Algebra II
(two semester course)

Algebra II is a fourth theoretical course in Classic Math School’s Enrichment Program, and intended for students from 8th to 10th grade. The course prerequisites include fluency in making and solving linear and quadratic equations and inequalities (Algebra I).

The key elements of this Algebra II course:
Exploring functions’ behavior within the scope of elementary math.
Graphing functions. Translating graphs.
Using functions and equations as models for the word problems.

Concepts introduction, including proofs of theorems and derivation of formulas, as well as problem solving formed an integral part of each class session. Students learn extensively from and by examples, and through problem discussions. A variety of instructional methods are used to enhance students' problem-solving abilities. Students tackle many complicated problems using inductive and deductive reasoning approaches. Some of the topics and problems that were studied in this course include:

Relations and Functions
Domain and Range.
3 Ways of Assigning Functions: Mapping Diagrams (Tables), Graphs, Equations (Formulas)
One-To-One and Many-To-One Functions. Vertical Line and Horizontal Line Tests.
Even and Odd Functions.
Composition of Functions.
Inverse Functions.

Power Functions and their Graphs
Natural, Integral and Rational Exponents and their Properties.
Direct and Inverse Variations.
Joint and Combined Variations.

Parabolas: Vertex, Line of Symmetry, Minimum, Maximum.
Introduction to Complex Numbers.

Polynomial Functions and their Graphs
Factoring. Division of Polynomials. Synthetic Division.
Polynomial Equations. Remainder and Factor Theorems.
Fundamental Theorem of Algebra.
Descartes’ Rule of Signs. Boundaries of the Roots. Rational Roots.