Irish Mathematical Olympiad ManualLulu.com, 29 juil. 2013 - 166 pages This Manual was primarily written to assist Irish secondary-school students who are preparing to compete in the Irish Mathematical Olympiad (held in May each year) or the International Mathematical Olympiad (held each July). It has also proved useful in other countries, and is popular among people who simply enjoy mathematics. The Mathematical Olympiads are written examinations, based on what is called "second--level mathematics". There are significant variations between countries in the content of second--level programmes in Mathematics. Thus, Irish competitors find themselves faced with problems that require background knowledge that is not covered in the Senior Cycle programme for Irish schools. In order to have a reasonable chance of success, they need to master this material. The authors are academics who have many years experience as voluntary trainers of Olympiad contestants and in other mathematical enrichment activities for young people. The selection of material is based on this experience. |
Table des matières
Introduction | 1 |
Trigonometry | 15 |
Induction | 47 |
Combinatorics | 79 |
Inequalities | 89 |
Complex Numbers | 101 |
More Algebra | 109 |
More Geometry | 121 |
Functional Equations | 145 |
Autres éditions - Tout afficher
Irish Mathematical Olympiad Manual James Cruickshank,Gary McGuire,Anthony G. O'Farrell Aucun aperçu disponible - 2023 |
Expressions et termes fréquents
algebraic Algorithm angles answer argument arithmetic arrangements base calculation called centre Chapter circle coefficients common divisor complex numbers congruences consecutive Consider coordinates corresponding denoted divides division equal equation example Exercises expression fact factor Figure Find Find all functions formula functions f geometric given gives hence holds identity induction inequality Irish known least length Mathematical mean method multiply Note occur Olympiad opposite pair perpendicular plane polynomial positive integer possible powers prime problems proof Prove Pythagorean triple quadrilateral question radius rational numbers real numbers remainder Remark require result roots of unity rule satisfy segment Show sides similar Solution solve sometimes square statement Step Suppose tangent Theorem things triangle true unit vowels write written