Algebra II Description
The main theme in Algebra II is expanding the notion of a function through the study of a variety of function types. Logic and reasoning skills learned in Geometry continue to be applied in proving logical statements about the various functions studied. The function concept is thoroughly explored at the beginning of the course, and properties of functions are highlighted. Knowledge of quadratic equations and transformations is linked as quadratic functions are graphed in the plane. The complex number system is introduced as a way of describing certain solutions obtained from the quadratic formula. The concept of the root or zero of a quadratic function is connected to x-intercepts and expanded to polynomial functions and the factor theorem. The difference between the expansion (including the Binomial theorem) and factorization is highlighted. The roots and graphs of polynomial functions are thoroughly analyzed. Previous knowledge of circles and the graphs of quadratic functions, provide the foundation for the study of conic sections. The concepts of the rational numbers and rational expressions are expanded to the analysis of rational functions. The poles and asymptotes of a rational function are thoroughly explored, as well as operations on these functions, and finding intersections of these functions. The connections between inverses and compositions are made, with a clear illustration of the relationship of the domain and range of a function and its inverse. The concept of inverses is then discussed in the context of radical functions. Rational exponents are used to rewrite radical expressions. Inverses are also used to establish the connection between exponential and logarithmic functions. These functions are analyzed, and exponential and logarithmic equations are solved in a real world context, with a focus on exponential growth and decay and compound interest. Knowledge of linear equations is needed for the study of linear systems. Basic notions of counting and probability are then discussed. Arithmetic and geometric series are discussed, as well as methods of finding partial sums.
Units- Analyzing Polynomial Functions
- Analyzing Rational Functions and Equations
- Compositions and Inverses
- Inverses and Radical Functions
- Analyzing Exponential & Logarithmic Functions
- Arithmetic & Geometric Sequences and Series