How to prepare for AMC 8? The following books are highly recommended for serious minds ...
Throughout the years, I had many friends asked "what are good materials to prepare kids for math competitions?" Depending on the level of your kids, here are some good ones for your reference that should cover your child from elementary school to high school (all used by the Math Clubs I was/am involved in).
Elementary School Level
These three are highly recommended:
Creative Problem Solving in School Mathematics
Math Olympiad Contest Problems for Elementary and Middle Schools Vol I
Math Olympiad Contest Problems for Elementary and Middle Schools Vol II
These three books were praised by every parent who used them. The authors are terrific. You can use them together for your child, if you child can finish just half of the books, he or she will be called a Math Whiz by every school, I can guarantee that.
Middle School Level
This one is quite new but already receive rave reviews and quickly becomes a must have for every middle school's math team -
Math Competition for Middle School
I cannot over emphasize that it's a must have for any kids who are serious about middle school level math competitions, such as AMC 8.
Another excellent one for middle school students:
Hard Math for Middle School: IMLEM Plus Edition
High School Level
While the above middle school level book could be used by some lower level high school kids, these three books will definitely keep your kids busy and get them well prepared for AMC 10 and AMC 12:
The Contest Problem Book VIII
It covers AMC 10 problems from 2001 to 2007, the authors were joint directors of AMC 10 and AMC 12 of that period. This is probably the best book to prepare for AMC 10 and 12.
The Contest Problem Book IX
It covers problems for AMC 12 from 2001 to 2007. The authors were joint directors of AMC 10 and 12 during that period.
The Contest Problems Book VII
It covers AMC 10 and AMC 12 problems from 1995 to 2000.
You may have noticed that these three books above are just the recent volumes, if your child has more time, of course you could try the earlier volumes, starting from Vol I (great AHSME problems).
The above books should have your child's math education from elementary to high school level well covered and make to the top national levels, you shouldn't have to spend extra money on anything else.
Finally, this blog is a good source of information about math education, including some more recent AMC 8 problems and answers, you can check it out -