Advanced Algebra through Functions
(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.
Power Functions and their Graphs
Natural, Integral and Rational Exponents and their Properties.
Direct and Inverse Variations.
Joint and Combined Variations.
Quadratic Functions and their Graphs
Parabolas: Vertex, Line of Symmetry, Minimum, Maximum.
Vieta Theorem. Factoring. Quadratic Equations. Derivation of Quadratic Formula.
Introduction to Complex Numbers.
Quadratic Inequalities. Biquadratic Equations.
Word Problems Leading to Quadratic Equations.
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.
Radical Functions and their Graphs
Radical Equations. Extraneous Solutions.
Word Problems Leading to Radical Equations.
Rational Functions and their Graphs
Vertical, Horizontal and Slant Asymptotes.
Rational Equations. Extraneous Solutions.
Word problems Leading to Rational Equations.
Exponential Functions and their Graphs
Exponential Growth and Decay. Related Word Problems.
Logarithmic Functions and their Graphs
Properties of Logarithms. Change-of-Base Formula.
Logarithmic Equations. Extraneous Solutions.