TexasPrecalculus
Texas Precalculus Curriculum
Video lessons and practice for every Precalculus topic. Aligned to Texas Essential Knowledge and Skills (TEKS) standards for high school math.
Texas Precalculus Curriculum | StudyPugHelp
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ID | Strand & Expectation | StudyPug Topic |
|---|---|---|
TX.P.2.A | Use the composition of two functions to model and solve real-world problems |
TX.P.2.C | Represent a given function as a composite function of two or more functions |
TX.P.2.D | Describe symmetry of graphs of even and odd functions |
TX.P.2.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 |
TX.P.2.F | Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions |
TX.P.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 |
TX.P.2.H | Graph arcsin x and arccos x and describe the limitations on the domain |
TX.P.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 |
TX.P.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 |
TX.P.2.K | Analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes |
TX.P.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 |
TX.P.2.N | Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems |
TX.P.2.O | Develop and use a sinusoidal function that models a situation in mathematical and real-world problems |
TX.P.2.P | Determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems |
TX.P.3.A | Graph a set of parametric equations |
TX.P.3.C | Use parametric equations to model and solve mathematical and real-world problems |
TX.P.3.D | Graph points in the polar coordinate system and convert between rectangular coordinates and polar coordinates |
TX.P.3.E | Graph polar equations by plotting points and using technology |
TX.P.3.F | Determine the conic section formed when a plane intersects a double-napped cone |
TX.P.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 |
TX.P.4.B | Describe the relationship between degree and radian measure on the unit circle |
TX.P.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 |
TX.P.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 |
TX.P.4.E | Determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical and real-world problems |
TX.P.4.F | Use trigonometry in mathematical and real-world problems, including directional bearing |
TX.P.4.G | Use the Law of Sines in mathematical and real-world problems |
TX.P.4.H | Use the Law of Cosines in mathematical and real-world problems |
TX.P.4.I | Use vectors to model situations involving magnitude and direction |
TX.P.4.J | Represent the addition of vectors and the multiplication of a vector by a scalar geometrically and symbolically |
TX.P.4.K | Apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems |
TX.P.5.A | Evaluate finite sums and geometric series, when possible, written in sigma notation |
TX.P.5.B | Represent arithmetic sequences and geometric sequences using recursive formulas |
TX.P.5.C | Calculate the nth term and the nth partial sum of an arithmetic series in mathematical and real-world problems |
TX.P.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 |
TX.P.5.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 |
TX.P.5.G | Use the properties of logarithms to evaluate or transform logarithmic expressions |
TX.P.5.H | Generate and solve logarithmic equations in mathematical and real-world problems |
TX.P.5.I | Generate and solve exponential equations in mathematical and real-world problems |
TX.P.5.J | Solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and real-world problems |
TX.P.5.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 |
TX.P.5.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 |
TX.P.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 |
TX.P.5.N | Generate and solve trigonometric equations in mathematical and real-world problems |
Texas Precalculus Topics Covered
StudyPug's Texas Precalculus course covers all major topic areas required by the Texas Essential Knowledge and Skills (TEKS) for high school Precalculus. Students get video lessons and practice problems for each of the following areas:
- Functions: Composition of functions, even and odd symmetry, inverse functions, and piecewise-defined functions including step functions
- Graphing and Transformations: Exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise functions and their transformations
- Key Features and End Behavior: Domain, range, zeros, asymptotes, relative extrema, intervals of increase/decrease, and infinity notation
- Rational Functions: Horizontal, vertical, and oblique asymptotes; discontinuities and left/right-sided behavior
- Trigonometry: Unit circle, radian and degree measure, reference angles, special angles, Law of Sines, Law of Cosines, sinusoidal models, and directional bearing
- Parametric Equations: Graphing, converting to rectangular form, and modeling real-world problems
- Polar Coordinates: Graphing points and equations in the polar coordinate system
- Conic Sections: Ellipses and hyperbolas with center (h, k), locus definitions, and connections to rectangular equations
- Vectors: Magnitude, direction, vector addition, and scalar multiplication
- Sequences and Series: Arithmetic and geometric sequences, recursive formulas, sigma notation, partial sums, infinite geometric series, and the Binomial Theorem
- Exponential and Logarithmic Equations: Properties of logarithms, solving exponential and logarithmic equations
- Polynomial and Rational Inequalities: Solving and writing solution sets in interval notation
- Trigonometric Identities and Equations: Reciprocal, quotient, Pythagorean, cofunction, even/odd, and sum and difference identities
How StudyPug Helps Texas Precalculus Students
Precalculus introduces some of the most challenging topics in high school math. StudyPug breaks each TEKS standard into short, focused video lessons that students can watch at their own pace. After each lesson, practice problems let students check whether they've understood the concept before moving on.
Whether a student is preparing for a unit test, catching up after missing class, or getting ahead before the semester starts, StudyPug has the lessons and practice they need — aligned to what Texas schools teach.
Preparing for College Math
Texas Precalculus is designed to prepare students for calculus and other college-level math courses. Mastering topics like function analysis, trigonometric identities, and sequences gives students a strong foundation for AP Calculus, dual enrollment courses, and college entrance assessments. StudyPug's Texas math curriculum supports students at every level of high school math.