Syllabus
Fall 2008
Instructor: 
Mrs.
Regina Ramey 
School: 
Boone County Honors Academy 
Email 

TEXT:
Calculus Graphical, Numerical, Algebraic, 3rd edition; Finney, Demana, Waits, Kennedy
REQUIREMENTS:
3ring binder, Pencil, Notebook, Graph Paper, and Graphing Calculator
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:
I. Limits
1. Use graphical and
numerical evidence to estimate limits and identify situations where limits fail
to exist.
2. Apply rules to
calculate limits.
3. Use the limit
concept to determine where a function is continuous.
II. Derivatives
1. Use the limit
definition to calculate a derivative, or to determine when a derivative fails
to exist.
2. Calculate
derivatives (of first and higher orders) with pencil and paper, without
calculator or computer algebra software, using:
(a) Linearity of the
derivative;
(b) Rules for products and
quotients and the Chain Rule;
(c) Rules for powers,
trigonometric and inverse trigonometric functions, and for logarithms and
exponentials.
3. Use the derivative
to find tangent lines to curves.
4. Calculate
derivatives of functions defined implicitly.
5. Interpret the
derivative as a rate of change.
6. Solve problems
involving rates of change of variables subject to a functional relationship.
7. Approximate
functions by using linearization (differentials).
III. Applications of the Derivative
1. Find critical
points, and use them to locate maxima and minima.
2. Use critical
points and signs of first and second derivatives to sketch graphs of functions:
(a) Use the first
derivative to find intervals where a function is increasing or decreasing.
(b) Use the second
derivative to determine concavity and find inflection points.
(c) Apply the first
and second derivative tests to classify critical points.
3. Use Differential Calculus to solve
optimization problems.
4. Apply the Mean Value Theorem.
5. Use
IV. The Integral
1. Find
antiderivatives of functions; apply antiderivatives to solve separable
firstorder differential equations.
2. Use the definition
to calculate a definite integral as a limit.
3. Apply the
Fundamental Theorem of Calculus to evaluate definite integrals and to
differentiate functions defined as integrals.
4. Calculate
elementary integrals with pencil and paper, without calculator or computer
algebra software, using:
(a) Linearity of the
integral;
(b) Rules for powers
(including exponent 1) and exponentials, the six trigonometric functions and
the inverse sine, tangent and secant;
(c) Simple
substitution.
V. Transcendental Functions
1. Use the relation
between the derivative of a one to one function and the derivative of its inverse.
2. Calculate with
exponentials and logarithms to any base.
3. Calculate
derivatives of logarithmic, exponential and inverse trigonometric functions;
interpret and apply such derivatives as usual.
4. Use logarithmic
differentiation.
5. Use models describing
exponential growth and decay.
TENTATIVE PACING GUIDE
Chapter 1 Prerequisites for Calculus 11
days
Chapter 2 Limits and Continuity 10
days
Chapter 3 Derivatives 30
days
Chapter 4 Applications of Derivatives 28
days
Chapter 5 The Definite
Integral 26 days
Chapter 6 Differential Equations and Mathematical
Modeling 22 days
Chapter 7 Applications of Definite Integrals 21
days
This timeline gives approximately 15 days to “review” the course before the exam.
Put your knowledge to the test: The AP Calculus AB Exam
assesses your mastery of
The AP Calculus AB
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:
Karl's Calculus Tutor http://www.karlscalculus.org/
Ask Dr. Math http://mathforum.org/dr.math/drmath.html
TI Graphing
Calculators http://education.ti.com/educationportal/
Tutorials for the
Calculus Phobe http://www.calculushelp.com/funstuff/phobe.html
Mr. Calculus http://users.adelphia.net/~sismondo/index.html
CyberCalc http://www.npac.syr.edu/REU/reu94/williams/calcindex.html
AP:
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