1
I made some research for my history project.
I did some research for my history project.
Use do, not make, with research: ‘I did some research for my history project.’
Check our grammar lesson on do and make.
2
Our teacher asked us to do a research on sleep.
Our teacher asked us to do some research on sleep.
Research is usually an uncountable noun, so do not put a before it. Say ‘some research’ or ‘a research project’.