## 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 (AMC) have been given for more than 50 years to millions of high school students. First Steps for Math Olympians 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. 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. First Steps for Math Olympians 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. |

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### Contents

Arithmetic Ratios | 1 |

Polynomials and their Zeros | 9 |

Exponentials and Radicals | 19 |

Defined Functions and Operations | 31 |

Triangle Geometry | 37 |

Circle Geometry | 55 |

Polygons | 71 |

Examples for Chapter 7 | 78 |

Statistics | 135 |

Trigonometry | 143 |

ThreeDimensional Geometry | 155 |

Functions | 167 |

Logarithms | 179 |

Complex Numbers | 187 |

Solutions to Exercises | 197 |

37 | 242 |

### 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

AABC addition AHSME altitude AMC 10A angle Answer D arithmetic average base chair choices choose chosen circle collection common complex number consequence consider contains cosine cube defined DEFINITION denote determine digits distance distinct divides divisible equal equation Example is number Exercise Exercise 9 Answer Exercises for Chapter expression face fact factor figure final formula function geometric given gives graph Hence implies intersection involving least length line segment Mathematical mean multiple objects occurs original places plane polygon polynomial positive integer possible prime probability problem professor properties radius real numbers remainder result right triangle roots satisfy scores sequence shown sides similar solution solve square Suppose taking Theorem triangle true unit volume zeros