Difference between revisions of "2021 AIME II Problems"
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{{AIME Problems|year=2021|n=II}} | {{AIME Problems|year=2021|n=II}} | ||
==Problem 1== | ==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 <math>777</math> or <math>383</math>.) | |
[[2021 AIME II Problems/Problem 1|Solution]] | [[2021 AIME II Problems/Problem 1|Solution]] | ||
Revision as of 12:48, 22 March 2021
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| 2021 AIME II (Answer Key) | AoPS Contest Collections • PDF | ||
|
Instructions
| ||
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
to 
, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.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
In the diagram below, 
is a rectangle with side lengths 
and 
, and 
is a rectangle with side lengths 
and 
as shown. The area of the shaded region common to the interiors of both rectangles is 
, where 
and 
are relatively prime positive integers. Find 
.
[asy/]
pair A, B, C, D, E, F;
A = (0,3);
B=(0,0);
C=(11,0);
D=(11,3);
E=foot(C, A, (9/4,0));
F=foot(A, C, (35/4,3));
draw(A--B--C--D--cycle);
draw(A--E--C--F--cycle);
filldraw(A--(9/4,0)--C--(35/4,3)--cycle,gray*0.5+0.5*lightgray);
dot(A^^B^^C^^D^^E^^F);
label("
", A, W);
label("
", B, W);
label("
", C, (1,0));
label("
", D, (1,0));
label("
", F, N);
label("
", E, S);
[/asy]
Someone please help with the diagram
Problem 3
Find the number of positive integers less than 
that can be expressed as the difference of two integral powers of 
Problem 4
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 5
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
Problem 6
These problems will not be available until the 2021 AIME II is released on Thursday, March 18, 2021.
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. 
