Classroom:
316
Subject:
Pre-AP Pre-Calculus
Teacher:
Mr. Schievenin
Livingston American School Quarterly Lesson Plan
Week 1
Concept / Topic To Teach:
Functions/Domains
Standards Addressed:
Week 2
Week 4
Polynomial Functions
Polynomial Functions
Interpret functions that
Understand the concept of
a function and use function arise in applications in
notation
terms of the context
Understand the
relationship between zeros
and factors of polynomials
Rewrite rational
expressions
1. Understand that a function
from one set (called the
domain) to another set
(called the range) assigns to
4. For a function that models
a relationship between two
quantities, interpret key
features of graphs and
2. Know and apply the
Remainder Theorem: For a
polynomial p(x) and a
number a, the remainder on
each element of the domain
exactly one element of the
range. If f is a function and x
is an element of
tables in terms of the
quantities, and sketch graphs
showing key features given
a verbal description of
division by x – a is p(a), so
p(a) = 0 if and only if (x – a)
is a factor of p(x).
its domain, then f(x) denotes
the output of f corresponding
to the input x. The graph of f
is the graph of
the relationship. Key
features include: intercepts;
intervals where the function
is increasing, decreasing,
the equation y = f(x).
positive, or negative;
relative maximums and
minimums; symmetries; end
behavior; and periodicity.�
2. Use function notation,
evaluate functions for inputs
in their domains, and
interpret statements that use
function notation in terms of
a context.
Functions
Week 3
5. Relate the domain of a
function to its graph and,
where applicable, to the
quantitative relationship it
3. Identify zeros of
polynomials when suitable
factorizations are available,
and use the zeros to
construct a
rough graph of the function
defined by the polynomial.
c. Graph polynomial
functions, identify zeros
when suitable factorizations
are available, and
6. Rewrite simple rational
expressions in different
forms; write a(x)/b(x) in the
form q(x) + r(x)/b(x), where
a(x), b(x), q(x), and r(x) are
polynomials with the degree
of r(x) less than the degree
of b(x), using
inspection, long division, or,
for the more complicated
examples, a computer
algebra system.
7. (+) Understand that
rational expressions form a
system analogous to the
rational numbers, closed
under
addition, subtraction,
multiplication,
Classroom:
316
Subject:
Pre-AP Pre-Calculus
describes. For example, if
the function h(n) gives the
number of person-hours it
takes to assemble n
engines in a factory, then the
positive integers would be
an appropriate domain for
the function.�
6. Calculate and interpret the
average rate of change of a
function (presented
symbolically or as a table)
over a specified interval.
Estimate the rate of change
from a graph.
Analyze functions using
different representations
7. Graph functions
expressed symbolically and
show key features of the
graph, by hand in simple
cases
and using technology for
more complicated cases.�
a. Graph linear and quadratic
functions and show
intercepts, maxima, and
minima.
b. Graph square root, cube
root, and piecewise-defined
functions, including step
functions and
absolute value functions.
Teacher:
Mr. Schievenin
show end behavior.
d. (+) Graph rational
functions, identifying zeros
and asymptotes when
suitable factorizations are
available, and showing end
behavior.
Classroom:
316
Subject:
Pre-AP Pre-Calculus
Build new functions from
existing functions
3. Identify the effect on the
graph of replacing f(x) by
f(x) + k, k f(x), f(kx), and f(x
+ k) for specific values of k
(both positive and negative);
find the value of k given the
graphs. Experiment with
cases and illustrate an
explanation of the effects on
the graph using technology.
Include recognizing even
and odd functions from
their graphs and algebraic
expressions for them.
3.1 Solve problems
involving functional
concepts, such as
composition, defining the
inverse function
and performing arithmetic
operations on functions.
(CA Standard Algebra II –
24.0)
4. Find inverse functions.
a. Solve an equation of the
form f(x) = c for a simple
function f that has an inverse
and write an
expression for the inverse.
For example, f(x) =2 x3 or
Teacher:
Mr. Schievenin
Classroom:
316
Subject:
Pre-AP Pre-Calculus
Teacher:
Mr. Schievenin
f(x) = (x+1)/(x–1) for x ≠ 1.
b. (+) Verify by composition
that one function is the
inverse of another.
c. (+) Read values of an
inverse function from a
graph or a table, given that
the function has an
inverse.
d. (+) Produce an invertible
function from a noninvertible function by
restricting the domain.
Specific Objectives:
SWBAT write domains in
function notation and
determine the domain of a
function
SWBAT employ the
operations to combine
functions through addition,
multiplication, and division
SWBAT evaluate a function
and its inverse
SWBAT write domains in
function notation and
determine the domain of a
function.
SWBAT determine the
domain of a combined
function
SWBAT test whether a
function is even, odd, or
neither
SWBAT determine the
inverse of a function, and
evaluate whether or not
given functions have an
inverse relationship
SWBAT graph polynomial
functions, identify zeros
when suitable factorizations
are available, and show end
behavior.
SWBAT evaluate whether or
not a function approaches
infinity algebraically and
calculate the points at which
a vertical asymptote exists
Classroom:
316
General Goal(s):
Subject:
Pre-AP Pre-Calculus
Intro to the Class
Teacher:
Mr. Schievenin
Graphing Polynomial
equations
Ratio Zeros (roots) test
Slope of a line
Increasing and decreasing
functions
Function notation
Inverse functions
Finding Zeros
Synthetic Division
Domain and Range
Finding inverse functions
End behavior
Remainder theorem
Piecewise functions
Checking using composition
of a function and its inverse
Ratio Zeros (roots) test
Representing polynomials as
quotients and remainders
Graphical representations of
inverse
Remainder theorem
Using inverses to solve
equations
Long division
Long division
Representing polynomials as
quotients and remainders
One-to-one or restricting
domain to create an inverse
function
Correlation coefficients
Linear Regressions
Assessment Based On
Objectives:
Core Values Addressed
Formative assessment on
guided and independent
practice
Quiz 1
Formative Assessment
Formative Assessment
Classwork
Classwork
Classwork
Formative assessment on
guided and independent
practice
Homework
Homework
Assessment of homework
Assessment of homework
Compassion,
Communication, Creativity,
Confidence
Compassion,
Communication, Creativity,
Confidence
Test 1
Compassion,
Communication, Creativity,
Confidence
Compassion,
Communication, Creativity,
Confidence
Classroom:
316
Subject:
Pre-AP Pre-Calculus
Teacher:
Mr. Schievenin
Livingston American School Quarterly Lesson Plan
Week 5
Week 6
Week 7
Week 8
Concept / Topic To Teach:
Polynomial Functions
Logarithmic and
Exponential Functions
Logarithmic and
Exponential Functions
Logarithmic and
Exponential Functions
Standards Addressed:
SWBAT graph polynomial
functions, identify zeros
when suitable factorizations
are available, and show end
behavior.
3. Choose and produce an
equivalent form of an
expression to reveal and
explain properties of the
quantity
e. Graph exponential and
logarithmic functions,
showing intercepts and end
behavior, and
5. (+) Understand the
inverse relationship between
exponents and logarithms
and use this relationship to
trigonometric functions,
showing period, midline,
and amplitude.
solve problems involving
logarithms and exponents.
e. Graph exponential and
logarithmic functions,
showing intercepts and end
behavior, and
trigonometric functions,
showing period, midline,
and amplitude.
represented by the
expression.�
c. Use the properties of
exponents to transform
expressions for exponential
functions. For example the
expression 1.15t can be
rewritten as (1.151/12)12t ≈
1.01212t to reveal the
approximate equivalent
monthly
interest rate if the annual
rate is 15%.
d. Prove simple laws of
logarithms. (CA Standard
Algebra II – 11.0)
e. Use the definition of
logarithms to translate
Classroom:
316
Subject:
Pre-AP Pre-Calculus
Teacher:
Mr. Schievenin
between logarithms in any
base. (CA Standard
Algebra II – 13.0)
f. Understand and use the
properties of logarithms to
simplify logarithmic
numeric expressions
and to identify their
approximate values. (CA
Standard Algebra II – 14.0)
Specific Objectives:
SWBAT determine the
minimum and maximum
values of a quadratic
expression
SWBAT use logarithms to
determine what power a
number would need to be
raised to in order to become
another given number
SWBAT conduct a leading
coefficient test to determine
whether a function’s degree
is even or odd
SWBAT use logarithms to
model growth and decay
with applications in
economics and chemistry
SWBAT determine the
intercepts of a logarithmic
expression
SWBAT determine
situations in which the
employment of a logarithm
would be useful in solving a
problem, and then properly
employ the logarithm to
solve for a given value.
Writing corresponding
exponential and logarithmic
equations
Properties of logarithms
Solving exponential and
logarithmic equations using
inverse functions
Graphing logarithms
SWBAT evaluate the zeroes
of a polynomial function
General Goal(s):
Graphing Rational
Functions
Finding vertical and
horizontal asymptotes
Solving rational functions
Domain and range of
rational functions
Change of base formula
Re-writing equations using
properties of logs
Classroom:
316
Assessment Based On
Objectives:
Subject:
Pre-AP Pre-Calculus
Formative assessment on
guided and independent
practice
Teacher:
Formative assessment on
guided and independent
practice
Assessment of homework
Mr. Schievenin
Formative assessment on
guided and independent
practice
Formative assessment on
guided and independent
practice
Assessment of homework
Assessment of homework
Quiz 3
Test 2
Assessment of homework
Core Values Addressed
Compassion,
Communication, Creativity,
Confidence
Compassion,
Communication, Creativity,
Confidence
Compassion,
Communication, Creativity,
Confidence
Compassion,
Communication, Creativity,
Confidence