Is it possible to know the composer?

Clical music is broken down into different eras: Baroque,Clical,Romantic, Impressionism and Modern. Learn the stylistic differences between the different eras and it will help you to identify the composers better. Some composers are transitional and their style evolves. I think your teacher wants you to know the difference between the eras, so when she plays drop the needle you can identify the eras style. Naming the composer would be a plus but that's a lot of music to digest at one time! Get yourself a good history of music text that identifies the stylistic differences and listen to their sound examples. You will be ready after some time in the library and the listening lab. Good luck and enjoy your listening sessions.