Main goal: The main goal of UCSMP Advanced Algebra is to improve and extend the algebra skills of students accumulated during the previous years of study to accommodate the topics traditional to a second algebra course.

Main theme I: Functions provide a unifying theme throughout. Linear, quadratic, exponential, logarithmic, and trigonometric functions are covered, as well as functions of variation, sequences, and transformations. Functions are treated as special kinds of relations and quadratic relations are covered in more detail. The corresponding equations and inequalities are solved symbolically and graphically, with and without CAS technology.

Main theme II: Both the content and the logical approach begun in UCSMP Geometry are applied. A review of linear functions and systems utilizes geometric properties of points, lines, and planes. Terms are carefully defined and theorems proved. Formulas and graphs of functions are examined using reflections, translations and scale change transformations. Congruence and symmetry are applied to the study of triangle trigonometry. Geometric applications and representations of all matrix operations are presented.

Main theme III: Mathematical modeling and applications are carefully developed through detailed examination of the basic properties of a situation that cause it to be modeled by each type of function studied in the course. Data abound in the selection of models and provide rationales for the study of each type of function. A wide variety of problems are designed to enhance algebra skills and properties, and quantitative literacy.

Using a CAS to show the changing height and area of a triangle in a table and graph

Comparison between this and earlier editions: Significantly larger numbers of students now take a second course of algebra than did so when the earlier editions were written.Recognizing this larger population, the major changes in this course have been to make the content more accessible to this wider range of students while keeping standards high.

Some distinctive lessons: Fitting a model to data I and II (2-7, 2-8); Rotations and perpendicular lines (4-9); Solving systems using tables, graphs, or a CAS (5-2); Continuous compounding (9-3); Trigonometry, Earth, moon, and stars (10-3); Lotteries (13-8).

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