Texas Algebra II Curriculum

Texas Algebra II: What Students Learn

Algebra II builds on the foundation set in Algebra I and introduces Texas high school students to more advanced mathematical concepts. Aligned to the Texas Essential Knowledge and Skills (TEKS), the course spans functions, systems of equations, quadratic and polynomial operations, exponential and logarithmic relationships, rational and radical expressions, and statistical modeling.

Functions and Their Inverses

Students begin by graphing parent functions including f(x) = √x, f(x) = 1/x, f(x) = x³, f(x) = ³√x, and exponential and logarithmic forms. From there, they learn to write and analyze inverse functions using notation like f⁻¹(x), understand domain restrictions, and use function composition to verify whether two functions are inverses of each other.

Systems of Equations and Inequalities

Algebra II students formulate and solve systems of three linear equations in three variables using Gaussian elimination, matrix methods, and substitution. They also solve systems combining a linear equation and a quadratic equation, and determine the reasonableness of solutions. The course extends to systems of linear inequalities in two variables, including identifying possible solution sets.

Quadratic Functions and Equations

• Write quadratic functions given three points in the plane
• Write the equation of a parabola using vertex, focus, directrix, and axis of symmetry
• Transform f(x) = ax² + bx + c into vertex form f(x) = a(x − h)² + k
• Solve quadratic and square root equations, and identify extraneous solutions
• Solve quadratic inequalities

Exponential and Logarithmic Relationships

Students analyze transformations of f(x) = bˣ and f(x) = log_b(x) where b is 2, 10, or e. They formulate and solve exponential equations of the form y = abˣ, rewrite exponential equations as logarithmic equations and vice versa, and determine the reasonableness of logarithmic solutions. Real-world modeling with recursive notation is also covered.

Polynomial and Rational Expressions

The course covers adding, subtracting, and multiplying polynomials and complex numbers, as well as polynomial long division for degree-three and degree-four polynomials. Students determine linear and quadratic factors, factor the sum and difference of two cubes, and simplify rational expressions with integral exponents. Radical expressions and equations involving rational exponents round out this section.

Absolute Value, Rational, and Cube Root Equations

• Formulate and solve absolute value linear equations and inequalities
• Analyze transformations of f(x) = 1/x and f(x) = ³√x
• Solve cube root equations with real roots
• Formulate, solve, and check rational equations for real-world situations
• Determine asymptotic restrictions on rational functions and express domain and range using interval notation

Data Analysis and Regression

Students analyze data sets to determine whether a linear, quadratic, or exponential model is most appropriate. Using technology, they write regression equations and use those models to make predictions and critical judgments from real-world data.

StudyPug covers every one of these TEKS-aligned Algebra II topics with video lessons and practice problems. Students can work through topics at their own pace, replay lessons as needed, and build confidence before tests.