They found out that I'd cheated and I was rejected.
I failed the entrance exam for a public university, which was my first choice, but I passed for a private college, which was my second choice.
I’m so embarrassed I failed such an easy test. I wish I could sink through the floor.
You know that 合格する is "to pass a test," so what's the opposite of that? Fail a test or failure.
If you know the reading for 合格, all you have to do is add 不 to it! You've learned all these readings, yay!