CBTis 116 Tijuana, BC, Mxico Academia de Matemticas

Formulario de Matemticas CBTis 116

Fracciones

=

=

=

= ( )

Leyes de los Exponentes

= +

= () = () =

=

=

Productos Notables ( + )( ) = 2 2 ( )( ) = ( )2 ( )2 = 2 2 + 2 ( + )( + ) = 2 + ( + ) + ( )3 = 3 32 + 32 3 Propiedades de los Logaritmos

= = = +

=

= =

Formula general para ecuaciones de 2do grado

2 + + = 0 = 2 42

Teorema de Pitgoras = 2 + 2 Ley de Senos

= = Ley de Cosenos

2 = 2 + 2 2 2 = 2 + 2 2 2 = 2 + 2 2 = 2 + 2 22 = 2 + 2 22 = 2 + 2 22

Radianes Grados 2 360 180 2 90 3 60 1 57.3 4 45 6 30

Relaciones Trigonomtricas =

=

= =

= =

Angulo Sen Cos Tan 0 0 1 0 30 12 32 13 45 12 12 1 60 32 12 3 90 1 0

Identidades Trigonomtricas

= 1 = 1 = 1 =

=

2 + 2 = 1 1 + 2 = 2 1 + 2 = 2 ( ) = ( ) = ( ) = 1 2 = 2 2 = 2 2 2 = 2 1 2 2 = 12 (1 2) 2 = 12 (1 + 2) + = 2 1

2 ( + ) 1

2 ( )

= 2 12

( ) 12

( + ) + = 2 12 ( + ) 12 ( ) = 2 12 ( + ) 12 ( ) = +

+ 2 = 1 2 2 = 1 + 2 2 = = 1 1 + = 2 = + 2

Distancia entre 2 puntos

= (2 1)2 + (2 1)2 Punto medio

= 1 + 22 = 1 + 22 Punto que divide a un segmento en la razn r1: r2

= 12 + 211 + 2 = 12 + 211 + 2

Distancia de un punto a una reta

= 1 + 1 + 2 + 2 Pendiente

= 2 12 1

= : = 2 11 + 12 : 1 = 2 : 1 = 12 Ecuacin de la Recta

= + 1 = ( 1) + = 0 + + = 0

Ecuacin de la Circunferencia ( )2 + ( )2 = 2 Ecuacin de la Parbola ( )2 = 4( ) ( )2 = 4( ) Ecuacin de la Elipse ( )2

2+ ( )2

2= 1 2 = 2 + 2 ( )2

2+ ( )2

2= 1 =

Ecuacin de la Hiprbola ( )22

( )2

2= 1 2 = 2 + 2 ( )2

2

( )22

= 1 =

Limites lim 0 = lim = 0 lim 00 = lim = Derivadas

() = = lim0 ( + ) () = lim0

= 0

= 1

=

= 1

=

+

( ) =

=

2

() = 1

() = ()

=

= ()

= 1

+ ()

=

=

= 2

= 2

=

=

= 1

1 2

= 11 2

= 11 + 2

= 11 + 2

= 1

2 1

= 1

2 1

ALGEBRA

GEOMETRA PLANA

GEOMETRA ANALTICA

TRIGONOMETRA

CLCULO

CBTis 116 Tijuana, BC, Mxico Academia de Matemticas

Formulario de Matemticas CBTis 116

Integrales

= + = [ ] = = +1

+ 1 + 1

= || +

= + =

+ = + = + = | | + = | | + = | + | + = | | + 2 = + 2 = + = + = + =

2 + 2 = 1 +

2 2= 12 + +

2 2= 12 + +

2 2=

+

2 2 = + 2 2 +

2 2= 1

+

Integracin por sustitucin trigonomtrica

Si contiene Se sustituye Utilizar la identidad

2 2 = 1 2 = 2 2 + 2 = 1 + 2 = 2 2 2 = 2 1 = 2

Distribucin de frecuencias

= 1 + 3.322 () =

Medidas de Tendencia Central

Concepto Datos Sin Agrupar Datos Agrupados

Moda Dato ms repetido 1 + 11 + 2 Mediana

Par Impar 1 + 2 ()1 2+2+12 +12

Media Aritmtica = =

Media Geomtrica =

Media Armnica

= 1

Medidas de Dispersin Concepto Datos Sin Agrupar Datos Agrupados

Rango (2) (1) Desviacin

Media = | | = | | Desviacin

Tpica = | |2 = | |2 Varianza = 2 = 2

Medidas de Forma Concepto Formula

Sesgo

3( )

Curtosis 4 = 44 Momentos = | |

Medidas de Correlacin Concepto Formula

Coeficiente de

Correlacin =

[2 ()2][2 ()2] = Recta de

Regresin

= 1 + 0 1 = 2 ()2 0 = 1

Error estndar de estimacin

= 2 0 1 2

Tcnicas de Conteo Concepto Formula

Principio de Multiplicacin = 1234 .. Permutaciones = !( )! Combinaciones = !( )! !

Probabilidad

() = ""

Probabilidad de eventos independientes ( ) = ()() Probabilidad de eventos mutuamente excluyentes ( ) = () + () Probabilidad Condicional

(/) = ( )()

Teorema de Bayes

(1/) = (1 )(1 ) + (2 ) + (2 ) + (1/) = (/1)()(/1)() + (/2)() + (/3)() + Constantes

= 2.7182818246 .. = 3.14159265359 ..

Rectas Notables

Triangulo

Alturas

Medianas

Mediatrices

Bisectrices

Circulo

reas, permetros y volmenes

Figura Permetro rea

Triangulo

= + + = ()2 Rectngulo

= 2 + 2 =

Circulo

= 2 = 2

Figura rea Volumen

Cubo

= 62 = 3

Cilindro

= 2 + 22 = 2

Cono

= 4 + 2 + 2 = 23

Esfera

= 42 = 433

PROBABILIDAD Y ESTADSTICA