## First Steps for Math Olympians: Using the American Mathematics CompetitionsA major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions have been given for more than fifty years to millions of 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 preparing for the Mathematical Olympiads will find many useful ideas here, but people generally interested in logical problem solving should also find the problems and their solutions stimulating. The book can be used either for self-study or as topic-oriented material and samples of problems for practice exams. Useful reading for anyone who enjoys solving mathematical problems, and equally valuable for educators or parents who have children with mathematical interest and ability. |

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### Contents

Arithmetic Ratios | 1 |

Polynomials and their Zeros | 9 |

Exponentials and Radicals | 19 |

Triangle Geometry | 37 |

Circle Geometry | 55 |

Polygons | 71 |

Counting | 85 |

Probability | 97 |

Statistics | 135 |

Trigonometry | 143 |

ThreeDimensional Geometry | 155 |

Functions | 167 |

Logarithms | 179 |

Complex Numbers | 187 |

Solutions to Exercises | 197 |

Epilogue | 291 |

### Other editions - View all

First Steps for Math Olympians: Using the American Mathematics Competitions J. Douglas Faires No preview available - 2006 |

First Steps for Math Olympians: Using the American Mathematics Competitions J. Douglas Faires No preview available - 2006 |

### Common terms and phrases

9 Answer AABC ABCD addition AHSME altitude AMC 10A American Mathematics Competitions arithmetic sequence base binary operation central angle chair chord coefficients complex number consider cube defined denote diameter digits divided divisible equation equilateral exam Example is number Examples for Chapter Exercise 4 Answer Exercise 8 Answer Exercise 9 Exercises for Chapter face card factor figure final Example formula function geometric sequence gives graph Hence inscribed angle interior angles International Mathematical Olympiads intersection length line segment log8 loga logarithm median multiple occur permutations perpendicular plane polygon polynomial positive integer prime decomposition probability problem-solving quadratic quadrilateral radius ratio real numbers result right triangle scores secant line shown sides sine and cosine Solutions for Chapter solve square Suppose tangent Theorem implies Titu Andreescu triangle geometry unit circle USAMO vertex Youngstown State University ZABC zeros