2002 AMC 12B 真题
The arithmetic mean of the nine numbers in the set is a -digit number , all of whose digits are distinct. The number does not contain the digit
What is the value of
For how many positive integers is a prime number?
Let be a positive integer such that is an integer. Which of the following statements is not true:
Let and be the degree measures of the five angles of a pentagon. Suppose that and and form an arithmetic sequence. Find the value of .
Suppose that and are nonzero real numbers, and that the equation has solutions and . Then the pair is
The product of three consecutive positive integers is times their sum. What is the sum of their squares?
Suppose July of year has five Mondays. Which of the following must occur five times in August of year ? (Note: Both months have 31 days.)
If are positive real numbers such that form an increasing arithmetic sequence and form a geometric sequence, then is
How many different integers can be expressed as the sum of three distinct members of the set ?
The positive integers and are all prime numbers. The sum of these four primes is
For how many integers is the square of an integer?
The sum of consecutive positive integers is a perfect square. The smallest possible value of this sum is
Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?
How many four-digit numbers have the property that the three-digit number obtained by removing the leftmost digit is one ninth of ?
Juan rolls a fair regular octahedral die marked with the numbers through . Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of 3?
Andy’s lawn has twice as much area as Beth’s lawn and three times as much area as Carlos’ lawn. Carlos’ lawn mower cuts half as fast as Beth’s mower and one third as fast as Andy’s mower. If they all start to mow their lawns at the same time, who will finish first?
A point is randomly selected from the rectangular region with vertices . What is the probability that is closer to the origin than it is to the point ?
If and are positive real numbers such that and , then is
Let be a right-angled triangle with . Let and be the midpoints of legs and , respectively. Given that and , find .
For all positive integers less than , let
For all integers greater than , define . Let and . Then equals
In , we have and . Side and the median from to have the same length. What is ?
A convex quadrilateral with area contains a point in its interior such that . Find the perimeter of .
Let , and let denote the set of points in the coordinate plane such thatThe area of is closest to