Difference between revisions of "2008 AMC 10A Problems"
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==Problem 1== | ==Problem 1== | ||
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==Problem 2== | ==Problem 2== | ||
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==Problem 3== | ==Problem 3== | ||
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==Problem 4== | ==Problem 4== | ||
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==Problem 5== | ==Problem 5== | ||
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==Problem 6== | ==Problem 6== | ||
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==Problem 7== | ==Problem 7== | ||
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==Problem 8== | ==Problem 8== | ||
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==Problem 9== | ==Problem 9== | ||
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==Problem 10== | ==Problem 10== | ||
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==Problem 11== | ==Problem 11== | ||
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==Problem 12== | ==Problem 12== | ||
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==Problem 13== | ==Problem 13== | ||
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==Problem 14== | ==Problem 14== | ||
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==Problem 15== | ==Problem 15== | ||
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==Problem 16== | ==Problem 16== | ||
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==Problem 17== | ==Problem 17== | ||
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==Problem 18== | ==Problem 18== | ||
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==Problem 19== | ==Problem 19== | ||
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==Problem 20== | ==Problem 20== | ||
+ | Trapezoid <math>ABCD</math> has bases <math>\overline{AB}</math> and <math>\overline{CD}</math> and diagonals intersecting at <math>K</math>. Suppose that <math>AB = 9</math>, <math>DC = 12</math>, and the area of <math>\triangle AKD</math> is <math>24</math>. What is the area of trapezoid <math>ABCD</math>? | ||
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+ | <math>\mathrm{(A)}\ 92\qquad\mathrm{(B)}\ 94\qquad\mathrm{(C)}\ 96\qquad\mathrm{(D)}\ 98 \qquad\mathrm{(E)}\ 100</math> | ||
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==Problem 21== | ==Problem 21== | ||
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==Problem 22== | ==Problem 22== | ||
+ | Jacob uses the following procedure to write down a sequence of numbers. First he chooses the first term to be 6. To generate each succeeding term, he flips a fair coin. If it comes up heads, he doubles the previous term and subtracts 1. If it comes up tails, he takes half of the previous term and subtracts 1. What is the probability that the fourth term in Jacob's sequence is an integer? | ||
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+ | <math>\mathrm{(A)}\ \frac{1}{6}\qquad\mathrm{(B)}\ \frac{1}{3}\qquad\mathrm{(C)}\ \frac{1}{2}\qquad\mathrm{(D)}\ \frac{5}{8}\qquad\mathrm{(E)}\ \frac{3}{4}</math> | ||
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==Problem 23== | ==Problem 23== | ||
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==Problem 24== | ==Problem 24== | ||
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==Problem 25== | ==Problem 25== | ||
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Revision as of 02:55, 25 April 2008
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
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Problem 2
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Problem 3
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Problem 4
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Problem 5
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Problem 6
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Problem 7
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Problem 8
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Problem 9
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Problem 10
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Problem 11
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Problem 12
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Problem 13
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Problem 14
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Problem 15
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Problem 16
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Problem 17
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Problem 18
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Problem 19
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Problem 20
Trapezoid has bases
and
and diagonals intersecting at
. Suppose that
,
, and the area of
is
. What is the area of trapezoid
?
Problem 21
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Problem 22
Jacob uses the following procedure to write down a sequence of numbers. First he chooses the first term to be 6. To generate each succeeding term, he flips a fair coin. If it comes up heads, he doubles the previous term and subtracts 1. If it comes up tails, he takes half of the previous term and subtracts 1. What is the probability that the fourth term in Jacob's sequence is an integer?
Problem 23
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Problem 24
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Problem 25
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