Hi
I cannot speak for the Andover or Exeter placement test, but at our school students are sent online math and language tests that they self select based on their past math/language level. The school looks at the test, previous class level, grade/comments. And re: math the test scoring.
They are then placed in a level class that is usually correct, however, there is time for students to move up or down as needed at the start of the year. If your student is coming from a school that has not been as rigorous as the new boarding school they may be moved to a lower level.
The school wants the students to learn and be successful. Having a strong foundation in math and language is key for harder level classes. I do not suggest learning for the placement test as it will not be an accurate account of your child’s ability which will hinder them as the work and thinking picks up.
The test should be low stress. Your child only takes the placement test after they are accepted and enrolled. Your child is in now; it is only about getting your child the best placement to support their learning.
Hope that helps, good luck.