The basic function of a microphone is to receive radio signals. In other words, all microphones will do.
If you want better sound quality, buy a combination of condenser microphone and live sound card. If you want something with similar sound quality, you can buy a USB microphone. If you want a working one, you can buy a game microphone or a conference microphone.
Secondly, unless the school arranges the online examination in a unified way, if you arrange the examination place yourself, you should choose a quiet and soundproof place, and the income noise will be judged as cheating, which is not worth the candle.