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My university just allows anyone into first semester, but then has quite hard courses and exams there already – by the end of the second semester, 90% have already failed.

That’s another way to solve the >10x applicants issue.

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That's actually a genius way to reduce administrative overhead as well. Problem is that the exams select only for people that are good at taking exams. Not always the most interesting/well rounded students.

It's the best solution yet — going by entrance exams prefers those who already have knowledge, going by SAT is completely unfair, etc.

My university (at least the engineering department, but I think all the STEM departments) uses a weighting scheme to adjust grades. They look at the average that students from that school gets after the first year and adjusts the entrance grades down accordingly. So, if a student who had a 95% average coming out of high school went to a school where people generally had about a 75% after first year and an entrance average of 90%, you'd reduce that student's entrance average by 15% so they'd count as having an 80% for comparison to other students. It's not quite as simple as this as the calculations are more detailed (one needs to account for comparing courses and schools with no or few previous students), but it's roughly the idea.

With this scheme, if a school inflates their grades it will have a larger adjustment down. It's entirely based on past performance of people from the school, so there's no standardized tests to worry about. Theoretically, one could have an adjustment upwards, but I've never heard of it happening (I participated in department meetings where they discussed admissions in general). The adjustments are usually somewhere between 20 and mid to high 20s percent. Some are higher (not many), but a few are lower but not by much.

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