Difference between revisions of "2000 AMC 10 Problems"
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== Problem 5 == | == Problem 5 == | ||
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+ | Points <math>M</math> and <math>N</math> are the midpoints of sides <math>PA</math> and <math>PB</math> of <math>\triangle PAB</math>. As <math>P</math> moves along a line that is parallel to side <math>AB</math>, how many of the four quantities listed below change? | ||
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+ | (a) the length of the segment <math>MN</math> | ||
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+ | (b) the perimeter of <math>\triangle PAB</math> | ||
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+ | (c) the area of <math>\triangle PAB</math> | ||
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+ | (d) the area of trapezoid <math>ABNM</math> | ||
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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> | ||
[[2000 AMC 10 Problems/Problem 5|Solution]] | [[2000 AMC 10 Problems/Problem 5|Solution]] |
Revision as of 18:56, 5 January 2009
Contents
[hide]- 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
- 26 See also
Problem 1
In the year 2001, the United States will host the International Mathematical Olympiad. Let , , and be distinct positive integers such that the product . What is the largest possible value of the sum ?
Problem 2
Problem 3
Each day, Jenny ate of the jellybeans that were in her jar at the beginning of that day. At the end of the second day, remained. How many jellybeans were in the jar originally?
Problem 4
Chandra pays an on-line service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was , but in January her bill was because she used twice as much connect time as in December. What is the fixed monthly fee?
Problem 5
Points and are the midpoints of sides and of . As moves along a line that is parallel to side , how many of the four quantities listed below change?
(a) the length of the segment
(b) the perimeter of
(c) the area of
(d) the area of trapezoid
Problem 6
The Fibonacci sequence starts with two s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence?