Algebra Arrayan
Transcript of Algebra Arrayan
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Índice de Contenidos – Álgebra Arrayán Capitulo 1: Álgebra en los Números Reales 1.1 LENGUAJE ALGEBRAICO 1.2 VALORIZACIÓN DE EXPRESIONES ALGEBRAICAS 1.3 REDUCCIÓN DE TÉRMINOS SEMEJANTES Y USO DE PARÉNTESIS 1.4 MULTIPLICACIÓN ALGEBRAICA 1.5 PRODUCTOS NOTABLES 1.6 FACTORIZACIÓN 1.6.1 Factor común (Monomio y Polinomio) 1.6.2 Factor común compuesto 1.6.3 Diferencia de cuadrados 1.6.4 Trinomios ordenados 1.6.5 Sumas o diferencias de cubos 1.7 FRACCIONES ALGEBRAICAS 1.7.1 Simplificación 1.7.2 Multiplicación y División de fracciones algebraicas 1.7.3 Adición y Sustracción de fracciones algebraicas
PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 2: Ecuaciones e inecuaciones de primer grado 2.1 ECUACI0NES 2.1.1 Ecuaciones de primer grado con coeficientes enteros 2.1.2 Ecuaciones de primer grado con coeficientes fraccionarios 2.1.3 Ecuaciones fraccionarias de primer grado 2.1.4 Ecuaciones literales de primer grado 2.1.5 Ecuaciones con valor absoluto 2.2 PROBLEMAS 2.3 DESIGUALDADES E INECUACIONES 2.3.1 Desigualdades 2.3.2 Inecuaciones 2.3.3 Inecuaciones simultáneas 2.3.4 Inecuaciones con valor absoluto
PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 3: Relaciones y funciones 3.1 LÓGICA 3.2 CONJUNTOS 3.2.1 Conceptos básicos 3.2.2 Operaciones entre conjuntos 3.3 RELACIONES 3.3.1 Conceptos básicos 3.3.2 Relación de equivalencia y de orden 3.4 FUNCIONES 3.4.1 Conceptos básicos 3.4.2 La función de primer grado (Ecuación de la recta) 3.4.3 Tipos de funciones. Función inversa 3.4.4 Funciones de primer grado simultáneas. Sistemas de ecuaciones de primer grado 3.4.5 Inecuaciones con dos variables. Sistemas y problemas de programación lineal PRUEBA DE SELECCIÓN MÚLTIPLE
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Capitulo 4: Ecuaciones e inecuaciones de segundo grado 4.1 ECUACIÓN CUADRÁTICA 4.1.1 Solución de la ecuación por factorización 4.1.2 Solución de la ecuación cuadrática aplicando la fórmula general 4.1.3 Ecuaciones bicuadráticas 4.1.4 Relación entre los coeficientes de una ecuación cuadrática
y sus raíces o soluciones y naturaleza de ellas 4.2 LA FUNCIÓN CUADRÁTICA 4.3 INECUACIONES DE SEGUNDO GRADO 4.4 SISTEMAS DE ECUACIONES DE SEGUNDO GRADO 4.4.1 Sistemas que contienen una ecuación lineal y una ecuación cuadrática 4.4.2 Sistemas en que ambas ecuaciones son de la forma ax2 ± y2 = c 4.4.3 Sistemas formados por una ecuación de la forma x2 ± y2 = a
y la otra ecuación, de la forma xy = b 4.4.4 Sistemas homogéneos formados por ecuaciones cuyos términos
son todos de segundo grado 4.4.5 Otros sistemas y problemas
PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 5: Polinomios y teoría de ecuaciones 5.1 DEFINICIÓN Y OPERACIONES CON POLINOMIOS 5.1.1 Suma 5.1.2 Resta 5.1.3 Producto 5.1.4 División 5.2 TEORÍA DE ECUACIONES 5.2.1 Cálculo de las raíces de un polinomio. Factorización 5.2.2 Relación entre los coeficientes de una ecuación P (x) = 0 y sus raíces
PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 6: Potencias y Raíces 6.1 POTENCIAS 6.1.1 Potencias de exponente natural 6.1.2 Potencias de exponente cero y exponente entero negativo 6.2 PROPIEDADES DE LAS POTENCIAS 6.2.1 Multiplicación de potencias de igual base 6.2.2 División de potencias de igual base 6.2.3 Elevación de potencia a potencia 6.2.4 Multiplicación de potencias de igual exponente 6.2.5 División de potencias de igual exponente 6.2.6 Potencia de un producto 6.2.7 Potencia de un cociente 6.3 ECUACIONES EXPONENCIALES 6.4 RAÍCES 6.5 PROPIEDADES 6.5.1 Potencia de exponente fraccionario 6.5.2 Multiplicación de raíces de igual índice 6.5.3 División de raíces de igual índice 6.5.4 Raíz de una raíz 6.6 RACIONALIZACIÓN 6.6.1 Técnicas de racionalización 6.7 ECUACIONES IRRACIONALES
PRUEBA DE SELECCIÓN MÚLTIPLE
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Capitulo 7: Logaritmos 7.1 DEFINICIÓN DE LOGARITMO 7.2 PROPIEDADES 7.3 ECUACIONES EXPONENCIALES y LOGARÍTMICAS PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 8: Trigonometría 8.1 SISTEMAS DE MEDICIÓN DE ANGULOS 8.2 RAZONES TRIGONOMÉTRICAS PARA ANGULOS AGUDOS 8.3 IDENTIDADES TRIGONOMÉTRICAS 8.4 FUNCIONES TRIGONOMÉTRICAS DE UN ANGULO CUALQUIERA 8.5 FUNCIONES TRIGONOMÉTRICAS DE 60°, 30° Y 45°, 0°, 90°, 180° Y 270° 8.6 FUNCIONES PERIÓDICAS 8.7 FUNCIONES PARES E IMPARES 8.8 ECUACIONES TRIGONOMÉTRICAS 8.9 RESOLUCIÓN DE TRIANGULOS NO RECTANGULOS 8.9.1 Teorema del seno (o de los senos) 8.9.2 Teorema del coseno (o de los cosenos) 8.9.3 Ángulos de elevación y depresión
PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 9: Números Complejos 9.1 DEFINICIONES Y PROPIEDADES 9.1.1 Igualdad 9.1.2 Representación geométrica 9.1.3 Forma canónica de un complejo 9.1.4 Operaciones con números complejos 9.1.5 Estructura del conjunto 9.1.6 Potencias de i 9.2 CONJUGADO Y MÓDULO DE UN COMPLEJO 9.2.1 Conjugado de un complejo 9.2.2 Módulo de un complejo 9.3 REPRESENTACIÓN TRIGONOMÉTRICA O FORMA POLAR DE UN
NÚMERO COMPLEJO 9.3.1 Definición de razones trigonométricas 9.3.2 Representación trigonométrica del complejo z = a + bi 9.3.3 Producto y cociente de complejos en forma polar 9.3.4 Potenciación de números complejos en forma polar 9.3.5 Radicación de números complejos en forma polar
PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 10: Vectores 10.1 DEFINICIONES 10.2 OPERACIONES CON VECTORES 10.2.1 Suma de vectores 10.2.2 Producto por escalar 10.2.3 Propiedades de la suma y el producto por escalar 10.2.4 Resta de vectores 10.3 VECTOR UNITARIO 10.3.1 Definición 10.3.2 Normalizar un vector 10.4 DESCOMPOSICIÓN DE UNVECTOR 10.5 PRODUCTO PUNTO (O PRODUCTO ESCALAR)
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10.5.1 Definición 10.5.2 Propiedades 10.5.3 Ángulo entre vectores 10.5.4 Proyección de un vector sobre otro 10.6 VECTORES EN EL ESPACIO R3 10.6.1 Definiciones 10.6.2 Producto vectorial o producto cruz
PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 11: Matrices y determinantes 11.1 CONCEPTOS BÁSICOS 11.2 IGUALDAD Y ADICIÓN DE MATRICES 11.2.1 Matrices iguales 11.2.2 Adición de matrices 11.2.3 Propiedades de la adición 11.3 PONDERACIÓN DE UNA MATRIZ POR UN ESCALAR 11.3.1 Definición 11.3.2 Propiedades 11.4 MULTIPLICACIÓN DE MATRICES 11.4.1 Procedimiento 11.4.2 Propiedades de la multiplicación 11.4.3 Matrices inversas y ecuaciones multiplicativas 11.5 DETERMINANTES Y SISTEMAS DE ECUACIONES 11.5.1 Determinantes y Sistemas lineales de orden 11.5.2 Determinantes y Sistemas lineales de orden 3
PRUEBA DE SELECCIÓN MULTIPLE Capitulo 12: Sumatoria y progresiones 12.1 SUMATORIA 12.2 SUCESIONES 12.2.1 Definición 12.2.2 Sucesiones convergentes 12.2.3 Sucesiones divergentes 12.2.4 Sucesiones crecientes y decrecientes 12.3 PROGRESIÓN ARITMÉTICA 12.4 PROGRESIÓN GEOMÉTRICA 12.4.1 Definición 12.4.2 Cálculo de intereses de capital 12.5 PROGRESIÓN ARMÓNICA 12.6 INDUCCIÓN MATEMÁTICA
PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 13: Análisis combinatorio, Teorema del binomio y Elementos de probabilidades 13.1 ANÁLISIS COMBINATORIO 13.1.1 Conceptos básicos 13.1.2 Permutaciones 13.1.3 Arreglos o variaciones 13.1.4 Combinaciones 13.2 TEOREMA DEL BINOMIO 13.2.1 Conceptos y observaciones básicas 13.2.2 Teorema del binomio 13.2.3 El triángulo de Pascal 13.3 ELEMENTOS DE PROBABILIDADES
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13.3.1 Conceptos básicos 13.3.2 Probabilidad de la unión y de la intersección de dos eventos
PRUEBA DE SELECCIÓN MÚLTIPLE Capitulo 14: Problemas 14.1 APLICACIÓN DE ECUACIONES LINEALES ENTERAS 14.2 APLICACIÓN DE ECUACIONES LINEALES FRACCIONARIAS 14.3 APLICACIÓN DE SISTEMAS DE ECUACIONES LINEALES 14.4 PROBLEMAS MISCELÁNEOS
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