a. Convert between and among radical and exp onential
forms of numerical expressions.
b. Simplify and perform operations on numerical expressions containing
radicals.
c. Apply the laws of exponents to numerical expressions with rational and
negative exponents to order and rewrite them in alternative forms.
O2. Complex numbers
a. Represent complex numbers in the form a+bi, where
a and b are real; simplify powers of pure imaginary numbers.
b. Perform operations on the set of complex numbers.
O3. Algebraic expressions
a. Convert between and among radical and exponential
forms of algebraic expressions.
b. Simplify and perform operations on radical algebraic expressions.
c. Apply the laws of exponents to algebraic expressions, including those
involving rational and negative exponents, to order and rewrite them in
alternative forms.
d. Perform operations on polynomial expressions .
e. Perform operations on rational expressions, including complex
fractions .
f. Identify or write equivalent algebraic expressions in one or more
variables to extract information.
Equations and Inequalities (Priority: 20%)
a. Solve equations and inequalities involving the
absolute value of a linear expression.
b. Express and solve systems of linear equations in three variables with
and without the use of technology.
c. Solve systems of linear inequalities in two variables and graph the
solution set.
d. Recognize and solve problems that can be represented by single variable
linear equations or inequalities or
systems of linear equations or inequalities involving two or more variables.
Interpret the solution(s) in
terms of the context of the problem.
E2. Nonlinear equations and inequalities
a. Solve single-variable quadratic, exponential,
rational, radical, and factorable higher-order polynomial
equations over the set of real numbers, including quadratic equations involving
absolute value.
b. Solve single variable quadratic equations and inequalities over the
complex numbers; graph real solution
sets on a number line.
c. Use the discriminant, D = b^2 – 4ac , to determine the nature of the
solutions of the equation ax^2 + bx + c = 0.
d. Graph the solution set of a two-variable quadratic inequality in the
coordinate plane.
e. Rewrite nonlinear equations and inequalities to express them in
multiple forms in order to facilitate finding
a solution set or to extract information about the relationships or graphs
indicated.
Polynomial and Rational Functions (Priority: 30%)
P1. Quadratic functions
a. Determine key characteristics of quadratic
functions and their graphs.
b. Represent quadratic functions using tables, graphs, verbal statements,
and equations. Translate among these representations.
c. Describe the effect that changes in the parameters of a quadratic
function have on the shape and position of its graph.
d. Recognize, express, and solve problems that can be modeled using
quadratic functions. Interpret their
solutions in terms of the context.
P2. Higher-order polynomial and rational functions
a. Determine key characteristics of power functions
in the form f (x) = ax^n, a ≠ 0, for positive integral values
of n and their graphs.
b. Determine key characteristics of polynomial functions and their graphs.
c. Represent polynomial functions using tables, graphs, verbal statements,
and equations. Translate among
these representations.
d. Determine key characteristics of simple rational functions and their
graphs.
e. Represent simple rational functions using tables, graphs, verbal
statements, and equations. Translate
among these representations.
f. Recognize, express, and solve problems that can be modeled using
polynomial and simple rational
functions. Interpret their solutions in terms of the context.
Exponential Functions (Priority: 20%)
X1. Exponential functions
a. Determine key characteristics of exponential
functions and their graphs.
b. Represent exponential functions using tables, graphs, verbal
statements, and equations. Represent
exponential expressions in multiple forms. Translate among these
representations.
c. Describe the effect that changes in a parameter of an exponential
function have on the shape and position
of its graph.
d. Recognize, express, and solve problems that can be modeled using
exponential functions, including those
where logarithms provide an efficient method of solution . Interpret their
solutions in terms of the context.
Function Operations and Inverses (Priority: 15%)
F1. Function operations
a. Combine functions by addition, subtraction,
multiplication, and division .
b. Determine the composition of two functions, including any necessary
restrictions on the domain.
F2. Inverse functions
a. Describe the conditions under which an inverse
relation is a function.
b. Determine and graph the inverse relation of a function.
F3. Piecewise-defined functions
a. Determine key characteristics of absolute value,
step , and other piecewise-defined functions.
b. Represent piecewise-defined functions using tables, graphs, verbal
statements, and equations. Translate
among these representations.
c. Recognize, express, and solve problems that can be modeled using
absolute value, step, and other
piecewisedefined functions. Interpret their solutions in terms of the context.
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