Advanced Placement Calculus AB
Syllabus
Teacher: Mr. Marsico
E-Mail: mathew1.marsico@cms.k12.nc.us
Room #: 738
Website: http://mathew1-marsico.cmswiki.wikispaces.net
Introduction:
This course is intended to provide students with a sound understanding of the concepts of Calculus and
its applications. It covers all topics included in the Calculus AB topic outline as it appears in the AP®
Calculus Course Description.
Our study of Calculus is divided into two major topics: differential and integral Calculus. Differential
Calculus enables us to calculate rates of change, find the slope of a curve and calculate velocities and
accelerations of moving bodies. Integral Calculus is used to find the area of an irregular region in a
plane, measure lengths of curves and calculate centers of mass of arbitrary solids. Our task is to perfect
each student’s mechanics and to develop his or her understanding of the theory of Calculus and the
ability to use these ideas in applied Calculus. Through additional practice of the mechanics and the
development of the applications of derivatives and antiderivatives in problem solving, each student may
accomplish this task.
The first seven months of the class will be devoted to studying differential and integral Calculus while
the next four weeks will be review and preparation for the AP exam. During the year, information
concerning the administration, scoring and content of the exam will be discussed.
Throughout the course, a multirepresentational approach will be utilized. This means that problems
and solutions will be presented analytically, graphically and numerically, and there will be an emphasis
on the connection between these representations. Furthermore, the students must be able to explain
these multiple representations both verbally and in written form.
Course Outline:
Unit One: Limits and Their Properties (3 weeks)
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Find limits graphically and numerically
Evaluate limits analytically
Continuity and one-sided limits
Intermediate Value Theorem
Infinite limits and vertical asymptotes
Unit Two: Differentiation (9 weeks)
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The derivative and the tangent line problem
Differentiability and continuity
Basic differentiation rules and rates of change (average and instantaneous)
Product and Quotient Rules and Higher Order derivatives
The Chain Rule
Implicit differentiation
Related Rates
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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
Limits at Infinity (horizontal asymptotes)
Summary of Curve Sketching (including monotonicity)
Optimization problems
Differentials
Local linear approximations
Unit Three: Introduction to Integral Calculus (5 weeks)
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Antiderivatives and indefinite integration
Differential equations
Position, velocity, acceleration problems
Riemann sums
Definite integrals solved using geometric formulas
Properties of definite integrals
Trapezoidal Rule
The Fundamental Theorem of Calculus
Average value of a function
Second Fundamental Theorem of Calculus
Integration using u-substitution
Displacement and definite integrals
Midterm Exam: The midterm exam includes problems from past AP exams that test the students’
abilities to connect concepts graphically, analytically, numerically, and verbally.
Unit Four: Transcendental Functions (7 weeks)
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The Natural Logarithmic Function and Differentiation
The Natural Logarithmic Function and Integration
Inverse Functions
Exponential Functions: Differentiation and Integration
Bases other than e and applications
Differential equations: Growth and decay
Differential equations: Separation of variables
Differential equations: Slope fields
Inverse trigonometric functions and Differentiation
Inverse trigonometric functions and Integration
Unit Five: Applications of Integration (2 weeks)
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Area of a region between two curves
Volume: Known cross-sections
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Volume: Disc method
Volume: Washer method
Unit Six: Additional Topics
 Differential Equations and Slope Fields
 L’Hopital’s Rule
 Integration by Parts (time permitting)
Unit Seven: AP Review (3 to 4 weeks)
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1997, 1998, and 2003 AP Exams
Free response questions; 2000 to present
**AP Exam Date: Wednesday, May 9 at 8:00 am.
Technology:
The use of technology allows Calculus to come alive for students, enabling them to gain a level of
understanding that may otherwise be unattainable. Specifically, graphing calculators will be used to
model concepts, help students find solutions to problems and allow students to see a connection
between analytical, numerical and graphical representations. For example, when studying limits, the
students will be able to explore and visualize what it means for a function to have a limit by graphing
the function and viewing it through multiple viewing windows (both as x approaches a number and as x
approaches infinity). The students will also be taught how to numerically calculate the derivative of a
function and the value of a definite integral. Demonstrations of how to use the calculators for these
and other functions will be shown using a TI-84 and a TI-89. The students will be required to have their
calculators in class every day since we will use them to find the solutions to many types of problems
and to explore new topics.
Other technology that will be utilized throughout the course includes a Promethean Board (which is
how the demonstrations with the graphing calculators will be shown to the class) and interactive,
dynamic sketches (for example, these are used to help students overcome some of the misconceptions
about limits and better understand the formal definition of a limit).
Student Evaluation:
Grades will be determined based on the student’s performance in the following areas:
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Tests: Tests will be given at the end of each chapter. They will consist of both
multiple choice and free response questions, much like the AP Exam. Furthermore,
some questions will not allow the use of a calculator and will require solutions to be
presented in multiple ways (numerically, analytically and graphically). These will
account for approximately 60% of your grade.
Quizzes: At least one quiz will be given throughout each chapter. These are intended
to give a quick assessment of where the students are doing well and where they are
struggling. Overall, they will focus heavily on the mechanics of the chapter more
than the tests will. These will account for approximately 20% of your grade.
AP Question Packets: Students will be given a packet of questions either used on
previous AP Exams or questions similar to those seen on the AP Exam every, or every
other week. Students are encouraged to work on these questions with other students
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and ask me for extra help when they experience difficulties. The emphasis of these
packets is to develop the student’s ability to justify solutions both verbally and in
written form. Moreover, they will emphasize the skills mirrored in the nightly
homework assignments. These will account for approximately 10% of your grade.
Projects: Various projects will be assigned throughout the year. They will be highly
interactive, hands-on assignments that will help concepts that are difficult to visualize
become tangible. For example, when studying surfaces of revolution, the students
are divided into groups and given Play Doh, a ruler, a straw and about 20 index cards
(either left as rectangles or cut into triangles). The students place the straw into a
flattened piece of Play Doh (to represent the y-axis) and place the index cards around
the straw to simulate a solid of revolution. They can then set up the integral and
determine the volume of the figure. The students will then use their graphing
calculators to check their solutions and make sure they can use them to numerically
calculate the value of a definite integral. Finally, to take it to the next level, students
move the index cards an inch away from the straw and try to calculate the volume of
this solid. By working in groups, students continue to practice verbally justifying
their answers, and by solving the integral both numerically and graphically, they are
continuing to connect the multiple representations. The grades for the various
projects will fall into the other categories depending on the length and difficulty of
the project.
Other: You will also have homework assigned on a nightly basis and other individual
and group class work. Along with participation, this will count for approximately 10%
of your overall average.