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Algebra II

Extend algebraic reasoning to polynomial, rational, radical, exponential, and logarithmic functions. Complex numbers, sequences, series, and advanced modeling with Desmos visualizations. TEKS §111.40 aligned.

14 Units

40-55 minutes per unit

What You Will Learn

Advanced Functions

Polynomial, rational, exponential, and logarithmic functions — transformations, inverses, and compositions.

Desmos Explorations

Interactive graphing of every function family. Parameter sliders reveal how algebra controls shape.

TEKS §111.40 Aligned

Covers Texas Essential Knowledge and Skills for Algebra II.

All Units

Equations and Inequalities Review

Review and extend multi-step equations, absolute value equations and inequalities, and literal equations as a bridge from Algebra I into Algebra II.

•Solve multi-step equations involving distribution, combining like terms, and variables on both sides
•Solve absolute value equations and interpret their solutions graphically
•Solve and graph absolute value inequalities using compound inequality reasoning
+1 more objectives

Functions and Relations

Formalize function notation, determine domain and range, perform function operations and compositions, and find inverse functions.

•Use function notation to evaluate functions and interpret statements about functions in context
•Determine the domain and range of functions from equations, graphs, and contexts
•Perform operations on functions (addition, subtraction, multiplication, division) and find compositions
+1 more objectives

Linear Systems and Matrices

Solve systems of two and three linear equations using substitution, elimination, and matrix methods including Gaussian elimination and determinants.

•Solve systems of two linear equations using substitution and elimination
•Extend solving techniques to systems of three equations in three variables
•Represent linear systems as augmented matrices and apply Gaussian elimination
+1 more objectives

Quadratic Functions: Advanced

Deepen understanding of quadratic functions through completing the square, vertex form, the quadratic formula derivation, the discriminant, and complex number solutions.

•Convert quadratic functions to vertex form by completing the square
•Derive the quadratic formula from the general form by completing the square
•Use the discriminant to classify the number and type of solutions
+1 more objectives

Polynomial Functions

Analyze polynomial functions through end behavior, zeros and multiplicity, the Factor Theorem, the Remainder Theorem, and graphing techniques.

•Describe the end behavior of a polynomial function using its degree and leading coefficient
•Identify zeros of polynomial functions and their multiplicities from factored form
•Apply the Factor Theorem and Remainder Theorem to analyze polynomial functions
+1 more objectives

Polynomial Operations

Divide polynomials using long division and synthetic division, factor higher-degree polynomials, and apply the Rational Root Theorem to find zeros.

•Perform polynomial long division and interpret the quotient and remainder
•Use synthetic division as an efficient tool for dividing by linear factors
•Apply the Rational Root Theorem to generate a list of possible rational zeros
+1 more objectives

Rational Functions

Simplify, multiply, and divide rational expressions, identify asymptotes and discontinuities, and graph rational functions.

•Simplify rational expressions by factoring and canceling common factors
•Multiply and divide rational expressions, stating domain restrictions
•Identify vertical asymptotes, horizontal asymptotes, and holes in rational functions
+1 more objectives

Radical Functions and Equations

Graph square root and cube root functions, apply transformations, solve radical equations, and identify extraneous solutions.

•Graph square root and cube root functions and describe their key features
•Apply transformations (shifts, reflections, stretches) to radical functions
•Solve radical equations and check for extraneous solutions
+1 more objectives

Exponential Functions

Model exponential growth and decay, understand the number e, graph exponential functions with transformations, and apply compound interest formulas.

•Distinguish exponential growth from decay by examining the base of the function
•Graph exponential functions and apply translations, reflections, and stretches
•Solve real-world problems involving compound interest and continuous growth
+1 more objectives

Logarithmic Functions

Define logarithms as inverses of exponential functions, apply log properties to simplify and solve equations, and use the change of base formula.

•Convert between exponential and logarithmic form
•Evaluate logarithms using the definition and properties of logs
•Apply the product, quotient, and power rules to simplify logarithmic expressions
+1 more objectives

Sequences and Series

Analyze arithmetic and geometric sequences, use sigma notation, compute partial sums, and determine convergence of infinite geometric series.

•Write explicit and recursive formulas for arithmetic and geometric sequences
•Use sigma notation to express and evaluate sums
•Derive and apply formulas for partial sums of arithmetic and geometric series
+1 more objectives

Introduction to Trigonometry

Define trigonometric functions using the unit circle, convert between degrees and radians, and graph sine and cosine functions with transformations.

•Define sine, cosine, and tangent using the unit circle
•Convert between degree and radian measure
•Evaluate trigonometric functions at key angles without a calculator
+1 more objectives

Probability and Statistics

Count outcomes with permutations and combinations, expand expressions with the binomial theorem, and analyze probability distributions including the normal distribution.

•Distinguish between permutations and combinations and apply the correct counting formula
•Expand binomial expressions using the binomial theorem and Pascal's triangle
•Construct and interpret probability distributions
+1 more objectives

Algebra II Capstone

Compare function families, select appropriate models for real-world data, and synthesize Algebra II concepts through multi-step problem solving.

•Compare and contrast the key features of linear, quadratic, polynomial, rational, radical, exponential, logarithmic, and trigonometric functions
•Select the appropriate function type to model a real-world scenario based on data patterns
•Solve multi-step problems that integrate concepts from across the course
+1 more objectives

Algebra II. Texas FHSP/DLA graduation requirement. TEKS §111.40 aligned. Prerequisite: Geometry.