數(shù)學-山東省煙臺德州東營2024年高考診斷性測試試題和答案

ACBCBDAA 由題意知f'(2)=2，12因為f(x)0，設(shè)g(x)=?x22因為f(x)0，設(shè)g(x)=?x22?x+2lnx,x(0,+)，則bg(x)max.xxx······················································································當x(0,1)時，g'(x)0，所以g(x)在(0,1)單調(diào)遞增，當x(1,+)時，g'(x)0，所以g(x)在(1,+)單調(diào)遞減，···············11分······························································2所以A1O軸正方向，建立如圖所示的空間直角坐標系O?xyz.······8分 3 322設(shè)m=(x,y,z)為平面ABA1的一個法向量，|33故m=(,3,1)，·····························12分17.解1）兩人得分之和大于100分可分為甲得40分、乙得70分，甲得70分、乙得40（2）搶答環(huán)節(jié)任意一題甲得15分的概率p=（3）X的可能取值為2,3,4,5. ························434所以X的分布列為,······································X2345P 1 9 4 27··································13分所以E(X)=2x 1 9 4 =.222設(shè)直線l的方程為x=my+3，22不妨設(shè)P(x1,y1),Q(x2,y2)，,且y1+y2=4m21y2.4m2.··················································所以kAPkAQ=. y1y2m2y1y2+5m(y1+y2)+25··········································4··························································（2）設(shè)直線AP的方程為y=k(x+2)，則直線DM:y=?(x?3)，M=用?替換上式中的k可得yN=5kk2+1.25k2+16.··········································································································································································································3125 kk5因為25k2+22x2kk5 所以x=|OB|?sint=t?sint， （2）證明：由復合函數(shù)求導公式y(tǒng)=y.x，sinθ+cosθtanθ+1()2()2所以為定值所以為定值1.·········································10分y0