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. |
Contents
Arithmetic Ratios | 1 |
Polynomials and their Zeros | 9 |
Exponentials and Radicals | 19 |
Defined Functions and Operations | 31 |
Triangle Geometry | 37 |
1 | 55 |
1 | 71 |
Counting | 85 |
Trigonometry | 143 |
ThreeDimensional Geometry | 155 |
Functions | 167 |
Logarithms | 179 |
Complex Numbers | 187 |
Solutions to Exercises | 197 |
37 | 242 |
42 | 248 |
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 a₁ AABC ABCD AHSME AHSME 11 altitude AMC 10A AMC problems arithmetic sequence binary operation central angle chair chord coefficients complex number consider cube defined DEFINITION denote diameter digits divided divisible domain equation equilateral Euler's Formula exam Example is number Examples for Chapter Exercise 10 Answer Exercise 9 Exercises for Chapter face card factor figure final Example formula geometric sequence gives graph Hence inscribed angle interior angles intersection length line segment loga logarithm logg Mathematical median multiple occurs permutations perpendicular plane polygon positive integer prime decomposition probability quadratic quadrilateral radius ratio real numbers result right angle 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 vertex ZABC