Download SEMESTER 1

Pre-Calculus
Unit 1 – Functions and Their Graphs
Scoring Criteria
Performance Indicators
U1.PI 1
Use multiple representations to
describe linear functional
relationships.
U1.PI 2
Graph piecewise functions.
“1” – Emerging
I have demonstrated the most
basic knowledge/skills relevant
to this standard.
“2” – Developing
I have demonstrated relevant
knowledge/skills, but have not
yet demonstrated convincing
evidence of fully meeting the
standard.
Level 1
I can calculate slope using two
points on a line. I can identify
and justify the slope of a
vertical line (undefined) and
horizontal line.
L2: Level 1, plus…
I can represent linear
functions using slopeintercept form, graph a line
given slope-intercept form
and identify the slope and x
and y-intercepts of a line.
I can accurately plot the
endpoints of all segments of a
piecewise function.
I can graph a linear piecewise
function.
CCSS Domain(s): Functions
“3” – Achieving
I have demonstrated that I
have the knowledge/skills
defined in the standard.
“4” – Excelling
I have demonstrated the
knowledge/skills defined by
the standard with a high level
of understanding/ability as
defined by the discipline.
L3: Level 2, plus…
I can demonstrate algebraic and
graphical equivalence of linear
functions using point-slope,
slope-intercept and standard
forms.
L4: Level 3, plus…
I can graph a piecewise function
including linear and non-linear
segments by hand and using
graphing technology.

I can determine the slope of a
line using the difference
quotient and explain how to
derive the formula using
function notation.

U1.PI 3
Identify the domain and range of
a function given an algebraic
expression.
Identify and verify inverse
functions.
I can identify the domain or
range of a single function
family from an algebraic
expression.
I can find an inverse of a given
function given in a table,
equation or graph and I can
write the inverse function
using appropriate notation.
I can identify the domain and
range of a single function
family from an algebraic
expression.
I can create inverse functions
algebraically and use
composition of functions to
verify the inverse relationship.
I can create figures using
transformations of
multiple parent functions
and domain restrictions.
I can write a piecewise
function for a given graph.
I can identify the domain of a
complex function from an
algebraic expression.
I can identify the domain and
range of a complex function
from an algebraic expression.
I can explain if a function is
invertible using domain/range
and one-to-one terminology.
I can produce an invertible
function from a non-invertible
function by restricting the
domain.
I can demonstrate an inverse
function graphically.
Pre-Calculus
Unit 2 – Polynomial Functions and Rational Functions
“1” – Emerging
I have demonstrated the most
basic knowledge/skills relevant to
this standard.
Scoring Criteria
Performance Indicators
U2PI4
Graphing and interpreting
quadratic functions using
key characteristics.
U2PI5
Graphing higher order
polynomials using the end
behavior and multiplicity of
zeroes.
Identifying real (rational
and irrational) zeros of
higher order polynomials.
“2” – Developing
I have demonstrated relevant
knowledge/skills, but have not yet
demonstrated convincing evidence
of fully meeting the standard.
Level 1, plus…
Level 2, plus…
U2PI7
Graphing rational
functions using key
function characteristics.
“4” – Excelling
I have demonstrated the
knowledge/skills defined by the
standard with a high level of
understanding/ability as defined by
the discipline.
Level 3, plus…

I can identify the zeros of a
quadratic function in standard
form by using the quadratic
formula or factoring.

I can find an equation in standard
form given the vertex and a point on
the parabola or given the zeros and
a point on the parabola.

I can identify the vertex and zeros
of a standard form quadratic
function by completing the square
when 𝑎 ≠ 1.

I can identify key attributes of a
quadratic function (vertex, axis of
symmetry, zeros, y-intercept)
from a graph.

I can identify the vertex and zeros of
a standard form quadratic function
by completing the square when
𝑎 = 1.

I can graph quadratic functions
from standard, factored or vertex
form.

I can use the Leading Coefficient
Test to determine the end
behavior of graphs of polynomial
functions and accurately describe
the end behavior using limit
notation.

I can identify a polynomial equation
in completely factored form.


I can use transformations
multiplicities of zeroes to sketch
graphs of polynomial functions.
I can identify the correct y-intercept
and the leading coefficient “a”
when graphing polynomial
functions or when writing equations
for polynomials from graphs.
I can identify the zeros of a polynomial
function using long or synthetic
division.
I can apply the Remainder and Factor
Theorems.
I can use the Rational Zero Test to
determine possible rational zeros of
polynomial functions.
U2PI6
Graphing polynomials with
real and complex zeros
(Fundamental Theorem of
Algebra).
“3” – Achieving
I have demonstrated that I have
the knowledge/skills defined in the
standard.
 I can use the imaginary unit “I” to
write complex numbers.
 I can use commutative,
associative and distributive
properties to add, subtract and
multiply complex numbers.
I can identify vertical and horizontal
asymptotes of rational functions.
I can use complex conjugates to write
the quotient of two complex numbers in
standard form.

I can use the Intermediate Value
Theorem to help locate zeros of
polynomial functions.
I can use Descartes’ Rule of Signs and
the Upper and Lower Bound Rules to
find zeros of polynomials.
 I can apply the Fundamental
Theorem of Algebra to determine
the number of zeros of a
polynomial function.
 I can find all zeros of polynomial
functions including complex zeros.
 I can create a sketch of a rational
function involving vertical and
horizontal asymptotes.
 I can identify hole in the graph of a
rational function.
I can create a sketch of a rational
function with two vertical asymptotes or
a slant asymptote showing the end
behavior.
I can solve real life situation
problems using key
attributes of quadratic
functions.
I can identify rational and
irrational zeroes of a
polynomial equation given in
factored form and sketch an
accurate graph involving
irrational zeroes.
I can find the real zeros of a
polynomial algebraically and
use the zeros, end behavior
and additional points to
sketch a graph of the
function.
I can find all zeros of any
higher order polynomial
(real and complex) by
factoring and can sketch the
resulting graph.
I can graph rational
functions and accurately
identify zeroes, asymptotes,
y-intercepts and additional
points as needed.
CCSS Domains and Standards:
NUMBER AND QUANTITY:
The Complex Number System
N-CN 1. Know there is a complex number 𝑖 such that 𝑖² = −1, and every complex number has the form 𝑎 + 𝑏𝑖 with 𝑎 and 𝑏 real.
N-CN 2. Use the relation 𝑖² = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
N-CN 3. Find the conjugate of a complex number, use conjugates to find moduli and quotients of complex numbers.
Use complex numbers in polynomial identities and equations.
N-CN 7. Solve quadratic equations with real coefficients that have complex solutions
N-CN 8. Extend polynomials identities to the complex number. For example, rewrite 𝑥² + 4 = (𝑥 + 2𝑖)(𝑥 − 2𝑖)
N-CN 9. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
ALGEBRA:
Interpret Structure of expressions
A-SSE 2. Use the structure of expression to identify ways to rewrite it. For example, x 4 − y 4 = (x 2 )2 − (y 2 )2 = (x 2 − y 2 )(x 2 + y 2 )
Understand the relationship between zeros and factors of a polynomial
A-APR 2. Know and apply the Remainder Theorem : For a polynomial 𝑝(𝑥) and a number 𝑎, the remainder on division by 𝑥 – 𝑎 is 𝑝(𝑎), so 𝑝(𝑎) = 0 if and only if (𝑥 −
𝑎) is a factor of 𝑝(𝑥).
A-APR 3. Identify zeroes of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the
polynomial.
A-APR 6. Rewrite simple rational expressions in different forms.
FUNCTIONS:
Analyze functions using different representations
F-IF 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases, using technology for more complicated
cases.
F-IF 7c. Graph polynomial functions, identify zeroes when suitable factorizations are available, and showing end behavior.
F-IF 8. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph,
and interpret quadratics graphically
F-IF 7a. Graph rational functions, identifying zeroes and asymptotes when suitable factorizations are available, and showing end behavior.
Pre-Calculus
Unit 3 – Exponential and Logarithmic Functions
“1” – Emerging
I have demonstrated the most
basic knowledge/skills relevant to
this standard.
Scoring Criteria
“2” – Developing
I have demonstrated relevant
knowledge/skills, but have not yet
demonstrated convincing evidence
of fully meeting the standard.
Level 1, plus…
Performance Indicators
U3PI 8
Graphing exponential and
Logarithmic functions
U3PI 9
Evaluating common and
natural logarithms,
properties of logarithms,
and solving equations
U3PI 10
Exponential and
logarithmic application



Graph exponential function
including the asymptote and
any intercepts.
Identify the domain of a
logarithmic function.

Graph logarithmic function
including the asymptote and any
intercepts.
Convert between exponential
and logarithmic expressions.

Evaluate single-step exponential
and logarithmic equations.


Setting up and solving basic
exponential application
problems.
CCSS Domains and Standards:
NUMBER AND QUANTITY:
The Complex Number System
N-CN
Use complex numbers in polynomial identities and equations.
N-CN
ALGEBRA:
Interpret Structure of expressions
A-SSE
FUNCTIONS:
Analyze functions using different representations
F-IF

Setting up and solving complex
exponential application
problems involving continuous
compounding.
“3” – Achieving
I have demonstrated that I have
the knowledge/skills defined in the
standard.
“4” – Excelling
I have demonstrated the
knowledge/skills defined by the
standard with a high level of
understanding/ability as defined by
the discipline.
Level 2, plus…
Level 3, plus…
 Demonstrate
 Graph natural logarithmic
graphically and
functions including the
algebraically the
asymptote and any intercepts.
inverse relationship
between exponential
and logarithmic
functions including a
comparison of
domain and range.
 Apply properties of logarithms
Evaluate multi-step
to expand and condense
exponential and
logarithmic expressions.
logarithmic equations.
 Evaluate single-step natural
logarithmic equations.

Solve complex logarithmic
application problems.

Write the exponential or
logarithmic equation for a
given graph.
Solving exponential or
logarithmic models
requiring calculation of
the rate of change.