(a) General requirements. Students shall be awarded
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 problemsolving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying
the solution, and evaluating the problemsolving 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 Algebraic Reasoning, students will build on
the knowledge and skills for mathematics in KindergartenGrade 8 and
Algebra I, continue with the development of mathematical reasoning
related to algebraic understandings and processes, and deepen a foundation
for studies in subsequent mathematics courses. Students will broaden
their knowledge of functions and relationships, including linear,
quadratic, square root, rational, cubic, cube root, exponential, absolute
value, and logarithmic functions. Students will study these functions
through analysis and application that includes explorations of patterns
and structure, number and algebraic methods, and modeling from data
using tools that build to workforce and college readiness such as
probes, measurement tools, and software tools, including spreadsheets.
(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 problemsolving model that incorporates analyzing
given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problemsolving 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) Patterns and structure. The student applies mathematical
processes to connect finite differences or common ratios to attributes
of functions. The student is expected to:
(A) determine the patterns that identify the relationship
between a function and its common ratio or related finite differences
as appropriate, including linear, quadratic, cubic, and exponential
functions;
(B) classify a function as linear, quadratic, cubic,
and exponential when a function is represented tabularly using finite
differences or common ratios as appropriate;
(C) determine the function that models a given table
of related values using finite differences and its restricted domain
and range; and
(D) determine a function that models realworld data
and mathematical contexts using finite differences such as the age
of a tree and its circumference, figurative numbers, average velocity,
and average acceleration.
(3) Patterns and structure. The student applies mathematical
processes to understand the connections among representations of functions
and combinations of functions, including the constant function, f(x) = x, f(x) = x ^{2 }, 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 10 or e; functions
and their inverses; and key attributes of these functions. The student
is expected to:
(A) compare and contrast the key attributes, including
domain, range, maxima, minima, and intercepts, of a set of functions
such as a set comprised of a linear, a quadratic, and an exponential
function or a set comprised of an absolute value, a quadratic, and
a square root function tabularly, graphically, and symbolically;
(B) compare and contrast the key attributes of a function
and its inverse when it exists, including domain, range, maxima, minima,
and intercepts, tabularly, graphically, and symbolically;
(C) verify that two functions are inverses of each
other tabularly and graphically such as situations involving compound
interest and interest rate, velocity and braking distance, and FahrenheitCelsius
conversions;
(D) represent a resulting function tabularly, graphically,
and symbolically when functions are combined or separated using arithmetic
operations such as combining a 20% discount and a 6% sales tax on
a sale to determine h(x), the total
sale, f(x) = 0.8
x, g(x) = 0.06(0.8x), and h(x) = f(x) + g(x);
(E) model a situation using function notation when
the output of one function is the input of a second function such
as determining a function h(x) = g(f(x)) = 1.06(0.8x) for
the final purchase price, h(x) of
an item with price x dollars representing
a 20% discount, f(x) = 0.8x followed by a 6% sales tax, g(x) = 1.06x; and
(F) compare and contrast a function and possible functions
that can be used to build it tabularly, graphically, and symbolically
such as a quadratic function that results from multiplying two linear
functions.
(4) Number and algebraic methods. The student applies
mathematical processes to simplify and perform operations on functions
represented in a variety of ways, including realworld situations.
The student is expected to:
(A) connect tabular representations to symbolic representations
when adding, subtracting, and multiplying polynomial functions arising
from mathematical and realworld situations such as applications involving
surface area and volume;
(B) compare and contrast the results when adding two
linear functions and multiplying two linear functions that are represented
tabularly, graphically, and symbolically;
(C) determine the quotient of a polynomial function
of degree three and of degree four when divided by a polynomial function
of degree one and of degree two when represented tabularly and symbolically;
and
(D) determine the linear factors of a polynomial function
of degree two and of degree three when represented symbolically and
tabularly and graphically where appropriate.
(5) Number and algebraic methods. The student applies
mathematical processes to represent, simplify, and perform operations
on matrices and to solve systems of equations using matrices. The
student is expected to:
(A) add and subtract matrices;
(B) multiply matrices;
(C) multiply matrices by a scalar;
(D) represent and solve systems of two linear equations
arising from mathematical and realworld situations using matrices;
and
(E) represent and solve systems of three linear equations
arising from mathematical and realworld situations using matrices
and technology.
(6) Number and algebraic methods. The student applies
mathematical processes to estimate and determine solutions to equations
resulting from functions and realworld applications with fluency.
The student is expected to:
(A) estimate a reasonable input value that results
in a given output value for a given function, including quadratic,
rational, and exponential functions;
(B) solve equations arising from questions asked about
functions that model realworld applications, including linear and
quadratic functions, tabularly, graphically, and symbolically; and
(C) approximate solutions to equations arising from
questions asked about exponential, logarithmic, square root, and cubic
functions that model realworld applications tabularly and graphically.
(7) Modeling from data. The student applies mathematical
processes to analyze and model data based on realworld situations
with corresponding functions. The student is expected to:
(A) represent domain and range of a function using
interval notation, inequalities, and set (builder) notation;
(B) compare and contrast between the mathematical and
reasonable domain and range of functions modeling realworld situations,
including linear, quadratic, exponential, and rational functions;
(C) determine the accuracy of a prediction from a function
that models a set of data compared to the actual data using comparisons
between average rates of change and finite differences such as gathering
data from an emptying tank and comparing the average rate of change
of the volume or the second differences in the volume to key attributes
of the given model;
(D) determine an appropriate function model, including
linear, quadratic, and exponential functions, for a set of data arising
from realworld situations using finite differences and average rates
of change; and
(E) determine if a given linear function is a reasonable
model for a set of data arising from a realworld situation.
