1. Write down four friends' names in the name column in the table.

2. You can communicate with others in groups with the five questions on the blackboard.

3. What is her mother asking of her?

4. I'd like you to introduce one of your friends in the table to the classmates.

5. History is not only interesting but also informative.

6. Math is complex but useful.
7. Social science is exciting but not important.
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Would you check the sentences and correct errors, please?

All look good to me!

The only things I'd add are commas in sentences 6 and 7 -- after "complex" and after "exciting" --
http://grammar.ccc.commnet.edu/grammar/commas.htm
Scroll down to #7.

1. The sentence is grammatically correct. It asks you to write down four friends' names in the name column of a table.

2. The sentence is grammatically correct. It suggests that you can communicate with others in groups using the five questions written on the blackboard.

3. The sentence is asking for clarification. It is not clear who "her" refers to or what the context of the question is. In order to correct it, we would need more information.

4. The sentence is grammatically correct. It asks you to introduce one of your friends from the table to your classmates.

5. The sentence is grammatically correct. It states that history is both interesting and informative.

6. The sentence is grammatically correct. It states that math is complex but also useful.

7. The sentence is grammatically correct. It states that social science is exciting but not considered important.