Frieren wasn't picked as a first class mage because she's weak for an elf who has lived 1000yrs. Other people passed the exam because they are strong compared to most other humans , Frieren isn't a human so Serie won't compare her to humans. Lastly on Frierens way to the exam she already stated she has lost fight against 6 different humans (which is embarrassing since she is over 1000 yrs old )