For over fifty years, the Mathematical Association of America (MAA) has been engaged in the construction and administration of challenging contests for students in American and Canadian high schools at every level of ability. This is the ninth book of problems and solutions from the American Mathematics Competitions 12 (AMC), aimed at students of high school age, and featuring 325 problems from the 13 AMC contests held in the years 2001-2007. Graphs and figures have since been redrawn to make them more consistent in form and style, and the solutions to the problems have been both edited and supplemented. The Problem Index contained classifies the problems into the following major subject areas: Algebra and Arithmetic, Sequences and Series, Triangle Geometry, Circle Geometry, Quadrilateral Geometry, Polygon Geometry, Counting Coordinate Geometry, Solid Geometry, Discrete Probability, Statistics, Number Theory, and Logic. These are then broken down into subcategories and cross-referenced for ease of use.
This is a book that should be on the active use desk of every high school math teacher in the world. The problems were created for the American Mathematics Competitions (AMC) exams that are for high school students so there is a wide variation in difficulty but none require any mathematics beyond the level of precalculus. The problems are multiple-choice and detailed solutions to all are included. Therefore, it is a perfect resource for the teacher looking for problems to challenge the class or to present a topic in a different way. The book concludes with an index of the problems according to type, so it is very easy to find any problem that will conform to your needs and interests of the moment. It is also fun for more advanced mathematicians, I kept a notepad at my side as I was reading it and on many occasions picked it up and quickly verified what I considered to be the solution. Obviously, it is also an excellent resource for teachers training their students for math competitions.
Published in Journal of Recreational Mathematics, reprinted with permission and this review appears on Amazon