TEXT:
Calculus Graphical, Numerical, Algebraic, 3rd edition; Finney, Demana, Waits, Kennedy
REQUIREMENTS:
3ring
binder, Pencil,
Notebook, and Graphing Calculator (TI83+, TI84, TI84 Silver, TI89, or
TINspire
)
Before studying
calculus, all students should complete four courses of secondary mathematics
designed for collegebound students: courses in which they study algebra,
geometry, trigonometry, analytic geometry, and elementary functions. These
functions include those that are linear, polynomial, rational, exponential,
logarithmic, trigonometric, inverse trigonometric, and piecewise defined. In
particular, before studying calculus, students must be familiar with the
properties of functions, the algebra of functions, and the graphs of functions.
Students must also understand the language of functions (domain and range, odd
and even, periodic, symmetry, zeros, intercepts, and so on) and know the values
of the trigonometric functions of the numbers 0, pi/6, pi/4, pi/3, pi/2, and
their multiples.
DESCRIPTION:
Advanced
Placement (AP)
Students should be able to:
work with functions represented in a variety
of ways: graphical, numerical, analytical, or verbal. They should understand
the connections among these representations.
understand the meaning of the derivative in
terms of a rate of change and local linear approximation and they should be
able to 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 change
and should be able to use integrals 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.
communicate mathematics both orally and in
wellwritten sentences and should be able to explain solutions to problems.
model a written description of a physical
situation with a function, a differential equation, or an integral.
use technology to help solve problems, experiment,
interpret results, and verify conclusions.
determine the reasonableness of solutions,
including sign, size, relative accuracy, and units of measurement.
develop an appreciation of calculus as a
coherent body of knowledge and as a human accomplishment.
TOPICAL OUTLINE:
The topic outline for Calculus BC includes all Calculus AB topics. Additional
topics are found in paragraphs that are marked with a plus sign (+) or an
asterisk (*). The additional topics can be taught anywhere in the course. Some
topics will naturally fit immediately after their Calculus AB counterparts.
Other topics may fit best after the completion of the Calculus AB topic outline.
Although the examination is based on the topics listed here, the course may be
enriched with additional topics.
With the aid of technology, graphs of functions are often easy to produce. The emphasis is on the interplay between the geometric and analytic information and on the use of calculus both to predict and to explain the observed local and global behavior of a function.
The analysis of planar curves includes those given in parametric form, polar form, and vector form.
Appropriate integrals are used in a variety of applications to model physical, social, or economic situations. Although only a sampling of applications can be included in any specific course, students should be able to adapt their knowledge and techniques to solve other similar application problems. Whatever applications are chosen, the emphasis is on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. To provide a common foundation, specific applications should include finding the area of a region (including a region bounded by polar curves), the volume of a solid with known cross sections, the average value of a function, the distance traveled by a particle along a line, and for BC only the length of a curve (including a curve given in parametric form).
Use of Riemann sums (using left, right, and midpoint evaluation points) and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values.
A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence or divergence.
PACING GUIDE:
Chapter 1 Prerequisites for Calculus 
4 days 
Chapter 2 Limits and Continuity 
6 days 
Chapter 3 Derivatives 
22 days 
Chapter 4 Applications of Derivatives 
14 days 
Chapter 5 The Definite Integral 
16 days 
Chapter 6 Differential Equations and Mathematical
Modeling 
22 days 
Chapter 7 Applications of Definite Integrals 
15 days 
Chapter 8 L'Hôpital's Rule, Improper Integrals, and Partial Fractions 
7 days 
Chapter 9 Infinite Series 
23 days 
Chapter 10 Parametric, Vector, and Polar Functions 
16 days 
This timeline gives approximately 15 days to “review”
the course before the exam.
Put your knowledge to the test: The AP Calculus BC Exam
assesses your mastery of
The AP Calculus BC
Exam is 3 hours and 15 minutes. The 105minute, 45question multiplechoice
section tests your proficiency on a wide variety of topics. The 90minute,
sixproblem freeresponse section gives you the chance to demonstrate your
ability to solve problems using an extended chain of reasoning.
The multiplechoice
section of the exam has two parts. For Part A, you'll have 55 minutes to
complete 28 questions without a calculator. For Part B, you'll have 50 minutes
to answer 17 questions using a graphing calculator. For more information, see
the calculator policy for the AP Calculus Exams.
Unlike other
multiplechoice tests, random guessing can hurt your final score. While you
don't lose anything for leaving a question blank, one quarter of a point is
subtracted for each incorrect answer on the test. But if you have some
knowledge of the question and can eliminate one or more answers, it's usually
to your advantage to choose what you believe is the best answer from the
remaining choices.
The freeresponse
section tests your ability to solve problems using an extended chain of
reasoning. You'll have 45 minutes for each of the two parts of the
freeresponse section. In Part A, you'll answer three questions using a
graphing calculator. In Part B, you'll answer three questions without a
calculator. During the second timed portion of the freeresponse section (Part
B), you are permitted to continue work on problems in Part A, but you are not
permitted to use a calculator during this time. For more information, see the
calculator policy for the AP Calculus Exams.
The multiplechoice
and freeresponse sections each account for onehalf of your final exam grade. Since
the exams are designed for full coverage of the subject matter, it is not
expected that all students will be able to answer all the questions.
AP Grade Reports are
sent in July to the college you designated on your answer sheet, to you, and to
your high school. Each report is cumulative and includes grades for all the AP
Exams you have ever taken, unless you have requested that one or more grades be
withheld from a college or canceled.
RESOURCES:
AP: 
http://www.collegeboard.com/student/testing/ap/sub_calbc.html?calcbc 
Ask
Dr. Math 

Calculus textbook website 
http://www.phschool.com/webcodes10/index.cfm?fuseaction=home.gotoWebCode&wcprefix=bkk&wcsuffix=1000 
CyberCalc 

InterAct Math 

Karl's
Calculus Tutor 

Mr. Calculus


PowerPoint Lectures 

Slopefields on TI89 
http://www.jamesrahn.com/Calculator/TI89/ti893.htm 
TI
Graphing Calculators


Tutorials for the Calculus Phobe


Using the TI89 Calculator 
http://www.prenhall.com/divisions/esm/app/graphing/ti89/index.html 
Visual Calculus 
Grade Scale: 

A 
93 and above 
B 
85  92 
C 
75 – 84 
D 
65  74 
F 
64 and below 
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