2000AMC12Problems
Problem1
In the year,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?
xianjianProblem2
黑龙江五大连池
Problem3
Each day,Jenny ate of the jellybeans that were in her jar at the beginning of that day. At the end of the cond day,remained.How many jellybeans were in the jar originally?
Problem4
The Fibonacci quence starts with two1s,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 quence?
Problem5
If where then
Problem6
Two different prime numbers between and are chon.When their sum is subtracted from their product,which of the following numbers could be obtained?
Problem7成字开头的成语
How many positive integers have the property that is a positive integer?
Problem8
Figures,,,and consist of,,,and non-overlapping squares.If the pattern continued,how many non-overlapping squares would there be in figure?
Problem9
Mrs.Walter gave an exam in a mathematics class of five students.She entered the scores in random order into a spreadsheet,which recalculated the class average after each score was entered.Mrs. W
alter noticed that after each score was entered,the average was always an integer.The scores (listed in ascending order)were71,76,80,82,and91.What was the last score Mrs.Walters entered?
Problem10
The point is reflected in the-plane,then its image is rotated
by about the-axis to produce,and finally,is translated by5units in the positive-direction to produce.What are the coordinates of?
Problem11
Two non-zero real numbers,and satisfy.Which of the following is a possible value of?
Problem12
消防安全月Let A,M,and C be nonnegative integers such that.What is the maximum value of+++?
Problem13
One morning each member of Angela’s family drank an8-ounce mixture of coffee with milk.The amounts of coffee and milk varied from cup to cup,but were never zero.Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee.How many people are in the family?
Problem14
When the mean,median,and modeof the list
are arranged in increasing order,they form a non-constant arithmetic progression.What is the sum of all possible real values of?
Problem15
Let be a function for which.Find the sum of all values of for which.
Problem16
A checkerboard of rows and columns has a number written in each square,beginning in the upper left corner,so that the first row is numbered,the cond row, and so on down the board.If the board is renumbered so that the left column,top to bottom, is,the cond column and so on across the board,some squares have the same numbers in both numbering systems.Find the sum of the numbers in the squares (under either system).
真理大学Problem17
A centered at has radius and contains the point.The gment is tangent to the circle at and.If point lies on and bicts,
then
Problem18
松下电熨斗In year,the day of the year is a Tuesday.In year,the day is also a Tuesday.On what day of the week did th day of year occur?
Problem19
triangle,,,.Let denote the midpoint
85年多少岁of and let denote the interction of with the bictor of angle.Which of the following is clost to the area of the triangle?
Problem20
If and are positive numbers satisfying
Then what is the value of latex?
Problem21
因式分解公式
Through a point on the hypotenu of right triangle,lines are drawn parallel to the legs of the triangle so that the triangle is divided into asquare and two smaller right triangles.The area of one of the two small right triangles times the area of the square.The ratio of the area of the other small right triangle to the area of the square is
Problem22
The graph below shows a portion of the curve defined by the quartic
polynomial.Which of the following is the smallest?
