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Matemáticas I: Cónicas, Recta, Sistemas y Fractales

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Quiz de temas selectos de Math I

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Matemáticas I: Cónicas, Recta, Sistemas y Fractales
 

Matemáticas I: Cónicas, Recta, Sistemas y FractalesOnline version

Quiz de temas selectos de Math I

by Ana Maria Hernández
1

¿Cuál es la ecuación general de una elipse centrada en el origen?

2

La ecuación de una circunferencia de radio r y centro (h,k) es:

3

La ecuación de la recta en forma explícita es:

4

Un sistema lineal 2x2 puede resolverse por:

5

Si las rectas de un sistema son paralelas, la solución es:

6

La determinante de A = [[a,b],[c,d]] define si el sistema tiene:

7

Un fractal es:

8

Ejemplo simple de fractal conocido:

9

El conjunto de Sierpinski se genera eliminando:

10

En un sistema 2x2, si det(A) = 0 y hay soluciones, estas son:

Explicación

La elipse tiene suma de cuadrados igual a 1 con fracciones positivas.

Deriva de la definición de distancia al cuadrado.

Forma pendiente-intersección y = mx + b.

Métodos comunes: sustitución, igualación, eliminación (reducción).

Rectas paralelas no se intersectan.

Solución única si det(A) ≠ 0.

Propiedad de autosimilitud típica de fractales.

Conjunto de Cantor es clásico fractal.

Patrón triangular repetido a múltiples escalas.

Det=0 puede dar infinitas o ninguna; aquí asume consistencia.

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