What if an exercise wasn't uniquely defined?

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In summary, the math exam question asked for the ratio of two wheels based on the number of revolutions made along a certain distance. Some students gave the ratio of the radii while others gave the ratio of the areas. The examiner should accept both answers as it is their fault for not clearly defining the question. While some argue that other interpretations such as ratios of volume or angles could also be valid, using the ratio of the areas seems to be the most reasonable measure for a two-dimensional region. Overall, the examiner should take into consideration all possible interpretations and accept them accordingly.
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grzz
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TL;DR Summary
Points of view of examiner and student may not be coincident.
A math exam question asked for the ratio of two wheels given the required information about the number of revolutions made along a certain distance by the two wheels of a penny-farthing bike.

Some students gave the ratio of the radii while others gave the ratio of the areas.

What should an examiner do when confronted with these two types of answers?

Thanks for any help.
 
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  • #2
Accept them both, since it is the fault of the examiner for writing an ill-defined question!
 
  • #3
grzz said:
Summary:: Points of view of examiner and student may not be coincident.

revolutions made along a certain distance
... indicates, that the ratio of the circumferences, i.e. of the radii is asked for. Nothing in the text points to areas.
 
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  • #4
Fresh is right. Would ratios of volume or mass have to be accepted as well?
 
  • #5
Volume and mass are different; you'd need to know the three-dimensional geometry of the wheel for the former as well as material properties for the latter. Meanwhile, area is a perfectly reasonable measure of 'size' of a two-dimensional region.
 
  • #6
One can always find interpretations that are not intended if one only is willing to. E.g. one could solve for the ratio of angles, which are defined by all revolutions of the wheels along the given distance.
 
  • #7
Isn't the "ratio of wheels" equal to 1? One front wheel and one back wheel.
 
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  • #8
I am inclined to be in favour with the reply of "etotheipi', though I totally missed the perfectly logical reply of 'Vanadium 50'!

Anyway, thanks for all contributions.
 
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FAQ: What if an exercise wasn't uniquely defined?

What does it mean for an exercise to not be uniquely defined?

When an exercise is not uniquely defined, it means that there is not enough information or parameters given to determine the specific outcome or solution. This can lead to multiple possible interpretations or solutions for the exercise.

How does an exercise become uniquely defined?

An exercise becomes uniquely defined when all necessary information and parameters are provided, leaving no room for ambiguity. This can be achieved through clear instructions, specific variables, and defined constraints.

What are the consequences of an exercise not being uniquely defined?

The consequences of an exercise not being uniquely defined can include confusion, frustration, and inaccurate results. It can also lead to different interpretations and solutions, making it difficult to compare results or replicate the exercise.

Can an exercise still be useful even if it is not uniquely defined?

Yes, an exercise can still be useful even if it is not uniquely defined. It can serve as a starting point for exploration and experimentation, and can also promote critical thinking and problem-solving skills. However, it is important to acknowledge and address the lack of uniqueness in the exercise.

How can we ensure that an exercise is uniquely defined?

To ensure that an exercise is uniquely defined, it is important to carefully consider and provide all necessary information and parameters. This can involve reviewing and refining instructions, clearly defining variables and constraints, and testing the exercise to ensure that there is only one possible solution.

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