*The Contest Problem Book IX* is the ninth book of problems and solutions from the American Mathematics Competitions AMC 12 contests. It chronicles 325 problems from the 13 AMC 12 contests given in the years 2001 through 2007. The authors were the joint directors of this and the AMC 10 competitions during that period, and are also joint authors of a book that includes the AMC 10 exams from the years 2000 through 2007.

A Problem Index at the back of the book classifies the problems into the subject areas of Algebra, Arithmetic, Complex Numbers, Counting, Functions, Geometry, Graphs, Logarithms, Logic, Number Theory, Polynomials, Probability, Sequences, Statistics, and Trigonometry. A problem that uses a combination of these areas is listed multiple times.

### Table of Contents

Preface

A Brief History of the Contests

Construction of the Contests

Acknowledgements

Problems

2001 AMC 12 Problems

2002 AMC 12A Problems

2002 AMC 12B Problems

2003 AMC 12A Problems

2003 AMC 12B Problems

2004 AMC 12A Problems

2004 AMC 12B Problems

2005 AMC 12A Problems

2005 AMC 12B Problems

2006 AMC 12A Problems

2006 AMC 12B Problems

2007 AMC 12A Problems

2007 AMC 12B Problems

Solutions

2001 AMC 12 Solutions

2002 AMC 12A Solutions

2002 AMC 12B Solutions

2003 AMC 12A Solutions

2003 AMC 12B Solutions

2004 AMC 12A Solutions

2004 AMC 12B Solutions

2005 AMC 12A Solutions

2005 AMC 12B Solutions

2006 AMC 12A Solutions

2006 AMC 12B Solutions

2007 AMC 12A Solutions

2007 AMC 12B Solutions

Index of Problems

About the Editors

### About the Editors

**J. Douglas Faires** received his BS in mathematics from Youngstown State University in 1963, and earned his PhD in mathematics from the University of South Carolina in 1970. He has been a Professor at Youngstown State University since 1980, and has been actively involved in the MAA for many years. For example, he was Chair of the Ohio Section in 1981-1982 and Governor from 1997-2000. He is currently a member of the MAA’s Undergraduate Research and Undergraduate Student Activities Committees and he was the National Director of the AMC 10 Competition of the American Mathematics Competitions until 2007.

Faires is a past President of Pi Mu Epsilon and he was a member of their Council for many years. Faires has been the recipient of many awards and honors. He was named the Outstanding College-University Teacher of Mathematics by the Ohio Section of the MAA in 1996; he has also received five Distinguished Professorship awards from Youngstown State University, and an honorary Doctorate of Science Degree in May 2006. Faires has authored and coauthored numerous books including *Numerical Analysis* (now in its eight edition!), *Numerical Methods* (third edition), *PreCalculus* (fourth edition), and *First Steps for Math Olympians*, a book in the MAA Problem Book Series.

**David Wells** received a PhD in mathematics from the University of Pittsburgh in 1973. He taught at Ohio Dominican University for six years and has been at the New Kensington campus of Penn State University since 1979. During his career at Penn State he has received both the Teresa Cohen Service Award from the Department of Mathematics and the Excellence in Teaching Award from the New Kensington Campus. He has been a member of the MAA since 1974, holding several sectional and national positions during that time. He served as Governor of the Allegheny Mountain Section from 1996 to 1999 and has recently been appointed as Chair of the MAA Committee on the American Mathematics Competitions. He has chaired the AMC 12 Contest Committee since 2001. Dr. Wells received the Meritorious Service Award from the Allegheny Mountain Section of the MAA in 2005. His non-mathematical interests include hiking and songwriting.