2024届湖南省长沙市一中高三下学期月考（七）数学试题及答案

长沙市一中2024届高三月考试卷(七)数学试卷:8,5,共40.,.1.15131231292343191738(((())))(A)19(B)23(C)21(D)18{ꢀ}ꢀ2.A=xex2−2x⩽1,B={−1,0,1},A∩Bꢀ(A)4(B)3(C)8(D)73.3zz·(1−2i),则|z|=√√32352(A)2(B)(C)(D)54.{a}a=3n−b(n∈N,b∈),b<3”是“{|a|}∗n(A)(C)nn(B)(D)sin2θ2cos2θ+4sin2θ5.tanθ=2,则=()1329(A)(B)2(C)1(D)6.E:y2=2px(p>0)FE,B,交ElC,⊥l,点D.若F是,且|AF|=3,则|AB|=()√√(A)4(B)23(C)32(D)37.C:kx−y=1F,P(3−4)(m>0)为C,且P与FC22,则C()√√√55(A)(B)3(C)2(D)28.已知函数f(x)的定义域为,且满足f(x)+f(3−x)=4,f(x)的导函数为g(x),函数y=g(x−1)的图象关()3(2,1),则f+g(2024)=()2(A)3(B)−3(C)1(D)−1二、多项选择题:本题共3,每小题6,共18.在每小题给出的选项中,有多项符合题目要求,全部选对的得6,,0.119.f(x)=cos2x+sin2x,则()22()π(A)fx−8πkπ(B)y=f(x)x=+,k∈Z1221{#{QQABAQ4UogAAAoBAABgCAQUwCgAQkBAAAIoGgEAEMAAACQFABAA=}#}()π5π(C)f(x),88(D)y=f(x)(0,f(0))2x−2y+1=02π10.A−CD−B(A)ABD,⊥CD,BD⊥CD,且CD=1,+BD=2,则()3(B)与BC√√3(C)[2,5)(D)A−BCD411.甲、乙两同学参加普法知识对抗赛,规则是每人每次从题库中随机抽取一题回答.若回答正确,得1,答题继1;若回答错误,得0,同时换成对方进行下一轮答题.据经验统计,甲、乙每次答题正确的概率分别是和22,1.iP,第iK,ii3则()145(A)P2=(C)Pi+1(B)P(2=1)=2416131=Pi+(D)E(i)=Pi+i−1(i⩾2)2:3,5,共15.12.(x+3y)(x−y)xy.83613.PM:(x−m+1)+(y−)=1,Qy=lnx.m∈,|PQ|⩾n22,则n.√√14.已知正六棱锥的高是底面边长的23,侧棱长为13,正六棱柱内接于正六棱锥,即正六棱柱的所有顶点均在,.:5,共77..15.6,1,2,2,3,3,3.(1),1;(2)若每次随机取出两张卡片后不放回,直到将所有标记数字为2的卡片全部取出,记此时盒中剩余的卡片数量X,求XE(X).16.P−ABC,PA=BC,=PC,⊥PB.(1):=BC;√(2)PAC⊥ABC,=2AB,A−PB−C.PACB2{#{QQABAQ4UogAAAoBAABgCAQUwCgAQkBAAAIoGgEAEMAAACQFABAA=}#}17.(0,π)f(x)=cos2x+sinx.(1)求f(x);1(2):x∈(0,1),f(x)>x−x+1.424x2y218.C:+=1(a>b>0)(0,1),B(0,−1),F,且·=·.a2b2(1)C;(2)P(2,−1),BPP,P·=.分2121212CM,N(),:P,M,N.19.△ABCa,b,c,(a,b,c).记D,即(a,b,c)∈D.√√√(1):“(a,b,c)∈D”是“(a,b,c)∈D;(2)△ABCO,且xO+yO+zO=0,设I=(x,y,z)(x,y,z>0).①若I=(3,4,5),求S△AOB:S△AOC②:I∈D.;3{#{QQABAQ4UogAAAoBAABgCAQUwCgAQkBAAAIoGgEAEMAAACQFABAA=}#}{#{QQABAQ4UogAAAoBAABgCAQUwCgAQkBAAAIoGgEAEMAAACQFABAA=}#}{#{QQABAQ4UogAAAoBAABgCAQUwCgAQkBAAAIoGgEAEMAAACQFABAA=}#}{#{QQABAQ4UogAAAoBAABgCAQUwCgAQkBAAAIoGgEAEMAAACQFAB