AP Calculus BC Syllabus (Mr.Greek)
Course Overview
Calculus BC is a full year (2 semester) course. The course teaches all topics associated
with Functions, Graphs, and Limits; Derivatives; Integrals; and Polynomial
Approximations and Series as delineated in the Calculus BC Topic Outline in the AP
Calculus college board syllabus. Concepts are introduced graphically and numerically
and skills using the concepts are developed analytically and verbally. Mastery of AB
topics is a prerequisite for this class. First quarter we will review every AB calculus
topic required for the BC exam. The quarter 1 Final will be an actual released AP AB
Calculus exam and will be graded according to the AP Rubric. Ten years of AP results
shows that nearly every one of the students enrolled in my AP classes take the AP exam
and 65% to 100% of them pass(usually above 90% pass). This should provide clear
evidence that every syllabus topic is taught. The AP scores have consistently reflected
the grades students have earned in my class. That is, those with a C or better in my class
usually pass the AP exam. I thoroughly cover every College Board syllabus topic as well
as add physics and computer science applications to reinforce the subject
Marks are determined from exams (40%), quizzes (30%), homework (5%), labs (5%),
and a final exam (20%). Quizzes and homework collection will be used as start up
activities. Tests and quizzes have been designed to correlate with how well a student
should perform on the AP examination in May.
Assistance:
Assignments, some labs, tutorials, and helpful math sites will be found at my web site
http://www.laquintahs.org/apps/staff/
Instructional Materials
Primary Textbook: Larson, Hoestetler, Edwards. Calculus 6th edition. Boston, Mass.:
Houghton Mifflin.
Graphing Calculators: TI-83 or TI-83 plus or TI-89 or TI-89 titanium
Supplemental Materials: AP test preparation books, old AP exams and software
(Python,).
Course Planner
Section
Chapter 6
Topics
Applications of Integration
Volumes of Revolution: Shell Method
Arc Length and Surface of Revolution
Work
Moments, Centers of Mass and Centroids
Fluid Pressure and Fluid Force
Chapter 7
Integration Techniques, L’Hopitals Rule, Improper Integrals
Integration by Parts (physics apps include Fourier series)
Trigonometric Integrals
Trigonometric Substitution
Partial Fractions and Logistic Growth
Indeterminate Forms and L’Hopital’s Rules
Improper Integrals (physics apps include Laplace transforms to solve
ODE’s)
Chapter 8
Infinite Series
Sequences
Series and Convergence
Integral Test and p-Series
Comparison of Series
Alternating Series
Ratio and Root Test
Taylor Polynomials and Approximations
Power Series
Representation of Functions by Power Series (including generating
functions for solving simple recursion equations)
Taylor and Maclaurin Series
Chapter 9
Conics, Parametric Equations and Polar Coordinates
Conic Sections
Plane Curves and Parametric Equations
1st and 2nd Derivatives and Arclength of Parametric Equations
Polar Coordinates and Polar Graphs and tangents to the curve
Area and Arclength in Polar Coordinates
Kepler’s 3 Laws, Derivation of the equations for planetary motion
Vectors and Vector Valued Functions
Vectors and Vector Notation
Vector Valued Functions
Differentiation and Integration of Vector Valued Functions
Velocity and Acceleration
Many physics applications in Mechanics and E&M
Chapter 10/11
Additional
Euler’s Method and Differential Equations
Review of AB Calculus topics Through-out the year
First Quarter
Sections
1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Topics (review)
Homework
What is calculus
Finding limits graphically and
numerically
Evaluating limits analytically
Continuity and one-sided limits
Infinite limits
Definition of derivative and
tangent line problem
Basic differentiation rules and
rates of change
Product rule, quotient rule, and
higher-order derivatives
Chain rule and composite
functions
Implicit differentiation
Related rates
Rectilinear motion, (velocity
and acceleration)
Extrema on an interval
Mean value theorem
Increasing and decreasing
functions
The First Derivative Test
Concavity
The Second Derivative Test
Limits at infinity (Horizontal
Asymptotes)
Summary of curve sketching
Optimization (many AP exam
max-min problems)
Newton’s Method
Differentials (error estimates)
4.1
4.2
4.3
4.4
4.5
4.6
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6.1
Antiderivative and indefinite
integrals
Differential equations (with
physics applications)
Slope fields
Area
Properties of sigma notation
Finding limits of a sum
Riemann Sums
Definite integrals (computed by
Riemann Sums)
Fundamental Theorem of
Calculus
Mean Value Theorem for
integrals
Second Fundamental Theorem
of Calculus
Integration by substitution
Numerical integration:
Trapezoidal Rule and
Simpson’s Rule (including
error calculations)
Natural Log Function and
differentiation, method
logarithmic differentiation
Natural Log Function and
integration
Inverse functions and
derivatives
Natural Exponential Functions:
differentiation and integration
Applications of exponential
functions
Exponential growth and decay
Integration by separation of
variables (with physics
applications, friction fall)
Area between curves
6.2
Volume : The disk method
After the AP Exam (LABS)
Cover additional topics in the textbook to prepare those students who will be continuing
calculus in college. Prepare for a second semester cumulative final. Students work on
calculus lab projects using symbolic manipulators such as MAPLE. (see the maple-soft
application site for 100’s of project topics in calculus). In previous years students used
java and visual basic to generate a web based calculus tutorial similar to the college
boards APCD (they called it “AP circle”). Last year students wrote “python” computer
programs to generate slope fields and programmed in Euler’s method to graph the
particular solution on top of the slope field. They generated fractals and wrote programs
to investigate various types of cellular automata.
Student Evaluation and Activities
Students will be engaged in activities, experiences, and/or projects that include:
• investigating functions, graphs, limits, derivatives and integrals.
• comparing functions represented graphically, numerically, analytically, and verbally
and make the connections among these representations.
• communicating mathematics and explaining solutions to problems both verbally as
well written and presented on white boards
• using graphing calculators and write computer programs to help solve problems,
experiment, interpret results, and support conclusions.
 using symbolic manipulators such as MAPLE
 various physics applications including friction fall, Snell’s law, damped and driven
harmonic motion, rectilinear motion, differential equations, Gauss’ law, Line and
Surface integrals used in Mechanics and Electricity and Magnetism. (Note many BC
students are also in my calculus based AP Physics C Class)