2002 AMC 10P Problems
2002 AMC 10P (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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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
The ratio equals
Problem 2
The sum of eleven consecutive integers is What is the least of these integers?
Problem 3
Mary typed a six-digit number, but the two s she typed didn't show. What appeared was How many different six-digit numbers could she have typed?
Problem 4
Which of the following numbers is a perfect square?
Problem 5
Let be a sequence such that and for all Find
Problem 6
The perimeter of a rectangle is and its diagonal has length What is the area of this rectangle?
Problem 7
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 8
How many ordered triples of positive integers satisfy
Problem 9
The function is given by the table
If and for , find
Problem 10
Let and be distinct real numbers for which
Find
Problem 11
Let Find the sum of all real numbers for which is a factor of
Problem 12
For and consider
Which of these equal
Problem 13
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 14
The vertex of a square is at the center of square The length of a side of is and the length of a side of is Side intersects at and intersects at If angle the area of quadrilateral is
Problem 15
What is the smallest integer for which any subset of of size must contain two numbers that differ by 8?
Problem 16
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 17
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 18
For how many positive integers is a prime number?
Problem 19
If are real numbers such that , and , find
Problem 20
How many three-digit numbers have at least one and at least one ?
Problem 21
Let be a real-valued function such that
for all Find
Problem 22
In how many zeroes does the number end?
Problem 23
Let
and
Find the integer closest to
Problem 24
What is the maximum value of for which there is a set of distinct positive integers for which
Problem 25
Under the new AMC scoring method, points are given for each correct answer, points are given for each unanswered question, and no points are given for an incorrect answer. Some of the possible scores between and can be obtained in only one way, for example, the only way to obtain a score of is to have correct answers and one unanswered question. Some scores can be obtained in exactly two ways, for example, a score of can be obtained with correct answers, unanswered question, and incorrect, and also with correct answers and unanswered questions. There are (three) scores that can be obtained in exactly three ways. What is their sum?
See also
2002 AMC 10P (Problems • Answer Key • Resources) | ||
Preceded by 2001 AMC 10 Problems |
Followed by 2002 AMC 10A 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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.