(a) General requirements. Students shall be awarded
one-half to one credit for successful completion of this course. Prerequisite:
Algebra I.
(b) Introduction.
(1) The desire to achieve educational excellence is
the driving force behind the Texas essential knowledge and skills
for mathematics, guided by the college and career readiness standards.
By embedding statistics, probability, and finance, while focusing
on fluency and solid understanding, Texas will lead the way in mathematics
education and prepare all Texas students for the challenges they will
face in the 21st century.
(2) The process standards describe ways in which students
are expected to engage in the content. The placement of the process
standards at the beginning of the knowledge and skills listed for
each grade and course is intentional. The process standards weave
the other knowledge and skills together so that students may be successful
problem solvers and use mathematics efficiently and effectively in
daily life. The process standards are integrated at every grade level
and course. When possible, students will apply mathematics to problems
arising in everyday life, society, and the workplace. Students will
use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying
the solution, and evaluating the problem-solving process and the reasonableness
of the solution. Students will select appropriate tools such as real
objects, manipulatives, paper and pencil, and technology and techniques
such as mental math, estimation, and number sense to solve problems.
Students will effectively communicate mathematical ideas, reasoning,
and their implications using multiple representations such as symbols,
diagrams, graphs, and language. Students will use mathematical relationships
to generate solutions and make connections and predictions. Students
will analyze mathematical relationships to connect and communicate
mathematical ideas. Students will display, explain, or justify mathematical
ideas and arguments using precise mathematical language in written
or oral communication.
(3) In Algebra II, students will build on the knowledge
and skills for mathematics in Kindergarten-Grade 8 and Algebra I.
Students will broaden their knowledge of quadratic functions, exponential
functions, and systems of equations. Students will study logarithmic,
square root, cubic, cube root, absolute value, rational functions,
and their related equations. Students will connect functions to their
inverses and associated equations and solutions in both mathematical
and real-world situations. In addition, students will extend their
knowledge of data analysis and numeric and algebraic methods.
(4) Statements that contain the word "including" reference
content that must be mastered, while those containing the phrase "such
as" are intended as possible illustrative examples.
(c) Knowledge and skills.
(1) Mathematical process standards. The student uses
mathematical processes to acquire and demonstrate mathematical understanding.
The student is expected to:
(A) apply mathematics to problems arising in everyday
life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing
given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process
and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives,
paper and pencil, and technology as appropriate, and techniques, including
mental math, estimation, and number sense as appropriate, to solve
problems;
(D) communicate mathematical ideas, reasoning, and
their implications using multiple representations, including symbols,
diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record,
and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and
communicate mathematical ideas; and
(G) display, explain, or justify mathematical ideas
and arguments using precise mathematical language in written or oral
communication.
(2) Attributes of functions and their inverses. The
student applies mathematical processes to understand that functions
have distinct key attributes and understand the relationship between
a function and its inverse. The student is expected to:
(A) graph the functions *f(x)=√x,
f(x)=1/x, f(x)=x*^{3 }, f(x)=^{3 }√x, f(x)=b^{x },
f(x)=|x|, and *f(x)=log*_{b }(x) where *b * is
2, 10, and *e, * and, when applicable,
analyze the key attributes such as domain, range, intercepts, symmetries,
asymptotic behavior, and maximum and minimum given an interval;
(B) graph and write the inverse of a function using
notation such as *f *^{-1 }(x);
(C) describe and analyze the relationship between a
function and its inverse (quadratic and square root, logarithmic and
exponential), including the restriction(s) on domain, which will restrict
its range; and
(D) use the composition of two functions, including
the necessary restrictions on the domain, to determine if the functions
are inverses of each other.
(3) Systems of equations and inequalities. The student
applies mathematical processes to formulate systems of equations and
inequalities, use a variety of methods to solve, and analyze reasonableness
of solutions. The student is expected to:
(A) formulate systems of equations, including systems
consisting of three linear equations in three variables and systems
consisting of two equations, the first linear and the second quadratic;
(B) solve systems of three linear equations in three
variables by using Gaussian elimination, technology with matrices,
and substitution;
(C) solve, algebraically, systems of two equations
in two variables consisting of a linear equation and a quadratic equation;
(D) determine the reasonableness of solutions to systems
of a linear equation and a quadratic equation in two variables;
(E) formulate systems of at least two linear inequalities
in two variables;
(F) solve systems of two or more linear inequalities
in two variables; and
(G) determine possible solutions in the solution set
of systems of two or more linear inequalities in two variables.
(4) Quadratic and square root functions, equations,
and inequalities. The student applies mathematical processes to understand
that quadratic and square root functions, equations, and quadratic
inequalities can be used to model situations, solve problems, and
make predictions. The student is expected to:
(A) write the quadratic function given three specified
points in the plane;
(B) write the equation of a parabola using given attributes,
including vertex, focus, directrix, axis of symmetry, and direction
of opening;
(C) determine the effect on the graph of *f(x) = √x * when *f(x)
* is replaced by *af(x), f(x) + d, f(bx), * and *f(x - c) * for specific positive and negative
values of *a, b, c, * and *d; *
(D) transform a quadratic function *f(x) = ax*^{2 } + bx +
c to the form *f(x) = a(x - h)*^{2 } + k to identify the different attributes
of *f(x); *
(E) formulate quadratic and square root equations using
technology given a table of data;
(F) solve quadratic and square root equations;
(G) identify extraneous solutions of square root equations;
and
(H) solve quadratic inequalities.
(5) Exponential and logarithmic functions and equations.
The student applies mathematical processes to understand that exponential
and logarithmic functions can be used to model situations and solve
problems. The student is expected to:
(A) determine the effects on the key attributes on
the graphs of *f(x) = b*^{x } and *f(x) = log*_{b }(x) where *b * is 2, 10, and *e * when *f(x) * is replaced by *af(x),
f(x) + d, * and *f(x - c) * for
specific positive and negative real values of *a,
c, * and *d; *
(B) formulate exponential and logarithmic equations
that model real-world situations, including exponential relationships
written in recursive notation;
(C) rewrite exponential equations as their corresponding
logarithmic equations and logarithmic equations as their corresponding
exponential equations;
(D) solve exponential equations of the form *y = ab*^{x } where *a * is a nonzero real number and *b * is greater than zero and not equal to
one and single logarithmic equations having real solutions; and
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