あなたのおかげでテストに受かりました！って英語でなんて言うの？

"Because of you, I passed the test!"
"Because of you" - you could also say, "you are the reason." You are telling the person or teacher, that they are the one who helped you do well on the test.

"Thanks for your help, I passed the test!"
Here you are thanking the person first, then explaining why you are thanking them. You could also say, "I passed the test, thanks for your help!"

Use the expression 'couldn't have done it without you' to express that you feel that that person's support/ teachings were essential to your success. It's a very kind thing to say to someone.

In this case it seems that the function of your communication is both to inform and thank the teacher for assisting your preparation. The most casual way would be sentence 2 which seems more natural thsn sentence 1.

Simple sentences expressing gratitude for the work done by the teacher in preparing the student for his or her exam. Help could be substituted with assistance or input without altering meaning

Because of you is telling the person that they helped you do something and couldn't have done it without their help