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Algebra 2
In this course, students learn the advanced concepts of Algebra and application of these concepts to problem solving. The stress of this course is done on three key elements:
1. Exploring functions’ behavior within the scope of elementary math.
2. Graphing. Translating graphs.
3. Using functions and equations as models for the word problems.
Concepts introduction and problem solving form an integral part of each class session. Students have learned extensively from and by examples, and a variety of instructional methods were used to enhance students' problem-solving abilities. Students tackled many complicated problems using inductive and deductive reasoning approaches. Some of the topics and problems that are 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
Direct and inverse variations
Joint and combined variations
Quadratic Functions and their Graphs
Parabolas:(Vertex, line of symmetry, minimum, maximum)
Viet Theorem. Factoring. Quadratic equations. Derivation of quadratic formula
Introduction to complex numbers
Quadratic Inequalities. Biquadratic equations
Word problems
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
Rational Functions and their Graphs
Rational equations. Extraneous solutions
Word problems
Exponential Functions and their Graphs
Number e
Exponential growth and decay. Word problems.
Logarithmic Functions and their Graphs
Properties of logarithms. Change-of-base formula.
Logarithmic equations. Extraneous solutions
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