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ADVANCED MATH Algebra Standard

H.A.1 Relations and Functions: Evaluate, analyze, model and perform operations
on polynomial, absolute value, rational, radical, logarithmic, exponential,
algebraic, piece-wise and step functions and relations with and without
technology.

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.1.1. Demonstrate an understanding
of the concept of a function, use function
notation, and determine whether or not a
given relation is a function.
         
H.A.1.2. Given the graph of a relation,
graph its inverse, demonstrating an
understanding of the reversing roles of
domain and range.
         
H.A.1.3 Evaluate and interpret functions.          
H.A.1.4 Determine, with or without
technology, the domain and range of a
relation defined by a graph, a table of
values, or a symbolic equation including
those with restricted domains and
whether a relation is a function.
         
H.A.1.4. Determine, with and without
technology, the domain and range of a
relation defined by a graph, or a table of
values, or a symbolic equation , including
those with restricted domains.
         
H.A.1.5. Represent a given relation in
multiple ways: as a table of values, a
graph, and a symbolic equation.
         
H.A.1.6 Analyze the effect on the graph
of a function by changing coefficients ,
exponents, and other parameters of the
function.
         
H.A.1.7 Find the zeros of a function.          
H.A.1.8 Determine whether a given
relation is even, odd or both
         
H.A.1.9 Perform operations ( addition ,
subtraction , division and multiplication) of
functions algebraically, numerically, and
graphically
         

H.A.2 Linear and Absolute Value Equations and Inequalities and Systems of Equations
and Inequalities:
Construct and model linear and absolute value equations and
inequalities and systems of linear equations and inequalities in two and three
variables and solve them with and without technology.

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.2.1 Analyze and apply various
methods to graph and solve linear and
absolute value equations and
inequalities.
         
H.A.2.2 Develop and apply the basic
operations and properties of matrices
(associative, commutative, identity, and
inverse).
         
H.A.2.3 Analyze and explain the
reasoning used to solve systems of linear
equations and inequalities in two
variables via substitution , elimination,
graphing, and matrix algebra.
         
H.A.2.4 Solve systems of linear equations
with two and three variables using
graphing and algebraic methods
(including matrices) and interpret the
solution in the appropriate context.
         
H.A.2.5 Graph, solve, and analyze
absolute value equations and inequalities
in two variables.
         
H.A.2.6 Interpret, analyze, and solve
linear programming problems with
technology.
         

H.A.3 Quadratic Equations and Functions: Students solve, model and interpret
quadratic equations and functions and systems of quadratic equations.

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.3.1 Define, plot and compute with
complex numbers and describe how the
associative, commutative, and distributive
properties of operations on real numbers
extend to operations on complex
numbers.
         
H.A.3.2 Complete the square to solve a
quadratic equation and to develop the
quadratic formula and apply this formula
to the solution of quadratic equations and
the interpretation of the nature of their
roots.
         
H.A.3.3 Sketch a quadratic function’s
graph without technology, and recognize
the relationships between the coefficients
of a quadratic function and characteristics
of its graph (e.g. shape, position,
intercepts, zeros, maximum, minimum,
symmetry, vertex .)
         
H.A.3.4 Construct and solve quadratic
inequalities in one and two variables and
represent their solutions graphically.
         
H.A.3.5 Solve equations that contain
radical expressions.
         
H.A.3.6 Solve nonlinear systems of
equations, including linear-quadratic and
quadratic-quadratic, algebraically and
graphically.
         

H.A.4 Conic Sections: Students will identify, analyze and sketch the graphs of the
conic sections and relate their equations and graphs.

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.4.1 Identify, graph, analyze and write
the equations of conic sections in
standard form and general form, in order
to identify the conic section and to find its
geometric properties (foci, asymptotes,
eccentricity, etc.).
         
H.A.4.2 Solve, with and without
appropriate technology, systems of
equations and inequalities involving
conics and other types of equations
         

H.A.5 Polynomials: Perform operations with polynomials and apply these
operations to analyze the graphical behavior of polynomial functions.

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.5.1 Add, subtract, multiply and divide
( division of polynomials by monomials
only) polynomial expressions using
symbolic manipulation and physical
models.
         
H.A.5.2 Understand and apply the
binomial theorem to expand binomial
expressions raised to positive integer
powers .
         
H.A.5.3 Analyze and describe graphs of
polynomial functions by examining their
intercepts, zeros, domain and range, and
local (turning points) and global (end)
behavior.
         
H.A.5.4 Factor polynomials completely
and apply properties of exponents to
transform
polynomial expressions and
solve polynomial equations.
         
H.A.5.5 Use graphing technology to find
approximate solutions for polynomial
equations.
         
H.A.5.6 Write a polynomial equation
given its solutions (i.e. real and/or
complex).
         

H.A.6 Algebraic Fractions: Simplify algebraic and complex fractions, solve
equations involving algebraic fractions, and understand negative and fractional
exponents

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.6.1 Understand and simplify
expressions using properties of negative
and fractional exponents.
         
H.A.6.2 Perform operations (i.e. addition,
subtraction, multiplication, and division)
on and simplify algebraic fractions and
radical expressions.
         
H.A.6.3 Simplify complex fractions.          
H.A.6.4 Solve equations involving
algebraic fractions.
         

H.A.7 Rational and Radical Functions: Interprets, solve and graph rational and
radical equations and functions with and without technology.

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.7.1 Convert between rational
exponent and radical forms of
expressions.
         
H.A.7.2 Add, subtract, multiply, divide
and evaluate rational functions and
simplify rational expressions with linear
and quadratic denominators.
         
H.A.7.3 Investigate, draw and analyze
characteristics of rational and radical
functions including domain and range,
asymptotes, zeros, intercepts, intervals of
increase and decrease, and rate of
change.
         
H.A.7.4 Solve graphically, algebraically
and numerically equations involving
radical and rational expressions.
         
H.A.7.5 Use properties of radicals to
solve equations and identifies extraneous
roots when they occur
         

H.A.8 Logarithmic and Exponential Equations and Functions: Interpret, solve and
graph logarithmic and exponential equations and functions, develop and apply
laws of exponents and logarithms to perform computations with and without
technology.

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.8.1 Investigate, draw and analyze
characteristics of exponential and
logarithmic functions including domain
and range, asymptotes, zeros, intercepts,
intervals of increase and decrease, and
rate of change.
         
H.A.8.2 Define a logarithm as a solution
to an exponential equation, and
recognize the inverse relationship
between functions defined by logarithms
and exponential expressions, showing
this relationship graphically.
         
H.A.8.3 Describe the effects of changes
in the parameters of logarithmic and
exponential functions graphically.
         
H.A.8.4 Solve graphically, algebraically
and numerically, with and without
appropriate technology, equations
involving exponential and logarithmic
expressions.
         
H.A.8.5 Approximate solutions to an
exponential equation, and relate the
solutions to the points of intersection of
the graph of the exponential equation and
the graph of a horizontal line.
         
H.A.8.6 Develop and apply the laws of
logarithms and the change-of-base
formula to simplify and evaluate natural
and common logarithmic expressions and
to find their approximate values.
         

H.A.9 Sequences and Series: Analyze and evaluate sequences and series
(including but not limited to arithmetic and geometric) and fluently apply sigma
notation with and without technology.

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.9.1 Define, recognize, and
discriminate between arithmetic and
geometric sequences and series.
         
H.A.9.2 Use the properties of such
sequences and series to solve problems,
including finding the general term and
sum recursively and explicitly.
         
H.A.9.3 Find partial sums of arithmetic
and geometric series.
         
H.A.9.4 Solve, with and without
appropriate technology, problems
involving the sum (including Sigma
notation) of finite and infinite sequences
and series and apply sigma notation to
describe a series.
         
H.A.9.5 Translate between the numeric
and symbolic form of a sequence or
series.
         
H.A.9.6 Describe limits of sequences and
apply their properties to investigate
convergent and divergent series; and
apply sequences and series to solve
problems including sums and binomial
expansion.
         
H.A.9.7 Explore and use other sequences
found in nature such as the Fibonacci
sequence and the golden ratio.
         

H.A.10 Mathematical Reasoning and Problem Solving: Students use a variety of
strategies to solve problems.

ADVANCED MATH

ALGEBRA STANDARD

This standard should be an advanced math
standard in the algebra strand
Strongly
Agree
Agree No
Opinion
Disagree Strongly
Disagree
H.A.10.1 Use a variety of problem-solving
strategies, such as drawing a diagram,
guess-and-check, solving a simpler
problem, writing an equation, and working
backwards.
         
H.A.10.2 Decide whether a solution is
reasonable in the context of the original
situation.
         
H.A.10.3 Decide if a given algebraic
statement is true always, sometimes, or
never (statements involving rational or
radical expressions or logarithmic or
exponential functions).
         
H.A.10.4 Use the properties of number
systems and the order of operations to
justify the steps of simplifying functions
and solving equations.
         
H.A.10.5 Understand that the logic of
equation solving begins with the
assumption that the variable is a number
that satisfies the equation and that the
steps taken when solving equations
create new equations that have, in most
cases, the same solution set as the
original. Understand that similar logic
applies to solving systems of equations
simultaneously.
         
H.A.10.6 Use counterexamples to show
that statements are false.
         
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