Algebra I
(two semester course)
Algebra I is the second theoretical course in Classic Math School’s Enrichment Program, and is intended for students from 6th to 9th grade. This course prerequisites include the fluency in solving one-variable linear equations. The scope and depth of the course may vary significantly depending on the actual students’ level and duration of the course.
This course generally covers the same topic area as most of Algebra I courses around the country, but with conceptual approach and significant depth. It also covers some topics from Algebra II.
The key elements of this Algebra I course:
Absolute value equations and inequalities.
Systems of linear equations and inequalities with geometric interpretation involving slope concept.
Quadratic equations.
Concepts introduction and problem solving form 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.
The topics and problems that are studied in Algebra I course may 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. Finite and Infinite Sets. Cardinality of Sets.
Operations on Sets: Unions and Intersections. Venn Diagram Problems.
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. Interval Method. 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, Slope-Intercept Form, 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 Leading to the Systems of Linear Equations.
Linear Inequalities in Two Variables. Graphing the Solution Set.
Linear Programming. Linear programming Major Theorem and its Geometric Interpretation. Solving Problems Using Linear Programming Method.
Monomials and Polynomials. 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. Special Product Formulas with Derivation.
Factoring Quadratic Trinomials. Identical polynomials. Factoring Techniques and Strategies for Polynomials. Prime Polynomials.
Fundamental Theorem of Algebra.
Long Division for Polynomials. Synthetic Division of Polynomials.
Solving Quadratic Equations.
Derivation of Quadratic Formula by Completing the Square.
The Complete Analysis of Quadratic Equation Real Roots Based on the Nature of Discriminant.
Vieta Theorem and its Converse.
Solving Quadratic Equations versus Factoring Corresponding Quadratic Trinomials.
Rational Expressions. (Algebraic Fractions.).
Operations on Algebraic Fractions. Complex Rational Expressions.
Word Problems Leading to Quadratic and Rational Equations.