Mathematical Theory.

Mathematical theory includes the study of fractions, analytic geometry etc. These topics will allow to understand better a material and will answer questions in your math problems.

Divisibility rules Divisibility by 2 Divisibility by 3 Divisibility by 4 Divisibility by 5 Divisibility by 6 Divisibility by 9 Divisibility by 10 Divisibility by 11

Fraction Forms of fractions The basic property of fraction Simplifying fractions Least common denominator of fractions Converting improper fractions (composed fractions) to mixed numbers Converting mixed numbers to improper fractions (composed fractions) Addition and Subtraction of fractions Multiplication of fractions Division of fractions Comparing fractions Convert Decimals to Common Fractions

Percent Percent Definition. Main information Decimal to Percent. Percent to Decimal The method of solving problems with percentage Find P percent of A B is P percent of what? B is what percent of A? Find the number which is greater (less) than a given number by P percent.

Factoring: Some special cases Square of the sum Square of the difference Difference of squares Cube of sum Cube of difference Sum of cubes Difference of cubes

Arithmetic mean

Vectors Vectors Definition. Main information Component form of a vector with initial point and terminal point Length of a vector Direction cosines of a vector Equal vectors Orthogonal vectors Collinear vectors Coplanar vectors Angle between two vectors Vector projection Addition and subtraction of vectors Scalar-vector multiplication Dot product of two vectors Cross product of two vectors (vector product) Scalar triple product (mixed product) Linearly dependent and linearly independent vectors Decomposition of the vector in the basis

Matrix Matrix Definition. Main information System of linear equations - matrix form Types of matrices Matrix scalar multiplication Addition and subtraction of matrices Matrix multiplication Transpose matrix Elementary matrix operations Determinant of a matrix Minors and cofactors of a matrix Inverse matrix Linearly dependent and independent rows Rank of a matrix

Analytic geometry Distance between two points Midpoint. Coordinates of midpoint Equation of a line Equation of a plane Distance from point to plane Distance between two planes Distance from a point to a line - 2-Dimensional Distance from a point to a line - 3-Dimensional Angle between two planes Angle between line and plane

I will add new theoretical material in this section gradually.

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