## Concepts in Competitive MathematicsThis short reference book contains fundamental concepts crucial to solving math competition problems such as those found on the Mathematical Association of America's AMC 10, AMC 12, and AIME, as well as those found in local or regional competitions. Full of formulas as well as examples and solutions, this book shows how specific problems can be best solved in order to succeed in math competitions. Content is organized by mathematical topic and has been selected for its diversity. Topics include Number Theory, Combinatorics, Probability, Statistics, Sequences and Series, Algebra, Geometry, Trigonometry, and Coordinate Mathematics. The book even contains a section containing the author's own tips from past experience in math competitions. All in all, this is a must buy for math competition participants and teachers alike. Contains: Nine Chapters, Table of Contents, Index. |

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### Contents

Number Theory | 7 |

Combinatorics | 15 |

Probability and Statistics | 37 |

Sequences and Series | 47 |

Algebra | 53 |

Geometry | 61 |

Trigonometry | 75 |

The Coordinate Plane | 81 |

### Common terms and phrases

ABCD area of Q arithmetic sequence Bag1 Bag2 black balls black sock cevian Choice and Chance color combination Combinatorics combinatorics problems Cubic Function cyclic quadrilateral Dashes and Dividers data points deﬁnition diﬀerent distinct objects dominos double counted equal equation equilateral triangle exactly Example exponent and logarithm expressed f attains Fibonacci numbers ﬁnd ﬁnite ﬁrst ﬁve ﬂag geometric sequence harmonic mean hypotenuse inﬁnite integers intersection last digit law of cosines letter pairs loga median multiples Natural Numbers Notation number of arrangements number of objects number of positive odd number pairs are glued parabola pay check permutation Pigeonhole Principle Platonic Solids polygon polynomial prime factorization Pythagorean quadratic quadrilateral question radius rankings real roots rectangle red ball relative minimum relatively prime repetition rhombus right triangle selections sign changes Solution square tangent Theorem Tips Tip total number Totient vertex violation W. A. Whitworth what’s