2021 AIME II Problems
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2021 AIME II (Answer Key) | AoPS Contest Collections • PDF | ||
Instructions
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Contents
Problem 1
Find the arithmetic mean of all the three-digit palindromes. (Recall that a palindrome is a number that reads the same forward and backward, such as or .)
Problem 2
Equilateral triangle has side length . Point lies on the same side of line as such that . The line through parallel to line intersects sides and at points and , respectively. Point lies on such that is between and , is isosceles, and the ratio of the area of to the area of is . Find .
Someone please help with the diagram
Problem 3
Find the number of permutations of numbers such that the sum of five products is divisible by .
Problem 4
There are real numbers and such that is a root of and is a root of These two polynomials share a complex root where and are positive integers and Find
Problem 5
For positive real numbers , let denote the set of all obtuse triangles that have area and two sides with lengths and . The set of all for which is nonempty, but all triangles in are congruent, is an interval . Find .
Problem 6
For any finite set , let denote the number of elements in . FInd the number of ordered pairs such that and are (not necessarily distinct) subsets of that satisfy
Problem 7
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 8
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 9
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 10
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 11
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 12
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 13
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 14
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 15
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
See also
2021 AIME II (Problems • Answer Key • Resources) | ||
Preceded by 2021 AIME I |
Followed by 2022 AIME I | |
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.