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Muncy Junior-Senior High School
Mathematics Department
Course Number/Name: 468 Advanced Placement Calculus BC
Instructor: Mr. Smith
Meeting Times: Period 6
Meeting Locations: Room 260
Prerequisite Course: Advanced Placement Calculus AB
Phone Number: 546-3127 ext. 3000
Email: gsmith@muncysd.org
2017 Advanced Placement Calculus BC Exam
Tuesday, May 9, 2017
Morning Testing Session (8 a.m.)
Course Overview
Advanced Placement Calculus BC is a continuation of the Advanced Placement Calculus AB
course. AP Calculus BC is roughly equivalent to both first and second semester college calculus
courses and extends the content learned in AB to different types of equations and introduces the
topic of sequences and series. The AP course covers topics in differential and integral calculus,
including concepts and skills of limits, derivatives, definite integrals, the Fundamental Theorem
of Calculus, and series. The course teaches students to approach calculus concepts and problems
when they are represented graphically, numerically, analytically, and verbally, and to make
connections amongst these representations. Students learn how to use technology to help solve
problems, experiment, interpret results, and support conclusions.
Assessment Overview
The AP Calculus BC Exam questions measure students’ understanding of the concepts of
calculus, their ability to apply these concepts, and their ability to make connections among
graphical, numerical, analytical, and verbal representations of mathematics. Adequate
preparation for the exam also includes a strong foundation in algebra, geometry, trigonometry,
and elementary functions, though the course necessarily focuses on differential and integral
calculus. Students may not take both the Calculus AB and Calculus BC Exams within the
same year. A Calculus AB sub-score is reported based on performance on the portion of the
Calculus BC Exam devoted to Calculus AB topics.
The free-response section tests students’ ability to solve problems using an extended chain of
reasoning. During the second timed portion of the free-response section (Part B), students are
permitted to continue work on problems in Part A, but they are not permitted to use a calculator
during this time.
All students enrolled in this course are expected to take the AP Calculus BC Exam at their own
expense. Failure to take the AP Exam will result in no class weight being awarded (for class
ranking purposes) and will also result in the student taking a comprehensive final exam, if
applicable. Students earning a score of 3 or higher on the AP Calculus BC Exam will have their
exam fee reimbursed by the school district.
Primary Textbook th
Larson, Ron and Bruce H. Edwards. Calculus of a Single Variable, AP Edition, 10 Edition.
Brooks/Cole, Cengage Learning. 2014.
Supplemental Textbooks nd
Rogawski, Jon and Ray Cannon. Rogawski’s Calculus for AP, Early Transcendentals, 2
Edition. W.H. Freeman and Company. 2012.2015.
Rogawski, Jon and Colin Adams. Calculus, 3rd Edition. W.H. Freeman and Company.
Best, George, Stephen Carter and Douglas Crabtree. Calculus: Concepts and Calculators, 2nd
Edition. Venture Publishing. 2006.
Additional Resources
Curriculum Modules and Special Focus materials from The College Board.
Graphing Calculators
Students will be required to use a graphing calculator throughout the course. Students will be
provided with a TI-84 Plus graphing calculator and/or a TI-89 Titanium graphing calculator. For
in-class demonstration, TI Smartview will be used with the TI-84 Plus and TI-Presenter will be
used to project the TI-89 Titanium.
Course Goals
Students who are enrolled in AP Calculus BC are expected to
Work with functions represented in multiple ways: graphical, numerical, analytical, or
verbal. They should understand the connections among these representations.
Understand the meaning of the derivative in terms of a rate of change and local linear
approximation and use derivatives to solve problems.
Understand the meaning of the definite integral as a limit of Riemann sums and as the net
accumulation of change and use integrals to solve problems.
Understand the relationship between the derivative and the definite integral as expressed
in both parts of the Fundamental Theorem of Calculus.
Communicate mathematics and explain solutions to problems verbally and in writing.
Model a written description of a physical situation with a function, a differential
equation, or an integral.
Use technology to solve problems, experiment, interpret results, and support conclusions.
Determine the reasonableness of solutions, including sign, size, relative accuracy, and
units of measurement.
Develop an appreciation of calculus as a coherent body of knowledge and as a human
accomplishment.
Content Outline
The outline that follows is structured around the Enduring Understandings within the four big
ideas that are described in the AP Calculus Course and Exam Description:
Big Idea 1: Limits
Big Idea 2: Derivatives
Big Idea 3: Integrals and The Fundamental Theorem of Calculus
Big Idea 4: Series (BC only)
Many of the Enduring Understandings from the first three Big Ideas were covered in our AB
course, but there are additional EUs added to those ideas for the BC course.
Unit 1 Review of AP Calculus AB
While review of all AB topics will be ongoing through Bell Ringers, Bell Ringer Quizzes, and
items included on assessments throughout the year, the course will begin with a review unit. The
maximum time that will be allotted for this unit will be 20 class periods.
I. Limits and Continuity
A. Finding Limits Graphically and Numerically
B. Finding Limits Analytically
C. Limits and Infinity and Infinity Limits
D. Continuity at a Point
E. Intermediate Value Theorem
II. Differentiation
A. Limit Definition of Derivative
B. Average and Instantaneous Rates of Change (e.g., velocity, acceleration, distance
traveled, displacement)
C. Basic Differentiation Rules
D. Product and Quotient Rules
E. Trigonometric Functions
F. The Chain Rule
G. Implicit Differentiation
H. Inverse Functions
I. Exponential and Logarithmic Functions
J. Logarithmic Differentiation
K. Inverse Trigonometric Functions
III. Applications of Derivatives
A. Related Rates
B. Extreme Value Theorem and Extrema on a Closed Interval
C. The Mean Value Theorem and Rolle’s Theorem
D. Increasing and Decreasing and the First Derivative Test
E. Concavity and the Second Derivative Test
F. Curve Sketching
G. Optimization
H. Newton’s Method
I. Linearization and Differentials
IV. Integration
A. Antiderivatives and Indefinite Integrals (all formulas)
B. Rectangle Approximation Methods and Area
C. Riemann Sums and Definite Integrals
D. The Fundamental Theorem of Calculus
E. Mean Value Theorem for Integrals and Average Value of a Function
F. Net Change Theorem (including distance and displacement revisited)
G. Integration by Substitution
H. Trapezoidal Approximations
V. Applications of Integration
A. Area Under a Continuous Non-negative Curve
B. Area Between Two Curves
C. Volume of Solid with Known Cross-Sections
D. Volume: Disk Method
E. Volume: Washer Method
F. Slope Fields and Separable Differential Equations
Review exercises and examples will consist of selected textbook exercises, released AP Calculus
AB Exams, worksheets and other materials found online and teacher-prepared materials. The last
review topic – slope fields and separable differential equations – will lead into the content of this
course that will be new.
Unit 2 (Chapter 6) Differential Equations
I. Slope Fields and Euler’s Method
II. Differential Equations: Growth and Decay
III. Separation of Variables and the Logistic Equation
IV. First-Order Linear Differential Equations
Unit 3 (Chapter 7) Additional Applications of Integration
I. Volume: Shells
II. Arc Length and Surfaces of Revolution
III. Work
IV. Moments, Centers of Mass and Centroids
V. Fluid Pressure and Fluid Force
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