As you mentioned, if you avoid saying your actual score/grade and they pry enough for you to have to say your score, it will look like you think you're smart. It will look like you are acting like you know more than them or that they needn't undermine your abilities. People always tend to assume that you knew you were going to tell them your scores and you wanted to build it up before you told it to them.
Just tell them your score off the bat. The best way to do that without coming off as conceited is to undermine yourself. Not act like you're dumb and then tell them your high score. That will be worse. But start the sentence off with something like:
Surprisingly, I got an A+
Act like you're shocked about how well you've done in the test. Make them feel like you didn't expect yourself to perform so well.
Of course, this only can work so many times. After that, it will go back to: "Yeah OK, we get it. You're smart". So after a while, after you tell them your (high) score, move to something like this:
I've taken a few tests in this field now, so I am getting slightly better at this. I'm glad these classes are working out so well for me.
After a few times of saying this, again, you need to change your tone a little bit. Go to something like this:
I don't know, having taken so many tests in this field, I expected to score more than an A, but I guess the difficulty goes up as I go through more tests.
Once they've adequately understood that you are capable of doing well in tests, you can be straight up factual to them. Like this:
Got an A+ in my test. I'm glad I'm still doing well in my tests and haven't lost interest in these classes yet. I usually get tired of tests but this subject has really kindled my interest.
For your first sentence, you could use a few variations so that you can delay the second phase a little bit. Here are a few examples:
My teacher is amazing! He practically got us an A+.
The test was hard, but I studied the right things and took a lot of notes in my classes. It came a long way in helping me get this A.
Stayed up all night the past week so I can make absolutely sure I do well in this test! It paid off.
I was worried if I got a lot of the answers wrong, but thankfully, I didn't. This subject is still a bit confusing for me.
If the questions are not exactly as I studied them to be, I get thrown off. Luckily, I had questions that I expected to have.
Telling someone you scored high in a test in itself doesn't make you conceited. It is all about how you tell them you got a good grade.
In addition, always add a tiny little sentence that gives the person an opportunity to "share their wisdom" with you. This makes it look like you're still down-to-earth and not on your high horse.
I hope this helps.