2021年必威体育精装版美国数学竞赛2021 AMC 10B（学习版）.pdf

批注[c1]: 2021 AMC 10B Problem 1 How many integer values of satisfy ? Solution 1 Problem 2 What is the value of ? Solution Problem 3 In an after-school program for juniors and seniors, there is a debate team with an equal number of students from each class on the team. Among the students in the program, of the juniors and of the seniors are on the debate team. How many juniors are in the program? Solution 1 1 / 12 Problem 4 At a math contest, students are wearing blue shirts, and another students are wearing yellow shirts. The students are assigned into pairs. In exactly of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts? Solution Problem 5 The ages of Jonies four cousins are distinct single-digit positive integers. Two of the cousins ages multiplied together give , while the other two multiply to . What is the sum of the ages of Jonies four cousins? Solution Problem 6 Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is , and the afternoon classs mean score is . The ratio of the number of students in the morning class to the number of students in the afternoon class is . What is the mean of the scores of all the students? Solution 1 2 / 12 Problem 7 In a plane, four circles with radii and are tangent to line at the same point but they may be on either side of . Region consists of all the points that lie inside exactly one of the four circles. What is the maximum possible area of region ? Solution 1 Problem 8 Mr. Zhou places all the integers from to into a by grid. He places in the middle square (eighth row and eighth column) and places other numbers one by one clockwise, as