Basic Mathematical Topics of American Mathematics Competition 12

• Main Authors: Yu-Chi Huang, 黃昱祺
• Other Authors: Fu-Chuen Chang
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/85559786287561194300

碩士 === 國立中山大學 === 應用數學系研究所 === 101 === This study investigates the art of solving problems in American Mathematics Competition 12 (AMC 12) from year 2000 to 2013. These exam problems are classified as 16 basic mathematical topics. The important definitions and theorems are summarized in the paper. The topics includes: 1. arithmetic, including properties of proportionality; 2. polynomials, including Bolzano’s theorem; 3. exponential and logarithmic, including law of exponential and law of logarithmic; 4. number of coordinate systems, including formula of division point; 5. triangle, including the Pythagorean theorem and Menelaus’ theorem; 6. circle, including power of a point theorem; 7. polygons, including Ptolemy’s theorem; 8. solid geometry, including the volume of the sphere; 9. counting, including set theory, permutations and combinations; 10. probability, including exclusive inclusive principle; 11. number theory, including prime factorization and binary system; 12. sequences and series, including arithmetic, geometric sequence with other common sequence; 13. statistics, including the weighted average and median; 14. trigonometric functions, including law of sines and double angle formula; 15. functions, including domain and range with other common functions; 16. complex, including complex conjugate complex with common properties.