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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