智慧上进·2023届高三限时特训·40分钟·分科模拟卷化学(十)10答案考试试卷
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21.【命题意图】本题考查椭圆的标准方程及其简单几何性质、直线与椭圆的位置关系,考查转化与化归思想、函数与方程思想,体现了逻辑推理、数学运算等核心素养(1)【解】显然A(0,b),设P(%),则1PA=√号+(ob=又因为a2-b2=1,所以1PA1=√J6-2+26+1令%)=-2+26+1(-b≤o≤b.因为该二次函数图像的对称轴方程为y。=-b<-b,所以此二次函数在区间[-b,b]上单调递减.当y=-b时,f(yo)取得最大值,所以f(o)=f(-b).结合题意知,f(-b)=-1+262+262+1=12,解得62=3,所以a2=4.因此椭圆C的标准方程为号号=1(5分)(2)【证明】当直线ST的斜率存在时,设直线ST的方程为y=k(x-1),S(x1,y1),T(22),则直线BS和BT的斜率之和为ks+km=名+x1-4名2-4k(x-1)(-4)+(名-1)(名-4)(x1-4)(x2-4)2kx12-5k(x1+x2)+8①(8分)】(x1-4)(2-4)将y=k(x-1)代入椭圆方程并化简,得(4k2+3)x28k2x+4k2-12=0,8k2则名场4+3名4k2-12(10分)42+3所以2x名2-5k(x1+名)+8k=2k(42-12)-5k·8k+8k(4K+3=0,4k2+3因此,kas+kr=0,此时BF平分∠SBT(11分)当直线ST的斜率不存在时,根据椭圆的对称性知BF平分∠SBT综上,BF平分∠SBT(12分)】
第四部分写作第一节审题指导)本篇书面表达要求考生代表学生会写一则通知,对象为全体学生,所以应用第一人称进行写作;文章要明确活动目的,以激发参与者的兴趣和热情:活动尚未开始,所以时态以一般将来时为主;此外在文章中必须将活动时间及相应的活动安排介绍清楚。【参考范文】NOTICEDear fellow students,In order to be close to nature and experience the joy oflabor,an activity called Tea-Leaf-Picking will take place thisSaturday on the Xishan Farm.We're planning to gather at our school gate at 8:00 amand leave for the farm by bus at 8:30 am.Arriving at 9:00am,we'll set about picking tea leaves with everything ready.We'll have lunch and have a rest from 11:30 am to 2:00 pm.We may go home round 4:00 pm by bus.We're supposed to be punctual.Besides,wearing clotheswith long sleeves is necessary,and we'd better bring a littlebasket to hold tea leaves.Most importantly,it's no doubt thatwe're required to write a passage about this activity and handit in next Monday.May us a good weekend!Students'Union亮点评析)》本篇书面表达要点齐全,层次分明,逻辑清晰。文章第一段交代了活动目的、时间和地,点:第二段详细介绍了活动安排:第三段介绍了活动的注意事项:最后一段表达期待。整篇文章语言流畅,并且作者在文章中使用了一些高分词汇,知be close to,take place,leave for,besupposed to等。此外作者还使用了一些高分结构,如过去分词短语作后置定语“.,an activity called Tea-Leaf-Pickingwill take place this Saturday on the Xishan Farm.”和that引导的主语从句“Most importantly,it's no doubt that we'rerequired to write a passage about this activity and hand it innext Monday.”等。这些高分词汇和句型的使用为文章增色不少。