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n a v i g a t i o n :

Algebra 1


 

(two semester course)

 

Algebra I course is part of the Classic Math School Enrichment Program. Students meet twice a week for a two-hour session. Each of two semesters is comprised of 15 sessions. Students complete 45-60 minutes homework each week. This course generally covers the same topic area as most of Algebra I courses around the country, but with enhanced depth and emphasis on conceptual approach.

 

Concepts introduction and problem solving form an integral part of each class session. Students learn extensively from and by examples, and 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 are studied in this course include:

        Algebra Prerequisites:

Variables. Algebraic Expressions. Order of  Operations.

Commutative Properties for Addition and Multiplication.

Associative Properties for Addition and Multiplication.

Identity Properties for Addition and Multiplication.

Distributive Property for Multiplication  over Addition.

Properties of Equality. Properties of Comparison (Order).

Linear Equations and Inequalities. Equivalent Transformations of Equations and Inequalities.

 

        Literal Equations and Formulas. Unit Analysis. Converting Formulas.

        Elements of Set Theory. 

Set Notations. Cardinality of Sets. Operations on Sets.

 

        Introduction to Number Theory.

Number Sets.

Relationship between the Subsets of Real Numbers Set.

 

        Elements of Math Logic. Compound Sentences. Truth Tables.

Conjunctions and Intersections.  Disjunctions and Unions. Venn Diagrams.

 

        Absolute Value of a Real Number. Algebraic Definition and Geometric Interpretation. Properties.

Absolute Values Equations. Extraneous Solutions. Interval Method.

Absolute Values Inequalities. Graphing. Geometric Interpretation.

 

        Linear Equations in Two Variables. A Line as a Graph of the Equation. X- and Y- intercepts.

Slope of a Line. A Slope as a Rate of Change. Horizontal and Vertical Lines.

Different forms of Linear Equations: Standard, the Slope- Intercept Form, the Point-Slope form.

Parallel and Perpendicular Lines.

        Systems of Linear Equations in Two Variables. Geometric Interpretation.

Solving Systems of Linear Equations by Graphing, Substitution, and Linear Combination Methods.

Solving Word Problems Using the Systems of Linear Equations.

        Linear  Inequalities in Two Variables. Graphing the Solution Set.

Linear Programming. Linear programming Major Theorem and its Geometric Interpretation.

 

        Monomials and Polynomials. Their Degrees, Coefficients, and Terms. Leading Term of a Polynomial.

Ascending and Descending Order for Polynomials.

Addition and Subtraction of  Polynomials. Multiplication of Polynomials.

FOIL Rule for Multiplication of Binomials. Shortcut Multiplication Formulas.

Factoring Quadratic Trinomials. Identical polynomials. Factoring Uniqueness. Prime polynomials.

 

        Solving Quadratic Equations.

Derivation of Quadratic Formula by Completing the Square.

The Complete Analysis of the Real Roots Based on the Discriminant.

Viete Theorem and its Converse.

The Relationship between Solving Quadratic Equations and Factoring Corresponding Quadratic Trinomials.

 

        Rational Expressions. (Algebraic Fractions.).

Operations on Algebraic Fractions. Complex Rational Expressions.

 

        Word Problems Leading to Quadratic and Rational Equations.