Selection to the USAMO is based on the USAMO index which is defined as AMC 12 Score plus 10 times AIME Score.
Selection to the USAJMO is based on the USAJMO index which is defined as AMC 10 Score plus 10 times AIME Score.
The AIME is a 15 question, 3 hour exam taken by high scorers on the AMC 10 and AMC 12. Each answer is an integer from 0 to 999, inclusive, making guessing almost futile. Wrong answers receive no credit, while correct answers receive one point of credit. No partial credit is given. Thus AIME scores are integers from 0 to 15 inclusive.
Both the AMC 10 and AMC 12 are 25 question, 75 minute multiple choice contests. The AMC 10/12 is scored in a way that penalizes guesses. Correct answers are worth 6 points, incorrect questions are worth 0 points, and unanswered answers are worth 1.5 points, to give a total score out of 150 points.
Recent USAMO and USAJMO Qualification Indices
| Year | AMC 12 | AMC 10 | Total number of qualifiers |
| 2024 | USAMO cutoff with AIME I: 245 (AMC 12A), 248 (AMC 12B)
USAMO cutoff with AIME II: 220 (AMC 12A), 228 (AMC 12B) |
USAJMO cutoff with AIME I: 236 (AMC 10A), 232 (AMC 10B)
USAJMO cutoff with AIME II: 230 (AMC 10A), 220 (AMC 10B) |
|
| 2023 | USAMO cutoff with AIME I: 223 (AMC 12A), 227 (AMC 12B)
USAMO cutoff with AIME II: 214.5 (AMC 12A), 226 (AMC 12B) |
USAJMO cutoff with AIME I: 194 (AMC 10A), 190.5 (AMC 10B)
USAJMO cutoff with AIME II: 188 (AMC 10A), 180 (AMC 10B) |
|
| 2022 | USAMO cutoff with AIME I: 222 (AMC 12A), 227.5 (AMC 12B)
USAMO cutoff with AIME II: 208.5 (AMC 12A), 203 (AMC 12B) |
USAJMO cutoff with AIME I: 203.5 (AMC 10A), 190.5 (AMC 10B)
USAJMO cutoff with AIME II: 196.5 (AMC 10A), 182 (AMC 10B) |
|
| 2021 | USAMO cutoff with AIME I: 229.5 (AMC 12A), 231.5 (AMC 12B)
USAMO cutoff with AIME II: 238 (AMC 12A), 238 (AMC 12B) |
USAJMO cutoff with AIME I: 217 (AMC 10A), 213 (AMC 10B)
USAJMO cutoff with AIME II: 223 (AMC 10A), 214.5 (AMC 10B) |
|
| 2020 | USAMO cutoff with AIME I: 233.5 (AMC 12A), 235 (AMC 12B)
USAMO cutoff with AIME II: 234 (AMC 12A), 234.5 (AMC 12B) |
USAJMO cutoff with AIME I: 229.5 (AMC 10A), 230 (AMC 10B)
USAJMO cutoff with AIME II: 233.5 (AMC 10A), 229.5 (AMC 10B) |
|
| 2019 | USAMO cutoff with AIME I: 220 (AMC 12A), 230.5 (AMC 12B)
USAMO cutoff with AIME II: 230.5 (AMC 12A), 236 (AMC 12B) |
USAJMO cutoff with AIME I: 209.5 (AMC 10A), 216 (AMC 10B)
USAJMO cutoff with AIME II: 216.5 (AMC 10A), 220.5 (AMC 10B) |
|
| 2018 | USAMO cutoff with AIME I: 215 (AMC 12A), 235 (AMC 12B)
USAMO cutoff with AIME II: 216 (AMC 12A), 230.5 (AMC 12B) |
USAJMO cutoff with AIME I: 222 (AMC 10A), 212 (AMC 10B)USAJMO cutoff with AIME II: 222 (AMC 10A), 212 (AMC 10B) | |
| 2017 | USAMO cutoff with AIME I: 225.5 (AMC 12A), 235 (AMC 12B)
USAMO cutoff with AIME II: 221 (AMC 12A), 230.5 (AMC 12B) |
USAJMO cutoff with AIME I: 224.5 (AMC 10A), 233 (AMC 10B)
USAJMO cutoff with AIME II: 219 (AMC 10A), 225 (AMC 10B) |
280 USAMO; 208 USAJMO |
| 2016 | 220.0 for USAMO with AIME I, 205.5 for USAMO with AIME II | 210.5 for USAJMO with AIME I, 200.0 for USAJMO with AIME II | 318 USAMO; 198 USAJMO |
| 2015 | 219.0 for USAMO with AIME I, 229.0 for USAMO with AIME II | 213.0 for USAJMO with AIME I, 223.5 for USAJMO with AIME II | 286 USAMO; 244 USAJMO |
| 2014 | 211.5 for USAMO | 211.0 for USAJMO | 266 USAMO; 231 USAJMO |
| 2013 | 209.0 for USAMO | 210.5 for USAJMO | 264 USAMO; 231 USAJMO |
| 2012 | 204.5 for USAMO | 204.0 for USAJMO | 268 USAMO; 233 USAJMO |
| 2011 | 188.0 (AIME I); 215.5 (AIME II) for USAMO | 179.0 (AIME I); 196.5 (AIME II) for USAJMO | 282 USAMO; 222 USAJMO |
| 2010 | 208.5 (USAMO); 204.5 (USAMO—11th and 12th) | 188.5 (USAJMO) or 11/15 on AIME (USAMO) | 277 USAMO; 235 USAJMO |
Click HERE find out more about Math Competitions!
Ivy League Education Center 
Pingback: 2016 AMC 12B Problems and Answers | Ivy League Education Center
Pingback: 2016 AIME I Problems and Answers | Ivy League Education Center
Pingback: 2016 USA(J)MO SELECTION SCORES ANNOUNCED | Ivy League Education Center