TeXercises.com

Umfang und Fläche

About points...

We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.

That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/umfang-und-flache/

Question

Solution

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Exercise:
Die folgen Teilaufgaben sind unabhängig voneinander. Die volle Punktzahl wird nur erteilt wenn die Endlösung komplett vereinfacht ist. abclist abc Ein Kreis habe den gleichen Umfang wie vier Kreise mit Radius r insgesamt. Wie gross ist sein Radius R? abc Ein Kreis habe den gleichen Flächeninhalt wie vier Kreise mit Radius r insgesamt. Wie gross ist sein Radius R? abclist

Solution:
abclist abc Jeder einzelne der vier Kreise hat einen Umfang von al u_ pi r. Alle Kreise zusammen haben deshalb einen Umfang von al u pi r pi r. Ein Kreis mit einem solchen Umfang hat einen Radius von al R fracupi r. abc Jeder einzelne der vier Kreise hat eine Fläche von al A_ pi r^. Alle Kreise zusammen haben deshalb einen Umfang von al A pi r^ Ein Kreis mit einer solchen Fläche hat einen Radius von al R sqrtfracApi sqrtfracpi r^pi r. abclist

Meta Information

\(\LaTeX\)-Code

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Attributes & Decorations

Tags	algebraisch, geometrie, kreisberechnungen
Content image
Difficulty	(2, default)
Points	8 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	pw
Decoration
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