2017 AIME I Problems
2017 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
Instructions
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Contents
Problem 1
Fifteen distinct points are designated on : the 3 vertices , , and ; other points on side ; other points on side ; and other points on side . Find the number of triangles with positive area whose vertices are among these points.
Problem 2
When each of 702, 787, and 855 is divided by the positive integer , the remainder is always the positive integer . When each of 412, 722, and 815 is divided by the positive integer , the remainder is always the positive integer . Fine .
Problem 3
For a positive integer , let be the units digit of . Find the remainder when is divided by .
Problem 4
A pyramid has a triangular base with side lengths , , and . The three edges of the pyramid from the three corners of the base to the fourth vertex of the pyramid all have length . The volume of the pyramid is , where and are positive integers, and is not divisible by the square of any prime. Find .
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
2017 AIME I (Problems • Answer Key • Resources) | ||
Preceded by 2016 AIME II |
Followed by 2017 AIME II | |
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The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.