Course Goals

In this course, students build on their understanding of math from Algebra 1. Algebra 2 uses problem situations, physical models, and appropriate technology to extend algebraic thinking and engage student reasoning. Algebra 2 is an in-depth study of linear, quadratic, exponential, logarithmic, polynomial, rational, and trigonometric functions and inequalities. Other topics of study include factoring, powers and roots, matrices, sequences and series, and probability and statistics.

The course is organized around the following foundational concepts of Algebra 2:

• Real Numbers, Expressions, and Algebraic Reasoning: Students will strengthen their understanding of the real number system and algebraic structure by simplifying expressions using operations on real numbers and properties of real numbers. Students will develop stronger mathematical habits, including organizing work clearly and using algebraic reasoning to support accurate computation.

• Equations, Inequalities, and Problem Solving: Students will solve linear equations and inequalities in one variable, including compound and absolute value inequalities. Students will apply algebraic techniques to interpret and solve real-world problemsusing formulas, models, and clear reasoning.

• Graphs and Functions: Students will connect equations, graphs, and tables through a deeper study of functions. Students will graph linear functions, interpret slope as rate of change, write equations of lines, and extend function thinking through piecewise-defined functions and function transformations.

• Systems of Equations, Matrices, and Linear Models: Students will solve systems of linear equations in two and three variables and apply systems to problem-solving situations. Students will explore matrix methods for solving systems, use determinants in solving systems, and model real-world constraints through linear programming and systems of inequalities.

• Exponents, Polynomials, and Polynomial Functions: Students will build fluency with exponent rules and scientific notation anddeepen their understanding of polynomials as functions. Students will perform polynomial operations and use a variety of factoring strategies to rewrite expressions and solve equations efficiently.

• Rational Expressions and Rational Equations: Students will apply operations to rational expressions. Students will solverational equations and apply rational models to variation and real-world problem solving while attending to restrictions on the domain.

• Radicals, Rational Exponents, and Complex Numbers: Students will work flexibly with radicals and rational exponents,simplify radical expressions, and solve equations involving radicals. Students will also develop proficiency with complex numbers and extend prior algebraic tools to include non-real solutions.

• Quadratic and Higher-Degree Equations and Polynomial Behavior: Students will solve quadratic equations using completingthe square, the quadratic formula, and other quadratic methods. Students will analyze polynomial functions using zeros, the Fundamental Theorem of Algebra, and inequality reasoning to make conclusions about solutions and behavior.

• Exponential and Logarithmic Functions and Applications: Students will expand their understanding of functions through exponential and logarithmic relationships, including inverse functions and properties of logarithms. Students will solve exponential and logarithmic equations and apply these tools to real-world growth/decay and modeling contexts.

• Sequences and Series: Students will study arithmetic and geometric sequences and series, including partial sums, and connectthese patterns to real mathematical modeling situations.

• Counting Methods, Probability, and Statistics: Students will use the Fundamental Counting Principle, permutations, and combinations to compute probabilities and analyze outcomes. Students will explore probability concepts including conditional probability, expected value, and the normal distribution to interpret real-world uncertainty and decision-making.

• Trigonometric Functions, Identities, and Applications: Students will develop trigonometry from angle measure through right-triangle trig and trig functions of any angle, including periodic behavior and graphing sine, cosine, and tangent. Students will verify identities, solve trigonometric equations, and apply the Law of Sines and Law of Cosines to model and solve real-world problems.