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Math Formulas

Thinking Operations

General Information

Symbols, relationships

 

Number theory

ℕ⊂ℤ⊂ℚ⊂ℝ⊂ℂ

Number Sets

ℙ={ 2, 3, 5, 7, …}

Prime Numbers - Prime Factorization

a|m ⇔n·a=m

Divisibility Rules

(m;n)=l ; [m;n]=k

Greatest Common Divisor (factor) - Least Common Multiple

ab+cd=ad+bcbd

Operations with rational numbers

 

Binomial theorem

a+bn

Binomial theorem

 

Combinatorics

Pn=n!

Permutations

Cnk=(nk)

Combination

V n k = n ! ( n − k ) !

Variation

 

Sets

A∪B ; A∩B ; A B

Operations on Sets

A∪B=B∪A

Fundamental laws of set algebra

A∪B∪C

Cardinality of sets

A×B

Cartesian product

ρ⊆AxA

Relation

 

Logic

P∨Q ; P⇒Q

Logical Operations and Truth Tables

a∨b=b∨a

Properties of Logical Operators

 

Graph Theory

Graph Theory

Graph Theory - definitions, relationships

 

Algebra

Polynomials

a+b2

Special Binomials

 

Progressions

a n = a a + ( n − 1 ) d

Arithmetic progression

a n = a 1 ⋅ q n − 1

Geometric progression

 

Logarithm

logab=c ⇔ac=b

Logarithm

l o g a x = l o g b x l o g b a

Changing the base of a logarithm

 

Exponents

a·a·a=a3

Powers

 

Roots

an=b ⇒bn=a

Roots

 

Proportionality

a:b=c:d

Direct and Inversely Proportion

 

Inequalities

fx<gx

Inequalities

 

Equations

ax2+bx+c=0

Quadratic equation

 

Complex numbers

z=a+ib   ;  i=-1

Complex Numbers

zn

Power of complex numbers

zk=a+ibn

Roots of complex numbers

 

Kamatni račun

k=T·p100

Interest calculation,

 

Geometry

Trigonometry

a s i n α = b s i n β = c s i n γ

Law of Sines

c 2 = a 2 + b 2 − 2 a b c o s 2 γ

Law of Cosines

s i n 2 α + c o s 2 α = 1

Trygonometry Identities of same angle

sin(α±β)

Identities for the sum and difference of two angles

sin(2α)

Trigonometric identities of double angles

sinα2

Trigonometric identities of half angles

sinα±sinβ

Sum and difference of trigonometric functions

sinα=ac

Trigonometry of right triangles

 

Two-dimensional geometric shapes

B1B2¯B2B3¯=A1A2¯A2A3¯

Basic Proportionality Theorem

Triangle

Triangle

Special Triangles

Special Triangles - Right Triangle, Equilateral Triangles, Isosceles Triangles

Quadrilateral

Quadrilateral

Squere

Squere

Rectangle

Rectangle

Rhombus

Rhombus

Parallelogram

Parallelogram

Kite

Kite

Trapezoid

Trapezoid

Circle

Circle

Circular sector

Circular sector

Circular segment

Circular segment

 

Three-dimensional geometric shapes

Cube

Cube

Gömb

Sphere

Cone

Cone

Prism

Prism

Pyramide

Pyramide

Platonic solids

Platonic solids

Cylinder

Cylinder

 

Vectors

a → · b → = | a → | | b → | c o s α

Scalar Product of Vectors

c→=a→×b→

Vector Product of Vectors

 

Analytical Geometry 2D

d=|P1P2|¯

Distance between two points

x 2 + y 2 = r 2

Circle

y = m x + b

Linear equation

x2a2+y2b2=1

Ellipse

 

Mathematical analysis

Important functions

y=ax+b

Linear polynomial function

y=ax2+bx+c

Quatratic polynomial function

y=ax3+bx2+cx+d

Cubic polynomial function

y=1x

Rational function

y=x2k , k∈ℕ

Root function with even radical

y=x2k+1 , k∈ℕ

Root function with odd radical

y=ax

Exponential function

y=logax

Logarithmic function

y=sin x

Sine function

y=cos x

Cosine function

y=tg x

Tangent function

y=ctg x

Cotangent function

y=|x|

Absolute value functions

 

Function Transformations

f(x+c)

Variable and function value transformations

 

Limits

limx→x0fx=a

Limit of a function

 

Dervation

ddxfx=f‵x

Table of Derivatives

( f · g ) ′ = f ′ · g ± f · g ′

Differentiation rules

Tx

Taylor Series

 

Integration

∫fxdx=Fx+C

Table of Integrals

∫ c f ( x ) d x = c ∫ f ( x ) d x

Integration Rules

∫abfxdx=Fb-Fa

Definite Integrals

 

Probability and Statistics

Probability

∑i=1nAi=Ω

Events, Operations with events, Complete system of events

PA=AΩ

Probability of an event

PA|B=PA∩BPB

Conditional Probability

PA=∑i=1nPA|Bi·PBi

Law of Total Probability

PBi|A=PA|Bi·PBiPA

Bayes’ Theorem

 

Statistics

A=∑xii=1nn

Measures of Central Tendency

 
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