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The standards below
outline the content for a one-year
course in Algebra II.
Students enrolled in Algebra II
are assumed to have mastered those
concepts outlined in the Algebra
I standards. A thorough treatment
of advanced algebraic concepts is
provided through the study of functions, “families
of functions,” equations,
inequalities, systems of equations
and inequalities, polynomials, rational
expressions, complex numbers, matrices,
and sequences and series. Emphasis
will be placed on practical applications
and modeling throughout the course
of study. Oral and written communication
concerning the language of algebra,
logic of procedures, and interpretation
of results also should permeate
the course.
These standards include
a transformational approach to graphing
functions. Transformational graphing
uses translation, reflection, dilation,
and rotation to generate a “family
of graphs” from a given graph
and builds a strong connection between
algebraic and graphic representations
of functions. Students will vary
the coefficients and constants of
an equation, observe the changes
in the graph of the equation, and
make generalizations that can be
applied to many graphs.
Graphing utilities
(graphing calculators or computer
graphing simulators), computers,
spreadsheets, and other appropriate
technology tools will be used to
assist in teaching and learning.
Graphing utilities enhance the understanding
of realistic applications through
mathematical modeling and aid in
the investigation and study of functions.
They also provide an effective tool
for solving/verifying equations
and inequalities. Any other available
technology that will enhance student
learning should be used. |
| AII.1 |
The
student will identify field properties,
axioms of equality and inequality,
and properties of order that are
valid for the set of real numbers
and its subsets, complex numbers,
and matrices. |
| AII.2 |
The
student will add, subtract, multiply,
divide, and simplify rational
expressions, including complex
fractions. |
| AII.3 |
The
student will
- add,
subtract, multiply, divide, and
simplify radical expressions containing
positive rational numbers and
variables and expressions containing
rational exponents; and
- write
radical expressions as expressions
containing rational exponents
and vice versa.
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| AII.4 |
The
student will solve absolute value
equations and inequalities graphically
and algebraically. Graphing
calculators will be used as
a primary method of solution and
to verify algebraic solutions. |
| AII.5 |
The
student will identify and factor
completely polynomials representing
the difference of squares, perfect
square trinomials, the sum and
difference of cubes, and general
trinomials. |
| AII.6 |
The
student will select, justify,
and apply a technique to solve
a quadratic
equations over the set of
complex numbers. Graphing calculators
will be used for solving and for
confirming the algebraic solutions. |
| AII.7 |
The
student will solve equations containing
rational expressions and equations
containing radical expressions
algebraically and graphically. Graphing
calculators will be used for solving
and for confirming the algebraic
solutions. |
| AII.8 |
The
student will recognize multiple
representations of functions (linear,
quadratic, absolute value, step,
and exponential
functions) and convert between
a graph, a table, and symbolic
form. A transformational approach
to graphing will be employed through
the use of graphing calculators. |
| AII.9 |
The
student will find the domain,
range, zeros, and inverse of
a function; the value of a function
for a given element in its domain;
and the composition of multiple
functions. Functions will
include exponential, logarithmic,
and those that have domains
and ranges that are limited
and/or discontinuous. The graphing
calculator will be used as a
tool to assist in investigation
of functions.
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| AII.10 |
The
student will investigate and describe
through the use of graphs the
relationships between the solution
of an equation, zero of a function, x-intercept
of a graph, and factors of a polynomial expression. |
| AII.11 |
The
student will use matrix multiplication
to solve practical problems. Graphing
calculators or computer programs
with matrix capabilities will
be used to find the product. |
| AII.12 |
The
student will represent problem
situations with a system of linear
equations and solve the system,
using the inverse matrix method. Graphing
calculators or computer programs
with matrix capability will be
used to perform computations. |
| AII.13 |
The
student will solve practical problems,
using systems of linear inequalities
and linear programming, and describe
the results both orally and in
writing. A graphing calculator
will be used to facilitate solutions
to linear programming problems. |
| AII.14 |
The
student will solve nonlinear systems
of equations, including linear-quadratic and
quadratic-quadratic, algebraically
and graphically. The graphing
calculator will be used as a tool
to visualize graphs and predict
the number of solutions. |
| AII.15 |
The
student will recognize the general
shape of polynomial, exponential,
and logarithmic functions.
The graphing calculator will be
used as a tool to investigate
the shape and behavior of these
functions. |
| AII.16 |
The student will
investigate and apply the properties
of arithmetic and geometric
sequences and series to solve
practical problems, including
writing the first n terms,
finding the nth term,
and evaluating summation formulas. Notation
will include S and an. |
| AII.17 |
The
student will perform operations
on complex
numbers and express the results
in simplest form. Simplifying
results will involve using patterns
of the powers of i. |
| AII.18 |
The
student will identify conic
sections (circle, ellipse,
parabola, and hyperbola) from
his/her equations. Given the
equations in (h, k) form,
the student will sketch graphs
of conic sections, using transformations. |
| AII.19 |
The
student will collect and analyze
data to make predictions and solve
practical problems. Graphing
calculators will be used to investigate scatterplots and
to determine the equation for
a curve of best fit. Models will
include linear, quadratic, exponential,
and logarithmic functions. |
| AII.20 |
The
student will identify, create,
and solve practical problems involving
inverse variation and a combination
of direct and inverse
variations. |
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Equipment
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