Algebra 1B is the second half of a one-year UC A-G area C course. Algebra 1A and 1B are submitted and transcripted together; neither semester alone completes Algebra I. Students entering 1B from another school should have completed a first semester that covered one-variable statistics, linear equations and inequalities, systems and two-variable statistics. If they have not, the gaps that matter most in 1B are solving linear equations, slope as a rate of change and fitting a model to data; plan targeted support in the first two weeks rather than repeating Algebra 1A.

Standards. Across the two semesters, the course cites every one of the 71 CA CCSS Algebra I standards, and the build checks this. Algebra 1B carries the functions standards (F-IF, F-BF), the linear and exponential models standards (F-LE, including F-LE.6 on quadratic motion, a California placement), the number system standards (N-RN.1-3), polynomial arithmetic (A-APR.1), structure in expressions (A-SSE.2, A-SSE.3), quadratic equations (A-REI.4 with its parts) and linear-quadratic systems (A-REI.7). A-REI.11 (solving f(x) = g(x) graphically) is taught with absolute value functions in Unit 1. The CA version of A-REI.4.b asks students to recognize complex solutions and write them as a ± bi; the course introduces this in Lesson 4.3 as a preview, and Algebra 2 develops it.

The area C case for this semester. Point reviewers to four pieces of reasoning. Students prove that linear functions grow by equal differences and exponential functions by equal factors (Lesson 2.1, F-LE.1.a). They explain why rational exponents are defined as they are (Lesson 2.2, N-RN.1). They derive the quadratic formula by completing the square and justify every step (Lesson 4.3 and the Unit 4 portfolio). And they prove that a rational number plus an irrational number is irrational (N-RN.3). Alongside these proofs are four modeling tasks with real data or real design constraints: a utility rate schedule, a real growth or decay pattern, a filmed projectile and a design problem.

The California Mathematics Framework (2023). As in 1A, investigation comes before explanation and discourse carries the reasoning. The contexts are chosen for California students: tiered utility rates, census counts, school spaces. The Framework’s emphasis on data continues in 1B, where students fit exponential and quadratic models and judge them with residuals, building directly on Algebra 1A Unit 4.