For what it's worth, Rosen's introductory text on discrete mathematics is pretty good as well. (This sort of math crops up all the time in formal CS, for those of you who might otherwise wonder wtf discrete has to do with anything.)
http://www.amazon.com/s/ref=nb_sb_ss_i_0_13?url=search-alias...
(The study guide that is available to go with it is worth the money, imho.)
The Graham, Knuth, Patashnik book on concrete mathematics (a bit of a play on words for continuous and discrete) is a quality work as well but written to a considerably higher level that may or may not be pleasant to contend with depending on the reader's background.
http://www.amazon.com/Concrete-Mathematics-Foundation-Comput...
Thanks also for proposing the test and posting the papers online. It's hard to discover what level of knowledge is assumed of software developers if you've never worked in a large team and haven't entered the field via graduate or postgraduate study.
> I haven't looked to see if every question is covered by these, but here's some standard textbooks I like:
The good thing is @cpervica has suggested standard textbooks, as opposed to suggesting obtuse texts unreachable to a beginner.
Algorithms:
I think a beginner might be confused by Sedgewick's terse coding style.
Computer Architecture and Operating Systems:
I haven't read either of the books. I would add http://bcs.wiley.com/he-bcs/Books?action=index&itemId=04... to the list. Like most of the OS books, you won't get a full picture of the OS from this book, but you will know the topics which will help you understand a real OS. Also most of the non-recent book won't cover flat memory model http://en.wikipedia.org/wiki/Flat_memory_model That is not to say knowing about segmentation is going to hurt you.
Mathematics:
I haven't read any of the books. From TOC, the cryptography and the statistics book looks good. I would recommend skipping cryptography maths for starters. If you are a beginner, an application level understanding of cryptography is what you need.
Networking and Systems:
Tanenbaums books loves history and theory. It's a nice book nevertheless. Once you are done with it, you should read Stevens' book on TCP/IP http://www.kohala.com/start/tcpipiv1.html
Algorithms and Data Structures:
http://www.amazon.ca/Introduction-Algorithms-Thomas-H-Cormen...
http://www.amazon.ca/Algorithms-4th-Robert-Sedgewick/dp/0321...
Computer Architecture and Operating Systems:
http://www.amazon.ca/Computer-Architecture-Quantitative-John...
http://www.amazon.ca/Design-Implementation-FreeBSD-Operating...
Mathematics:
http://www.amazon.ca/Calculus-James-Stewart/dp/0495011606
http://www.amazon.ca/Introductory-Statistics-Prem-S-Mann/dp/...
http://www.amazon.ca/Introduction-Mathematical-Cryptography-...
Networking and Systems:
http://www.amazon.ca/Computer-Networks-5th-Andrew-Tanenbaum/...
http://www.amazon.ca/Database-Management-Systems-Raghu-Ramak...
http://www.amazon.ca/Distributed-Systems-Principles-Andrew-T...