What to do for my graduate school application if I think my GPA doesn't reflect my coursework mastery I am one of those people with low GPA but want to apply for graduate school in US. I am really having trouble with standardized tests in my institution. It's not uncommon for me to receive low grade in final exams(finals normally account for 60% to 70% percent of grading of corresponding courses) and this has led to a number of courses with poor grades that is already enough to ruin my GPA. It is not that I didn't spend time in studying, in fact I learned those courses quite well (perhaps, in other words, I am not a good test taker). I was initially thinking I should get the right GPA I deserve and was very angry with myself especially when I saw many of my peers could confidently gain much higher GPA than I do even with only a little understanding of course materials plus simply memorizing lecture notes by force(yes, our exams makes this kind of preparation really an effective way to get grades like 3.7/4.0 for most core courses). It seems to me like my classmates can have 3.7/4.0 with ease, but I was more likely to get only 2.7/3.0/3.3 even if I was well versed in coursework and fully prepared for exams. I talked to my classmates for help but they told me they were too surprised by my situation and don't know what I should do at all. I tried various methods to make a difference like making sure my homework/class attendance parts of scoring rubric are going well, even the above mentioned exam preparation strategy, but still received little improvement.  I never successfully found a solution throughout my undergrad, and I really want to defend this shortcoming in my statement of purpose, but I have worries about this.
MY QUESTION IS:
If I go ahead to explain this in my SOP, would it sound like merely an attempt to find an excuse? If your advice is &quot;do it&quot;, is there anything I should not talk about regarding the reason I mentioned above(i.e. don'ts)?
*. Some additional information, I am applying physics graduate program. I have first author publication in physics which I think could help me address that my knowledge mastery of related  maths and physics is not what my grade shows. But even so, my paper, of course, cannot address other poorly scored courses.
An application for grad study in the US contains many elements, of which GPA is only one. If the GPA is poor, then the other elements need to indicate a high likelihood of success in graduate study and thereafter. Research experience (published papers especially) is a good indicator. And in the US, the letters of recommendation from people who know you well and can be expected to give an honest assessment can be very important.
Talk to some of your current professors and get their advice about how to proceed and ask for letters as appropriate.
And, you need the knowledge from those early courses, even if your GPA doesn't reflect that you have mastered it.

To respond to your edit:
No, the SoP is not the place for this and it will sound like an excuse there. That isn't to say that you couldn't mention it elsewhere, though it is best if the explanation is given by others, such as letter writers.
But, the SoP should be entirely forward looking, saying what you want to do in the future and not giving explanations about the past. Say, in the SoP what your plans are for graduate study and thereafter, including any ideas you might have about research areas you hope to explore. You likely have a limited amount of space/words in the SoP. Use them effectively.