Transcript Presentation from May 3rd

Accelerated Integrated
Precalculus
May 3, 2010
Dr. Brian Wynne, Math Dept. Chair
Mrs. Sharon Bean, Math Teacher
H. Precalculus vs. AIP
FUNCTIONS
• Characteristics of functions—
domain, range, symmetry,
zeros, asymptotes,
boundedness, periodicity,
points of discontinuity,
intervals over which a
function increases/decreases,
relative extrema
• Operations with functions—
composing two or more
functions, finding a
function’s inverse, defining a
function parametrically
• Families of functions—
polynomial, rational,
exponential, logarithmic,
trigonometric
FUNCTIONS
• Characteristics of functions—
domain, range, symmetry,
zeros, asymptotes,
boundedness, periodicity,
points of discontinuity,
intervals over which a
function increases/decreases,
relative extrema
• Operations with functions—
composing two or more
functions, finding the inverse
of rational functions
• Families of functions—
rational, trigonometric
H. Precalculus vs. AIP
EQUATIONS/INEQUALITIES
• Solving polynomial
equations/inequalities over
the field of complex numbers
• Solving rational
equations/inequalities
• Solving
exponential/logarithmic
equations/inequalities
• Solving trigonometric
equations
EQUATIONS/INEQUALITIES
• Solving rational
equations/inequalities
• Solving trigonometric
equations
H. Precalculus vs. AIP
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TRIGONOMETRY
Converting angles between
degree measure and radian
measure
Sketching angles in standard
position and identifying coterminal and reference angles
Defining trigonometric functions
as circular functions as well as the
ratio of the sides of right triangles
Evaluates and graphs
trigonometric functions as well as
inverse trigonometric functions
Verifies trigonometric identities
Law of Sines/Law of Cosines
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TRIGONOMETRY
Converting angles between
degree measure and radian
measure
Sketching angles in standard
position and identifying coterminal and reference angles
Defining trigonometric functions
as circular functions as well as the
ratio of the sides of right triangles
Evaluates and graphs
trigonometric functions as well as
inverse trigonometric functions
Verifies trigonometric identities
Law of Sines/Law of Cosines
H. Precalculus vs. AIP
•
•
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VECTORS/POLAR
COORDINATES
Graphing vectors in a
plane, performing vector
operations, and applying
vectors to solve contextual
problems
Using DeMoivre’s Theorem
to re-express complex
numbers in polar form and
perform operations
Converting between polar
and rectangular coordinates
Graphing and analyzing
polar equations
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•
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•
VECTORS/POLAR
COORDINATES
Graphing vectors in a
plane, performing vector
operations, and applying
vectors to solve contextual
problems
Using DeMoivre’s Theorem
to re-express complex
numbers in polar form and
perform operations
Converting between polar
and rectangular coordinates
Graphing and analyzing
polar equations
H. Precalculus vs. AIP
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•
•
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•
DATA ANALYSIS/
PROBABILITY
Using combinations,
permutations, and the
Fundamental Principle of
Counting to “count” events
Applying the Binomial Theorem
to expand binomial expressions
Defining sample spaces,
outcomes, and events
Computing the probability of an
event—including independent,
dependent, and conditional
Analyzing data using mean,
median, mode, standard
deviation, and variance
DATA ANALYSIS/
PROBABILITY
• Applying the Central Limit
Theorem to calculate
confidence intervals for a
population
• Determining the margin or
error for a specified level of
confidence
• Using confidence intervals and
margins of error to make
inferences from data about a
population
H. Precalculus vs. AIP
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SEQUENCES/SERIES
Determining terms of
arithmetic/geometric
sequences
Using sigma notation
Finding partial sums of
arithmetic/geometric series
Proving the “truth” of a
statement using mathematical
induction
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SEQUENCES/SERIES
Determining terms of
arithmetic/geometric
sequences
Using sigma notation
Finding partial sums of
arithmetic/geometric series
Proving the “truth” of a
statement using mathematical
induction
H. Precalculus vs. AIP
•
•
•
•
MATRICES
Performing operations with
matrices
Solving 2 x 2 and 3 x 3
systems of equations using
matrices
Finding the inverse of a
square matrix—if it exists
Using matrices to decompose a rational
expression into partial
fractions
MATRICES
Nothing included in AIP
Curriculum
H. Precalculus vs. AIP
CONIC SECTIONS
• Identifying whether an
equation represents a
circle, a parabola, an
ellipse, or a hyperbola
• Writing an equation for
and graphing standard
conic sections
CONIC SECTIONS
Nothing included in AIP
Curriculum
Student Expectations:
1. Do homework every night – not just before
test or at end of semester so you can get
credit.
2. Take notes during class.
3. Exhibit good work ethic – no slacking off!
4. Come in for extra help when needed.
Teacher Expectations:
1. Have optional prerequisite skills packet online that can be done this summer
2. Hold before school help sessions 2 days each
week (after school sessions will be held when
needed)
3. Post calendar for periods of 1 or 2 weeks online
4. Hold study sessions in preparation for the
new GHSGT
Assessments:
1. Higher level thinking questions will be
included
2. Will have one or more assessments during
each chapter
3. Will prepare students to take NEW GHSGT
4. No more PLATO for recovery of low or
failing test grades or averages
Placement for
2011-2012 School Year
AP Calculus AB or
AP Calculus BC and/or
AP Statistics or
New Discrete Math
Placement will be determined by student’s work
ethic and grades. If a student does not exhibit
a good work ethic along with good grades, he
or she will not be recommended for the AP
Calculus BC class.
Contact Information:
Dr. Brian Wynne
[email protected]
Sharon Bean
[email protected]