Side-By-Side TEKS Comparison: Precalculus

Mathematical Process Standards

The process standards remain the foundation of mathematical learning in Texas. These skills are woven into the curriculum and should be integrated into all reporting categories.

Previous TEKS (111.41.c.1)	Current TEKS (111.41.c.1)
The student uses mathematical processes to acquire and demonstrate mathematical understanding.	The student uses mathematical processes to acquire and demonstrate mathematical understanding. (The content is largely consistent, with an emphasis on applying mathematics to problems arising in everyday life.)

Functions (111.41.c.2)

This section addresses the understanding and application of functions, including parent functions, transformations, and inverse functions.

Previous TEKS	Current TEKS
2(A) Describe and graph parent functions.	2(A) Graph the six parent functions: linear, absolute value, quadratic, cubic, square root, and cube root. (Change: Adds specificity regarding which parent functions must be graphed.)
2(B) Use the parent function to investigate parameters.	2(B) Describe and analyze the effects of parameter changes on the graphs of parent functions.
2(C) Determine and analyze the inverse of a function.	2(C) Determine and analyze the inverse of a function with and without technology.
	2(D) (New) Represent domain and range using interval notation, inequalities, and set notation. (Addition: Increases specificity on how domain and range are represented.)

Power and Polynomial Functions (111.41.c.3)

Changes in this strand focus on a deeper understanding of polynomial behavior, key attributes, and real-world application.

Previous TEKS	Current TEKS
3(A) Analyze graphs of polynomial functions.	3(A) Analyze graphs of polynomial functions, including end behavior, zeros, multiplicity, and symmetry.
3(B) Determine the sum, difference, product, and quotient of polynomial functions.	3(B) Perform operations with polynomial functions including addition, subtraction, multiplication, and division.
	3(C) (New) Determine the complex zeros of polynomial functions. (Addition: Explicitly includes complex zeros.)

Rational and Radical Functions (111.41.c.4)

The revised standards place a heavier emphasis on the analysis of discontinuities and the simplifying of expressions involving radicals.

Previous TEKS	Current TEKS
4(A) Sketch graphs of rational functions.	4(A) Sketch the graphs of rational functions, including identifying discontinuities, asymptotes, and intercepts. (Change: Adds specific requirements for analyzing graph features.)
4(B) Analyze the end behavior of rational functions.	4(B) Describe the end behavior of rational functions using limit notation. (Change: Introduces limit notation as a required tool.)
4(C) Determine domain and range of radical functions.	4(C) Determine the domain and range of radical functions and rational functions.

Exponential and Logarithmic Functions (111.41.c.5)

While the core concepts remain similar, the current TEKS clarify the relationship between exponential and logarithmic equations.

Previous TEKS	Current TEKS
5(A) Construct and analyze exponential models.	5(A) Construct exponential and logarithmic models to solve real-world problems.
5(B) Rewrite exponential equations as logarithmic equations.	5(B) Formulate exponential and logarithmic equations that model real-world situations.
	5(C) (New) Solve exponential and logarithmic equations using a variety of methods, including technology.

Trigonometric Functions (111.41.c.6)

Significant shifts occurred in Trigonometry, particularly regarding the unit circle and trigonometric identities.

Previous TEKS	Current TEKS
6(A) Analyze trigonometric functions graphically.	6(A) Analyze the graph of trigonometric functions, including periodicity, amplitude, midline, and phase shift.
6(B) Use trigonometric ratios to solve problems.	6(B) Use the unit circle to determine the values of trigonometric functions.
	6(C) (New) Apply trigonometric functions to model periodic phenomena.

Trigonometric Equations and Identities (111.41.c.7)

This section consolidates the solving of equations and verification of identities.

Previous TEKS	Current TEKS
7(A) Use trigonometric identities.	7(A) Verify trigonometric identities using fundamental identities such as Pythagorean, reciprocal, quotient, and co-function.
7(B) Solve trigonometric equations.	7(B) Solve trigonometric equations, including those arising from real-world applications.

Vectors and Matrices (111.41.c.8)

Standards regarding matrices have been streamlined, while vectors have been reinforced with clearer applications.

Previous TEKS	Current TEKS
8(A) Manipulate matrices and solve matrix equations.	8(A) Represent vectors as directed line segments and write component form.
8(B) Add, subtract, and multiply matrices.	8(B) Perform operations on vectors, including addition, subtraction, and scalar multiplication.
	8(C) (Reallocated/Modified) Use matrices to represent and solve systems of equations.

Conics (111.41.c.9)

The definitions and applications of conic sections have been updated to align with college-readiness standards.

Previous TEKS	Current TEKS
9(A) Identify conic sections.	9(A) Define conic sections in terms of a locus of points and write equations of conic sections.
9(B) Sketch graphs of conic sections.	9(B) Sketch graphs of conic sections from given equations, including showing vertices, foci, and asymptotes for hyperbolas.

Sequences and Series (111.41.c.10)

There is a distinct shift toward using sigma notation and understanding the convergence of series.

Previous TEKS	Current TEKS
10(A) Define arithmetic and geometric sequences.	10(A) Use sigma notation to represent mathematical series.
10(B) Find sums of series.	10(B) Calculate the sum of finite and infinite arithmetic and geometric series.

Calculus Concept Preview (111.41.c.11)

Added as a precursor to calculus, this section now explicitly addresses limits and continuity.

Previous TEKS	Current TEKS
(Generally covered under functions, not explicit)	11(A) (New) Apply concepts of limits to describe the behavior of functions.
	11(B) (New) Determine the continuity of functions.

Conclusion
The updated Precalculus TEKS are designed to bridge the gap between high school mathematics and college-level calculus. By emphasizing real-world modeling, increasing specificity on mathematical representation (such as interval and limit notation), and explicitly covering complex numbers and vectors, the new standards demand a higher level of conceptual understanding from students. Teachers are encouraged to shift their instructional focus toward deeper analysis of function behavior and verification.