AIME Training AIME竞赛培训
American Invitational Mathematics Examination 美国数学邀请赛
What is the AIME? 什么是AIME？
The American Invitational Mathematics Examination (AIME) is a prestigious, invitation-only competition for students who excel on the AMC 10 or AMC 12. Organized by the Mathematical Association of America (MAA), AIME serves as the second stage in the pathway to the International Mathematical Olympiad (IMO). 美国数学邀请赛（AIME）是一项享有盛誉的邀请制竞赛，面向在AMC 10或AMC 12中表现优异的学生。 由美国数学协会（MAA）组织，AIME是通往国际数学奥林匹克（IMO）的第二阶段。
The questions on the AIME are significantly more challenging than those on the AMC 10 and AMC 12, requiring deep mathematical insight, creative problem-solving, and mastery of advanced techniques. Top-scoring AIME participants are invited to take the USAMO or USAJMO. AIME的题目比AMC 10和AMC 12难度大得多，需要深刻的数学洞察力、创造性的问题解决能力和高级技巧的掌握。 AIME高分选手将被邀请参加USAMO或USAJMO。
📝 Exam Format 📝 考试形式
Understanding the AIME structure is key to success 了解AIME结构是成功的关键
🏆 Road to the IMO 🏆 通往IMO之路
AIME is your gateway to the world's most prestigious math competition AIME是通往世界最负盛名数学竞赛的大门
AIME Topic Areas AIME考试内容
Master these four pillars of competition mathematics 掌握竞赛数学的四大支柱
Algebra 代数
Advanced Algebraic Techniques 高级代数技巧
- Polynomials & Vieta's Formulas多项式与韦达定理
- Functional Equations函数方程
- Complex Numbers & Roots of Unity复数与单位根
- Sequences & Series数列与级数
- Inequalities (AM-GM, Cauchy-Schwarz)不等式（AM-GM，柯西-施瓦茨）
- Symmetric Polynomials对称多项式
- Logarithms & Exponentials对数与指数
Geometry 几何
Euclidean & Coordinate Geometry 欧几里得与坐标几何
- Circle Theorems (Power of a Point)圆定理（点的幂）
- Trigonometry & Law of Sines/Cosines三角函数与正弦/余弦定理
- Coordinate Geometry & Vectors坐标几何与向量
- Similar & Congruent Triangles相似与全等三角形
- Ceva's & Menelaus's Theorems塞瓦定理与梅涅劳斯定理
- Ptolemy's Theorem托勒密定理
- 3D Geometry & Spatial Reasoning三维几何与空间推理
Combinatorics 组合数学
Counting & Probability 计数与概率
- Permutations & Combinations排列与组合
- Inclusion-Exclusion Principle容斥原理
- Generating Functions生成函数
- Recursion & Recurrence Relations递归与递推关系
- Probability & Expected Value概率与期望值
- Pigeonhole Principle鸽巢原理
- Bijections & Counting Arguments双射与计数论证
Number Theory 数论
Properties of Integers 整数性质
- Modular Arithmetic模运算
- Prime Factorization & Divisibility质因数分解与整除
- Fermat's Little Theorem费马小定理
- Euler's Totient Function欧拉函数
- Diophantine Equations丢番图方程
- Chinese Remainder Theorem中国剩余定理
- Lifting the Exponent (LTE)提升指数引理
📊 Problem Difficulty Distribution 📊 题目难度分布
AIME problems progressively increase in difficulty AIME题目难度逐渐递增
Build confidence with accessible problems. Master these to score 5+ reliably. 通过可达题目建立信心。掌握这些可稳定得5分以上。
Require deeper insight and technique. Scoring 7+ opens USAMO/USAJMO doors. 需要更深入的洞察力和技巧。得7分以上可开启USAMO/USAJMO之门。
Challenge problems requiring creative solutions. Scoring 10+ virtually guarantees USAMO. 需要创造性解决方案的挑战题。得10分以上几乎确保USAMO资格。
🎯 Qualification to USAMO/USAJMO 🎯 USAMO/USAJMO资格
Your combined AMC and AIME scores determine Olympiad eligibility 你的AMC和AIME综合成绩决定奥赛资格
🏆 USAMO Index USAMO指数
For students who qualified through AMC 12. Top scorers are invited to the USA Mathematical Olympiad. 适用于通过AMC 12晋级的学生。高分者将被邀请参加美国数学奥林匹克。
🥇 USAJMO Index USAJMO指数
For students who qualified through AMC 10. Top scorers are invited to the USA Junior Mathematical Olympiad. 适用于通过AMC 10晋级的学生。高分者将被邀请参加美国青少年数学奥林匹克。
📅 2025 AIME Competition Dates 📅 2025年AIME竞赛日期
Students may only take AIME once (either I or II) 学生只能参加一次AIME（I或II）
AIME I
AIME II
Why Train With Us for AIME? 为什么选择我们的AIME培训？
Expert guidance to maximize your AIME score 专家指导，最大化你的AIME成绩
40+ Years of Problems 40+年真题
Comprehensive practice with every AIME problem since 1983, organized by topic and difficulty 1983年以来每道AIME真题的全面练习，按主题和难度分类
Advanced Techniques 高级技巧
Learn powerful methods: generating functions, complex bashing, projective geometry 学习强大方法：生成函数、复数运算、射影几何
Strategic Training 策略训练
Time management, problem selection, and when to "bash" vs. find elegant solutions 时间管理、题目选择，以及何时"暴力计算"vs寻找优雅解法
Mock Exams 模拟考试
Timed practice under real conditions with detailed solution analysis 真实条件下的计时练习，配有详细解答分析
USAMO Preparation USAMO准备
Bridge to proof-based Olympiad mathematics for top performers 为顶尖学生搭建通往证明型奥赛数学的桥梁
Small Classes 小班教学
Maximum 6 students for personalized problem-solving guidance 每班最多6人，个性化问题解决指导
🏆 Our Students' AIME Achievements 🏆 我们学生的AIME成就
Student Success Stories 学生成功故事
I went from scoring 6 on my first AIME to 12 on my second attempt. The advanced techniques and strategic training completely transformed my approach to competition math. 我从第一次AIME的6分进步到第二次的12分。高级技巧和策略训练完全改变了我对竞赛数学的方法。
As an 8th grader taking AIME for the first time, I was terrified. The structured problem sets and mock exams gave me the confidence to score 9 and qualify for USAJMO! 作为第一次参加AIME的8年级学生，我曾经非常害怕。系统的习题集和模拟考试给了我信心，最终得到9分并晋级USAJMO！
The number theory and combinatorics training was exceptional. I finally understood generating functions and scored my first double-digit AIME score! 数论和组合数学的训练非常出色。我终于理解了生成函数，并取得了第一个两位数的AIME成绩！
Elevate Your AIME Performance! 提升你的AIME成绩！
Join elite students on the path to USAMO and beyond 加入精英学生，踏上通往USAMO及更高目标的道路