How come whenever you take a test they test you on things they don't teach you?

I think you're confusing memorization of details with being able to comprehend, analyze and apply information. The last is what the Common Core Standards emphasize. For example, if you've learned that 2+2 equals 4, the old tests would have asked 2+2=? But the new tests will give you a situation- you have a couple of apples and your friend has the same number of apples. If you pool your apples, how many will you have?

A test can be a spit-back of a section of a book or class or could test the concepts offered and require a more advanced answer. In colleges and universities, the main purpose is teaching people how to learn on their own and to apply concepts and knowledge. Younger grades are more frequently a test of memory.

It's been years since I've been in school, but we were taught before the test back then.

What test is this that doesn’t test you over material presented?