Illustrative Mathematics / Open Up Resources HS Algebra 2 (2021) by the Illustrative Mathematics team. HS Algebra 2 with Trigonometry textbook in the IM/OUR HS Math curriculum, openly licensed (CC BY 4.0) and free to use; problem-based, IM-aligned (this IS the canonical IM-aligned course). Eleven units (called Units rather than Chapters) covering: sequences and functions, polynomials and rational functions, exponential and logarithmic functions, trigonometric functions and the unit circle (Unit 6 Trig in the IM/OUR parlance), statistical inference, and a closing modeling unit.
Parent functions and transformations; transformations of linear and absolute value functions; modeling with linear functions; solving linear systems (review of Alg 1 systems).
Transformations of quadratic functions; characteristics (vertex, axis of symmetry, max/min); focus of a parabola (geometric definition); modeling with quadratic functions.
Solving quadratic equations by factoring/square roots; complex numbers; completing the square; the quadratic formula and discriminant; nonlinear systems; quadratic inequalities.
Graphing polynomial functions; polynomial arithmetic and division; factoring; solving polynomial equations; the Fundamental Theorem of Algebra; transformations and analyzing graphs; polynomial models.
nth roots and rational exponents; properties of rational exponents and radicals; graphing radical functions; solving radical equations and inequalities; function operations and inverse functions.
Exponential growth and decay; the natural base e; logarithms and logarithmic functions; transformations; properties of logarithms; solving exponential and logarithmic equations; modeling.
Inverse variation; graphing rational functions (asymptotes, holes); arithmetic of rational expressions; solving rational equations.
Sequences and series; arithmetic sequences/series; geometric sequences/series; infinite geometric series; recursive rules.
Right triangle trigonometry; angles and radian measure; trigonometric functions of any angle; graphs of sine, cosine, and other trig functions; modeling with trig; trigonometric identities; sum and difference formulas; Law of Sines; Law of Cosines.
Sample spaces; independent and dependent events; two-way tables and probability; disjoint and overlapping events; permutations and combinations; binomial distributions.