2024 AIME I Problems

2024 AIME I (Answer Key) | AoPS Contest Collections • PDF

Instructions This is a 15-question, 3-hour examination. All answers are integers ranging from to , inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers. No aids other than scratch paper, rulers and compasses are permitted. In particular, graph paper, protractors, calculators and computers are not permitted.

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Problem 1

Solution

Problem 2

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

The vertices of a regular octagon are coloured either red or blue with equal probability. The probability that the octagon can be rotated in such a way that all blue vertices end up at points that were originally red is , where and are relatively prime positive integers. What is ?

Solution

Problem 12

Define and . Find the number of intersections of the graphs of

Solution

Problem 13

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Problem 14

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Problem 15

Solution

See also

• American Invitational Mathematics Examination
• AIME Problems and Solutions
• Mathematics competition resources

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.