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Is it normal to do awful at one school but great at another? or does that just mean the student is stupid?
I swatched class, I'm doing better now. Yes, I think that if you are comfortable in school, you will do better.
I'd say it's possible.
I got A's for everything in High School, but there was one year when I did terrible at one subject because I got a teacher that didn't know what she was doing.
I'd say it's entirely possible that some schools as a whole teach the students better than others. (fortunately I just had one bad teacher, not all of them.)
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Other than that, it is also possible - as you suggested - that an underachieving student may score higher in a more lenient school.
It's entirely possible that one school may have a lower standard of education than another and the work is easier or marks are awarded more leniently.
This was not the case with the school I went to.
They had a reputation of having a high standard and regularly compared assignments with other schools in the district to ensure that they were at the same level or higher.
They purposely made internal tests more difficult than the national exams so that the students would be better prepared for the national exams.
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TL;DR: Either is possible. You'd have to compare the teaching and marking standards at the two schools.
Your environment and the expectations placed on you have an enormous impact on how you perform.