Texas Administrative Code
Title 19 - EDUCATION
Part 2 - TEXAS EDUCATION AGENCY
Chapter 111 - TEXAS ESSENTIAL KNOWLEDGE AND SKILLS FOR MATHEMATICS
Subchapter C - HIGH SCHOOL
Section 111.42 - Geometry, Adopted 2012 (One Credit)
Universal Citation: 19 TX Admin Code ยง 111.42
Current through Reg. 49, No. 38; September 20, 2024
(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 (-[infinity],[infinity]) 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;
(B) describe the
relationship between degree and radian measure on the unit circle;
(C) represent angles in radians or degrees
based on the concept of rotation and find the measure of reference angles and
angles in standard position;
(D)
represent angles in radians or degrees based on the concept of rotation in
mathematical and real-world problems, including linear and angular
velocity;
(E) determine the value
of trigonometric ratios of angles and solve problems involving trigonometric
ratios in mathematical and real-world problems;
(F) use trigonometry in mathematical and
real-world problems, including directional bearing;
(G) use the Law of Sines in mathematical and
real-world problems;
(H) use the
Law of Cosines in mathematical and real-world problems;
(I) use vectors to model situations involving
magnitude and direction;
(J)
represent the addition of vectors and the multiplication of a vector by a
scalar geometrically and symbolically; and
(K) apply vector addition and multiplication
of a vector by a scalar in mathematical and real-world problems.
(5) Algebraic reasoning. The
student uses process standards in mathematics to evaluate expressions, describe
patterns, formulate models, and solve equations and inequalities using
properties, procedures, or algorithms. The student is expected to:
(A) evaluate finite sums and geometric
series, when possible, written in sigma notation;
(B) represent arithmetic sequences and
geometric sequences using recursive formulas;
(C) calculate the nth term
and the nth partial sum of an arithmetic series in
mathematical and real-world problems;
(D) represent arithmetic series and geometric
series using sigma notation;
(E)
calculate the nth term of a geometric series, the
nth partial sum of a geometric series, and sum of an infinite
geometric series when it exists;
(F) apply the Binomial Theorem for the
expansion of (a + b)n in powers of a and
b for a positive integer n, where
a and b are any numbers;
(G) use the properties of logarithms to
evaluate or transform logarithmic expressions;
(H) generate and solve logarithmic equations
in mathematical and real-world problems;
(I) generate and solve exponential equations
in mathematical and real-world problems;
(J) solve polynomial equations with real
coefficients by applying a variety of techniques in mathematical and real-world
problems;
(K) solve polynomial
inequalities with real coefficients by applying a variety of techniques and
write the solution set of the polynomial inequality in interval notation in
mathematical and real-world problems;
(L) solve rational inequalities with real
coefficients by applying a variety of techniques and write the solution set of
the rational inequality in interval notation in mathematical and real-world
problems;
(M) use trigonometric
identities such as reciprocal, quotient, Pythagorean, cofunctions, even/odd,
and sum and difference identities for cosine and sine to simplify trigonometric
expressions; and
(N) generate and
solve trigonometric equations in mathematical and real-world
problems.
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