Difference between revisions of "2017 AIME I Problems"

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==Problem 1==
 
==Problem 1==
 
[[2017 AIME I Problems/Problem 1 | Solution]]
 
[[2017 AIME I Problems/Problem 1 | Solution]]
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Fifteen distinct points are designated on <math>\triangle ABC</math>: the 3 vertices <math>A</math>, <math>B</math>, and <math>C</math>; <math>3</math> other points on side <math>\overline{AB}</math>; <math>4</math> other points on side <math>\overline{BC}</math>; and <math>5</math> other points on side <math>\overline{CA}</math>. Find the number of triangles with positive area whose vertices are among these <math>15</math> points.
  
 
==Problem 2==
 
==Problem 2==

Revision as of 14:28, 8 March 2017

2017 AIME I (Answer Key)
Printable version | AoPS Contest CollectionsPDF

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.
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Problem 1

Solution Fifteen distinct points are designated on $\triangle ABC$: the 3 vertices $A$, $B$, and $C$; $3$ other points on side $\overline{AB}$; $4$ other points on side $\overline{BC}$; and $5$ other points on side $\overline{CA}$. Find the number of triangles with positive area whose vertices are among these $15$ points.

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

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

2017 AIME I (ProblemsAnswer KeyResources)
Preceded by
2016 AIME II
Followed by
2017 AIME II
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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