Last Updated February 17, 2001
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Platte Canyon High School Mathematics and Science |
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Syllabus University
of Colorado at Denver (UCD): Math
1401 Platte
Canyon High School: AP Calculus BC Instructor:
Debbi Marks September
5, 2000 through January 25, 2001 General InformationThis
class meets every school day for 90 minutes from 9:05 to 10:35. Instructor InformationDebbi
Marks Platte
Canyon High School, Room 215 303-838-4642
Ext 219 email:
debbimarks@uswest.net I
am available before school, after school and during 3rd period.
You may drop in or make an appointment to see me. Course PrerequisitesPrecalculus
with a ‘B’ or better or permission of instructor. Required Textbook
Calculus:
Graphical, Numerical, Algebraic
by Finney, Demana, Waits, Kennedy publisher:
Scott Foresman Addison Wesley, 1999 Objectives This course is an academically challenging program that
has been designed with the following objectives: •
To
understand the meaning of the derivative in terms of rate of change and local
linear approximation. •
To be able to work with functions represented graphically, numerically,
analytically or verbally and understand the connections among these
representations. •
To understand the meaning of the definite integral both as a limit of
Riemann sums and as a net accumulation of a rate of change. •
To be able to model problem situations with functions, differential
equations or integrals. •
To read, analyze, and solve challenging problems. •
To work and communicate effectively in groups. •
To take the AP Calculus (BC) test and score a 3, 4, or a 5. Classroom
Procedures and Grades Instruction in the AP Calculus class (Math
1401 and Math 2411) will include a variety of activities. Lecture and discussion, calculator explorations, lab
activities, and guided practice will all be used regularly. Students are expected to actively participate in all of these
activities. Class discussion is
important to assist understanding and to build on the ideas of classmates. Frequent tests and quizzes will be used to monitor the
progress of students. “Pop”
quizzes will be given regularly to ensure that students keep up with their work
and understanding. Each test will
follow the format of the AP Calculus test which includes four sections.
There are two sections of multiple choice, one using a calculator and one
not. There are two sections of free
response questions, one using a graphing calculator and one not. Grades will be based on the accumulation of points.
Homework will be worth 5 – 10 points for each assignment.
Quizzes range from 10 – 40 points.
Tests range from 60 – 145 points.
Other activities and assessments will be given points as well. No late work will be accepted. Materials pencils, red grading pen, TI-83 or TI-83 Plus graphing
calculator or TI-89 graphing calculator, loose-leaf binder, notebook paper,
graph paper Credit
Options PCHS:
2 units of high school credit will be awarded to students passing this
class. University
of Colorado at Denver:
This class is offered under the CU-Succeed program.
Students signing up for the CU credit will receive 4 semester hours of
first semester calculus credit.
Platte Canyon School District
will pay for this credit for any student who wishes to receive it. Please check with the college or university you plan to
attend to see if they will accept this credit. AP Credit:
In order to receive AP credit, you must take the AP Calculus (AB or BC) test offered on the
morning of May 10, 2001. Most
colleges and universities will accept this credit if the student earns a 3, 4 or
5 on the test. Check with the
college or university you plan to attend
to determine their policy. The
cost of taking this test is approximately $75 and must be paid prior to taking
the test. Calculators A graphing calculator is essential for this class.
The College Board gives the AP tests and expects every student to know
how to use a graphing calculator. Students
are allowed to use up to two different graphing calculators on the AP test.
The test is divided into two parts, one that is calculator active and the
other that is not. The most
powerful TI (Texas Instruments) graphing calculator that is allowed on the test
and in this class is the TI-89, a relatively new calculator that came out in
late 1998. Other calculators that
can be used are the TI family of TI-81 through TI-86. The TI-92 may not be used.
Please ask if you want to know what other brands of graphing calculators
may be used. Expectations
•
You
are expected to assume responsibility for your own learning as this is a college
class. You are expected to ask
questions to clarify your understanding and to enhance your learning experience. •
You are expected to attend class and be on time. •
All assignments must be turned in. All
homework is due the next day. Late
assignments will not receive credit but must be turned in. •
Homework and tests must be done
in pencil. You will grade your homework with a different
color pen. •
You are expected to actively participate in classroom discussion and
activities. •
Each student must bring their materials (paper, pencils, red pen, book,
calculator) to class each day to be prepared. •
Each student is expected to keep and organized notebook with all of their
calculus materials. This should be
brought to class every day. •
Any test grade of lower than a C must schedule a conference within the
next 24 hours to correct mistakes and relearn the material. Course Objectives
I.
Prerequisites for Calculus
A.
Lines
1.
Use increments to calculate slopes.
2.
Write an equation and sketch a graph of a line given specific
information.
3.
Identify the relationships between parallel lines, perpendicular lines,
and slopes.
4.
Use linear regression equations to solve problems.
B.
Functions and Graphs
1.
Identify the domain and range of a function using its graph or equation.
2.
Recognize even functions and odd functions using equations and graphs.
3.
Interpret and find formulas for piecewise defined functions.
4.
Write and evaluate compositions of two functions.
C.
Exponential Functions
1.
Determine the domain, range, and graph of an exponential function.
2.
Solve problems involving exponential growth and decay.
3.
Use exponential regression equations to solve problems.
D.
Parametric Equations 1.
Graph curves that are described using parametric equations.
2.
Find parametrizations of circles, ellipses, line segments, and other
curves.
E.
Functions and Logarithms
1.
Identify a one-to-one function.
2.
Determine the algebraic representation and the graphical representation
of a function and its inverse.
3.
Use parametric equations to graph inverse functions.
4.
Apply the properties of logarithms.
5.
Use logarithmic regression equations to solve problems.
F.
Trigonometric Functions
1.
Convert between radians and degrees, and find arc length.
2.
Identify the periodicity and even-odd properties of the trigonometric
functions.
3.
Generate the graphs of the trigonometric functions and explore various
transformations upon these graphs.
4.
Use the inverse trigonometric functions to solve problems. II.
Limits and Continuity
A.
Rates of Change and Limits
1.
Calculate average and instantaneous speeds.
2.
Define and calculate limits for function values and apply the properties
of limits.
3.
Use the Sandwich Theorem to find certain limits indirectly.
B.
Limits Involving Infinity
1.
Find and verify end behavior models for various functions.
2.
Calculate limits as x approaches +/- infinity and to identify vertical
and horizontal asymptotes.
C.
Continuity
1.
Identify the intervals upon which a given function is continuous and
understand the meaning of a continuous function.
2.
Remove removable discontinuities by extending or modifying a function.
3.
Apply the Intermediate Value Theorem and the properties of algebraic
combinations and composites of continuous functions.
D.
Rates of Change and Tangent Lines
1.
Apply directly the definition of the slope of a curve in order to
calculate slopes.
2.
Find the equations of the tangent line and normal line to a curve at a
given point.
3.
Find the average rate of change of a function. III.
Derivatives
A.
Derivative of a Function
1.
Calculate slopes and derivatives using the definition of the derivative.
2.
Graph f from the graph of f ′, graph f ′ from the graph of f,
and graph the derivative of a function given numerically with data.
B.
Differentiability
1.
Find where a function is not differentiable and distinguish between
corners, cusps, discontinuities, and vertical tangents.
2.
Approximate derivatives numerically and graphically.
C.
Use the rules of differentiation to calculate derivatives, including
second and higher order derivatives.
D.
Use derivatives to analyze straight line motion and solve other problems
involving rates of change.
E.
Use the rules for differentiating the six basic trigonometric functions.
F.
Chain Rule
1.
Differentiate composite functions using the Chain Rule.
2.
Find slopes of parametrized curves.
G.
Implicit Differentiation
1.
Find derivatives using implicit differentiation.
2.
Find derivatives using the Power Rule for Rational Powers of x.
H.
Calculate derivatives of functions involving the inverse trigonometric
functions.
I.
Calculate derivatives of exponential and logarithmic functions. IV.
Applications of Derivatives
A.
Determine the local or global
extreme values of a function.
B.
Apply the Mean Value Theorem and to find the intervals on which a
function is increasing or decreasing. C.
Use the First and Second Derivative Tests to determine the local extreme
values of a function. D.
Determine the concavity of a function and locate the points of inflection
by analyzing the second derivative. E.
Graph f using information about f ′. F.
Solve application problems involving finding minimum or maximum values of
functions. G.
Find linearizations and use Newton’s method to approximate the zeros of
a function. H.
Estimate the change in a function using differentials. I.
Solve related rate problems. V.
The Definite Integral A.
Approximate the area under the graph of a nonnegative continuous
function by using rectangle approximation methods. B.
Interpret the area under a graph as a net accumulation of a rate of
change. C.
Express the area under a curve as a definite integral and as a limit of
Riemann sums.
D.
Compute the area under a curve using a numerical integration procedure. E.
Apply rules for definite integrals and find the average value of a
function over a closed interval.
F.
Apply the Fundamental Theorem of Calculus. G.
Understand the relationship between the derivative and the definite
integral as expressed in both parts of the Fundamental Theorem of Calculus. H.
Approximate the definite integral by using the Trapezoidal Rule and by
using Simpson’s Rule, and estimate the error in using the Trapezoidal and
Simpson’s Rules.
UCD – CU Succeed Gold Incomplete PolicyIf
a student’s final grade is below a “C”, a student may accept and “IW”
(Incomplete Withdrawal) in lieu of a final grade. Students receiving and “IW” in lieu of a grade will not
receive a tuition refund. This
option is made available to protect a student’s chances of college admittance.
An “IW” on a student’s record will not negatively affect a
student’s GPA at CU – Denver. UCD- High School Academic Honor CodeStudents
are to submit only their own work for evaluation, to acknowledge the work and
conclusion of others, and to do nothing that would provide an unfair advantage
in their academic efforts. Students
who fail to comply with the CU-Denver Academic Honor Code are subject to
disciplinary action. |
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Last Updated February 17, 2001
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