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

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

P.1: : Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

P.1.A: : The student is expected to: apply mathematics to problems arising in everyday life, society, and the workplace;

P.1.B: : The student is expected to: 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;

P.1.C: : The student is expected to: 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;

P.1.D: : The student is expected to: communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

P.1.E: : The student is expected to: create and use representations to organize, record, and communicate mathematical ideas;

P.1.F: : The student is expected to: analyze mathematical relationships to connect and communicate mathematical ideas; and

P.1.G: : The student is expected to: display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

P.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.

P.2.D: : The student is expected to: describe symmetry of graphs of even and odd functions;

P.2.E: : The student is expected to: 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;

P.2.F: : The student is expected to: graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions;

P.2.G: : The student is expected to: 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;

P.2.I: : The student is expected to: 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;

P.2.J: : The student is expected to: 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;

P.2.K: : The student is expected to: analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes;

P.2.L: : The student is expected to: determine various types of discontinuities in the interval (negative 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;

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

P.2.O: : The student is expected to: develop and use a sinusoidal function that models a situation in mathematical and real-world problems; and

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

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

P.3.F: : The student is expected to: determine the conic section formed when a plane intersects a double-napped cone;

P.3.G: : The student is expected to: make connections between the locus definition of conic sections and their equations in rectangular coordinates;

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

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

P.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.

P.4.A: : The student is expected to: determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in mathematical and real-world problems;

P.4.B: : The student is expected to: describe the relationship between degree and radian measure on the unit circle;

P.4.C: : The student is expected to: represent angles in radians or degrees based on the concept of rotation and find the measure of reference angles and angles in standard position;

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

P.4.E: : The student is expected to: determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical and real-world problems;

P.4.F: : The student is expected to: use trigonometry in mathematical and real-world problems, including directional bearing;

P.4.I: : The student is expected to: use vectors to model situations involving magnitude and direction;

P.4.J: : The student is expected to: represent the addition of vectors and the multiplication of a vector by a scalar geometrically and symbolically; and

P.4.K: : The student is expected to: apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems.

P.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.

P.5.B: : The student is expected to: represent arithmetic sequences and geometric sequences using recursive formulas;

P.5.C: : The student is expected to: calculate the nth term and the nth partial sum of an arithmetic series in mathematical and real-world problems;

P.5.E: : The student is expected to: 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;

P.5.F: : The student is expected to: 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;

P.5.I: : The student is expected to: generate and solve exponential equations in mathematical and real-world problems;

P.5.M: : The student is expected to: 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

P.5.N: : The student is expected to: generate and solve trigonometric equations in mathematical and real-world problems.

Correlation last revised: 2/10/2025

Texas - Mathematics: Precalculus

Essential Knowledge and Skills | Adopted: 2012

P.1: : Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

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

P.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.

P.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.