Esta es la pregunta para la semana 4 del curso MA100 en el LSE. Examina el material de los capítulos 7 y 8. A continuación se describe cómo se definió un polinomio en la pregunta. Esto puede ser útil para cualquier persona que necesite editar esta pregunta.

Para las partes a a c, utilizamos un polinomio definido como m * (x ^ 4 - 2a ^ 2 x ^ 2 + a ^ 4 + b), donde las variables "a" y "b" se seleccionan al azar de un conjunto de tamaño reajustable, y la variable $ m $ se elige aleatoriamente del conjunto {+1, -1}. Podemos ver fácilmente que este polinomio tiene puntos estacionarios en -a, 0 y a. Introdujimos la variable "m" para que estos puntos estacionarios no siempre tuvieran la misma clasificación. La variable "b" es siempre positiva, y esto asegura que nuestro polinomio no cruce el eje x. Los primeros y segundos derivados; puntos estacionarios; la evaluación de la segunda derivada en los puntos estacionarios; la clasificación de los puntos estacionarios; y las intersecciones de los ejes se pueden expresar fácilmente en términos de las variables "a", "b" y "m". En efecto,

A ball is thrown vertically upwards from a position above ground level. Find its greatest height, and the total time its in the air.

This question asks a student to draw a straight line graph by dragging points.

Graphing $y=ab^{\pm x+d}+c$

Graphing $y=ab^x+c$

Graphing $y=a\log_{b}(\pm x+d)+c$

Graphing $y=a\log_{b}(x)+c$

Using $F=ma$ to find magnitudes of unknown forces acting on an accelerating body.

sin vertically shifted WORKING 1_11_16

sin vertically shifted 

sin vertically shifted WORKING 1_11_16

sin vertically shifted Working 1_11_16

sin vertically shifted Working 1_11_16

Given th original formula the student enters the transformed formula

sin vertically shifted Working 1_11_16

Questions on angles on parallel lines (vertically-opposite, alternate, corresponding and co-interior), and angles along a straight line and in a circle.

This task is part of a set of three assessment tasks for 7.RP.2.

7.RP.2 Robot Races asks students to "explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation" and to "compute unit rates associated with ratios of fractions." Students also need to compare the speeds of the robots.

A mass is inside a box which is suspended vertically by a cord. Question uses $F=ma$ for different accelerations.

A mass attached to a vertical rope. Finding the tension in the rope for different accelerations. Using $F=ma$.

Using $F=ma$ to find magnitudes of unknown forces acting on an accelerating body.

Ball projected vertically within water of a swimming pool. Find the acceleration, greatest height above the swimming pool floor reached, speed and time. Uses SUVAT equations and $F=ma$.

Given the original formula the student enters the transformed formula

Given th original formula the student enters the transformed formula

A ball is thrown vertically upwards from a position above ground level. Find its greatest height, and the total time its in the air.

Ball projected vertically within water of a swimming pool. Finding the acceleration, greatest height above the swimming pool floor reached, speed and time. Uses SUVAT equations and $F=ma$.