This book is mostly for middle school and high school students who are interested in math competitions. Such competitions are not easy. You have most likely learned many concepts, formulas, theorems, and general information about several areas of math during your middle school and high school years. Still, you may not know how to apply all that knowledge to solve the difficult and daunting problems in competitions. This book helps bridge the gap between math classes and math competitions. As such, it will help you build intuition and develop strong problem-solving skills beyond reciting formulas or doing calculations. Such capabilities make it much easier to simplify and solve math problems and are immensely valuable in your future study of any fields and careers that you may pursue. It is important to note, however, that this book does not teach you algebra, number theory, counting, probability, or geometry. We review essential knowledge about such topics but assume that you already have a solid grasp of them.
We strongly recommend that you try to solve each problem on your own first before reading the answer. It will help improve your problem-solving skills, familiarize yourself with some common approaches in tackling math problems, and stimulate your interest in math. Do not feel discouraged if the solutions to some problems are not immediately obvious. Some problems are challenging ones that require you to apply the knowledge in thoughtful and creative ways. Solving hard problems helps you focus on key areas of improvement so that you can develop strong problem-solving skills.
If you need to look at the solution, try your best to understand the reasoning behind it, rather than just the answer. Purely memorizing the answers will not help much with math competitions. You will not be able to answer problems that use similar concepts unless you truly understand the concepts themselves, rather than the answers, and can analyze the problems yourself. You are likely to encounter some problems in exams that are similar to, or the same as, the problems in this book. Remember that the goal of the book is not to feed you the answers! Instead of providing answers to the problems, we make significant efforts to review essential concepts, present solution strategies, analyze the solutions, and derive general rules. The building blocks can be learned, but how you analyze the problems and implement the concepts make an enormous difference—and these are the skills that you acquire through practice, practice, and more practice.
We thank Mollee Ye and Jason Zhong for their thoughtful inputs and discussions. We are grateful to the many friends who have spent precious time reviewing this book. Because of the limitation of our knowledge and capacity, there may be better ways to solve some problems. A few of the answers may even contain errors. Please email us at annabel@eazeducation.com or xinfeng@eazeducation.com if you have better approaches or corrections to any of the questions. We are grateful for your feedback and will post your corrections and constructive ideas on the book’s companion website https://www.eazeducation.com.
We hope you enjoy reading this book!
Annabel Zhou
Xinfeng Zhou