Download 2016 precalc_syllabus

Honros Pre-Calculus Syllabus - 2016-2017
September
October
November
a) determining whether a
given relation is or is not a
function.
b) distinguishing between
verbal, numerical,
algebraic, and graphical
representations of functions.
c) correctly determining
domain and range and
sketching graphs of selected
functions (including split
domain functions).
d) correctly performing
operations with functions,
including composition.
e) describing various forms
of symmetry and correctly
identifying functions as
even, odd, or neither.
f) graphing functions using
transformations (reflections,
translations, dilations, etc.).
g) correctly finding the
inverse of a relation or a
function and describing the
relationship between a
function and its inverse.
h) using terms such as “oneto-one”, “increasing”, and
“decreasing” in describing
functions and their graphs.
i) identifying appropriate
functions to model and
solve real-world problems.
a) correctly graphing
linear relationships.
b) correctly determining
the equation of linear
functions.
c) using linear functions to
“model” and solve realworld problems.
d) using a graphing
calculator to perform
linear regressions on data
sets.
a) recognizing power
functions and correctly
sketching their graphs.
b) correctly using synthetic
division to divide a
polynomial by a 1st deg.
binomial.
c) using the “factor
theorem” to decide if a
binomial is or is not a
factor of a polynomial.
d) determining the rational
zeros of a polynomial
function.
e) using the graphing
calculator to sketch
polynomial functions and
determine zeros and
extreme values.
f) correctly using the
“principle of dominance.”
g) using the concept of
derivative to identify
possible local extrema.
h) using polynomial
functions to model and
solve real-life problems.
a) identifying any
quadratic function as a
translation, reflection, or
dilation of y=x2 .
b) sketching graphs of
quadratic functions by
rewriting in standard form
and identifying vertex,
axis of symmetry, and
intercepts.
c) correctly determining
the “extreme” value of a
quadratic function.
d) correctly determining
the quadratic function
given a graph.
e) using quadratic
functions to “model” and
solve real-life problems.
f) using the graphing
calculator to sketch graphs
and determine extreme
values.
December
a) determining vertical
and horizontal
asymptotes for selected
rational functions.
b) sketching graphs of
selected rational
functions.
c) using the graphing
calculator to sketch the
graphs of rational
functions.
d) using rational
functions to model and
solve real-life problems.
January
a) correctly sketching the graphs
of functions in the form y=bx .
b) correctly computing simple
and compound interest and
deriving and using the
compound interest formula.
c) discovering the value of “e”
and graphing natural exponential
functions.
d) sketching the graphs of
exponential growth and
exponential decay functions
(including bounded and logistic
growth).
e) correctly solving real-life
problems involving exponential
growth or decay.
f) identifying logarithmic
functions as the inverse of
exponential functions.
g) correctly evaluating natural
and common logarithms.
h) correctly sketching the graphs
of logarithmic functions.
i) using the “laws of logarithms”
to express logs in expanded or
condensed form and to help
solve logarithmic and
exponential equations.
j) using logs to solve exponential
equations, especially those
involving growth or decay.
k) using the graphing calculator
to sketch graphs of logarithmic
and exponential functions and to
perform exponential and
logarithmic regression analysis.
February
March
April
May
June
a) deriving the distance
formula and using it to find
the distance between two
points.
b) describing the properties
of the four quadratic
relations.
c) using the definitions of
the quadratic relations to
derive the standard forms of
their equations.
d) using the definitions and
the standard forms to sketch
graphs of quadratic
relations.
e) using the graphing
calculator to sketch graphs
of quadratic relations.
f) correctly using
vocabulary associated with
quadratic relations (center,
foci, eccentricity, focal
radius, focal chord, etc.).
g) solving real-life
problems involving
quadratic relations.
h) correctly identifying the
specific quadratic relation
when its equation is written
in “general” form.
a) correctly using right
triangle trig to solve right
triangles.
b) correctly using the Law
of Cosines and the Law of
Sines to solve non-right
triangles.
e) using the Unit Circle to
find the values of the trig
functions of “special”
numbers and to estimate
the values of the functions
for non-special numbers.
f) using the Unit Circle to
find t given the value of the
trig function.
g) correctly sketching
graphs of sinusoidal
functions and correctly
using terms such as
amplitude, period, and
phase shift.
h) using the graphing
calculator to sketch the
graphs of sinusoidal
functions and investigate
their properties.
i) using circular functions
to model and solve realworld problems (emphasis
on harmonic motion).
j) correctly using the
methods of “addition of
ordinates” and
“multiplication of
ordinates” to sketch graphs
of composite trig functions.
k) determining properties
of the tangent function and
sketching its graph.
l) using reciprocal graphing
techniques to sketch graphs
of sec, cos, & tan
functions.
a) correctly defining the
inverse sine, inverse
cosine, and inverse
tangent functions.
b) correctly evaluating
expressions involving
inverse trig functions.
c) correctly graphing the
inverse trig functions.
d) applying the concepts
of trigonometry to solve
real-world problems.
a) properly differentiating
between discrete and continuous
variables.
b) correctly employing the
multiplication principle and
using it to determine numbers of
permutations and combinations.
c) explaining the difference
between experimental and
theoretical probability.
d) correctly identifying a sample
space and calculating
probabilities and conditional
probabilities.
e) solving problems involving
random variables and
“mathematical expectation.”
a) correctly defining
“radian.”
b) correctly converting
radians to degrees and
degrees to radians.
c) correctly computing arc
length and arc measure.
d) using the “Unit Circle”
to define the six circular
functions.
a) explaining the
difference between an
identity and an equation.
b) proving the
“fundamental identities.”
c) using the fundamental
identities to prove
selected identities.
d) deriving the sum and
difference identities and
using them to prove other
identities.
e) deriving the double
angle identities and using
them to prove other
identities.
f) using the trig identities
to help solve
trigonometric equations.
g) using trig identities
and equations to solve
real-world problems.