AP Audit Syllabus BC

Triscia Hochstatter

Informations

• Publié par: Enku
• Nombre de lectures: 10
• Langue: English

Extrait

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

#

D

a

y

s

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.