I self-studied as well. I used the Mike Meyers book. Although his book was good, after writing the exams (and passing the first time) I felt that Mike's book was designed to help you pass, not ace, the exams.
In general, it's important to know how to install all the various components in a computer. You also need to know all the Pentium-class processors including the slot/socket type, L1 and L2 cache sizes. I memorized all the IRQs, I/O addresses, DMA assignments, number of Pins for each memory type, cables and connectors and the maximum lengths of every type of cable I found in the book.
Unfortunately, most of what I memorized was not on the exams!
If I was going to do it all again, here's what I would suggest:
1. Read a competent book (yours is probably fine).
2. Go to
and print out the A+ objectives. Make sure you know something about each objective.
3. Buy a book on PC upgrading/troubleshooting. The A+ exam does not test you on "complex" PC problems but there is a strong emphasis on troubleshooting on the Core exam.
4. Beg, borrow or steal (err, well, don't actually steal) a copy of Win95, Win98, WinNT and Win2K. Familiarize yourself with installing each OS and, more importantly, do an upgrade from each OS to the other. I remember having a lot of questions involving upgrading from Win95 to Win98 or WinNT to Win2K.