Mathematics I: Algebra

Mathematics I: Algebra

1. Stage 1

   • Operations with polynomials
     • 1.1 Algebraic terminology
       • 1.1.1 Reduction of like terms
       • 1.2 Operation with polynomials
         • 1.2.1 Addition of polynomials
         • 1.2.2 Subtraction of polynomials
         • 1.2.3 Algebraic multiplication
         • 1.2.4 Algebraic division
         • 1.3 Simplification of expressions with grouping symbols
           • 1.4 Scientific notation

2. Stage 2

   • Special products and factoring polynomials
     • 2.1 Special products and factoring polynomials
       • 2.1.1 Special products
       • 2.2 Greatest common factor
         • 2.3 Conjugated Binomials and Difference of squares
           • 2.4 Binomials with common term or like terms and general trinomial of second degree
             • 2.4.1 Factoring quadratic trinomials
             • 2.5 Square of a Binomial and perfect square trinomial
               • 2.5.1 Factoring perfect square trinomials
               • 2.6 Factoring of addition or differences of two cubes
                 • 2.7 Factoring by grouping (association)
                   • 2.8 Cube of a binomial

3. Stage 3

   • Rational algebraic expressions
     • 3.1 Introduction to rational algebraic expressions
       • 3.2 Simplifying rational algebraic expressions
         • 3.3 Operations with rational algebraic expressions
           • 3.3.1 Multiplication and division
           • 3.3.2 Least common multiple. Addition of numerical fractions
           • 3.3.3 Addition and subtraction of rational expressions

4. Stage 4

   • Linear equations and fractional equations
     • 4.1 Linear equations in one variable
       • 4.1.1 Equations with decimal solutions
       • 4.1.2 Application problems
       • 4.2 Equations containing variables in both sides of the equality
         • 4.2.1 More application problems
         • 4.3 Literal equations and formulas
           • 4.4 The linear equations and extraneous solutions
             • 4.5 Fractional equations and extraneous solutions
               • 4.6 Problems involving ratio and proportion

5. Stage 5

   • System of linear equations
     • 5.1 Evaluating expressions and equations with two variables
       • 5.2 Cartesian coordinate system
         • 5.3 Graphing equations of two variables
           • 5.4 Finding the intersection of two graphs
             • 5.5 Solution of linear equation systems using analytical methods
               • 5.5.1 Substitution method
               • 5.5.2 Addition and subtraction method
               • 5.6 Problems involving two variables