美国数学竞赛AMC8

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1、2012 AMC 8 ProblemsProblem 1Rachelle uses  pounds of meat to make  hamburgers for her family. How many pounds of meat does she need to make hamburgers for a neighborhood picnic?SolutionProblem 2In the country of East Westmore, statisticians estimate there is a baby born ever

2、y  hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?SolutionProblem 3On February 13  listed the length of daylight as 10 hours and 24 minutes, the sunrise was , and the sunset as . The length of

3、daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?SolutionProblem 4Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?SolutionProblem 5In t

4、he diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is ,  in centimeters?SolutionProblem 6A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph

5、. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?SolutionProblem 7Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing

6、her score on the third test, she realized she can still reach her goal. What is the lowest possible score she could have made on the third test?SolutionProblem 8A shop advertises everything is "half price in today's sale." In addition, a coupon gives a 20% discount on sale prices. Usin

7、g the coupon, the price today represents what percentage off the original price?SolutionProblem 9The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were t

8、wo-legged birds?SolutionProblem 10How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?SolutionProblem 11The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, are all equal. What is the value of ?SolutionProblem 12What is the units digit o

9、f ?SolutionProblem 13Jamar bought some pencils costing more than a penny each at the school bookstore and paid . Sharona bought some of the same pencils and paid . How many more pencils did Sharona buy than Jamar?SolutionProblem 14In the BIG N, a middle school football conference, eac

10、h team plays every other team exactly once. If a total of 21 conference games were played during the 2012 season, how many teams were members of the BIG N conference?SolutionProblem 15The smallest number greater than 2 that leaves a remainder of 2 when divided by 3, 4, 5, or 6 lies between what numb

11、ers?SolutionProblem 16Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?SolutionProblem 17A square with integer side length is cut into 10 squares, all of

12、 which have integer side length and at least 8 of which have area 1. What is the smallest possible value of the length of the side of the original square?SolutionProblem 18What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?SolutionProblem

13、 19In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How many marbles are in the jar?SolutionProblem 20What is the correct ordering of the three numbers , , and , in increasing order?SolutionProblem 21Marla has a large wh

14、ite cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?SolutionProblem 22Let  be a se

15、t of nine distinct integers. Six of the elements are 2, 3, 4, 6, 9, and 14. What is the number of possible values of the median of  ?SolutionProblem 23An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 4, what is the area of the hexagon?Solu

16、tionProblem 24A circle of radius 2 is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is the ratio of the area of the star figure to the area of the original circle?SolutionProblem 25A square with area 4 is inscribed in a square with area 5, with one vertex

17、 of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length , and the other of length . What is the value of ?Solution华数教育专业中小学奥数辅导，专注美国数学竞赛AMC8、10、12，美国数学邀请赛AIME，美国普林斯顿数学竞赛PUMAC，13524602295，