Algebra 2 B is the second half of a single full-year course. Together with Algebra 2 A it is submitted to UC as one year of area C mathematics at the Algebra II / Mathematics III level. Students need both semesters for the year of credit, and the builder checks that every one of the 57 Algebra II codes is cited somewhere across the two semesters.

What Semester B covers. Four units follow the Illustrative Mathematics Algebra 2 sequence (CC BY 4.0), adapted rather than copied: Exponential Functions and Logarithms; Transformations of Functions; Trigonometric Functions; and Statistical Inferences. Several California additions to the standards live in this semester: F-LE.4.1-4.3 (proving and using logarithm laws, changing bases), G-GPE.3.1 (circles and parabolas from the general second-degree equation), A-REI.3.1 (absolute value equations and inequalities) and F-TF.2.1 (graphing all six trigonometric functions). Reviewers familiar with the national standards sometimes miss these; point them out.

The area C case for this semester. UC reviewers look for depth beyond Algebra 1 and Geometry, reasoning and proof, and application. Semester B supplies all three. Students prove the product, quotient and power laws of logarithms from the laws of exponents and derive the change-of-base formula from the definition (Lessons 1.2, 1.3). They prove the Pythagorean identity for every real number from the unit circle and critique proofs that cover only some cases (3.3). They argue from simulation in the inference unit, which is itself a form of mathematical argument about evidence (4.3, 4.4). Each unit ends in a modeling report on real data: U.S. Census counts of California’s population, the Golden Gate Bridge’s published dimensions with the student’s own measurement, a week of NOAA tide data from San Francisco, and a randomized experiment students run themselves. Each report passes through planning, a peer-reviewed draft, a revised final and a presentation with questions.

Keeping the case true. The proofs and discourse labs are what distinguish this course from a procedures course. If time is short, protect them and cut practice volume (Lesson 1.3 of this guide). The inference unit is the one most often squeezed at the end of the year; do not let it shrink to a single lesson, because the S-IC standards are assessed only there.

Unit assessments. Each unit has a proctored or synchronous component with at least one written proof or argument: a logarithm law, an identity, a completing-the-square derivation or a written inference conclusion.