关于美国数学竞赛[AMC10]

2025-02-09 07:54:57

推荐回答（5个）

回答1：

英文的题目：1.A bakery owner turns on his doughnut machine at . At the machine has completed one third of the day's job. At what time will the doughnut machine complete the job? 2.A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is . The ratio of the rectangle's length to its width is . What percent of the rectangle's area is inside the square? 3.For the positive integer , let denote the sum of all the positive divisors of with the exception of itself. For example, and . What is ? 4.Suppose that of bananas are worth as much as oranges. How many oranges are worth as much as of bananas? 5.Which of the following is equal to the product 6.A triathlete competes in a triathlon in which the swimming, biking, and running segments are all of the same length. The triathlete swims at a rate of 3 kilometers per hour, bikes at a rate of 20 kilometers per hour, and runs at a rate of 10 kilometers per hour. Which of the following is closest to the triathlete's average speed, in kilometers per hour, for the entire race? 7.The fraction simplifies to which of the following? 8.Heather compares the price of a new computer at two different stores. Store offers off the sticker price followed by a rebate, and store offers off the same sticker price with no rebate. Heather saves by buying the computer at store instead of store . What is the sticker price of the computer, in dollars? 9.Suppose that is an integer. Which of the following statements must be true about ? 10.Each of the sides of a square with area is bisected, and a smaller square is constructed using the bisection points as vertices. The same process is carried out on to construct an even smaller square . What is the area of ? 11.While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in more than 30 gallons of water. Steve starts rowing toward the shore at a constant rate of 4 miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking? 12.In a collection of red, blue, and green marbles, there are more red marbles than blue marbles, and there are more green marbles than red marbles. Suppose that there are red marbles. What is the total number of marbles in the collection? 13.Doug can paint a room in hours. Dave can paint the same room in hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by ? 14.Older television screens have an aspect ratio of . That is, the ratio of the width to the height is . The aspect ratio of many movies is not , so they are sometimes shown on a television screen by "letterboxing" - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of and is shown on an older television screen with a -inch diagonal. What is the height, in inches, of each darkened strip? 15.Yesterday Han drove 1 hour longer than Ian at an average speed 5 miles per hour faster than Ian. Jan drove 2 hours longer than Ian at an average speed 10 miles per hour faster than Ian. Han drove 70 miles more than Ian. How many more miles did Jan drive than Ian? 16.Points and lie on a circle centered at , and . A second circle is internally tangent to the first and tangent to both and . What is the ratio of the area of the smaller circle to that of the larger circle? 17.An equilateral triangle has side length 6. What is the area of the region containing all points that are outside the triangle but not more than 3 units from a point of the triangle? 18.A right triangle has perimeter 32 and area 20. What is the length of its hypotenuse? 19.Rectangle lies in a plane with and . The rectangle is rotated clockwise about , then rotated clockwise about the point moved to after the first rotation. What is the length of the path traveled by point ? 20.Trapezoid has bases and and diagonals intersecting at . Suppose that , , and the area of is . What is the area of trapezoid ? 21.A cube with side length is sliced by a plane that passes through two diagonally opposite vertices and and the midpoints and of two opposite edges not containing or , as shown. What is the area of quadrilateral ? 22.Jacob uses the following procedure to write down a sequence of numbers. First he chooses the first term to be 6. To generate each succeeding term, he flips a fair coin. If it comes up heads, he doubles the previous term and subtracts 1. If it comes up tails, he takes half of the previous term and subtracts 1. What is the probability that the fourth term in Jacob's sequence is an integer? 23.Two subsets of the set are to be chosen so that their union is and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter? 24.Let . What is the units digit of ? 25.A round table has radius . Six rectangular place mats are placed on the table. Each place mat has width and length as shown. They are positioned so that each mat has two corners on the edge of the table, these two corners being end points of the same side of length . Further, the mats are positioned so that the inner corners each touch an inner corner of an adjacent mat. What is ? Problem12345678910111213AnswerDAACBDEABEDCDProblem141516171819202122232425 AnswerDDBBBCDADBDC 你看，这才是一份……你能不能给我一个提供题目的方式

回答2：

AMC 10 竞赛是在每年的二月，不是三月。试题是全英语的。你可以在下面的网站上免费下载：
http://www.artofproblemsolving.com/Wiki/index.php/AMC_10_Problems_and_Solutions

美国高中数学物理教师
AMC 10、AMC 12 辅导教练

回答3：

AMC美国数学竞赛组成

1、AMC 8

考试时间40分钟，一共25道选择题，问题的难度随着考试进行逐渐增加。2007年前的AMC 8竞赛于需使用计算器，目前不允许使用。

评分方式：答对得一分，不同于AMC 10和AMC 12，答错或不答并不扣分。

2、AMC 10

竞赛考试时间75分，一共25道选择题，问题的难度随着考试进行逐渐增加。满分150分，2016年起，AMC 10不再允许使用计算器。

评分方式为：答对得6分，答错不得分，不答得1.5分，在2002-2006年间，不答得2.5分，2006-2007期间，不答得2分。前2.5%的AMC 10参赛者可受邀参加美国数学邀请（AIME）。

3、AMC 12

竞赛考试时间75分，一共25道选择题，问题的难度随着考试进行逐渐增加。满分150分，2008年起，AMC 12不再允许使用计算器。

评分方式为：答对得6分，答错不得分，不答得1.5分，在2002-2006年
间，不答得2.5分，2002年前，不答得2分。前5%的AMC 12参赛者可受邀参加美国数学邀请赛（AIME）。

4、AIME