1. She is good at dancing.

2. She is good at dance.

(Which one is correct? Are both correct?)

3. I am a student at Class 1-1.
4. I am a student in Class1-1.
5. I am in Class 1-1.
6. I am a first year student in Class
1-1.
7. I am a first grader of Class 1-1.

(Are all grammatical?)

She is good at dancing. (1)

Yes all are grammatical.

I agree that #1 is correct, but #2 is not. However, in #s 3-7, I agree with everything except #3. In #s 4-7, all phrasing is grammatical, but in #3, the word "at" is not used in this context.

Both 1. "She is good at dancing" and 2. "She is good at dance" are correct, but they have slightly different meanings.

1. "She is good at dancing" implies that she is skilled in the act of dancing and performs well when dancing.
2. "She is good at dance" implies that she is knowledgeable about dance as an art form, but may not necessarily be a skilled dancer herself.

Regarding the second set of sentences:

3. "I am a student at Class 1-1" is grammatically correct. It indicates that you are enrolled as a student in the class.

4. "I am a student in Class 1-1" is also grammatically correct. It conveys the same meaning as sentence 3, indicating that you are a student in that particular class.

5. "I am in Class 1-1" is grammatically correct and straightforward. It states that you are currently located or assigned to Class 1-1.

6. "I am a first-year student in Class 1-1" is grammatically correct. It specifies that you are in your first year of being a student in Class 1-1.

7. "I am a first grader of Class 1-1" is also grammatically correct. It suggests that you are in the first grade and part of Class 1-1.