入学試験って英語でなんて言うの？

An entrance exam is usually a requirement for a person to get into an institution. For example, you can say "I was required to write an entrance exam to be accepted into university."

The most common of these expressions in "Entrance Exam." "I am studying for my entrance exam into medical school."

Entrance Examination is the formal way of saying Entrance Exam. "We will grade the entrance Examinations tomorrow morning."

Entrance Test is very rare to hear but it gives the same idea as Entrance Exam, just meaning a test you take to be accepted into a school.

When speaking in terms of schools or colleges or universities, the name of the specific exam taken which leads to either acceptance or rejection is usually known as an 'entry' or 'entrance' exam. It may also be known as a 'selection exam' - especially if there are various rounds of the selection process such as interviews. doctors examinations, family or passport checks etc

An "entrance exam" is a test that must be taken and passed in order to get into a school.

Entrance exam and entrance examination are used interchangeably, they both are the test that you have to take in order to get into a school.

The best way to say you are taking an exam to get into a school/college would be 'an entrance exam'
An examination is the formal word used for exam - exam is the shortened word
An exam can also be called a test so when talking to your friend you might say 'Entrance test'