California Math Standards: Algebra I
Mathematics Framework for California Public Schools
Algebra I Standard 1.0:
Students identify and use the arithmetic properties of subsets
of integers and rational, irrational, and real numbers, including closure properties
for the 4 basic arithmetic operations.
Algebra I Standard 2:
Students understand and use such operations as taking the
opposite, finding the reciprocal, taking a root, and raising to a
fractional power. They understand and use the rules of exponents.
Algebra I Standard 3:
Stdents solve equations and inequalities involving absolute values.
Algebra I Standard 4:
Students simplify expressions before solving linear equations and
inequalities in one variable, such as 3(2x-5)+4(x-2)=12.
Algebra I Standard 5:
Students solve multistep problems, including word problems,
including word problems, involving linear equations and linear inequalities
in one variable and provide justification for each step.
Algebra I Standard 6:
Students graph a linear equation and compute the x and y intercepts
(i.e.: 2x+6y=4). They are also able to sketch the region defined by a
linear inequality.
Algebra I Standard 7:
Students verify that a point lies on a line, given an equation on
a line. Students are able to derive linear equations by using the
point/slope formula.
Algebra I Standard 8:
Students understand the concepts of parallel lines and perpendicular
lines and how their slopes are related. Find the equation of a line
perpendicular to a given line that passes through a given point.
Algebra I Standard 9:
Students solve a system of two linear equations in two variables
algebraically and are able to interpret the solution graphically. Students are able to
solve a system of two linear inequalities in two variables and sketch the solution sets.
Algebra I Standard 10:
Students add, subtract, multiply, and divide monomials and
polynomials. Students solve multistep problems, including word
problems, by using these techniques.
Algebra I Standard 11:
Students apply basic factoring techniques to second and simple
third degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
Algebra I Standard 12:
Students simplify fractions with polynomials in the numerator and
denominator by factoring both and reducing them to lowest terms.
Algebra I Standard 13: Students add, subtract, multiply and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.
Algebra I Standard 14: Students solve quadratic equations by factoring or completing the square.
Algebra I Standard 15: Students apply algebraic techniques to solve
rate problems, work problems, and percent mixture problems.
Algebra I Standard 16:
Students understand the concepts of a relation and a function,
determine whether a given relation defines a given relation defines a
function and give pertinent information about given relations and functions.
Algebra I Standard 17:
Students determine the domain of independent variables and the range of dependent variables
defined by a graph, a set of ordered pairs,
or a symbolic expression.
Algebra I Standard 18:
Students determine whether a relation defined by a graph, a set of ordered pairs, or a
symbolic expression is a function and justify.
Algebra I Standard 19:
Students use the quadratic formula to find the roots of a second-degree polynomial
and to solve quadratic equations.
Algebra I Standard 20:
Students use the quadratic formula to find the roots of a second-degree polynomial
and to solve quadratic equations.
Algebra I Standard 21:
Students graph quadratic functions and know that their roots are
the x intercepts.
Algebra I Standard 22:
Students use the quadratic formula or factoring techniques or both to determine whether the
graph of a quadratic function will intersect the x axis in zero, one, or 2 places.
Algebra I Standard 23:
Students apply quadratic equations to physical problems, such as
the motion of an object under the force of gravity.
Algebra I Standard 24:
Students use and know simple aspects of an argument
Algebra I Standard 25.0:
Use the properties of the number system to judge the validity of results,
to justify each step of a procedure, and to prove or disprove statements.
Algebra I Standard 25.1:
Students Use the properties of numbers to construct simple, valid arguments
for claimed assertions.
Algebra I Standard 25.2:
Students Judge the validity of an argument according to whether the properties of the
real number system and the order of operations have been applied correctly.
Algebra I Standard 25.3:
Given a specific algebraic statement involving linear, quadratic, or absolute
value expressions or equations or inequalities, determine whether the atatement is
true sometimes, always, or never.
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