Gizmos for Texas - Mathematics: Precalculus (Essential Knowledge and Skills (TEKS) adopted 2012)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

1: : The student uses mathematical processes to acquire and demonstrate mathematical understanding.

1.A: : apply mathematics to problems arising in everyday life, society, and the workplace;

1.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;

1.D: : communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

1.E: : create and use representations to organize, record, and communicate mathematical ideas;

1.G: : display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

2: : 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.

2.C: : represent a given function as a composite function of two or more functions;

2.F: : graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions;

2.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;

2.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;

2.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;

2.K: : analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes;

2.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;

2.M: : describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities;

2.N: : analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems;

2.O: : develop and use a sinusoidal function that models a situation in mathematical and real-world problems; and

2.P: : determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems.

3: : The student uses the process standards in mathematics to model and make connections between algebraic and geometric relations.

3.F: : determine the conic section formed when a plane intersects a double-napped cone;

3.H: : use the characteristics of an ellipse to write the equation of an ellipse with center (h, k); and

3.I: : use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k).

4: : The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.

4.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;

4.B: : describe the relationship between degree and radian measure on the unit circle;

4.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;

4.D: : represent angles in radians or degrees based on the concept of rotation in mathematical and real-world problems, including linear and angular velocity;

4.E: : determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical and real-world problems;

4.F: : use trigonometry in mathematical and real-world problems, including directional bearing;

4.I: : use vectors to model situations involving magnitude and direction;

4.K: : apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems.

5: : The student uses process standards in mathematics to evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.

5.B: : represent arithmetic sequences and geometric sequences using recursive formulas;

5.C: : calculate the nth term and the nth partial sum of an arithmetic series in mathematical and real-world problems;

5.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;

5.G: : use the properties of logarithms to evaluate or transform logarithmic expressions;

5.I: : generate and solve exponential equations in mathematical and real-world problems;

5.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

5.N: : generate and solve trigonometric equations in mathematical and real-world problems.

Correlation last revised: 2/11/2025

Texas - Mathematics: Precalculus

Essential Knowledge and Skills (TEKS) | Adopted: 2012

1: : The student uses mathematical processes to acquire and demonstrate mathematical understanding.

3: : The student uses the process standards in mathematics to model and make connections between algebraic and geometric relations.

4: : The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.

5: : The student uses process standards in mathematics to evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.