This online math reference is intended for schoolchildren, students and anyone who studies mathematics. The reference book contains both the theoretical part and detailed examples, and allows you to easily and quickly obtain the necessary information on various branches of mathematics, including arithmetic, algebra, trigonometry and geometry.

Arithmetic

Greatest common divisor

Least common multiple

Common fractions

            Definition and examples of common fractions

            Proper and improper fractions

            Mixed fractions

            The main property of a fraction. Reduction of fractions

Addition and subtraction of common fractions

            Addition and subtraction of fractions with the same denominators

             Reducing fractions to a common denominator

             Addition and subtraction of fractions with different denominators

             Addition and subtraction of mixed fractions

Multiplication and division of common fractions

             Multiplying a fraction by an integer

             Multiplication of common fractions

             Division of common fractions

Algebra

Complex numbers

Numerical sets and complex numbers

Algebraic notation of complex numbers

Operations with complex numbers represented in algebraic form

            Addition of complex numbers, examples

            Subtraction of complex numbers, examples

            Multiplication of complex numbers, examples

            Division of complex numbers, examples

            Exponentiation of complex numbers, examples

Modulus and arguments of a complex number

            Modulus of a complex number, example

            Modulus of the difference of complex numbers

            Arguments of a complex number, examples

Trigonometric notation of complex numbers, examples

Multiplication and division of complex numbers represented in trigonometric form

            Multiplication of complex numbers, examples

            Division of complex numbers, examples

Exponentiation and root extraction for complex numbers represented in trigonometric form

            Exponentiation of complex numbers, examples

            Extracting roots of complex numbers, examples

Polynomials

Methods of factorization of a polynomial: factoring out a common factor, abbreviated multiplication formulas, grouping

            Abbreviated multiplication formulas

Dividing a polynomial by a polynomial

            Dividing a polynomial by a polynomial by a column (angle)

            Method of undetermined coefficient

            Division of a polynomial by a binomial according to the Horner scheme

            Using the Horner's scheme to decompose a polynomial by powers of a binomial

            Calculating the value of a polynomial at a given point using Horner's scheme. Bezout's theorem

Factorization of polynomials

Factorization of a third degree polynomial

Equations with one variable

Equations with one variable, equivalent equations

General methods for solving equations

Algebraic equations

Linear equations

Quadratic equations, biquadratic equations

            Solving incomplete quadratic equations

            Solving complete quadratic equations

            Vieta's theorem for solving quadratic equations

            Solving of biquadratic equations

Cubic equations

            Solving cubic equations by factorization

            Solving symmetric cubic equations

            Cardano's formula for solving cubic equations

Quartic equations

            Solving equations of the fourth degree by factorization

            Solving of symmetric equations of the fourth degree

            The Ferrari's method for solving equations of the fourth degree

Equations of higher degrees

Fractional-rational equations

Equations with modulus

Irrational equations

Transcendental equations and inequalities

Trigonometric equations

Exponential equations

Logarithmic equations

Solving combined equations and inequalities

Systems of equations

Systems of two linear equations with two unknowns

Systems of three linear equations with three unknowns

Cramer's formulas for solving systems of linear equations

Solution of systems of linear equations by Gauss method

Functions

Linear

Quadratic

Cubic

Power

Hyperbolic

y = √x

Trigonometric

Exponential

Logarithmic

Geometry

Areas of figures

Formulas for finding the area of a triangle

            Heron's formula

            Formulas for calculating the area of an equilateral triangle

Formulas for finding the area of a convex quadrilateral

            Area of an arbitrary convex quadrilateral

            Area of a parallelogram

            Area of a rhombus

            Area of a trapezoid

Formulas for finding the area of a convex polygons

            Area of a convex polygon

            Area of a regular polygons

Area of a circle, sector of a circle and segment of a circle

Formulas for finding the area of a circle, a sector of a circle and a segment of a circle