Language qualifications are a separate category from entrance exams, and they are the piece most applicants forget. Germany asks for a TestDaF or a recognized language certificate for many programs, and the APS process checks your academic documents before you apply. France uses the DELF or DALF, Japan uses the JLPT, and China uses the HSK for Mandarin programs. Australia, Canada, the UK and the US do not usually ask for a language exam because the teaching is in English, which is why the English test replaces it.
For a year abroad or an exchange program, most of these do not apply. Those programs usually want your transcript, an English score, and a personal statement, because the point is to place you in existing classes rather than admit you to a degree. Our guide to college application deadlines covers the calendar side of a US application, which is where most missed deadlines cause lost places.
How should you sequence study abroad entrance exams?
English test first, six to twelve months out, because it has the earliest preparation curve and it is valid for two years. Then your academic test, ideally before your first application deadline rather than after, because the earliest deadlines are the ones with the most places. Take any subject specific exam last, once you know the exact program and its requirements. Subject specific exams are the most expensive mistake because they are usually booked on a date that cannot be moved, and a date that cannot be moved means you wait a full year for another sitting.
One practical warning. Read the requirements page of each program you are applying to, and write the list down with the date. Requirements change from year to year, and a program that waived an exam this cycle may ask for it next cycle, so the list you keep should have a date next to every entry. Requirements change, and a program that waived the GRE this year may require it next year, so do not rely on advice from a year ago.
Can you take them more than once?
Yes, and you should assume you will want a second attempt. Score validity is the other half of this question. English test scores are usually accepted for two years, GRE scores for five years, and GMAT scores for five years, while the SAT and ACT do not expire at all. That is why most study abroad entrance exams are planned around a two year window, because the English score is usually the first one to expire. TOEFL and IELTS have no limit in practice. The SAT and ACT allow retakes, with schools usually counting the higher score, though each has its own policy on how many times you may sit the test. The GRE allows retakes with a minimum gap between attempts. The GMAT also allows retakes, with a shorter waiting period for the second attempt.
Budget for one retake of each test in your plan, and take a full diagnostic under real conditions before you book. Most study abroad entrance exams can be retaken, but the waiting periods differ, so check the gap before you plan two attempts close together. Aiming a little above your target on the first try is cheaper than buying a second attempt, and it means you already know which section to fix.