Course – AP Calculus
Teacher – Mike Fox-Boyd
Campus
extension 448
CONTENT:
Functions
Review
Types of functions: linear, polynomial, rational,
absolute value, exponential, logarithmic, trigonometric, inverse trigonometric
and piece-wise
Limits
Intuitive definition of a limit, computational
techniques, estimating limits from graphs or tables, one-sided limits,
continuity, Intermediate Value Theorem, infinite limits, asymptotes, trigonometric
limits
Derivatives
Derivative defined as a limit of difference
quotient, derivatives of polynomials and functions with fractional and negative
exponents, product and quotient rules, chain rule, higher-order derivatives,
implicit differentiation, derivatives of trigonometric functions, “nDeriv(“ on
graphing calculator
Applications
of Derivatives
Tangent line to a curve at a point and local linear
approximation, instantaneous and average rates of change, approximate rate of
change from graphs and tables of values, comparing graph of function with graph
of derivative, related rates, extrema (absolute and relative), max/min
problems, Rolle’s Theorem, Mean Value Theorem, applications to graphing
(monotonocity, concavity), limits at infinity, horizontal motion, free-falling
objects
Integration
Antiderivatives: rewriting integrands to fit
fundamental formulas, substitution, Solving differential equations with initial
conditions, slope fields
Logarithmic,
Exponential, and Inverse Trigonometric Functions
Differentiation of inverse functions,
differentiation of logarithmic, exponential, and inverse trigonometric
functions, logarithmic differentiation, integration using logarithmic,
exponential, and inverse trigonometric functions
Applications
of Integration
Summation, area under the curve, upper and lower
sums, Reimann Sums, trapezoidal rule, Fundamental Theorem of Calculus, Second
Fundamental Theorem of Calculus, area of a region, average value of a function,
volume of a solid of revolution using the disk or washer methods, volume of a
solid with known cross-section, motion along a line, exponential growth,
numerical value of definite integral on graphing calculator
Summary:
Preparation for AP Exam
TEXT:
Calculus of a Single Variable, Eighth Edition, Larson, Hostetler, and
Edwards
CALCULATOR:
a graphing calculator, either a TI-83+ or TI-84+
QUARTER
GRADE: is based on test grades.
HOMEWORK
is assigned, reviewed, and NOT COLLECTED.
The midterm exam will cover material from the first semester. The final exam will be in the format of the
AP Exam and thus will cover material from the entire year.
If a test
is turned in without the honor code written on the back page, I will not
correct a test until the honor code is written.
Every student is expected to participate in
class. If a student chooses not to
volunteer answers, s/he will most likely be called upon.
Drinking
water only is allowed in class, as this “southern climate” is none too chilly,
and many of you participate in sports.
Water may not be kept in an open container, only water bottles with a
pressurized cap are allowed.
Answers to math problems should be boxed, except for
obvious exceptions. Deductions will be made
when appropriate. You will have to do
this in college, so it’s a good idea to get used to it now.
Please seek extra help with Mr. Fox-Boyd at any time. Try to make an appointment.
On Cyber Days, the class will move forward. Assignments will be posted, and you will
complete them. Grading regarding these
assignments will be announced when Cyber Days occur.