-数学-山西省三重教育联盟2023-2024学年高三上学期9月联考试题和答案

参考答案（数学）第1页共6页单项选择题_____、单项选择题12345678DACCBABD·:BE(0,兀:.sinB*0,..smA=Sm(A——)＋—,.fj.fj:.sinA=sinA—cosA+,'3.fj.fj·ππ4π:AE(0,兀:.A+·ππ4π:.A+=，解得A=ππ3(2)·:A=—，且MBC的面积为，·:D为BC的中点，:.2A=AB'+AC',-一2一2---2解得m了=7,:.AD的长为打.···············!分..............·2分···············3分..............·4分..............·5分..............·6分..............·7分..............·8分...............9分···············10分参考答案（数学）第2页共6页zz:.2a+—=29,a11,解得或I1,解得\d=3\a1=—,22—,93 +).l—3)·()曰又·:AC_l_BF,AC与BD相交，:.BF_l_平面ABCD;..............·2分..............·3分···············4分..............·6分...............7分...............8分...............9分···············10分···············11分···············12分···············1分..............·3分···············4分XFy参考答案（数学）第3页共6页...............7分•••.....•......8分•••.....•......9分...........................7分•••.....•......8分•••.....•......9分...............11分...............12分..............·2分..............·3分..............·4分...............11分...............12分..............·6分..............·6分设平面CBG的一个法向量为n=(x,y,z),则则令·:AC..lBF,AC..lBD,BF门BD=B,BF,BD已平面BGD,=2,兀五言]二2XXXX..............·6分..............·6分···············7分···············7分:.X的可能取值为0,I,2,3.P(X=0)=＝，P(X=1)=c:c='P(X=2)=c.c=,P(X=3)=1，c:14c:84:.x的分布列如下：X。123531E(X)=Ox—+Ix—+2x—+3x—=1.参考答案（数学）第4页共6页（或因为X服从超几何分布，所以E(X)=3x=1.)〈22_2')_2:x1-x2x1+x2x1-x22x。x1-x2x0a2x1-x2x1+x2x1-x22x。x1-x2x0a2,设直线MN的方程为y=kx+m,4y212,由得(4k23)x28kmx4m2124y212,14···············1分..............·2分···············3分..............·4分···············5分...............7分_k222)222k22k—2—-2+32—2,==,2—2解得m=2k(舍去）或m=-k,·:QM=(x1—2,Yi),4k2—:—2)(x2—2)+y心..............·9分参考答案（数学）第5页共6页——)—5k20':．点Q在以MN为直径的圆内.:.f'(x)=aex(I+lnx)+aex=aex·xlnx+x+I.XX令t(x)=xlnx+x+l,则t'(x)=lnx+2.·:t'(x)单调递增且t'()=0'e:.t(x):.t(x)t()=1—>0':.f'(x)>0,即f(x)在定义域(0,+oo)上单调由题g(x)—f(x)>0,即aex(I+Inx)<x2+x(I+Ina),aeXXXe···············11分...............12分..............·1分...............2分...............3分..............·4分···············5分•••.....•......6分..............·7分...............8分•••....••......9分eXeX