Hello-
About a month AGO I started taking an on line computer class- the beginning guide to MICROSOFT Word 2010.  I have been going to the public library for a few hour everyday to do my course work.  When I signed up for the course I called the library and asked what version of Word was installed on the computers.  They said version 2010 so I started the program.  I found out today August 1st that the library has updated all its software to Microsoft 2013.  I don't have a lot of computer experience and I am taking a 6 month online class.  Can I continue using a 2010 workbook and perform my practice activities and tests on the 2013 version at the library? Are the two programs similar?  Thanks!
Microsoft takes care to make its software backward compatible. You should have not trouble using the new software with an older tutorial.
Now if you com e upon some detail that  does not seem right, just  use the help feature.
Example: Let's say you want to enter a  symbol into the test. The method in the tutorial does not seem to be right.  Go to the help menu and kook for 'insert symbol' to see how it is done. 
ALSO, you might ask the librarian if that have one computer still running the older software. To reduce expenses, they might not have upgraded all computers.
http://office.microsoft.com/en-us/support/getting-started-with-office-2010-FX101822272.aspxOf course you can continue your practice. There wouldn't be any problem with that.
All MS Office 2010 documents will work in MS Office 2013. But you may(very rare) face sometimes when you will try to run 2013's document in MS Office 2010 (It is generally due to font(s) incompatibility, and its not a big issue).As far as I know you can do it, but not the contrary. Older versions are supported in newer ones, but the opposite is not workingThis topic was started a few weeks ago, so I imagine Beginner10 has made a decision by now.  As indicated in the discussion here, using Word 2013 would probably not cause any major problems if using it for a class on Word 2010.  Some minor issues might be encountered due a change in the command ribbon structure between the two versions of Word.  In other words, Word 2013 might not precisely conform to every aspect of the course material for Word 2010.  Any differences would require some effort to figure  out the difference. 

By the way, if the two versions of Word involved were 2003 and 2007, this idea of using the newer version for a class on the older version would definitely not be practical.  The 2003 and earlier versions had the older menu bar design, not the newer ribbon design.