“In Algebra II, a one-credit course, students build on their work with linear, quadratic, and exponential functions, to extend their repertoire of functions to include polynomial, rational, and radical functions. Students work closely with the expressions that define the functions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms. The Mathematical Practice Standards apply throughout this course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. The four critical areas of this course include (1) working extensively with polynomial operations; (2) building connections between geometry and trigonometric ratios; (3) understanding of a variety of function families; and (4) explore statistical data. Each critical area is described below:
- (1) Students develop the structural similarities between the system of polynomials and the system of integers. Students draw on analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students connect multiplication of polynomials with multiplication of multi-digit integers, and division of polynomials with long division of integers. Students identify zeros of polynomials, including complex zeros of quadratic polynomials, and make connections between zeros of polynomials and solutions of polynomial equations. The unit culminates with the fundamental theorem of algebra. A central theme of this unit is that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.
- (2) Building on their previous work with functions, and on their work with trigonometric ratios and circles in Geometry, students now use the coordinate plane to extend trigonometry to model periodic phenomena.
- (3) Students synthesize and generalize what they have learned about a variety of function families. They extend their work with exponential functions to include solving exponential equations with logarithms. They explore the effects of transformations on graphs of diverse functions, including functions arising in an application, in order to abstract the general principle that transformations on a graph always have the same effect regardless of the type of the underlying function. They identify appropriate types of functions to model a situation, they adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions” is at the heart of this unit. The narrative discussion and diagram of the modeling cycle should be considered when knowledge of functions, statistics, and geometry is applied in a modeling context.
- (4) Students see how the visual displays and summary statistics they learned in earlier grades relate to different types of data and to probability distributions. They identify different ways of collecting data—including sample surveys, experiments, and simulations—and the role that randomness and careful design play in the conclusions that can be drawn.
The content of this document is centered on the mathematics domains of Counting and Cardinality (Grade K), Operations and Algebraic Thinking (Grades 1-5); Numbers and Operations in Base Ten (Grades K-5); Numbers and Operations—Fractions (Grades 3-5); Measurement and Data (Grades K-5); Ratios and Proportional Relationships (Grades 6-7); the Number System, Expressions & Equations, Geometry, Statistics & Probability (Grades 6-8); Functions (Grade 8), and the high school conceptual categories of Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics & Probability. Instruction in these domains and
conceptual categories should be designed to expose students to experiences, which reflect the value of mathematics, to enhance students’ confidence in their ability to do mathematics, and to help students communicate and reason mathematically.
Printable Version of the Algebra 2 Standards: here