Matura m Teil 1: Vom Wagen springen
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
Short
Video
\(\LaTeX\)
Exercise:
Falls man einen möglichst schnellen Wagen will soll man dann mit einer Gruppe einzeln oder nacheinander von ihm springen?
Solution:
center tikzpicture filldrawcolorgreen!!white fill --.rectangle .-.; draw fillbrown ultra thick rectangle ..; draw fillgray . circle radius.; draw fillgray . circle radius.; drawcolorblu thick .---. nodemidway above sscvw; drawcolorred- thick --. nodemidway above sscvm; scopescale. draw .--+-:.; draw .--+-:.; draw .--..; draw ..--+-:.cm; draw ..--+-:.cm; draw .. circle .; scope tikzpicture center bf Alle gleichzeitig: unelastischer Stoss p_n &mustbe p mv_n Mv_a mv_r-v_a Mv_a mv_r M+mv_a v_a fracmM+m v_r bf Nacheinander: v_b _i^n Delta v_i Schwerpunktsystem des glqq Wagens mit i Männerngrqq: p_i &mustbe p_n-i mv_r-Delta v_i M+n-im Delta v_i mv_r M+n-i+m Delta v_i Delta v_i fracmM+n-i+m v_r Die Geschwindigkeit des Wagens nimmt also wenn die i. Person vom Wagen springt um Delta v_i zu. Endgeschwindigkeit: v_b _i^n Delta v_i _i^n fracmM+n-i+m v_r leftfracmM+m + fracmM+m + dots + fracmM+mright v_r v_bv_a; nacheinander besser. Raketenprinzip!
Falls man einen möglichst schnellen Wagen will soll man dann mit einer Gruppe einzeln oder nacheinander von ihm springen?
Solution:
center tikzpicture filldrawcolorgreen!!white fill --.rectangle .-.; draw fillbrown ultra thick rectangle ..; draw fillgray . circle radius.; draw fillgray . circle radius.; drawcolorblu thick .---. nodemidway above sscvw; drawcolorred- thick --. nodemidway above sscvm; scopescale. draw .--+-:.; draw .--+-:.; draw .--..; draw ..--+-:.cm; draw ..--+-:.cm; draw .. circle .; scope tikzpicture center bf Alle gleichzeitig: unelastischer Stoss p_n &mustbe p mv_n Mv_a mv_r-v_a Mv_a mv_r M+mv_a v_a fracmM+m v_r bf Nacheinander: v_b _i^n Delta v_i Schwerpunktsystem des glqq Wagens mit i Männerngrqq: p_i &mustbe p_n-i mv_r-Delta v_i M+n-im Delta v_i mv_r M+n-i+m Delta v_i Delta v_i fracmM+n-i+m v_r Die Geschwindigkeit des Wagens nimmt also wenn die i. Person vom Wagen springt um Delta v_i zu. Endgeschwindigkeit: v_b _i^n Delta v_i _i^n fracmM+n-i+m v_r leftfracmM+m + fracmM+m + dots + fracmM+mright v_r v_bv_a; nacheinander besser. Raketenprinzip!
Meta Information
Exercise:
Falls man einen möglichst schnellen Wagen will soll man dann mit einer Gruppe einzeln oder nacheinander von ihm springen?
Solution:
center tikzpicture filldrawcolorgreen!!white fill --.rectangle .-.; draw fillbrown ultra thick rectangle ..; draw fillgray . circle radius.; draw fillgray . circle radius.; drawcolorblu thick .---. nodemidway above sscvw; drawcolorred- thick --. nodemidway above sscvm; scopescale. draw .--+-:.; draw .--+-:.; draw .--..; draw ..--+-:.cm; draw ..--+-:.cm; draw .. circle .; scope tikzpicture center bf Alle gleichzeitig: unelastischer Stoss p_n &mustbe p mv_n Mv_a mv_r-v_a Mv_a mv_r M+mv_a v_a fracmM+m v_r bf Nacheinander: v_b _i^n Delta v_i Schwerpunktsystem des glqq Wagens mit i Männerngrqq: p_i &mustbe p_n-i mv_r-Delta v_i M+n-im Delta v_i mv_r M+n-i+m Delta v_i Delta v_i fracmM+n-i+m v_r Die Geschwindigkeit des Wagens nimmt also wenn die i. Person vom Wagen springt um Delta v_i zu. Endgeschwindigkeit: v_b _i^n Delta v_i _i^n fracmM+n-i+m v_r leftfracmM+m + fracmM+m + dots + fracmM+mright v_r v_bv_a; nacheinander besser. Raketenprinzip!
Falls man einen möglichst schnellen Wagen will soll man dann mit einer Gruppe einzeln oder nacheinander von ihm springen?
Solution:
center tikzpicture filldrawcolorgreen!!white fill --.rectangle .-.; draw fillbrown ultra thick rectangle ..; draw fillgray . circle radius.; draw fillgray . circle radius.; drawcolorblu thick .---. nodemidway above sscvw; drawcolorred- thick --. nodemidway above sscvm; scopescale. draw .--+-:.; draw .--+-:.; draw .--..; draw ..--+-:.cm; draw ..--+-:.cm; draw .. circle .; scope tikzpicture center bf Alle gleichzeitig: unelastischer Stoss p_n &mustbe p mv_n Mv_a mv_r-v_a Mv_a mv_r M+mv_a v_a fracmM+m v_r bf Nacheinander: v_b _i^n Delta v_i Schwerpunktsystem des glqq Wagens mit i Männerngrqq: p_i &mustbe p_n-i mv_r-Delta v_i M+n-im Delta v_i mv_r M+n-i+m Delta v_i Delta v_i fracmM+n-i+m v_r Die Geschwindigkeit des Wagens nimmt also wenn die i. Person vom Wagen springt um Delta v_i zu. Endgeschwindigkeit: v_b _i^n Delta v_i _i^n fracmM+n-i+m v_r leftfracmM+m + fracmM+m + dots + fracmM+mright v_r v_bv_a; nacheinander besser. Raketenprinzip!
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