Student “I Can Statements” for
Math Standards
Pre-calculus
I can statement
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Standard # met
I can determine if an equation defines a function by determining if it can
be solved for y, and if each x value determines a unique y value.
I can determine the (implied) domain for a given function.
I can determine a reasonable domain for a function describing a “real life”
problem.
I can evaluate a given function, obtaining a numerical or algebraic result.
Understand the
definition of a
function and be
able to use
functional notation,
evaluate a function,
and determine its
domain.
I can find a maximum or minimum value of a function on a closed interval
from graphical information.
I can find the zero of a function on a given interval using graphical
information.
Obtain
information and
draw conclusions
from graphs of
functions and
other relations.
I can complete the square to write a quadratic function in the form
Use various forms
for quadratic
functions to
identify vertex,
line of symmetry,
and intercepts. Be
able to graph a
quadratic, and
produce an
equation from a
given graph.
f ( x)  a  x  h   k given a more general form of the function.
2
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I can identify the vertex and axis of symmetry by utilizing the information
found in the form given in target #1, or by using the formula for the xcoordinate of the vertex, x  
b
.
2a
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I can solve a quadratic equation to determine the intercepts for the graph
of a given quadratic function.
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I can use the form given in target #1 to write the equation of a quadratic
function, given its graph.
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I can sketch the graph of a given quadratic equation, and identify the
vertex, axis of symmetry, and intercepts for the graph of the function.
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I can identify a right triangle from a diagram or when given sides a, b, and
c.
I can identify the legs and hypotenuse of a right triangle.
I can solve a2 + b2 = c2 for a missing value.
I can recognize common Pythagorean triples.
Apply the
Pythagorean
Theorem and its
converse to solve
problems and
logically justify
results.
Identify
intercepts, zeros,
maxima, minima,
and intervals of
increase and
decrease from the
graph of a
function.
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I can determine the objects defined in the given essential outcome by
examining the graph of a given function.
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I can identify a vertical translation, horizontal translation, or reflection over
the x or y-axis for a given function based on its equation, and I can rewrite
the equation for a given function using given transformations.
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I can sketch a graph for a translated function with or without the use of a
graphing utility.
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I can sketch a graph for any of the functions stated in essential outcome #6
with or without the use of a graphing utility.
Sketch the graphs
of common non
linear functions
(parent functions),
such as square
roots, absolute
value, and
quadratic
functions.
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I can add, subtract, and multiply given polynomials and recognize the
degree of the result.
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I can divide polynomials using long division, or synthetic division if
appropriate.
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I can express the quotient for a division of polynomials.
Perform basic
algebraic
operations with
polynomial
functions,
including division
and synthetic
division.
Determine how
translations affect
the symbolic and
graphical forms of
a function, and
use graphing
technology to
examine
translations.
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I can rewrite the result of a polynomial division using the form:
P( x)  D( x)Q( x)  R( x) or as a polynomial with a rational function
remainder.
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I can add, subtract, multiply and divide complex numbers and express the
results in standard form.
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I can solve a quadratic equation that has non-real solutions.
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I can use radian and/or degree measure to represent angles.
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I can evaluate trig function using the unit circle.
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I can use domain and period to evaluate sine and cosine functions.
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I can apply the formula for arc length (s = r  ), and use the concepts of
linear and angular speed to solve applied problems.
Find complex
solutions to
quadratic
equations, and
perform algebraic
operations with
complex numbers.
Translate problem
statements into
mathematical
models (equations
and inequalities)
including
quadratics and
solve the
problems using
appropriate
methods.
Develop skills with
graphing
calculator
operations
including
producing a graph
in a given window,
find function
values graphically
(tracing) or
numerically (use a
table), solve an
equation
numerically or
graphically.
Define and use the
properties of the
unit circle.
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I can use reference angles to evaluate trig functions.
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I can use trigonometric functions to model and solve real-life problems.
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I can use a calculator to evaluate trig functions, including the reciprocal
functions vis-à-vis the inverse functions.
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I can graph sine and cosine utilizing the properties of amplitude, period,
horizontal and vertical shift.
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I can find the sum of n terms of an arithmetic or geometric series, and can
determine the sum of a convergent infinite geometric series.
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I can solve applied problems involving sequences and series.
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I can prove summation formulas using the Principle of Mathematical
Induction.
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I can expand binomials using the Binomial Theorem
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I can use factorial notation to calculate binomial coefficients, and apply
counting principles, including permutations and combinations.
Find values of all
trig functions,
their reciprocals
and inverse
functions.
Apply properties
of sequences and
series, especially
arithmetic and
geometric
sequences.