YEAR 2: Algebra
Pass standardized tests (SAT, ASVAB, State Tests) with ease. Symbolic thinking. Modeling. Solving Equations. Connections Between Algebra and Geometry. Functional Relations Between Quantities. Symmetry and Geometric Transformations.
Course Outline
Part I

Formulation of Symbolic Equations from Verbal Information.

Equations of Lines.

Slope as Rate of Change.

Linear Systems.

Intersection of Lines.

Elimination Method. Substitution Method.


Equations of Parabolas.

Roots. Completing the Square. Discriminant. Formula for Roots.

Quadratic Inequalities. Maximum and Minimum Values of a Quadratic

Part II

Functions and Graphs.

Functional Relations. Notation.

Methods of Representing Functions. Graphs of Functions.

Elementary Functions. Transforming Graphs.

Implicit Functions. Inverse Functions.


Higher Degree Polynomials.

Fundamental Theorem of Algebra.

Qualitative Behavior from Multiplicity of Roots.Qualitative Behavior from Multiplicity of Roots.

Factoring Polynomials. Difference of Squares. Sum of Cubes.

Factoring Polynomials. Difference of Squares. Sum of Cubes.

Binomial Theorem. Combinations. Pascal's Triangle.

Vieta Formula, Elementary Symmetric Polynomials.

Remainder of Polynomial Division.


Conic Sections.

Ellipse. Parabola. Hyperbola. Circle.

Definition as Loci of Points.

Part III

Sequences and Series.

Geometric Sequences and Summations.

Triangular Numbers. Fibonnaci Numbers.


Group Theory.

Symmetry Groups. Permutations.

Geometric Transformations. Dihedral Groups.


Ring and Field Theory