作为基础学科,数学的重要性是众所周知的。在国际竞赛中,数学竞赛也是众多学科中参加人数最多、竞赛项目最多的。
今天我们要讲的就是其中两个非常著名的高含金量国际数学竞赛——AMC10和欧几里得!
AMC数学竞赛全称为“American Mathematics Competition”,由美国数学学会(MAA)主办,是全球范围内公信度最高、影响力最大的中学数学竞赛之一。
AMC数学竞赛是一个系列竞赛,目前国内学生可参加的包括AMC8、AMC10、AMC12以及AIME等竞赛。AMC10和AMC12都是可以晋级AIME竞赛的。
赛事规则
适合学生:10年级及以下学生,年龄小于17.5岁
报名时间:预计9月报名,A/B卷同时报
考试时间:预计11月,A/B卷相差1周
比赛形式:个人参与,在线机考
竞赛语言:中英双语
考试时长:75分钟
考试题型:25道选择题(5选1)
评分标准:满分150分,答对得6分,不答得1.5分,答错不扣分。
考察范围
● 代数综合:数列、方程、二次函数、不等式、乘法公式等。重点考查学生对知识点的掌握和问题分析能力。难点在于简化问题以及多项式和二次函数整除根问题的解法。
● 函数部分:坐标系、位置变换、一次函数、圆的方程等。重点考查学生理解问题和解题方法。难点在于求多边形面积,可灵活运用皮克定理和鞋带定理。
● 几何综合-解三角形、四边形与多边形:三角函数、相似和全等三角形、三角形相关定理、面积计算方法等。重点在于熟悉三角函数公式和算法,以及求不规则图形面积的方法。考查学生数形结合能力。
● 几何综合-圆与立体几何:圆的性质、立体几何的体积、表面积、欧拉公式等。难点在于圆的相关定理,考查学生空间想象能力和做辅助线的能力。
● 排列组合:加乘原理、单循环赛制、排列组合、容斥原理等。需要了解加法和乘法的区别,细心考虑情况全面性。考查学生分析情景的能力,复杂组合问题可使用二项式定理解决。
● 概率统计:各种统计量、古典概型、几何概型等。重点考查学生对事件可能发生情况的分析能力,难点在于条件概率。
● 数论部分:因数与倍数、数位、质数与合数、带余除法等。难点在于奇偶性分析、取余取整以及定义新运算问题,需要严谨的思维逻辑。
欧几里得竞赛(Euclid mathematics contest)创办于1945年,是加拿大滑铁卢大学的数学学院为全球高中生举办的数学竞赛,也是加拿大最具认可度的数学竞赛,含金量极高。主要针对12年级(高中最后一年)学生,低于12年级的学生也可以参加。
赛事规则
适合学生:任意年级高中生
考试形式:个人笔试,全英文试卷
竞赛时间:
预计2025年4月
竞赛形式:
全英文考试,时长150分钟;满分100分,共十道大题每题10分,每道大题2-3小题。
分为简答题和全解题,部分只需要答案,部分需要完整解答证明过程。根据答题步骤及思路技巧评分,如果答题步骤或方式过为散乱,即使结果正确可能也拿不到全分。
考察重点
欧几里得知识点考察集中在代数与方程、数列、多项式、平面几何、数列求和、解析几何、数论、三角恒等与三角函数、排列组合与概率、指数对数函数等若干模块。
相比AMC10/12竞赛,欧几里得竞赛考察的内容还是很接近的。不过欧几里得竞赛考的内容不包含复数。
● 平面几何和解析几何
是欧几里得备考的重点,题型占比约35%。几何题基本考察的是计算面积或边长,或者证明面积分割或边长比例关系或大小关系等。
● 代数运算或设方程求解
在欧几里得中占比30%左右,需要学生用未知数,根据题目提供信息构建等量关系方程,再求解,那么学生的代数运算能力要跟上。
● 排列组合与概率
是必考考点,一般都会放在第5-7题或者在第10题结合其他模块考察。
● 三角恒等与三角函数或求解三角函数
题目一般会放在7-9题,与对数题并称中国考生福利题。国内考生在这部分知识点学的比较扎实,做这部分的题目难度不大,而且这部分基本上只考一道题。
● 数论
在欧几里得数学竞赛出现的不多,常常是与计数结合,会放在第9或第10题。
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) 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