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2023 AIME II Problems

Revision as of 14:49, 16 February 2023 by MRENTHUSIASM (talk | contribs) (→‎Problem 3)
2023 AIME II (Answer Key)
Printable version | AoPS Contest Collections • PDF

Instructions

  1. This is a 15-question, 3-hour examination. All answers are integers ranging from $000$ to $999$, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.
  2. No aids other than scratch paper, graph paper, ruler, compass, and protractor are permitted. In particular, calculators and computers are not permitted.
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

Problem 1

The numbers of apples growing on each of six apple trees form an arithmetic sequence where the greatest number of apples growing on any of the six trees is double the least number of apples growing on any of the six trees. The total number of apples growing on all six trees is $990.$ Find the greatest number of apples growing on any of the six trees.

Solution

Problem 2

Recall that a palindrome is a number that reads the same forward and backward. Find the greatest integer less than $1000$ that is a palindrome both when written in base ten and when written in base eight, such as $292 = 444_{\text{eight}}.$

Solution

Problem 3

Let $\triangle ABC$ be an isosceles triangle with $\angle A = 90^\circ.$ There exists a point $P$ inside $\triangle ABC$ such that $\angle PAB = \angle PBC = \angle PCA$ and $AP = 10.$ Find the area of $\triangle ABC.$

Solution

Problem 4

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 5

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 6

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 7

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 8

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 9

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 10

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 11

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 12

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 13

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 14

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

Problem 15

These problems will not be available until the 2023 AIME II is released in February 2023.

Solution

See also

2023 AIME II (Problems • Answer Key • Resources)
Preceded by
2023 AIME I 		Followed by
2024 AIME I
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All AIME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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