Linsenkombination
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.
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 -
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 -
Question
Solution
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Video
\(\LaTeX\)
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Exercise:
Ein Gegenstand G steht vor einer Linse deren Brennpunkte F_ und F_ eingezeichnet sind. Er soll mit Hilfe einer weiteren Linse auf den das Bild B abgebildet werden. abclist abc Konstruiere das Bild welches durch die erste Linse entsteht. hfill abc Konstruiere die Linsenebene der zweiten Linse. hfill abc Konstruiere die Brennpunkte der zweiten Linse und beschrifte sie mit F_' und F_'. hfill abclist center tikzpicturelatex pgfmathsetmacror pgfmathsetmacroa pgfmathsetmacroyfpevalr*sina*pi/ fillBlue --y arc -a:a:r; fillBlue --y arc a:-a:-r; draw- very thick -. -- -. nodeaboveG; draw- very thick . -- . . nodeaboveB; fill - circle pt nodebelowF_; fill - circle pt nodebelowF_; draw - -- ; drawdashed - -- --; tikzpicture center
Solution:
center tikzpicturelatex pgfmathsetmacror pgfmathsetmacroa pgfmathsetmacroyfpevalr*sina*pi/ fillBlue --y arc -a:a:r; fillBlue --y arc a:-a:-r; draw- very thick -. -- -. nodeaboveG coordinate G; draw- very thick . -- . . nodeaboveB coordinate B; draw- darkred very thick . -- . -. nodebelowB' coordinate B'; fill - circle pt nodebelowF_; fill - circle pt nodebelowF_; draw - -- ; drawdashed - -- --; drawgray G -- B'; drawgray G -- - -- B'; drawgray B' -- B; drawdashed . -- .-; drawgray B' -- . -. -- B; drawgray B' -- . . -- B; fill . circle pt nodebelowF_'; fill . circle pt nodebelowF_'; tikzpicture center
Ein Gegenstand G steht vor einer Linse deren Brennpunkte F_ und F_ eingezeichnet sind. Er soll mit Hilfe einer weiteren Linse auf den das Bild B abgebildet werden. abclist abc Konstruiere das Bild welches durch die erste Linse entsteht. hfill abc Konstruiere die Linsenebene der zweiten Linse. hfill abc Konstruiere die Brennpunkte der zweiten Linse und beschrifte sie mit F_' und F_'. hfill abclist center tikzpicturelatex pgfmathsetmacror pgfmathsetmacroa pgfmathsetmacroyfpevalr*sina*pi/ fillBlue --y arc -a:a:r; fillBlue --y arc a:-a:-r; draw- very thick -. -- -. nodeaboveG; draw- very thick . -- . . nodeaboveB; fill - circle pt nodebelowF_; fill - circle pt nodebelowF_; draw - -- ; drawdashed - -- --; tikzpicture center
Solution:
center tikzpicturelatex pgfmathsetmacror pgfmathsetmacroa pgfmathsetmacroyfpevalr*sina*pi/ fillBlue --y arc -a:a:r; fillBlue --y arc a:-a:-r; draw- very thick -. -- -. nodeaboveG coordinate G; draw- very thick . -- . . nodeaboveB coordinate B; draw- darkred very thick . -- . -. nodebelowB' coordinate B'; fill - circle pt nodebelowF_; fill - circle pt nodebelowF_; draw - -- ; drawdashed - -- --; drawgray G -- B'; drawgray G -- - -- B'; drawgray B' -- B; drawdashed . -- .-; drawgray B' -- . -. -- B; drawgray B' -- . . -- B; fill . circle pt nodebelowF_'; fill . circle pt nodebelowF_'; tikzpicture center
Meta Information
Exercise:
Ein Gegenstand G steht vor einer Linse deren Brennpunkte F_ und F_ eingezeichnet sind. Er soll mit Hilfe einer weiteren Linse auf den das Bild B abgebildet werden. abclist abc Konstruiere das Bild welches durch die erste Linse entsteht. hfill abc Konstruiere die Linsenebene der zweiten Linse. hfill abc Konstruiere die Brennpunkte der zweiten Linse und beschrifte sie mit F_' und F_'. hfill abclist center tikzpicturelatex pgfmathsetmacror pgfmathsetmacroa pgfmathsetmacroyfpevalr*sina*pi/ fillBlue --y arc -a:a:r; fillBlue --y arc a:-a:-r; draw- very thick -. -- -. nodeaboveG; draw- very thick . -- . . nodeaboveB; fill - circle pt nodebelowF_; fill - circle pt nodebelowF_; draw - -- ; drawdashed - -- --; tikzpicture center
Solution:
center tikzpicturelatex pgfmathsetmacror pgfmathsetmacroa pgfmathsetmacroyfpevalr*sina*pi/ fillBlue --y arc -a:a:r; fillBlue --y arc a:-a:-r; draw- very thick -. -- -. nodeaboveG coordinate G; draw- very thick . -- . . nodeaboveB coordinate B; draw- darkred very thick . -- . -. nodebelowB' coordinate B'; fill - circle pt nodebelowF_; fill - circle pt nodebelowF_; draw - -- ; drawdashed - -- --; drawgray G -- B'; drawgray G -- - -- B'; drawgray B' -- B; drawdashed . -- .-; drawgray B' -- . -. -- B; drawgray B' -- . . -- B; fill . circle pt nodebelowF_'; fill . circle pt nodebelowF_'; tikzpicture center
Ein Gegenstand G steht vor einer Linse deren Brennpunkte F_ und F_ eingezeichnet sind. Er soll mit Hilfe einer weiteren Linse auf den das Bild B abgebildet werden. abclist abc Konstruiere das Bild welches durch die erste Linse entsteht. hfill abc Konstruiere die Linsenebene der zweiten Linse. hfill abc Konstruiere die Brennpunkte der zweiten Linse und beschrifte sie mit F_' und F_'. hfill abclist center tikzpicturelatex pgfmathsetmacror pgfmathsetmacroa pgfmathsetmacroyfpevalr*sina*pi/ fillBlue --y arc -a:a:r; fillBlue --y arc a:-a:-r; draw- very thick -. -- -. nodeaboveG; draw- very thick . -- . . nodeaboveB; fill - circle pt nodebelowF_; fill - circle pt nodebelowF_; draw - -- ; drawdashed - -- --; tikzpicture center
Solution:
center tikzpicturelatex pgfmathsetmacror pgfmathsetmacroa pgfmathsetmacroyfpevalr*sina*pi/ fillBlue --y arc -a:a:r; fillBlue --y arc a:-a:-r; draw- very thick -. -- -. nodeaboveG coordinate G; draw- very thick . -- . . nodeaboveB coordinate B; draw- darkred very thick . -- . -. nodebelowB' coordinate B'; fill - circle pt nodebelowF_; fill - circle pt nodebelowF_; draw - -- ; drawdashed - -- --; drawgray G -- B'; drawgray G -- - -- B'; drawgray B' -- B; drawdashed . -- .-; drawgray B' -- . -. -- B; drawgray B' -- . . -- B; fill . circle pt nodebelowF_'; fill . circle pt nodebelowF_'; tikzpicture center
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