Algebra 2

Students revisit functions through sequences, seeing arithmetic and geometric sequences as linear and exponential functions restricted to integer domains, and represent and model situations using sequences.

Students extend their work with linear and quadratic functions to polynomials of higher degree, moving flexibly between standard and factored forms, sketching graphs from key features (zeros, multiplicity, end behavior), and dividing polynomials to apply the Remainder Theorem.

Students transition from polynomials to rational functions and equations, analyzing asymptotic behavior, solving rational equations (including identifying extraneous solutions), proving polynomial identities, and deriving the finite geometric series sum formula.

Students extend exponent rules to rational exponents, solve equations involving square and cube roots, develop the concept of complex numbers, and solve quadratic equations with real or complex solutions.

Students extend exponential functions to rational and continuous inputs, introduce logarithms as a way to solve exponential equations, study the constant e, and use exponential and logarithmic functions and their graphs to model and solve problems.

Students examine how functions can be transformed by translations, reflections, and scaling of inputs and outputs, generalize even and odd symmetry, and apply transformations to model real-world data.

Students build trigonometric functions by extending right-triangle ratios to the unit circle, define cosine, sine, and tangent as functions on the real numbers, and apply transformations of periodic functions to model circular and periodic situations.

Students examine study types and the role of randomization, model bell-shaped distributions with normal curves, quantify sampling variability with margins of error, and analyze experimental data to assess whether observed effects are statistically significant.