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Difference between revisions of "2014 AMC 12B Problems"
(→Problem 17) |
(→Problem 17) |
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==Problem 17== | ==Problem 17== | ||
| − | Let <math>S</math> be the set of points on the graph of <math>y = x + \ | + | Let <math>S</math> be the set of points on the graph of <math>y = x + \sqrt{x}</math> such that <math>x</math> is an integer between <math>-100</math> and <math>100</math>, inclusive. How many distinct line segments with endpoints in <math>S</math> have integer side lengths? |
<math>\mathrm {(A) } 0 \qquad \mathrm {(B) } 1 \qquad \mathrm {(C) } 2 \qquad \mathrm {(D) } 3 \qquad \mathrm {(E) } 4</math> | <math>\mathrm {(A) } 0 \qquad \mathrm {(B) } 1 \qquad \mathrm {(C) } 2 \qquad \mathrm {(D) } 3 \qquad \mathrm {(E) } 4</math> | ||
Revision as of 21:36, 8 February 2014
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Amy, Bob, Charlie, and Dorothy each select distinct integers between 
and 
, inclusive. What is the probability that the four integers are side lengths of a cyclic quadrilateral?
Problem 15
Problem 16
Problem 17
Let 
be the set of points on the graph of 
such that 
is an integer between 
and 
, inclusive. How many distinct line segments with endpoints in have integer side lengths?
