Mathematics in Middle and High School: Techniques of Solving Problems

We have developed this book - Problems in Middle and High School Mathematics: Solving Techniques Edition II - to help middle and high school students acquire a deeper understanding of mathematics and prepare themselves for Olympiads and contests in this field, as well as having high levels of success in future related university courses. The wish is to instill in our students the art of reasoning and the power of evaluating and solving mathematical problems at a competitive level. However, this work can be counted on with assisting many more students (even those less inclined towards mathematics) with understanding proper methods of solving mathematical problems. We believe this work to be filling a gap in the area of high school mathematics in North-America, in terms of the material it covers, as well as the depth and rigor of the problems. While common elements with other works of this type do exist, we have tried to enrich its content through the addition of special features, important problems, and diversified solutions. Intending to often present to students multiple approaches in solving a problem, each chapter presents necessary core knowledge, problems grouped on thematic and solving ideas – as a result of a lengthy pedagogical career – with examples solved in great detail (sometimes with multiple solutions), followed by similar problems with answers in the back. Each chapter contains exercises that increase in difficulty, from solving simple algebraic expressions to problems up to par with major mathematics competitions and Olympiads. At the end of each chapter, we have included problems we have published in the “Mathematical Olympiads Correspondence Program” (http://www.math.ca/Competitions/MOCP/) in Ontario, Canada. Occasionally, some problems at the end of each chapter may appear very hard to solve. However, my thirty-year experience in teaching mathematics and my interactions with students enabled me to demonstrate the solutions in a clear, easy to understand manner. This second edition contains new problems, solutions and chapters that are sure to cover any Canadian high school curriculum and help students excel in their math-related courses. Additionally, the expertise gained from solving difficult problems through completing problem sets in this edition can be applied to many other courses and even daily life. We are confident that any students who pick up this book and solve one set of exercises can expand their knowledge, fuel their interest, and excel in their mathematics courses. We also can guarantee that solving problem sets within this book will be some of the best post-secondary preparation for students looking to pursue a degree in the field of mathematics. We also hope this work will become instrumental to mathematics teachers working both in the private and public education systems. Mihai Rosu rosumihai@yahoo.ca Vlad Rosu vladrosu20@gmail.com