functions 
                                                       o  Shifts, stretches, compressions 
                                               •   Working with functions in verbal, graphical, algebraic and 
                                                   tabular depictions 
                                               •   Comparing behavior of functions and dominance (calculator 
                                                   activity) 
                                                       o  Local and global behavior of functions 
                                                       o  Comparing relative magnitudes and their rates of 
                                                           change 
                                               •   Introduction to the concept of continuity 
                                                       o  Intuitive meaning 
                                                       o  Graphical interpretation 
                                                       o  Numerical interpretation 
                                                       o  Intermediate Value Theorem 
                                               •   Calculator Refresher (activity) 
                                                       o  Plotting graphs, finding roots, window manipulation, 
                                                           finding values of functions, using tables, “lies my 
                                                           calculator told me,” dangers of intermediate rounding 
                  
                    Unit 2                          •   Development of the derivative of a function at a point 
                    The Derivative                      using the derivation of instantaneous speed from average 
                    (10 days)                           speed 
                                                            o  Introduction of the concept of instantaneous rate 
                                                                 of change of a function at a point as the slope of 
                                                                 the curve of the graph of the function at that point 
                 AP Calculus BC Syllabus            •   Introduction to limits                                      Page 3 
                  
                                                            o  Intuitive concept of the limiting process 
                                                            o  Calculating limits from numerical data 
                                                            o  Calculating limits using algebra 
                                                            o  Calculating limits from graphs of functions 
                                                            o  Formal definition of limit 
                                                            o  Properties of limits 
                                                            o  One- and two-sided limits 
                                                            o  Proving limits exist 
                                                            o  Limits at infinity and end behavior 
                                                    •   Concept of the derivative 
                                                            o  Instantaneous rate of change from average rate of 
                                                                 change 
                                                            o  Definition of the derivative as the limit of the 
                                                                 difference quotient – analytical depiction 
                                                            o  Graphical depiction of limiting process – secant line 
                                                                 to tangent line 
                                                            o  Determining the derivative of a function 
                                                                 numerically 
                                                            o  Left- and right-hand derivatives and proving 
                                                                 differentiability 
                                                    •   Derivative of a function at a point 
                                                            o  Slope of tangent line to graph of a function at a 
                                                                 point including cases where there are vertical or 
                                                                 infinitely many tangents 
                                                            o  Slope of curve at a point 
                                                            o  Approximating rates of change of functions from 
                                                                 graphs and tables of data 
                                                            o  Finding derivatives of a function at a point using 
                                                                 calculators 
                                                    •   The derivative function 
                                                            o  Definition of first and second derivative functions 
                                                            o  What derivatives tells us graphically 
                                                                     ▪   Increasing/decreasing behavior, concavity 
                                                                         (signs of f’ and f”), inflection points 
                                                            o  What derivatives tell us about rates of change 
                                                            o  Working with derivative functions graphically, 
                                                                 analytically, verbally and numerically 
                                                                     ▪   Understanding the corresponding 
                                                                         characteristics between the graphs of f, f’ 
                                                                         and f” 
                                                    •   Interpreting the derivative 
                                                            o  Leibniz notation 
                                                            o  Dimension analysis 
                                                            o  Equations of motion 
                                                            o  As rates of change in various applications 
                 AP Calculus BC Syllabus                    o  Interpreting equations involving derivatives         Page 4