Algebra

Abstract algebra is the study of algebraic structures such as groups, rings, fields, and vector spaces. Learners will understand algebraic proofs and symmetry, allowing them to analyze abstract mathematical systems and solve advanced algebraic equations.

Algebra is the study of mathematical symbols and the rules for manipulating them. Learners will understand how to solve equations, analyze functions, and use variables to represent real-world relationships and quantitative problems.

Exponential functions are mathematical functions where a constant base is raised to a variable exponent. Learners will understand growth and decay models, Euler's number, and graphing techniques, enabling them to analyze population growth and financial interest.

Functions are mathematical relations that associate each input from a domain with exactly one output in a codomain. Learners will understand function notation, domain and range, composition, and inverses to model and analyze mathematical relationships.

Inequalities are mathematical statements comparing the relative size of two values or expressions using inequality symbols. Learners will understand how to solve, graph, and interpret linear, quadratic, and absolute value inequalities in one or more variables.

Linear equations are algebraic equations of the first degree, representing straight lines when graphed. Learners will understand how to solve for unknown variables, calculate slopes, and graph equations to model real-world relationships with constant rates of change.

Logarithms are the inverse operations of exponentiation, representing the power to which a base must be raised to yield a given number. Learners will understand logarithmic properties, change of base formulas, and how to solve logarithmic equations.

Polynomials are algebraic expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication. Learners will understand polynomial arithmetic, factoring techniques, and root-finding methods to analyze and graph polynomial functions of various degrees.

Quadratic equations are second-degree polynomial equations in a single variable. Learners will understand how to solve these equations using factoring, completing the square, and the quadratic formula, as well as how to graph and analyze parabolas.

Sequences are ordered lists of numbers, while series are the sums of those sequences. Learners will understand arithmetic and geometric progressions, convergence tests, and summation notation, enabling them to analyze infinite processes and approximate functions.

Systems of equations are collections of two or more equations sharing common variables. Learners will understand how to find simultaneous solutions using substitution, elimination, and matrix methods, allowing them to model complex scenarios with multiple constraints.