Difference between revisions of "2002 AMC 12P Problems"
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Revision as of 21:47, 29 December 2023
2002 AMC 12P (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 |
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
Which of the following numbers is a perfect square?
Problem 2
The function is given by the table
If and for , find
Problem 3
The dimensions of a rectangular box in inches are all positive integers and the volume of the box is in. Find the minimum possible sum of the three dimensions.
Problem 4
Let and be distinct real numbers for which Find
Problem 5
For how many positive integers is
Problem 6
Participation in the local soccer league this year is % higher than last year. The number of males increased by % and the number of females increased by %. What fraction of the soccer league is now female?
Problem 7
How many three-digit numbers have at least one and at least one ?
Problem 8
Let be a segment of length , and let points and be located on such that and . Let and be points on one of the semicircles with diameter for which and are perpendicular to . Find
Problem 9
Two walls and the ceiling of a room meet at right angles at point A fly is in the air one meter from one wall, eight meters from the other wall, and nine meters from point . How many meters is the fly from the ceiling?
Problem 10
Let For how many in is it true that
Problem 11
Let be the th triangular number. Find
Problem 12
For how many positive integers is a prime number?
Problem 13
What is the maximum value of for which there is a set of distinct positive integers for which
Problem 14
Find
Problem 15
There are red marbles and black marbles in a box. Let be the probability that two marbles drawn at random from the box are the same color, and let be the probability that they are different colors. Find
Problem 16
The altitudes of a triangle are and The largest angle in this triangle is
Problem 17
Let An equivalent form of is
Problem 18
If are real numbers such that , and , find
Problem 19
In quadrilateral , Find the area of
Problem 20
Let be a real-valued function such that
Problem 21
Let and be real numbers greater than for which there exists a positive real number different from , such that $$ (Error compiling LaTeX. Unknown error_msg)2(\log_a{c}
Problem 22
In rectangle , points and lie on so that and is the midpoint of . Also, intersects at and at . The area of the rectangle is . Find the area of triangle .
Problem 23
A polynomial of degree four with leading coefficient 1 and integer coefficients has two real zeros, both of which are integers. Which of the following can also be a zero of the polynomial?
Problem 24
In , . Point is on so that and . Find .
Problem 25
Consider sequences of positive real numbers of the form in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of does the term 2001 appear somewhere in the sequence?
See also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by 2000 AMC 12 Problems |
Followed by 2002 AMC 12A Problems |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.