2019年北京市中学生数学竞赛预赛(高一)

Preliminary Competition of Beijing for Senior High School of Grade 1 in 2019

1、1.B.经枚举,各元素之和为3的倍数的子集有{0}、{9}、{2,1}、{0,9}、{2,0,1}、{2,1,9}、{2,0,1,9},共7个.2.A.易知,tan∠CDE=EC/CD.考虑已知条件得2=AB/CD=AB/BF·BF/BE·BE/EC·EC/CD=cos30°·1/sin45°sin60°·tan∠CDE=√3/2×√2×√3/2tan∠CDE■∠CDE=8/3√2=4√2/3.