First Steps for Math Olympians: Using the American Mathematics Competitions

J. Douglas Faires

doi:10.5948/9781614444046

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 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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First Steps for Math Olympians

Using the American Mathematics Competitions

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Contents

Frontmatter
pp i-vi

Contents
pp vii-xii

Preface
pp xiii-xxii

1 - Arithmetic Ratios
pp 1-8

2 - Polynomials and their Zeros
pp 9-18

3 - Exponentials and Radicals
pp 19-28

4 - Defined Functions and Operations
pp 29-36

5 - Triangle Geometry
pp 37-54

6 - Circle Geometry
pp 55-70

7 - Polygons
pp 71-84

8 - Counting
pp 85-96

9 - Probability
pp 97-108

10 - Prime Decomposition
pp 109-114

11 - Number Theory
pp 115-126

12 - Sequences and Series
pp 127-134

13 - Statistics
pp 135-142

14 - Trigonometry
pp 143-154

15 - Three-Dimensional Geometry
pp 155-166

16 - Functions
pp 167-178

17 - Logarithms
pp 179-186

18 - Complex Numbers
pp 187-196

Solutions to Exercises
pp 197-290

Epilogue
pp 291-294

Sources of the Exercises
pp 295-300

Index
pp 301-306

About the Author
pp 307-307

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First Steps for Math Olympians

Using the American Mathematics Competitions

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