JOHN F. KENNEDY HIGH SCHOOL COURSE SYLLABUS DEPARTMENT OF MATHEMATICS

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Syllabus for JFK High School, Sacramento, CA

Chad Sweitzer, Principal

John F. Kennedy High School, Sacramento City USD Page
1

of
7

JOHN F. KENNEDY HIGH SCHOOL

COURSE S
YLLABUS

DEPARTMENT OF MATHEMATICS




1.

COURSE NUMBER, TITLE, UNITS AND PRINCIPAL/DEPARTMENT APPROVED
DESCRIPTION


Calculus AB 1
-
2 AP MCS 201
-
202 5 units + 5 units


Calculus AB curriculum foll
ows the recommendations listed in the AP Course
Description for Calculus AB by the College Board. It is a two
-
semester course in the
study of the Calculus of functions of a single variable using the concepts and
techniques of limits, differentiation, and i
ntegration. Besides using algebraic
process to develop these concepts and skills, written, verbal, numerical, and
graphical representations/ methods will be applied whenever appropriate.









2.

GENERAL INFORMATION



2013
-
2014

Jennifer Manzano
-
Tackett C308 (916) 433
-
5200 EXT 1308

jennifer
-
manzano@scusd.edu






3.

TEXTBOOKS AND/OR RECOMMENDED OR REQUIRED READINGS



Calculus of a Single Variable by Larson, Hostetler & Edwards ,8
th

Edition,

Published by Houghton Mifflin Company, copy right 2006


Syllabus for JFK High School, Sacramento, CA

Chad Sweitzer, Principal

John F. Kennedy High School, Sacramento City USD

Page
2

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7


4.

GENERAL OVERVIEW




The syllabus of Calculus AB submitted to AP Central of the College Board for
review has been appro
ved and is now used to guide the teaching of this course.
The Calculus AB syllabus begins with a review of the various concepts on function
learned in pre
-
Calculus course which are essential in the study of Calculus. The
first new concept introduced is the

limit of a function. An informal definition of this
new concept is used to replace the formal definition which is too abstract for most
high school students. After that, the concept of continuity of a function at a point
and on an interval will be introdu
ced to make way for the next two main concepts of
Calculus
-
Differentiation and Integration of function of a single variable. Students will
be required to memorize the limit definitions of the derivatives and be able to use
them to prove the rules of differ
entiation and later to apply these rules/short cuts to
solve word problems. After they have mastered the techniques of differentiation,
they will be introduced to the concept of Antidifferentiation,Riemann Sum and finally
the definition of a definite integ
ral. They will also learn five Existence Theorems
which are inter
-
related to one another. Eventually these theorems will be used to
prove the Fundamental Theorem of Calculus part I and part II. The Fundamental
Theorem is the most important part of our syll
abus. Many mathematicians would
like to call this theorem the most important theorem/break through in Mathematics.
In the past, many students got very excited when this Theorem was introduced to
them. The rest of the syllabus contains the applications of t
hese two important
techniques of Calculus
-
differentiation and integration to various types of functions
and their applications.


5.

COURSE OBJECTIVES



1. To provide the students the opportunities to acquire the concepts and
techniques in solving ap
plication problems of differential and integral calculus.



2. To provide the students the opportunities to use their graphing calculators to
expand and explore their understandi
ng of calculus.


3. To provide the students the opportunities to incorporate different ways
(analytical, numerical, and graphical approaches) to solve real world problems, as
well as the opportunity to verbalize explanations of their solutio
ns and thought
process.


4. To provide a strong Mathematics background for students who intend to major
in sciences, social sciences, or in any field in which the understanding of
Mathematics is very helpful.


5. To prepare students for the AP test in Ca
lculus AB so that they could be better
prepared for college.





6.

COURSE REQUIREMENTS, ATTENDANCE AND SPECIFIC GRADING POLICY


Syllabus for JFK High School, Sacramento, CA

Chad Sweitzer, Principal

John F. Kennedy High School, Sacramento City USD Page
3

of
7




AP Calculus is a pretty rigorous course and the problems in their homework
assignments or in the chapter tests are genera
lly more difficult than regular Math
classes. In order to encourage students to stay in the class, the grading scale is a
little bit lower than that in regular Math classes. But that doesn’t imply that students
could get an easy ‘A’ or ‘B’ in this class. T
hey have to work hard to earn good
grades.


Grading System in Calculus AB


Quizzes, Tests, and Final
------------
90%

Homework
--------------------------------
10%


85%
--

100% A

75%
--

84% B

60%
--

74% C

50%
--

59% D

49% and below F


Late work is usually not accepted without a good reason. Unit tests are given at the
end of each unit and there are quizzes in between. A correct answer to a non
-
calculator problem without showing work will at most get partial credit.


7.

DESCRIPTION OF MAJOR ACTIVITIES/EXERCISES/PROJECTS


Unit tests and a final exam at the end of each semester will be given through the
school year. Students who have signed up to take the AP test will be given a final
exam before the AP Calculus AB te
st in May.





8.

OUTLINE OF CLASS SESSIONS



Unit 1: Functions 15 days


Unit 2: Limits and Continuity of Functions

15 days

Unit 3: Differentiation 26 days


Unit 4: Applications of Derivatives

20 days

Unit 5: Antidifferentiation and Definite Integrals 16 days

Unit 6: Differentiation and Integration of Transcendental Functions 12 days


Unit 7: Applications of Definite Integrals 17 days

Unit 8: Techniques of Integration 13 days

Unit

9: Differential Equations 14 days







Syllabus for JFK High School, Sacramento, CA

Chad Sweitzer, Principal

John F. Kennedy High School, Sacramento City USD

Page
4

of
7


9.

GENERAL STATEMENTS



Students are expected to adhere t
o and be familiar with all school and district
policies pertaining to behavior, attendance, testing, cheating and plagiarism, and
final exams.





10.

CROSS INDEXING KEY OF COURSE OBJECTIVES TO REQUIRED
STANDARDS



Unit 1: Functions




1. Definitions of a function using a rule and using a set of ordered pairs.


2. Multiple representations of functions

verbal, graphical, numerical, and


algebraic.


3. Classifications of functions

algebraic and non
-
alge
braic.


4. Function transformations

horizontal and vertical shifting, reflecting,


compressing, and expanding.


5. Combinations of functions including composite functions.


6. Special

functions

absolute value, even and odd, piece
-
wise, and step


functions.


7. Use of graphing calculators to graph functions, to evaluate a function, to


find the zeros of a function, and to find the point of inters
ection of the



graphs of


two functions, in addition to being able to interpret the relevance of these



points and use them to justify arguments made about the function.


8. Applications

functions as mathematical

models.


Unit 2. Limits and Continuity of Functions


1.

Introduction to the concept of the limit of a function using graphical

and numerical approach.


2. Informal definition of the limit of a function, including written/verbal


expla
nations of cases in which limits do not exist, supported by evidence


found in tables/graphs of a graphing utility.


3. Evaluation of limits using algebraic methods

substitution,


cancellation, and rationalization.



4. Use the Squeeze Theorem to evaluate a special trigonometric limit.

Syllabus for JFK High School, Sacramento, CA

Chad Sweitzer, Principal

John F. Kennedy High School, Sacramento City USD Page
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7


5. Properties (or theorems) of limits of functions.


6. One
-
side limits.


7. Intuitive understanding of continuity of a functio
n at a point.


8. Definition of the continuity of a function at a point and on a closed interval.


9. Properties (or theorems) of continuity of a function.


10. The Intermediate Value Theorem.



11. Infinite limit and vertical asymptotes.


12. Limits at infinity.


13. Horizontal and oblique asymptotes.


Unit 3. Differentiation



1.

A graphical and numerical introduction of the concept of the deri
vative

using the classical tangent line problem and velocity of a falling object
problem.


2. Derivative interpreted as the slope of a secant line as it approaches


to the position of the tangent line.



3. Derivative as defined by the instantaneous rate of change of the


outputs in relation to the inputs.


4. Definition of the derivative of a function at a point

the limit definition.


5. Derivative as a number and

as a derived function.


6. Relationship between continuity and differentiability.


7. Derivative from the negative side and from the positive side.


8. Approximation of the derivative

of a function at a point


using graphical and numerical data.


9. Rules of differentiation of algebraic and trigonometric functions.


10. Implicit differentiation for implicit
ly defined functions.


11. Solving related rates problems using implicit differentiation.


Unit 4. Applications of Derivatives


1.

Use of derivatives to find the intervals of increasing or decreasing


for a give
n functions, including written/verbal explanations of the



significance of these intervals on both the original function and



derivative
function graphs.


2. The critical value of a function, including written/verbal explanati
ons of



the significance of this value on the both the original function and



derivative function graphs.


3. Use the First Derivative Test to find the relative (local) extrema of a



function and provide written/verbal ex
planations of the significance of



these points for both the original function and the derivative function



graphs.


4. The Extreme Value Theorem.


5. Find the absolute extrema of a function defined on a cl
osed interval,



both algebraically and by using the graphing utility, in addition to



Syllabus for JFK High School, Sacramento, CA

Chad Sweitzer, Principal

John F. Kennedy High School, Sacramento City USD

Page
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providing written/verbal explanations of the significance of these points



for
both the original function and the derivative function graphs.



6. The Second Derivative Test.


7. Use the second derivative of a function to determine the concavity and


point of inflection of the graph of a function.


8. Relationships of graphs of the fun
ction, its first derivative, and


its second derivatives, with a focus on the ability to provide written/
verbal explanations for these relationships using appropriate calculus
vocabulary.



9. Applications of derivatives

optimization and linear approximation.


10. Differential

definition and applications


11. Analysis of motion of a particle
---
position, velocity, and acceleration


1
2. The Rolle’s Theorem and the Mean Value Theorem.



13. Use of graphing utilities to verify and interpret the significance of all



maxima/minima, zeros, points of inflection, intervals of





decreasing/increasing, etc. o
f functions and their derivatives.


Unit 5. Antidifferentiation and the Definite Integrals.



1. Antiderivative of a given function, found both algebraically and by using



a graphing utility.


2. A partic
ular antiderivative that satisfies a given initial value condition.


3. Numerical Integrations
--
Approximation of the area under a curve


using n rectangles. Functions could be given in algebraic, numeric, or


graphica
l forms and various points of evaluation could be used, i.e., the


left
-
endpoint, the right
-
endpoints, or the midpoint in the ith subinterval.


4. The Riemann Sum of a function over a closed interval usin
g a regular



partition.


5. Definition of a Definite Integral

defined as the limit of a Riemann Sum.


7. Properties of Definite Integrals.


8. Applications and proofs of The Fundamental
Theorems of





Calculus
-
Part I and Part II.


9. The Mean Value Theorem for Integrals and the average value of a



function.

10.

The Trapezoidal Rule, in addition to the general co
ncept of finding
areas with trapezoids.


11. Integration by Substitution.



12. Written/verbal explanations of the relationships between functions,



their derivatives, and their antiderivatives, supported by evidence




found by using a graphing utility to find key characteristics of their



graphs
and interpreting the meaning of those characteristics.


Unit 6 Differentiation and Integration of Transcendental Functions



1. The

natural logarithmic function defined by a definite integral.

Syllabus for JFK High School, Sacramento, CA

Chad Sweitzer, Principal

John F. Kennedy High School, Sacramento City USD Page
7

of
7


2. The derivative of y=ln x and the completion of the Power Rule for



Integration.


3. The behavior of the graph of y=ln x.



4. The derivative of an inverse function.


5. The natural exponential Function defined as the inverse of the


natural logarithmic function.


6. The behavior of the graph o
f y=e^x.


7. The derivative of the inverse trigonometric functions.


8. Applications
--
exponential growth or decay models.


Unit 7 Applications of Definite Integrals



1. A
rea of a region between two curves.


2. Volume of a sold generated by revolving a bounded region


about a line

the Disc Method and the Washer Method.


3. Volume of solid with know
n cross sections.


4. Arc length
--
the length of a curve on a closed interval


5. Problems that require setting up a Riemann Sum and then taking its



limit.



Unit 8 Techniques of Integr
ation




1. Basic integration rules.


2. Trigonometric integration.


3. Partial Fractions.




Unit 9 Differential Equa
tions



1. Solving simple differentiations including initial values problems.


2. Solving separable differential equations.


3. Slope Fields

a graphical approach to solving problems



involving differential equations.


4. Exponential growth and decay models.


5 Learning Curve Model and Newton’s Law of Cooling Model.