Difference between revisions of "2024 AIME I Problems"
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{{AIME Problems|year=2024|n=I}} | {{AIME Problems|year=2024|n=I}} | ||
− | The | + | ==Problem 1== |
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+ | [[2024 AIME I Problems/Problem 1|Solution]] | ||
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+ | ==Problem 2== | ||
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+ | [[2024 AIME I Problems/Problem 2|Solution]] | ||
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+ | ==Problem 3== | ||
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+ | [[2024 AIME I Problems/Problem 3|Solution]] | ||
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+ | ==Problem 4== | ||
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+ | [[2024 AIME I Problems/Problem 4|Solution]] | ||
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+ | ==Problem 5== | ||
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+ | [[2024 AIME I Problems/Problem 5|Solution]] | ||
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+ | ==Problem 6== | ||
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+ | [[2024 AIME I Problems/Problem 6|Solution]] | ||
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+ | ==Problem 7== | ||
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+ | [[2024 AIME I Problems/Problem 7|Solution]] | ||
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+ | ==Problem 8== | ||
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+ | [[2024 AIME I Problems/Problem 8|Solution]] | ||
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+ | ==Problem 9== | ||
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+ | [[2024 AIME I Problems/Problem 9|Solution]] | ||
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+ | ==Problem 10== | ||
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+ | [[2024 AIME I Problems/Problem 10|Solution]] | ||
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+ | ==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 <math>\tfrac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. What is <math>m+n</math>? | ||
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+ | [[2024 AIME I Problems/Problem 11|Solution]] | ||
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+ | ==Problem 12== | ||
+ | Define <math>f(x)=|| x|-\tfrac{1}{2}|</math> and <math>g(x)=|| x|-\tfrac{1}{4}|</math>. Find the number of intersections of the graphs of <cmath>y=4 g(f(\sin (2 \pi x))) \quad\text{ and }\quad x=4 g(f(\cos (3 \pi y))).</cmath> | ||
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+ | [[2024 AIME I Problems/Problem 12|Solution]] | ||
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+ | ==Problem 13== | ||
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+ | [[2024 AIME I Problems/Problem 13|Solution]] | ||
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+ | ==Problem 14== | ||
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+ | [[2024 AIME I Problems/Problem 14|Solution]] | ||
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+ | ==Problem 15== | ||
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+ | [[2024 AIME I Problems/Problem 15|Solution]] | ||
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+ | ==See also== | ||
+ | {{AIME box|year=2024|n=I|before=[[2023 AIME II Problems|2023 AIME II]]|after=[[2025 AIME II Problems|2025 AIME II]]}} | ||
+ | * [[American Invitational Mathematics Examination]] | ||
+ | * [[AIME Problems and Solutions]] | ||
+ | * [[Mathematics competition resources]] | ||
+ | {{MAA Notice}} |
Revision as of 19:01, 2 February 2024
2024 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
Instructions
| ||
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |
Contents
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
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
?
Problem 12
Define and
. Find the number of intersections of the graphs of
Problem 13
Problem 14
Problem 15
See also
2024 AIME I (Problems • Answer Key • Resources) | ||
Preceded by 2023 AIME II |
Followed by 2025 AIME II | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
- American Invitational Mathematics Examination
- AIME Problems and Solutions
- Mathematics competition resources
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.