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| AII/T.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/T.2 |
The
student will add, subtract, multiply,
divide, and simplify rational
expressions, including complex
fractions. |
| AII/T.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.
|
| AII/T.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/T.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/T.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/T.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/T.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/T.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. |
| AII/T.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/T.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/T.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/T.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/T.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/T.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/T.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/T.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/T.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/T.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/T.20 |
The
student will identify, create,
and solve practical problems involving
inverse
variation and a combination
of direct and inverse variations. |
| AII/T.21 |
The
student will use the definitions
of the six trigonometric
functions to find the sine,
cosine, tangent,
cotangent, secant, and cosecant
of an angle in standard position,
given a point, other than the
origin, on the terminal side
of the angle. Circular function
definitions will be connected
with trigonometric function definitions. |
| AII/T.22 |
The
student, given the value of one
trigonometric function, will
find the values of the other trigonometric
functions. Properties of the
unit circle and definitions of
circular functions will be applied. |
| AII/T.23 |
The
student will find without the
aid of a calculating utility
the values of the trigonometric
functions
of the special angles and their
related angles as found in the
unit circle. This will include
converting radians to degrees
and vice versa. |
| AII/T.24 |
The
student will find with the aid
of a calculator the value of any
trigonometric function and inverse
trigonometric function. |
| AII/T.25 |
The
student will verify basic trigonometric
identities and make substitutions,
using the basic identities. |
| AII/T.26 |
The
student, given one of the six
trigonometric functions in standard
form [e.g., y = A sin (Bx
+ C) + D, where A, B, C, and D are
real numbers], will
- state
the domain and the range of
the function;
- determine
the amplitude, period, phase
shift, and vertical shift; and
- sketch
the graph of the function by
using transformations for at
least a one-period interval.
The
graphing calculator will be used
to investigate the effect of changing A,
B, C, and D on the graph
of a trigonometric functions. |
| AII/T.27 |
The
student will identify the domain
and range of the inverse trigonometric
functions and recognize the graphs
of these functions. Restrictions
on the domains of the inverse
trigonometric functions will
be included. |
| AII/T.28 |
The
student will solve trigonometric
equations that include both infinite
solutions and restricted domain
solutions and solve basic trigonometric
inequalities. Graphing utilities
will be used to solve equations,
check for reasonableness of results,
and verify algebraic solutions. |
| AII/T.29 |
The
student will identify, create,
and solve practical problems involving triangles. Techniques
will include using the trigonometric
functions, the Pythagorean
Theorem, the Law of Sines,
and the Law of Cosines. |
Equipment
Available
Updated
Thursday, December 1, 2005