Drei Quadrate
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
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Länge \(\ell\) / Masse \(m\) / Strecke \(s\) / Fläche \(A\) / Drehmoment \(\vec M\) / Radius \(r\) / Breite \(b\) /
The following formulas must be used to solve the exercise:
\(\sum \stackrel{\curvearrowleft}{M} \stackrel{!}{=} \sum \stackrel{\curvearrowright}{M} \quad \) \(A = \pi r^2 \quad \) \(A = s^2 \quad \) \(A = ab \quad \) \(\vec r_{\rm S} = \frac{1}{M} \sum_i m_i \vec r_i \quad \)
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Exercise:
Berechne die xy-Koordinaten des Schwerpunktes der unten abgebildeten Figur. Es handelt sich um drei aneinander gereihte Quadrate der Längen cm cm und cm. center tikzpicturescale. filldrawfillblack!!white ----------------; tikzpicture center
Solution:
NewQtyaecm NewQtyazcm NewQtyadcm % Wir legen folges Koordinatensystem fest: center tikzpicturescale. latex filldrawcolorblack fillblack!!white --------cycle; filldrawcolorblack fillblack!!white --------cycle; filldrawcolorblack fillblack!!white --------cycle; draw- colorgreen!!black thick -.--. nodebelow x; draw- colorgreen!!black thick -.--. nodeleft y; drawcolorblack fillyellow . . circle .cm; drawcolorblack fillblack . . circle .cm; drawcolorblack fillblack circle .cm; drawcolorblack fillblack . . circle .cm; tikzpicture center Ausserdem unterteilen wir den Körper in die drei offensichtlichen Quadrate. % Die Koordinaten der Schwerpunkte der einzelnen Quadrate sind SolQtyxefraca_aeX/cm SolQtyxza_ + fraca_aeX+azX/cm SolQtyxda_ + a_ + fraca_aeX+azX+adX/cm SolQtyyefraca_aeX/cm SolQtyyzfraca_azX/cm SolQtyydfraca_adX/cm al x_ xeF & y_ yeF x_ xzF & y_ yzF x_ xdF & y_ ydF. Ausserdem gilt für die Massen al m_i c a_i^. Mit der Schwerpunktformel finden wir schliesslich die Koordinaten des Schwerpunktes: SolQtyxfraca_^ + a_a_^ + a_^ + a_a_^+a_a_^+a_^a_^+a_^+a_^aeX**+*aeX*azX**+azX**+*aeX*adX**+*azX*adX**+adX**/*aeX**+azX**+adX**cm SolQtyyfraca_^+a_^+a_^a_^+a_^+a_^aeX**+azX**+adX**/*aeX**+azX**+adX**cm al x^* fracm_x_+m_x_+m_x_m_+m_+m_ fracc a_^xeF+c a_^qtyxzF+c a_^qtyxdFc a_^+c a_^+c a_^ xF fracqtyae^ + ae qtyaz^ +qtyaz^ + aeqtyad^+azqtyad^ + qtyad^qtyqtyae^+qtyaz^+qtyad^ xP y^* fracm_y_+m_y_+m_y_m_+m_+m_ fracc a_^yeF+c a_^ yzF+c a_^ydFc a_^+c a_^+c a_^ yF fracqtyae^+qtyaz^+qtyad^qtyqtyae^+qtyaz^+qtyad^ yP.
Berechne die xy-Koordinaten des Schwerpunktes der unten abgebildeten Figur. Es handelt sich um drei aneinander gereihte Quadrate der Längen cm cm und cm. center tikzpicturescale. filldrawfillblack!!white ----------------; tikzpicture center
Solution:
NewQtyaecm NewQtyazcm NewQtyadcm % Wir legen folges Koordinatensystem fest: center tikzpicturescale. latex filldrawcolorblack fillblack!!white --------cycle; filldrawcolorblack fillblack!!white --------cycle; filldrawcolorblack fillblack!!white --------cycle; draw- colorgreen!!black thick -.--. nodebelow x; draw- colorgreen!!black thick -.--. nodeleft y; drawcolorblack fillyellow . . circle .cm; drawcolorblack fillblack . . circle .cm; drawcolorblack fillblack circle .cm; drawcolorblack fillblack . . circle .cm; tikzpicture center Ausserdem unterteilen wir den Körper in die drei offensichtlichen Quadrate. % Die Koordinaten der Schwerpunkte der einzelnen Quadrate sind SolQtyxefraca_aeX/cm SolQtyxza_ + fraca_aeX+azX/cm SolQtyxda_ + a_ + fraca_aeX+azX+adX/cm SolQtyyefraca_aeX/cm SolQtyyzfraca_azX/cm SolQtyydfraca_adX/cm al x_ xeF & y_ yeF x_ xzF & y_ yzF x_ xdF & y_ ydF. Ausserdem gilt für die Massen al m_i c a_i^. Mit der Schwerpunktformel finden wir schliesslich die Koordinaten des Schwerpunktes: SolQtyxfraca_^ + a_a_^ + a_^ + a_a_^+a_a_^+a_^a_^+a_^+a_^aeX**+*aeX*azX**+azX**+*aeX*adX**+*azX*adX**+adX**/*aeX**+azX**+adX**cm SolQtyyfraca_^+a_^+a_^a_^+a_^+a_^aeX**+azX**+adX**/*aeX**+azX**+adX**cm al x^* fracm_x_+m_x_+m_x_m_+m_+m_ fracc a_^xeF+c a_^qtyxzF+c a_^qtyxdFc a_^+c a_^+c a_^ xF fracqtyae^ + ae qtyaz^ +qtyaz^ + aeqtyad^+azqtyad^ + qtyad^qtyqtyae^+qtyaz^+qtyad^ xP y^* fracm_y_+m_y_+m_y_m_+m_+m_ fracc a_^yeF+c a_^ yzF+c a_^ydFc a_^+c a_^+c a_^ yF fracqtyae^+qtyaz^+qtyad^qtyqtyae^+qtyaz^+qtyad^ yP.
Meta Information
Exercise:
Berechne die xy-Koordinaten des Schwerpunktes der unten abgebildeten Figur. Es handelt sich um drei aneinander gereihte Quadrate der Längen cm cm und cm. center tikzpicturescale. filldrawfillblack!!white ----------------; tikzpicture center
Solution:
NewQtyaecm NewQtyazcm NewQtyadcm % Wir legen folges Koordinatensystem fest: center tikzpicturescale. latex filldrawcolorblack fillblack!!white --------cycle; filldrawcolorblack fillblack!!white --------cycle; filldrawcolorblack fillblack!!white --------cycle; draw- colorgreen!!black thick -.--. nodebelow x; draw- colorgreen!!black thick -.--. nodeleft y; drawcolorblack fillyellow . . circle .cm; drawcolorblack fillblack . . circle .cm; drawcolorblack fillblack circle .cm; drawcolorblack fillblack . . circle .cm; tikzpicture center Ausserdem unterteilen wir den Körper in die drei offensichtlichen Quadrate. % Die Koordinaten der Schwerpunkte der einzelnen Quadrate sind SolQtyxefraca_aeX/cm SolQtyxza_ + fraca_aeX+azX/cm SolQtyxda_ + a_ + fraca_aeX+azX+adX/cm SolQtyyefraca_aeX/cm SolQtyyzfraca_azX/cm SolQtyydfraca_adX/cm al x_ xeF & y_ yeF x_ xzF & y_ yzF x_ xdF & y_ ydF. Ausserdem gilt für die Massen al m_i c a_i^. Mit der Schwerpunktformel finden wir schliesslich die Koordinaten des Schwerpunktes: SolQtyxfraca_^ + a_a_^ + a_^ + a_a_^+a_a_^+a_^a_^+a_^+a_^aeX**+*aeX*azX**+azX**+*aeX*adX**+*azX*adX**+adX**/*aeX**+azX**+adX**cm SolQtyyfraca_^+a_^+a_^a_^+a_^+a_^aeX**+azX**+adX**/*aeX**+azX**+adX**cm al x^* fracm_x_+m_x_+m_x_m_+m_+m_ fracc a_^xeF+c a_^qtyxzF+c a_^qtyxdFc a_^+c a_^+c a_^ xF fracqtyae^ + ae qtyaz^ +qtyaz^ + aeqtyad^+azqtyad^ + qtyad^qtyqtyae^+qtyaz^+qtyad^ xP y^* fracm_y_+m_y_+m_y_m_+m_+m_ fracc a_^yeF+c a_^ yzF+c a_^ydFc a_^+c a_^+c a_^ yF fracqtyae^+qtyaz^+qtyad^qtyqtyae^+qtyaz^+qtyad^ yP.
Berechne die xy-Koordinaten des Schwerpunktes der unten abgebildeten Figur. Es handelt sich um drei aneinander gereihte Quadrate der Längen cm cm und cm. center tikzpicturescale. filldrawfillblack!!white ----------------; tikzpicture center
Solution:
NewQtyaecm NewQtyazcm NewQtyadcm % Wir legen folges Koordinatensystem fest: center tikzpicturescale. latex filldrawcolorblack fillblack!!white --------cycle; filldrawcolorblack fillblack!!white --------cycle; filldrawcolorblack fillblack!!white --------cycle; draw- colorgreen!!black thick -.--. nodebelow x; draw- colorgreen!!black thick -.--. nodeleft y; drawcolorblack fillyellow . . circle .cm; drawcolorblack fillblack . . circle .cm; drawcolorblack fillblack circle .cm; drawcolorblack fillblack . . circle .cm; tikzpicture center Ausserdem unterteilen wir den Körper in die drei offensichtlichen Quadrate. % Die Koordinaten der Schwerpunkte der einzelnen Quadrate sind SolQtyxefraca_aeX/cm SolQtyxza_ + fraca_aeX+azX/cm SolQtyxda_ + a_ + fraca_aeX+azX+adX/cm SolQtyyefraca_aeX/cm SolQtyyzfraca_azX/cm SolQtyydfraca_adX/cm al x_ xeF & y_ yeF x_ xzF & y_ yzF x_ xdF & y_ ydF. Ausserdem gilt für die Massen al m_i c a_i^. Mit der Schwerpunktformel finden wir schliesslich die Koordinaten des Schwerpunktes: SolQtyxfraca_^ + a_a_^ + a_^ + a_a_^+a_a_^+a_^a_^+a_^+a_^aeX**+*aeX*azX**+azX**+*aeX*adX**+*azX*adX**+adX**/*aeX**+azX**+adX**cm SolQtyyfraca_^+a_^+a_^a_^+a_^+a_^aeX**+azX**+adX**/*aeX**+azX**+adX**cm al x^* fracm_x_+m_x_+m_x_m_+m_+m_ fracc a_^xeF+c a_^qtyxzF+c a_^qtyxdFc a_^+c a_^+c a_^ xF fracqtyae^ + ae qtyaz^ +qtyaz^ + aeqtyad^+azqtyad^ + qtyad^qtyqtyae^+qtyaz^+qtyad^ xP y^* fracm_y_+m_y_+m_y_m_+m_+m_ fracc a_^yeF+c a_^ yzF+c a_^ydFc a_^+c a_^+c a_^ yF fracqtyae^+qtyaz^+qtyad^qtyqtyae^+qtyaz^+qtyad^ yP.
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