# First Steps for Math Olympians: Using the American Mathematics Competitions

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*J. Douglas Faires*

MAA Press: An Imprint of the American Mathematical Society

Any high school student preparing for the
American Mathematics Competitions should get their hands on a copy of
this book!

A major aspect of mathematical training and its benefit to
society is the ability to use logic to solve problems. The American
Mathematics Competitions (AMC) have been given for more than fifty
years to millions of high school students. This book considers the
basic ideas behind the solutions to the majority of these problems,
and presents examples and exercises from past exams to illustrate the
concepts. Anyone taking the AMC exams or helping students prepare for
them will find many useful ideas here. But people generally interested
in logical problem solving should also find the problems and their
solutions interesting.

This book will promote interest in mathematics
by providing students with the tools to attack problems that occur on
mathematical problem-solving exams, and specifically to level the
playing field for those who do not have access to the enrichment
programs that are common at the top academic high schools. The book
can be used either for self-study or to give people who want to help
students prepare for mathematics exams easy access to topic-oriented
material and samples of problems based on that material. This is
useful for teachers who want to hold special sessions for students,
but it is equally valuable for parents who have children with
mathematical interest and ability.

As students' problem solving abilities improve, they will be able
to comprehend more difficult concepts requiring greater mathematical
ingenuity. They will be taking their first steps towards becoming math
Olympians!

#### Reviews & Endorsements

… This book should be included in the library of anyone involved in preparing high school students to the AMC. Highly recommended.

-- J. T. Noonan, CHOICE

Provides a wealth of opportunities for students to become experienced problem solvers.

-- David Webb, Penn State University

An impressive problem solving primer.The book presents a wide variety of problems and problem solving strategies.

-- Richard Gibbs, Fort Lewis College

# Table of Contents

## First Steps for Math Olympians: Using the American Mathematics Competitions

- Cover 11
- Title 44
- Contents 88
- Preface 1414
- 1. Arithmetic Ratios 2424
- 2. Polynomials and their Zeros 3232
- 3. Exponentials and Radicals 4242
- 4. Defined Functions and Operations 5252
- 5. Triangle Geometry 6060
- 6. Circle Geometry 7878
- 7. Polygons 9494
- 8. Counting 108108
- 9. Probability 120120
- 10. Prime Decomposition 132132
- 11. Number Theory 138138
- 12. Sequences and Series 150150
- 13. Statistics 158158
- 14. Trigonometry 166166
- 15. Three-Dimensional Geometry 178178
- 16. Functions 190190
- 17. Logarithms 202202
- 18. Complex Numbers 210210
- Solutions to Exercises 220220
- Epilogue 314314
- Sources of the Exercises 318318
- Index 324324
- About the Author 330330
- Back Cover 331331