(a) General requirements. Students shall be awarded
one-half to one credit for successful completion of this course. Prerequisites:
Algebra I, Geometry, and Algebra II.
(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) Precalculus is the preparation for calculus. The
course approaches topics from a function point of view, where appropriate,
and is designed to strengthen and enhance conceptual understanding
and mathematical reasoning used when modeling and solving mathematical
and real-world problems. Students systematically work with functions
and their multiple representations. The study of Precalculus deepens
students' mathematical understanding and fluency with algebra and
trigonometry and extends their ability to make connections and apply
concepts and procedures at higher levels. Students investigate and
explore mathematical ideas, develop multiple strategies for analyzing
complex situations, and use technology to build understanding, make
connections between representations, and provide support in solving
problems.
(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, and justify mathematical ideas
and arguments using precise mathematical language in written or oral
communication.
(2) Functions. The student uses process standards in
mathematics to explore, describe, and analyze the attributes of functions.
The student makes connections between multiple representations of
functions and algebraically constructs new functions. The student
analyzes and uses functions to model real-world problems. The student
is expected to:
(A) use the composition of two functions to model and
solve real-world problems;
(B) demonstrate that function composition is not always
commutative;
(C) represent a given function as a composite function
of two or more functions;
(D) describe symmetry of graphs of even and odd functions;
(E) determine an inverse function, when it exists,
for a given function over its domain or a subset of its domain and
represent the inverse using multiple representations;
(F) graph exponential, logarithmic, rational, polynomial,
power, trigonometric, inverse trigonometric, and piecewise defined
functions, including step functions;
(G) graph functions, including exponential, logarithmic,
sine, cosine, rational, polynomial, and power functions and their
transformations, including *af(x), f(x) +
d, f(x - c), f(bx) * for specific values of *a, b, c, * and *d, * in
mathematical and real-world problems;
(H) graph arcsin *x * and
arccos *x * and describe the limitations
on the domain;
(I) determine and analyze the key features of exponential,
logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric,
and piecewise defined functions, including step functions such as
domain, range, symmetry, relative maximum, relative minimum, zeros,
asymptotes, and intervals over which the function is increasing or
decreasing;
(J) analyze and describe end behavior of functions,
including exponential, logarithmic, rational, polynomial, and power
functions, using infinity notation to communicate this characteristic
in mathematical and real-world problems;
(K) analyze characteristics of rational functions and
the behavior of the function around the asymptotes, including horizontal,
vertical, and oblique asymptotes;
(L) determine various types of discontinuities in the
interval (-∞, ∞) as they relate to functions and explore
the limitations of the graphing calculator as it relates to the behavior
of the function around discontinuities;
(M) describe the left-sided behavior and the right-sided
behavior of the graph of a function around discontinuities;
(N) analyze situations modeled by functions, including
exponential, logarithmic, rational, polynomial, and power functions,
to solve real-world problems;
(O) develop and use a sinusoidal function that models
a situation in mathematical and real-world problems; and
(P) determine the values of the trigonometric functions
at the special angles and relate them in mathematical and real-world
problems.
(3) Relations and geometric reasoning. The student
uses the process standards in mathematics to model and make connections
between algebraic and geometric relations. The student is expected
to:
(A) graph a set of parametric equations;
(B) convert parametric equations into rectangular relations
and convert rectangular relations into parametric equations;
(C) use parametric equations to model and solve mathematical
and real-world problems;
(D) graph points in the polar coordinate system and
convert between rectangular coordinates and polar coordinates;
(E) graph polar equations by plotting points and using
technology;
(F) determine the conic section formed when a plane
intersects a double-napped cone;
(G) make connections between the locus definition of
conic sections and their equations in rectangular coordinates;
(H) use the characteristics of an ellipse to write
the equation of an ellipse with center *(h,
k); * and
(I) use the characteristics of a hyperbola to write
the equation of a hyperbola with center *(h,
k). *
(4) Number and measure. The student uses process standards
in mathematics to apply appropriate techniques, tools, and formulas
to calculate measures in mathematical and real-world problems. The
student is expected to:
(A) determine the relationship between the unit circle
and the definition of a periodic function to evaluate trigonometric
functions in mathematical and real-world problems;
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