Actually, in any science you need to show your work or not bother working the problem at all.
The reason is that other scientists need to be able to reproduce the same results given the same data or experiment.
If you don't show your work, this is not possible.
Also, on a test it will help you get partial credit, so you need to show your work all of the time.
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I am in lower VI at school, I don't noramally bother with working, It has not harmed my academic career.
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Doesn't make any difference that your teachers let you off easy, the fact of the matter is that in a science if you don't show your work your results are useless everyone, including yourself once you inevitably forget what you were doing at the time.