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

批注[c1]: 2021 AMC 10B Problem 1 How many integer values of satisfy ? Solution 1 Since is about , we multiply 9 by 2 for the numbers from to and the numbers from to and add 1 to account for the zero to get ~smarty101 and edited by Tony_Li2007 Problem 2 What is the value of ? Solution Note that the square root of any square is always the absolute value of the squared number because the square root function will only return a positive number. By squaring both and , we see that , thus is negative, so we must take the absolute value of , which is just . Knowing this, the first term in the expression equals and the second term is , and summing the two gives . 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? 1 / 20 Solution 1 Say there are juniors and seniors in the program. Converting percentages to fractions, and are on the debate team, and since an equal number of juniors and seniors are on the debate team, Cross-multiplying and simplifying we get Additionally, since there are students in the program, It is now a matter of solving the system of equations and the solution is Since we want the number of juniors, the answer is 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 t