2012 / AP Calculus bc

AP courses in calculus consist of a full high school academic year of work and are comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both, from institutions of higher learning. Syllabi

The AP program includes specifications for two calculus courses and the exam for each course. CalculusBC is a full-year course in the calculus of functions of a single variable. It includes all topics covered in CalculusAB plus additional topics.

Prerequisites: Before studying calculus all students should have studied algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions.

This AP course will develop students understanding of the concepts of calculus. CalculusBC will look at problems in four different methods: graphically, numerically, analytically, and verbally.

Primary Text:

Foerster, Paul A.Calculus: Concepts and Applications. Emeryville, CA: Key Curriculum Press.

Supplementary Textbooks used:

Anton, Howard. Calculus: A New Horizon. New York: John Wiley & Sons.

Hughes-Hallett, Devorah, et al. Calculus:Single Variable. New York: John Wiley & Sons.

Stewart, James. Calculus. Pacific Grove, CA: Brooks/Cole

Topics to be covered:

  1. Functions, graphs, and limits.
  • Analysis of graphs.
  • Limits of functions.
  • Asymptotic and unbounded behavior.
  • Continuity as a property of functions.
  • Parametric, polar, and vector functions. (BC only)
  1. Derivatives.
  • General concept.
  • Derivative at a point, as a function, applications.
  • Second derivatives.
  • Computation of derivatives.
  1. Integrals.
  • Interpretations and properties of definite integrals.
  • Applications. (BC only)
  • Fundamental theorem of Calculus.
  • Techniques and applications of antidifferentiation.
  • Numerical approximations to definite integrals.
  1. Polynomial Approximations and Series. (BC only)
  • Concept of series.
  • Series of constants
  • Taylor series.

Goals:

Students should be able

  • To continue to grow in our knowledge of what it means to be a disciple of Christ.
  • To work with functions in a variety of ways: graphically, numerically, analytically, or verbally. Students should understand the connections among these representations.
  • Understand the meaning of derivative in terms of rate of change and local linear approximation. Use derivatives to solve a variety of problems.
  • Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change. Use definite integral to solve a variety of problems.
  • Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
  • Model a written description of a physical situation with a function, a differential equation, or an integral.
  • To be able to model a written description of a physical situation with a function, a differential equation, or an integral.
  • To use technology to help solve problems, experiment, and verify conclusions.
  • To determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
  • To develop an appreciation for calculus.

AP Examination: Exam Date Wednesday May 8th2013Morning Session

AP Calculus Updates

Reminder: Multiple-Choice Section Scoring Change
Beginning with the May 2011 AP Exam administration, there will be a change to the way AP Exams are scored. Total scores on the multiple-choice section will be based on the number of questions answered correctly. Points will no longer be deducted for incorrect answers and, as always, no points will be awarded for unanswered questions.
Reminder: AP Calculus Free-Response Section—The format of the free-response sections of the AP Calculus AB and AP Calculus BC Exams is being modified. Beginning with the May 2011 AP Exam administration, Part A (graphing calculator required) consists of two problems to be completed in 30 minutes and Part B (no calculator is allowed) consists of four problems to be completed in 60 minutes.
This change in the free-response section format should not affect classroom instruction. In particular, students should use graphing calculators on a regular basis so they become adept in their use. Students should also have experience with the basic paper-and-pencil techniques of calculus and be able to apply them when technological tools are unavailable or inappropriate. The Development Committee believes that the change in exam format will help the AP Calculus Exams more accurately represent the broad range of calculus topics and concepts that need to be assessed.

A Calculus AB subscore grade is reported based on performance on the portion of the exam devoted to CalculusAB topics (approximately 60 percent of the exam).

Total length of AP CalculusBCexam is 3 hours 15 minutes.

Section I: Multiple-choice section testing proficiency in a wide variety of topics.

Part A: no calculator allowed (28 questions; 55 mins)

Part B: calculator may be used (17 questions; 50 mins)

Section II: Free response section

Part A: calculator required (2 questions; 30mins)

Part B: no calculator allowed (4 questions; 60mins)

Grades for Section I, II are weighted equally.

For Section II, if a student finishes Part A before the end of the timed 30 mins for Part A, he/she cannot begin working on Part B; the student must wait until the beginning of the timed 60 mins for Part B. However, during the timed portion for Part B, students may keep the green insert and go back and work on the problems in Part A without the use of a calculator.

Since the examinations are designed for full coverage of the subject matter, it is not expected that all students will be able to answer all the questions.

Grades:

First semester

Tests 40%

Homework 40%

Final 20%

Second semester

Tests 40%

Homework 40%

Final 20%

I am once again requiring that you have a separate notebook for your assignments. You will write the notes in one book and your assignments in one book. The assignment book will be labeled with the date and the section from the text that the assignment is from.

All work done in the assignment book will be done in pencil.

There will be no food allowed during class time. Come to class on time and prepared to be engaged in the material.

If absent, it is expected that you work through the assignment and be prepared for class the next day. If the absence is unexcused you will be given a zero for that days work.

This course involves a lot of work and getting behind at any stage is not a good idea. So do all homework when it is assigned. I wish you all the best in this course!

1