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Difference between revisions of "2014 AMC 12B Problems"

(→‎Problem 12)
(Cleaned up the trollers mess)
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==Problem 1==
 
==Problem 1==
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Find <math>1 + 2 + 3 + ... + 99 + 100</math>.
 
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<math>\mathrm {(A) } 4950 \qquad \mathrm {(B) } 5000 \qquad \mathrm {(C) } 5050 \qquad \mathrm {(D) } 5075 \qquad \mathrm {(E) } 5100</math>
 
  
 
[[2014 AMC 12B Problems/Problem 1|Solution]]
 
[[2014 AMC 12B Problems/Problem 1|Solution]]
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==Problem 4==
 
==Problem 4==
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A circle with radius <math>R</math> is circumscribed around a square. Another circle with radius <math>r</math> is inscribed in the square. Find <math>\frac{R}{r}</math>.
 
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<math>\mathrm {(A) } \frac{5}{4} \qquad \mathrm {(B) } \sqrt2 \qquad \mathrm {(C) } \frac{3}{2} \qquad \mathrm {(D) } \sqrt3 \qquad \mathrm {(E) } 2</math>
 
  
 
[[2014 AMC 12B Problems/Problem 4|Solution]]
 
[[2014 AMC 12B Problems/Problem 4|Solution]]
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==Problem 12==
 
==Problem 12==
  
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Find the remainder when <math>100! + 99! + 98! + ... + 3! + 2! + 1!</math> is divided by <math>100</math>.
 
  
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<math>\mathrm {(A) } 11 \qquad \mathrm {(B) } 33 \qquad \mathrm {(C) } 55 \qquad \mathrm {(D) } 77 \qquad \mathrm {(E) } 99</math>
 
  
 
[[2014 AMC 12B Problems/Problem 12|Solution]]
 
[[2014 AMC 12B Problems/Problem 12|Solution]]
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==Problem 14==
 
==Problem 14==
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Amy, Bob, Charlie, Dorothy, Edd, and Frank each select distinct integers between <math>2005</math> and <math>2014</math>, inclusive. What is the probability that the four integers are the lengths of the sides and diagonals of a cyclic quadrilateral?
 
  
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<math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ \frac{1}{42} \qquad \textbf{(C)}\ \frac{1}{30} \qquad \textbf{(D)}\ \frac{1}{21} \qquad \textbf{(E)}\ \frac{1}{7}</math>
 
  
 
[[2014 AMC 12B Problems/Problem 14|Solution]]
 
[[2014 AMC 12B Problems/Problem 14|Solution]]
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==Problem 17==
 
==Problem 17==
  
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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?
 
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<math>\mathrm {(A) } 0 \qquad \mathrm {(B) } 1 \qquad \mathrm {(C) } 2 \qquad \mathrm {(D) } 3 \qquad \mathrm {(E) } 4</math>
 
  
 
[[2014 AMC 12B Problems/Problem 17|Solution]]
 
[[2014 AMC 12B Problems/Problem 17|Solution]]

Revision as of 23:26, 8 February 2014

Problem 1

Solution

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

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

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