If you apply to Yale...You do not need to take the SATs, they accept A levels. I do believe Harvard may be starting as well (but you may want to check that.) A lot of ivy league schools, may also be fairly familiar with the A level, so if you send your details it may not even be necessary. I have heard also that Americans Uni's often accept the IB...so this would have been a good path to have had taken. But never minds.
There are several SATs that American Students usually take...
If I'm right it's obligatory to take...
1. SAT Reasoning Test (Which Includes Critical Reading, Writing and Mathematics). Which are all multiple question apart from the essay and grid in maths responses. They contain: Writing, Usage and Dictions (Approx 60 Mins), Critical Reading -Critical reading and sentence-level reading and Mathematics - Number and operations; algebra and functions; geometry; statistics, probability, and data analysis.
2. You will also have to take 3 Subject SAT Exams. I would choose if I were you: Mathematics (Level 1 or 2...or both if possible), Physics and Chemistry.
But you have a choice of 20:
SAT Subject Test in Literature
SAT Subject Test in United States History
SAT Subject Test in World History
SAT Subject Test in Mathematics Level 1
SAT Subject Test in Mathematics Level 2
SAT Subject Test in Biology E/M
SAT Subject Test in Chemistry
SAT Subject Test in Physics
SAT Subject Test in Chinese with Listening
SAT Subject Test in French
SAT Subject Test in French with Listening
SAT Subject Test in German
SAT Subject Test in German with Listening
SAT Subject Test in Modern Hebrew
SAT Subject Test in Italian
SAT Subject Test in Japanese with Listening
SAT Subject Test in Korean with Listening
SAT Subject Test in Latin
SAT Subject Test in Spanish Spanish
SAT Subject Test in Spanish with Listening
You would most likely be best off choosing the options you chose for a level...how ever as you can see, there is a lot less choice.
Good luck anyway.
Hope that helped.