USAMO Training USAMO竞赛培训
USA Mathematical Olympiad & Junior Mathematical Olympiad 美国数学奥林匹克与青少年数学奥林匹克
What is USA(J)MO? 什么是USA(J)MO？
The United States of America Mathematical Olympiad (USAMO) and Junior Mathematical Olympiad (USAJMO) are the most prestigious national-level math competitions in the United States. These proof-based examinations serve as a critical step in selecting the team that represents the USA at the International Mathematical Olympiad (IMO). 美国数学奥林匹克（USAMO）和青少年数学奥林匹克（USAJMO）是美国最负盛名的国家级数学竞赛。 这些证明型考试是选拔代表美国参加国际数学奥林匹克（IMO）团队的关键步骤。
Unlike the AMC and AIME which require only numerical answers, USAMO and USAJMO demand complete, rigorous mathematical proofs. This is where true mathematical reasoning and creativity are tested. Top performers are invited to the Mathematical Olympiad Program (MOP). 与只需要数值答案的AMC和AIME不同，USAMO和USAJMO要求完整、严谨的数学证明。 这里是真正测试数学推理和创造力的地方。顶尖选手将被邀请参加数学奥林匹克项目（MOP）。
✍️ Exam Format ✍️ 考试形式
A rigorous two-day proof-writing examination 严格的两天证明写作考试
USAMO
USA Mathematical Olympiad 美国数学奥林匹克
USAJMO
USA Junior Mathematical Olympiad 美国青少年数学奥林匹克
🏅 Awards & Recognition 🏅 奖项与荣誉
Official MAA award distribution for USAMO and USAJMO MAA官方USAMO和USAJMO奖项分布
🏆 USAMO Awards
Gold
Top ~6% of competitors 前约6%的参赛者
Silver
Top ~12% of competitors 前约12%的参赛者
Bronze
Top ~18% of competitors 前约18%的参赛者
Honorable Mention
14+ points 14分以上
🏆 USAJMO Awards
Winner
Top performers 顶尖选手
Recognition
~20% of contestants 约20%的参赛者
Honorable Mention
14+ points 14分以上
🌟 Road to IMO 🌟 通往IMO之路
USA(J)MO is your gateway to representing the United States internationally USA(J)MO是代表美国参加国际赛事的门户
Olympiad Topic Areas 奥赛核心内容
Master these four pillars of proof-based mathematics 掌握证明型数学的四大支柱
Algebra 代数
Olympiad Algebraic Methods 奥赛代数方法
- Functional Equations & Inequalities函数方程与不等式
- AM-GM, Cauchy-Schwarz, Jensen'sAM-GM、柯西-施瓦茨、詹森不等式
- Polynomial Theory & Roots多项式理论与根
- Sequences & Recurrences数列与递推
- Complex Numbers in Proofs证明中的复数
- Substitution Techniques代换技巧
Geometry 几何
Synthetic & Projective Methods 综合与射影方法
- Power of a Point & Radical Axes点的幂与根轴
- Projective Geometry & Cross-Ratio射影几何与交比
- Inversion & Transformations反演与变换
- Ceva, Menelaus, Stewart塞瓦、梅涅劳斯、斯图尔特定理
- Homogeneous Coordinates齐次坐标
- Spiral Similarity & Configurations螺旋相似与构型
Combinatorics 组合数学
Discrete Mathematics & Logic 离散数学与逻辑
- Graph Theory & Extremal Problems图论与极值问题
- Pigeonhole & Double Counting鸽巢原理与双计数
- Invariants & Monovariants不变量与单调量
- Coloring & Game Theory着色与博弈论
- Extremal Principle极端原理
- Algorithms & Constructions算法与构造
Number Theory 数论
Advanced Integer Properties 高级整数性质
- Quadratic Residues & Legendre二次剩余与勒让德符号
- Lifting the Exponent (LTE)提升指数引理
- Orders & Primitive Roots阶与原根
- Vieta Jumping & Descent韦达跳跃与下降法
- p-adic Valuationp进赋值
- Zsigmondy's Theorem齐格蒙迪定理
✍️ The Art of Proof Writing ✍️ 证明写作的艺术
USAMO grading rewards complete, rigorous solutions USAMO评分奖励完整、严谨的解答
7-Point Scale 7分制
Each problem is scored 0-7. Complete solutions get 7 points; partial credit is rare (mostly 0-1 or 6-7). 每题0-7分。完整解答得7分；部分分数很少（主要是0-1或6-7分）。
Key Ideas Matter 关键思想最重要
Graders look for main insights. Having all key ideas = "7-", missing one = "0+". Focus on core reasoning. 评分员寻找主要见解。有所有关键想法="7-"，缺少一个="0+"。专注于核心推理。
Clarity & Rigor 清晰与严谨
Write clearly, justify each step, and avoid gaps in logic. Elegance helps but completeness is essential. 写作清晰，证明每一步，避免逻辑漏洞。优雅有帮助，但完整性是必需的。
🎯 Qualification Index 🎯 资格指数
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. Higher AMC score and AIME score lead to higher index. Cutoffs vary by year. 适用于通过AMC 12晋级的学生。更高的AMC分数和AIME分数带来更高的指数。分数线每年不同。
🥇 USAJMO Index USAJMO指数
For students who qualified through AMC 10. Grade 10 and below. A stepping stone to USAMO for younger students. 适用于通过AMC 10晋级的学生。10年级及以下。年轻学生通往USAMO的踏脚石。
📅 2025 Competition Dates 📅 2025年竞赛日期
USAMO and USAJMO are held at official testing sites only USAMO和USAJMO仅在官方考点举行
Day 1 第一天
Day 2 第二天
Why Train With Us for USA(J)MO? 为什么选择我们的USA(J)MO培训？
Expert guidance to master proof-based olympiad mathematics 专家指导，掌握证明型奥赛数学
Proof Writing Mastery 证明写作精通
Learn to write clear, rigorous proofs that earn full marks from olympiad graders 学习撰写清晰、严谨的证明，从奥赛评分员那里获得满分
40+ Years of Problems 40+年真题
Comprehensive study of every USAMO/USAJMO problem with detailed solutions and insights 全面研究每道USAMO/USAJMO真题，配有详细解答和见解
Advanced Techniques 高级技巧
Master projective geometry, functional equations, extremal combinatorics, and more 掌握射影几何、函数方程、极值组合等
Mock Olympiads 模拟奥赛
Full-length practice under competition conditions with detailed feedback on proofs 竞赛条件下的全真模拟，配有证明的详细反馈
MOP Preparation MOP准备
Bridge training for those aiming to qualify for the Mathematical Olympiad Program 为希望晋级数学奥林匹克项目的学生提供桥梁培训
Small Classes 小班教学
Maximum 4 students for intensive, personalized proof-writing instruction 每班最多4人，进行深入、个性化的证明写作指导
🏆 Our Students' USA(J)MO Achievements 🏆 我们学生的USA(J)MO成就
Student Success Stories 学生成功故事
The proof writing training completely transformed my approach. I went from scoring 7 points total to 28 points and qualified for MOP. The personalized feedback on my proofs was invaluable. 证明写作培训完全改变了我的方法。我从总分7分进步到28分，并晋级MOP。对我证明的个性化反馈非常宝贵。
Learning advanced techniques like inversion and projective geometry opened up so many problems for me. The deep dives into each topic area were exactly what I needed to reach the next level. 学习反演和射影几何等高级技巧为我打开了许多问题。对每个主题领域的深入探讨正是我达到下一个水平所需要的。
As a 9th grader, I was intimidated by proof-based problems. The structured curriculum built my confidence step by step. Now I'm a USAJMO Winner and looking forward to USAMO next year! 作为9年级学生，我曾被证明题吓倒。系统的课程一步步建立了我的信心。现在我是USAJMO获奖者，期待明年的USAMO！
Master Olympiad Mathematics! 征服奥赛数学！
Join elite students on the path to MOP and the IMO 加入精英学生，踏上通往MOP和IMO的道路