(a) General requirements. Students shall be awarded
onehalf 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 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) 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 realworld 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 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, 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 realworld problems. The student
is expected to:
(A) use the composition of two functions to model and
solve realworld 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 realworld 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 realworld 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 leftsided behavior and the rightsided
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 realworld problems;
(O) develop and use a sinusoidal function that models
a situation in mathematical and realworld problems; and
(P) determine the values of the trigonometric functions
at the special angles and relate them in mathematical and realworld
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 realworld 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 doublenapped 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 realworld 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 realworld 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 realworld problems, including
linear and angular velocity;
(E) determine the value of trigonometric ratios of
angles and solve problems involving trigonometric ratios in mathematical
and realworld problems;
(F) use trigonometry in mathematical and realworld
problems, including directional bearing;
(G) use the Law of Sines in mathematical and realworld
problems;
(H) use the Law of Cosines in mathematical and realworld
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 realworld 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 n^{th } term and the n^{th } partial sum of an arithmetic series
in mathematical and realworld problems;
(D) represent arithmetic series and geometric series
using sigma notation;
(E) calculate the n^{th } term of a geometric series, the n^{th } 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 realworld problems;
(I) generate and solve exponential equations in mathematical
and realworld problems;
(J) solve polynomial equations with real coefficients
by applying a variety of techniques in mathematical and realworld
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
realworld 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 realworld
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 realworld problems.
