THUSSAT中学生标准学术能力2023年11月诊断性测试答案

一项是符合题目要求的.12345678CABBABDD项符合题目要求．全部选对的得5分，部分选对但不全的得2分，有错选的得0分.9ACABACD三、填空题：本题共4小题，每小题5分472四、解答题：本题共6小题，共70分．解答应写出文字说明sinCcosBsinCcosBbsinCcosB2sinsinCcosBsinB,12cosB=12,得B=············································································322222)，SESFSB=SC且==λ,：SE=SF·····················································6SBSC则AE=AF···································故ΔSEF与ΔAEF都是等腰三角形，取EF的中点G，则SG与AG均垂直于EF，Gλa,λa,(1−λ)h,SG=λa,λa,−λh,AG=λa,λa,(1−λ)h，平面AEF⊥平面SBC等价于SG⊥AG·················10分a2λ24λ=························12分nn:{an−2}是公比为的等比数列·······························································2分(1)n−1(1)n−1an「1(1)2(1)n−1]「(1)n]2n···························································(1)n(1)n1(1)n(1)n1:n取最小值14·················4{Cn}中最大项为C2,C3····································································}中最小值为λ2,:(bm)min−(Cn)max>，即λ2−λ>，:λ>·················································12分2012分）XP························································································································································2112分）=2a,:4a=4,:a=2·······························2:b=1，2(12)22222设Bx22④·····················································2④·····················································2A,F22x2: 2: 22222m:k<2，:m=:k<2，2:SΔF1BC=2BCd=2kx1−x2················································44k244k2−2x|2|4k2|=22224212242122221SF1BC···································································10分22设2k2设2k22t2t2tt66 6646644·····························································································2212分）由题意知又又:1<x2只需证x22·································((1))(2)(2)2)2)2)((1))