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Instructor: |
Mrs.
Regina Ramey |
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E-mail |
rnramey@access.k12.wv.us |
TEXT:
Calculus
Graphical, Numerical, Algebraic; Finney,
Demana, Waits, Kennedy 2003
REQUIREMENTS:
3-ring
binder, Pencil,
Notebook, and Graphing Calculator (TI-83+, TI-84, TI-84 Silver, or TI-89
recommended: TI-89)
Before studying
calculus, all students should complete four courses of secondary mathematics
designed for college-bound 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
well-written 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
first-order 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.
PACING GUIDE
|
Chapter 1 Prerequisites for Calculus |
0 days |
|
Chapter 2 Limits and Continuity |
8 days |
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Chapter 3 Derivatives |
12 days |
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Chapter 4 Applications of Derivatives |
14 days |
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Chapter 5 The Definite Integral |
7 days |
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Chapter 6 Differential Equations and Mathematical
Modeling |
7 days |
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Chapter 7 Applications of Definite Integrals |
9 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 105-minute, 45-question multiple-choice
section tests your proficiency on a wide variety of topics. The 90-minute,
six-problem free-response section gives you the chance to demonstrate your
ability to solve problems using an extended chain of reasoning.
The multiple-choice
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
multiple-choice 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 free-response
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
free-response 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 free-response 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 multiple-choice
and free-response sections each account for one-half 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:
|
Calculus textbook website |
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|
Karl's
Calculus Tutor |
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Ask
Dr. Math |
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|
TI
Graphing Calculators
|
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Tutorials for the Calculus Phobe
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|
Mr. Calculus
|
|
|
CyberCalc |
|
|
AP: |
http://www.collegeboard.com/student/testing/ap/sub_calab.html?calcab |
|
InterAct Math |
|
|
Visual Calculus |
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|
Calculus Graphical, Numerical, Algebraic
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|
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PowerPoint Lectures |