First Steps for Math Olympians: Using the American Mathematics Competitions

Front Cover
American Mathematical Soc., Oct 26, 2020 - Education - 307 pages

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!

 

Contents

1 Arithmetic Ratios
1
2 Polynomials and their Zeros
9
3 Exponentials and Radicals
19
4 Defined Functions and Operations
29
5 Triangle Geometry
37
6 Circle Geometry
55
7 Polygons
71
8 Counting
85
14 Trigonometry
143
15 ThreeDimensional Geometry
155
16 Functions
167
17 Logarithms
179
18 Complex Numbers
187
Solutions to Exercises
197
Epilogue
291
Sources of the Exercises
295

9 Probability
97
10 Prime Decomposition
109
11 Number Theory
115
12 Sequences and Series
127
13 Statistics
135
Index
301
About the Author
307
Back Cover
308
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