Selection to the USAMO is based on the USAMO index which is defined as AMC 12 Score + 10 * AIME Score.

Selection to the USAJMO is based on the USAJMO index which is defined as AMC 10 Score + 10 * 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 |

2016 |
220.0 for USAMO with AIME I,
210.5 for USAMO with AIME II |
205.0 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 |

**2015 USAMO and USAJMO Qualification Levels**

- Students taking the AMC 12 A, or AMC 12 B plus the AIME I need a USAMO index of 219.0 or higher to qualify for the USAMO.
- Students taking the AMC 12 A, or AMC 12 B plus the AIME II need a USAMO index of 229.0 or higher to qualify for the USAMO.
- Students taking the AMC 10 A, or AMC 10 B plus the AIME I need a USJAMO index of 213.0 or higher to qualify for the USAJMO.
- Students taking the AMC 10 A, or AMC 10 B plus the AIME II need a USJAMO index of 223.5 or higher to qualify for the USAJMO.

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