Advanced Math Competition for High School: Algebra and Number Theory

High school students participate in the math competition, algebra and number theory are two important test content. High school algebra curriculums include linear and exponential relationships, descriptive statistics, quadratic functions, polynomial, rational, radical, and trigonometric functions, sequences and series, probability distributions.Number theory is another very interesting test content. Even if you know addition and subtraction you can understand the simple concepts of number theory. But the study of it has been fascinating. Since ancient times, people have separated the natural numbers into a variety of different types. Here are some familiar and not-so-familiar examples:odd 1, 3, 5, 7, 9, 11, . . .even 2, 4, 6, 8, 10, . . .square 1, 4, 9, 16, 25, 36, . . .cube 1, 8, 27, 64, 125, . . .prime 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, . . .composite 4, 6, 8, 9, 10, 12, 14, 15, 16, . . .1 (modulo 4) 1, 5, 9, 13, 17, 21, 25, . . .3 (modulo 4) 3, 7, 11, 15, 19, 23, 27, . . .triangular 1, 3, 6, 10, 15, 21, . . .perfect 6, 28, 496, . . .Fibonacci 1, 1, 2, 3, 5, 8, 13, 21, . . .German mathematician Carl Friedrich Gauss (1777-1855) said, “Mathematics is the queen of the sciences–and number theory is the queen of mathematics.” This book will help students review the key points of high school algebra and number theory.The book also selects the representative questions of algebra and number theory from the AMC12 and AIME tests and analyze and solve them one by one. During the epidemic at home, the author collected algebra and number theory questions from famous math competitions in other countries, and analyzed the key points and problem solving points one by one. The author believe that the readers will obtain excellent scores in math competitions after reading and practice of the book carefully.