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AP Audit Syllabus BC

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®AP Calculus BC AP Calculus is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multirepresentational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. The connections among these representations also are important. (The College Board – AP Calculus Teacher’s Guide) Teaching Strategies Graphing Calculator Instruction will be given using primarily the TI-84. A graphing calculator will be used daily in the class and all chapter tests are divided in two halves: one without the use of any calculator and the other half requiring the use of a graphing calculator. The graphing calculator allows the student to support their work graphically, make conjectures regarding the behavior of functions and limits among other topics thus allowing students to view problems in a variety of ways. The calculator helps students develop a visual understanding of the material. 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, are used as a teaching tool. Expert Problems ...
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AP
®
Calculus BC
AP Calculus is primarily concerned with developing the students’ understanding of the
concepts of calculus and providing experience with its methods and applications. The course
emphasizes a multirepresentational approach to calculus, with concepts, results, and problems
being expressed geometrically, numerically, analytically, and verbally. The connections among
these representations also are important.
(The College Board – AP Calculus Teacher’s Guide)
Teaching Strategies
Graphing Calculator
Instruction will be given using primarily the TI-84. A graphing calculator will be used daily in the
class and all chapter tests are divided in two halves: one without the use of any calculator and
the other half requiring the use of a graphing calculator. The graphing calculator allows the
student to support their work graphically, make conjectures regarding the behavior of functions
and limits among other topics thus allowing students to view problems in a variety of ways. The
calculator helps students develop a visual understanding of the material. 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, are used as a teaching tool.
Expert Problems
Expert problems (problems from a daily assignment) are assigned to individual students and in
the event a classmate has a question or concern regarding a homework problem, he/she,
being the “expert” will come before the class and present the problem and discuss any areas
of concern. The use of a document camera makes this a very effective teaching strategy and
allows the “expert” the opportunity to communicate their reasoning verbally as well as the
opportunity to receive feedback on their written work from their classmates. Many discussions
arise as to what is sufficient justification and what is not.
Weekly AP Free Response Problem(s)
On a weekly basis, students are given up to six free response questions to solve. Students are
encouraged to work with each other on these, but individual written work is required on the part
of all students. These are graded in class using scoring guidelines similar to those developed
by the College Board. Students grade each other’s papers.
Daily Warm Up Multiple Choice Questions
At the beginning of each period, students are given up to 3 multiple choice questions to
complete. Differing methods of solution are shared and discussed.
Reworked Problem Notebook
Students have the opportunity to keep a “Reworked Problem Notebook” (RPN) that is turned in
on test days. A student can be eligible for up to 3 points added to a chapter test score. In order
to really understand mathematics, one needs to practice! Problems that need reworked are
those that a student:
1) had to look at the solution for help; 2) had to ask for help and/or 3)
worked the problem incorrectly. The RPN will be due on the day of the test and will not be
accepted late. To receive full credit, a student must have the following:
Reworked problems that are clearly labeled by chapter, section and number, neatly
organized and worked thoroughly and correctly
Commentary of what was learned, what to watch for in the future and what needs to be
studied, etc… The commentary is not necessary on every problem, but must be
included occasionally to receive full credit.
Calculus Book
Students create their own “Calculus Book” throughout the course chapter by chapter. Each
page has a specific topic where definitions, examples and commentary are required.
Tests
Chapter tests are divided into two parts: 1) no calculator, and 2) graphing calculator required.
Chapter tests are given over a two day period.
AP Calculus BC Course Outline
Primary Textbook
Finney, Ross L., Franklin Demana, Bert Waits, and Daniel Kennedy.
Calculus:
Graphical,
Numerical, Algebraic
. Reading, Mass.: Addison-Wesley, 1999. (Will be adopting the 2007
edition for the 2007/08 year.)
Other Resources
AP Calculus Course Description
AP Released Exams
D&S Marketing Systems, Inc. – Practice Exams
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Chapter 1:
Prerequisites for Calculus – 5 days
(Take home test)
(
1
-
1
)
L
i
n
e
s
0
(1-2) Functions and Graphs
0
(1-3) Exponential Functions
1
(1-4) Parametric Equations
2
(1-5) Inverse Functions and Logarithms
1
(1-6) Trigonometric Functions
1
Chapter 2:
Limits and Continuity – 8 days
(2-1) Rates of Change and Limits
2
(2-2) Limits Involving Infinity
1
(2-3) Continuity
1
(2-4) Rates of Change and Tangent Lines
1
Chapter 3:
Derivatives – 20 days
(3-1) Derivative of a Function
1
(3-2) Differentiability
1
(3-3) Rules of Differentiation
3
(3-4) Velocity and Other Rates of Change
3
(3-5) Derivatives of Trigonometric Functions
3
(3-6) Chain Rule
2
(3-7) Implicit Differentiation
2
(3-8) Derivatives of Inverse Trigonometric Functions
2
(3-9) Derivatives of Expo and Log Functions
1
Chapter 4:
Applications of Derivatives – 18 days
(4-6) Related Rates
5
(4-1) Extreme Values of Functions
2
(4-2) Mean Value Theorem
1
(4-3) Connecting f’ and f” with the Graph of f
2
(4-4) Modeling and Optimization
3
(4-5) Linearization and Newton’s method
3
Chapter 5:
The Definite Integral – 11 days (16)
(5-1) Estimating with Finite Sums
1
(5-2) Definite Integrals
2
(5-3) Definite Integrals and Antiderivatives
3
(5-4) Fundamental Theorem of Calculus
2
(5-5) Trapezoidal Rule
1
Chapter 6:
Differential Equations and Math Modeling – 15 days
(6-1) Antiderivatives and Slope Fields
2
(6-2) Integration by Substitution
2
(6-3) Integration by Parts
2
(6-4) Exponential Growth and Decay
2
(6-5) Population Growth
3
(6-6) Numerical Methods
1
Chapter 7:
Applications of Definite Integrals – 13 days
(7-1) Integral as Net Change
3
(7-2) Areas in the Plane
2
(7-3) Volumes
3
(7-4) Lengths of Curves
2
Chapter 8:
L’Hopital’s Rule –
11 days
(8-1) L’Hopital’s Rule
2
(8-2) Relative Rates of Growth
1
(8-3) Improper Integrals
3
(8-4) Partial Fractions and Integral Tables
1
Chapter 9:
Infinite Series – 17 days
(9-1) Power Series
3
(9-2) Taylor Series
2
(9-3) Taylor’s Theorem
2
(9-4)
Radius of Convergence
2
(9-5)
Testing Convergence at Endpoints
4
Chapter 10:
Parametric, Vector, and Polar Functions – 12 days
(10-1) Parametric Equations
1
(10-2) Vectors in Plane
1
(10-3) Vector-valued Functions
1
(10-5) Polar Coordinates and Polar Graphs
2
(10-6) Calculus of Polar Curves
3
Review and Preparation for the AP Exam – Approximately 3 weeks
Practice exams are given, scored and analyzed. Some are done in groups while others
are completed individually.
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