SYLLABUS : AP Calculus BC

SYLLABUS : AP Calculus BC
2013-14
INSTRUCTOR: VUCAJNK ROOM 312 avucajnk@bmhs-la.org
Student Textbook
Calculus of a Single Variable (2006)
Roland E. Larson/Robert P. Hostetler/Bruce H. Edwards
Houghton Mifflin (Eighth Edition)
Course Objectives
The objectives of teaching AP Calculus BC are not only for students to do well on the
AP
Calculus Exam but to enable students to appreciate the value of Calculus and to receive
a strong
foundation that will facilitate in the success of future math courses. Throughout the year,
students will work with functions represented graphically, numerically, analytically, and
verbally
and explore the connections among these representations. In addition to writing out
mathematical solutions to problems, students will learn to communicate mathematics
during
class discussions and group work, and will be expected to explain solutions in written
sentences
on various homework, test and quiz questions.
Technology
The teacher uses the TI83 graphing calculator. The TI83 or higher is recommended.
Graphing calculators are allowed and in some cases required to complete homework
assignments. However, students are allowed to use calculators on only about half of the
test and
quiz questions.
There are four functions that students must know for the AP Test and for successful
completion of this course. They are:
1. Finding a root.
2. Sketching a function in a specified window.
3. Approximating the derivative at a point.
4. Approximating the value of a definite integral.
In order to enhance learning and to help understand the concepts of calculus, graphing
calculators are used in the following specific ways:
• To estimate the limit of a function graphically and to use a table to reinforce the conclusion.
• To find a limit by analytic methods and compare to the above results.
• To graph functions and determine the x values at which the function is not continuous
• To locate the Absolute Extrema of a function over a given interval and then use differentiation
to
confirm the estimate.
• To identify horizontal asymptotes.
• To calculate the area under a curve and to both confirm results that students obtain by using

Riemann sums and by using antiderivatives.
• To evaluate definite integrals for functions that are difficult to solve analytically.
• To graph a function and determine whether it is one to one
on its entire domain.
• To graph a function and approximate the zeroes for functions whose zeroes are difficult to find
analytically.
• To graph the region bounded by the graphs of two or more functions.
• To draw a slope field for differential equations by picking, for example, 8 points such as
(0,0),(0,1),(1,0) etc.
• To obtain slopes at these points by using the differentiation capabilities of the calculator.
The above calculator activities are done using exponential, polynomial, trigonometric,
logarithmic and piecewise
functions. Students are encouraged to use calculators often to
develop familiarity and learn its strengths and weaknesses.
Course Outline:
AP Calculus AB Review Topics:
Chapter 1 Limits and Their Properties
2. Finding Limits Graphically and Numerically
3. Evaluating Limits Analytically
4. Continuity and One Sided Limits
5. Infinite Limits
Chapter 2 Differentiation
1. The Derivative and the Tangent Line Problem
2. Basic Differentiation Rules and Rates of Change
3. Product and Quotient Rules and HigherOrder
Derivatives
4. The Chain Rule
5. Implicit Differentiation
6. Related Rates
Chapter 3 Applications of Differentiation
1. Extrema on an Interval
2. Rolle’s Theorem and the Mean Value Theorem
3. Increasing and Decreasing Functions and the First Derivative Test
4. Concavity and the Second Derivative Test
5. Limits at Infinity
6. A Summary of Curve Sketching
7. Optimization Problems
8. Newton’s Method
9. Differentials

Chapter 4 Integration
1. Antiderivatives and Indefinite Integration
2. Area
3. Riemann Sums and Definite Integrals
4. The Fundamental Theorem of Calculus
5. Integration by Substitution
6. Numerical Integration
Chapter 5 Logarithmic, Exponential, and Other Transcendental Functions
1. The Natural Logarithmic Function: Differentiation
2. The Natural Logarithmic Function: Integration
3. Inverse Functions
4. Exponential Functions: Differentiation and Integration
5. Bases Other Than e and Applications
6. Inverse Trigonometric Functions: Differentiation
7. Inverse Trigonometric Functions: Integration
Chapter 6 Differential Equations
1. Slope Fields and Euler’s Method
2. Differential Equations: Growth and Decay
3. Separation of Variables and the Logistic Equation
Chapter 7 Applications of Integration
1. Area of a Region Between Two Curves
2. Volume: The Disk Method
4. Arc Length and Surfaces of Revolution
New Topics:
Chapter 8 Integration Techniques, L’Hopital’s Rule, and Improper Integrals
1. Basic Integration Rules
2. Integration by Parts
3. Trigonometric Integrals
4. Trigonometric Substitution
5. Partial Fractions
6. Integration by Tables and Other Integration Techniques
7. Indeterminate Forms and L’Hopital’s Rule
8. Improper Integrals
Chapter 9 Infinite Series
1. Sequences
2. Series and Convergence
3. The Integral Test and pSeries
4. Comparisons of Series
5. Alternating Series

6. The Ratio and Root Tests
7. Taylor Polynomials and Approximations
8. Power Series
9. Representation of Functions by Power Series
10. Taylor and Maclaurin Series
Chapter 10 Conics, Parametric Equations, and Polar Coordinates
1. Conics and Calculus
2. Plane Curves and Parametric Equations
3. Parametric Equations and Calculus
4. Polar Coordinates and Polar Graphs
5. Area and Arc Length in Polar Coordinates
Vectors handout
Please obey the following rules:
-ALWAYS BE ON TIME
-DON’T BE ABSENT FROM CLASS UNLESS ABSOLUTELY NECESSARY
-NO FOOD OR DRINKS IN CLASS
-FOLLOW ALL BMHS POLICIES
GRADING PERCENTAGES:
20% HOMEWORK
20% QUIZZES
40% TESTS
20% FINAL
HOMEWORK:
Homework is assigned daily and it is due next class. If a student does not have the homework
he or she receives 0.There is no homework makeup so it is important that every homework is
done. This policy will never change.
If a student is absent then the homework is due within 2 days upon return. The student is
responsible for turning the homework in. If the homework is not turned in within 2 days by the
student the grade is 0.
QUIZZES:

There will be random amount of quizzes administered at random times. Quizzes will not be
announced in advance so students have to be prepared at all times for a quiz.
EXAMS:
In general there will be one exam per chapter. Exams will be announced at least a day in
advance.
IF A STUDENT IS ABSENT DURING AN EXAM OR A QUIZ HE OR SHE IS RESPONSIBLE
FOR A MAKE UP WITHIN 3 DAYS UPON RETURN.IF THE EXAM OR A QUIZ IS NOT MADE
UP, THE GRADE IS 0.
FINAL:
There is a comprehensive final exam at the end of each semester
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