How do I translate 'do well on your test' into Chinese?
I basically agree with what Itux just said. But I would prefer to say “祝你考试顺利” instead of “祝你测试顺利”.

In your context, “考试” would be the word you look for when you want to translate "test" or "exam". As for "quiz", it's usually “小测”. “测验” means test indeed but in a much more general way. People tend to just use “考试” when they talk something about school, especially in daily conversations.