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山东省滨州市2019—2020学年下学期高一年级期末考试数学试题
山东 高一 期末 2020-09-17 15次

一、单选题添加题型下试题

1. 已知复数eqId67227f7bc6204fb9b11c9842fbf7e416是纯虚数,则实数m=(  )
A.﹣2B.﹣1C.0D.1
2. “幸福感指数”是指某个人主观地评价他对自己目前生活状态的满意程度的指标,常用区间eqId004160be53f9476a9f88ac1765c556d7内的一个数来表示,该数越接近10表示满意程度越高,现随机抽取6位小区居号,他们的幸福感指数分别为5,6,7,8,9,5,则这组数据的第80百分位数是(   )
A.7B.7.5C.8D.9
4. 已知在平行四边形eqId5ce7a06ae7a34393b92b5277978ac014中,点eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6分别是eqId0627be51821d4be7b3e024a354815d64eqId34c6b6e427744abfb88dc90b8c7c2111的中点,如果eqId9f7405ab55f141789b76d3eda62dc54aeqId3b580547e74e405991e9fb52977cb63a,那么向量eqId74a105416db74ad98abc382b80e4ea84(  )
A.eqId48fc30e5cf254c12b0d60cd9c75518ddB.eqId89f0386d81824fd7bb0f81185ada7cb1C.eqId24e376b40cac4a7080e53fa99529c968D.eqIdd24e803973ce45fbad001f6e5fb55aea
5. 已知圆锥的表面积为eqId5c266efbf3414de1a1d1e2d3553a9c42,且它的侧面展开图是一个半圆,则该圆锥的体积为(   )
A.eqId5beb71eacaaa44549c88e35d4b1a01eeB.eqIda80a557676ae4316a08672c32cf33de7C.eqIddcbaf093655d4ad9850f9791f0b28523D.eqIdc12500d69e0342b3be4db149b0244a7a
6. 《史记》中讲述了田忌与齐王赛马的故事,其中,田忌的上等马优于齐王的中等马,劣于齐王的上等马;田忌的中等马优于齐王的下等马,劣于齐王的中等马;田忌的下等马劣于齐王的下等马,若双方各自拥有上等马、中等马、下等马各1匹,且双方各自随机选1匹马进行1场比赛,则田忌的马获胜的概率为(   )
A.eqIdad04b6cca48b47cdbd0d239142650251B.eqId5f51ce9cc7fe4412baeb871cceb26665C.eqId9e311be638c64d4eaed28e15dcba7451D.eqId0dce1f07f2a0460f80cd56ad0d9328c2
7. 如图所示,为了测量山高eqId996e2048847f41d5a5fe0e2282909254,选择eqIdcc614bd3390c4d028df189b234dcc351和另一座山的山顶eqId19a4eb16029e4550a14f2afe4741a3c3作为测量基点,从eqIdcc614bd3390c4d028df189b234dcc351点测得eqId2381423d4cd146cab95f55527681a766点的仰角eqId4fdc7d076cf1413c94bb8533a5bbf1faeqId19a4eb16029e4550a14f2afe4741a3c3点的仰角eqId9eea2bcaec634a5dadef5b96e0edfe27eqIde1ea28630b5f43c992d34b72a58a4d0d,从eqId19a4eb16029e4550a14f2afe4741a3c3点测得eqId01dc4f6fd0894715854357e102c1cd34.已知山高eqId537dd193fffe4a229a6a81cb041491ce,则山高eqId996e2048847f41d5a5fe0e2282909254(单位:eqIda4be99d332154d13a4a6ed1ff6444fe7)为(  )
说明: figure
A.eqId91b4d2f0fe4c4e579a6ed407f100b2b2B.eqId1a9dca4e080e496b99fba6d5c070e878C.eqId1d457b4135934b75b205d61a6f83fbafD.eqIdcdf5edcc9b4042f19f5d9496a063788b
8. 如图,在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,原点eqId2efda802d5534f6d92d9f8af7aaec28b为正八边形eqId2c46275da31d47c8ad0699846ee50977的中心,eqIda7a4409e63024898afe796f52e670c19轴,若坐标轴上的点eqId2381423d4cd146cab95f55527681a766(异于点eqId2efda802d5534f6d92d9f8af7aaec28b)满足eqId840f4f887b51485885e51c29d540411e(其中eqId3f5d5e74a4154a20aa1bcbcf4644b20c,且eqIdb6e15e51d29a47a7aff44f98b1aafaeeeqId7a1e64cb03d64f6a909c3b35d53020f4),则满足以上条件的点eqId2381423d4cd146cab95f55527681a766的个数为(  )
说明: figure
A.eqIdc052ddfbd4524f67a79e0e77c2e5656aB.eqIdddd35c5d043e4ebeac32a99367053c68C.eqIddd4bf187d3fd47f6bcc24e568e09643eD.eqId401586f7a7f248b7904a4cfeaa2ed2f0

二、多选题添加题型下试题

9. 已知复数z满足(1﹣iz=2i,则下列关于复数z的结论正确的是(  )
A.eqId2a48785a780243f8bcd96f4de2b26b06
B.复数z的共轭复数为eqIdd97c066590474beb8b6a5abd6461c259=﹣1﹣i
C.复平面内表示复数z的点位于第二象限
D.复数z是方程x2+2x+2=0的一个根
10. 某市教体局对全市高三年级的学生身高进行抽样调查,随机抽取了100名学生,他们的身高都处在eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3eqId0cd8063abf2b458f80091bc51b75a904eqId93cbffaa5ae045d6ac45d1e979991c3a五个层次内,根据抽样结果得到统计图表,则下面叙述正确的是(   )
说明: figure 说明: figure
A.样本中女生人数多于男生人数B.样本中eqId8754ce8cf7f34f04abb9a0c041f57f5c层人数最多
C.样本中eqId93cbffaa5ae045d6ac45d1e979991c3a层次男生人数为6人D.样本中eqId0cd8063abf2b458f80091bc51b75a904层次男生人数多于女生人数
11. 已知事件eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c,且eqId5dfe84b0530c446b9e4c09a0742b030deqId28cbc59f61f94a829f7d2fdb7ea3597d,则下列结论正确的是(   )
A.如果eqId4ba4d0833b3746cdac653347b9d6e75d,那么eqId73ec9034cff345eba60fbfeac9770e5deqId1d294a05d25640329b63ad8e20894198
B.如果eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c互斥,那么eqId10edcd79375b4923a611d9937fd66602eqIdd48b15ee4a4342c7ae5de5d51ed6b91d
C.如果eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c相互独立,那么eqId10edcd79375b4923a611d9937fd66602eqIdd48b15ee4a4342c7ae5de5d51ed6b91d
D.如果eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c相互独立,那么eqId6f8c4ce241984240a17ed163faa33c6feqId276d1b4ff30943f7b41542ab2bfacba7
12. 如图,正方体eqId314fa9dac7e543429771aba186992c2c的棱长为1,则下列四个命题正确的是(   )
说明: figure
A.若点eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6分别是线段eqIdcd84a39aaa45434a837874b17614305ceqId58d78153efe44cd4aa53dcb230b9271a的中点,则eqIdffaae45e580044e58f4c430327fd2730
B.点eqId19a4eb16029e4550a14f2afe4741a3c3到平面eqId04b4ffa28cbd467bac8fde9505e251a5的距离为eqId317ed84d205b4156847380f7e9f38b08
C.直线eqId0627be51821d4be7b3e024a354815d64与平面eqId04b4ffa28cbd467bac8fde9505e251a5所成的角等于eqIdb47bf79338b1478a89eac53d16970cdf
D.三棱柱eqId60d9274ce0ca4d67acbf7a04e66d877b的外接球的表面积为eqId5c266efbf3414de1a1d1e2d3553a9c42

三、填空题添加题型下试题

解题方法
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13. 已知eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1分别为eqId64b9b599fdb6481e9f8d9a94c102300b三个内角eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的对边,且eqId42b177e380a74119938ec095604b8339,则eqIdce21b2b77d864971a29623b56f1cb6bb________.
14. 已知eqIdfc509a4be3594dc9bdf14b7ca31f8e37eqIdd6d010b4a532403892e1d514eb2303b0eqId377674d0dd234c37a35527088cf5b05e,则eqId7fa34c81fe764c5db19edc8249d4ccf5eqId9d9c58594a9b450888a060f3bbe0e37e的夹角为________.
15. 如图,在三棱锥eqIdf8dc44643cbe4fc8a134a58f9f33d0a4中,eqId861830ac839c45c8be1711197dedfe6eeqId4b0b3dc81c904869ad9cb5c18a37d440eqIde09bc9f58fbb40b8829481adb8f38962,且eqIda04aad3ceadd4b02960b9945d2cc3275eqId7a725a8549dd4ab0a962536d32c8c3b4,则二面角eqId56749bdd87ca4a5eba71091db5c25d30的余弦值是_____.说明: figure

四、双空题添加题型下试题

16. 已知数据eqId735b8047beee4dee870fc72ae837a245eqIdecaaaffea9af458c8e6dff16f15c1a73eqId2b48ba4c6112492987d51b451a7088c8,…,eqId0926f6c8f74748d784074f0759f0f374的平均数为10,方差为2,则数据eqIdf2f592b6c54340f8a4b0894c89688fb4eqIdf7531b3ff8ed4f598ab2eaa5573fb0f7eqId45fa66aa51a94e78ac49a4ae32d49391,…,eqId0e71fa662df24729b87f621378576c3a的平均数为________,方差为________.

五、解答题添加题型下试题

18. 已知eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1分别为eqId64b9b599fdb6481e9f8d9a94c102300b三个内角eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的对边,且eqId3b798648b226493888fd5abb334b9ecbeqIdda43591caa9542f780355a1d58dae3c1eqId1718cbf360734377b5e9f2c554f7e7e9
(1)求eqIdaea992e70d4943e49e893817eb885ed7eqId64b9b599fdb6481e9f8d9a94c102300b的面积eqId1b7d8b87b50e4cfdbf89d48980209a52
(2)若eqId0cd8063abf2b458f80091bc51b75a904eqId0627be51821d4be7b3e024a354815d64边上一点,且,______,求eqIdee1cbe7a8e3043db83620753699f6af3的正弦值.
从①eqId9244d0dcab2d4e348a49df61d474ae87,②eqIda26cb633916942c7a198adf44e734585这两个条件中任选一个,补充在上面问题中,并作答.
19. 在四面体eqId97af93bc48424679a970c09ac8f447cd中,点eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175eqId2381423d4cd146cab95f55527681a766分别是eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqId0627be51821d4be7b3e024a354815d64eqId34c6b6e427744abfb88dc90b8c7c2111的中点,且eqId76d7720851f643ebbe225e2bac80810aeqId9dd38d49033941988157d49ce91524dc.
说明: figure
(1)求证:eqIda5e4dd5d4b81428cbff4de50c7bf234c平面eqIda3c6f0e7f58b4f259c1664244e2084e8
(2)求异面直线eqIdcf2da96900c948a1b3ce7cbfd420c080eqId1b51efe7c2fa42748ac5a6be262e2fa4所成的角.
20. 溺水、校园欺凌等与学生安全有关的问题越来越受到社会的关注和重视,为了普及安全教育,某市组织了一次学生安全知识竞赛,规定每队3人,每人回答一个问题,答对得1分,答错得0分.在竞赛中,甲、乙两个中学代表队狭路相逢,假设甲队每人回答问题正确的概率均为eqId5f51ce9cc7fe4412baeb871cceb26665,乙队每人回答问题正确的概率分别为eqIdb6c439d70fd54c348ec88cefcd62be34,且两队各人回答问题正确与否相互之间没有影响.
(1)分别求甲队总得分为3分与1分的概率;
(2)求甲队总得分为2分且乙队总得分为1分的概率.
21. 如图,在三棱锥eqId12175c05cfe240a0b8270ee03df1962f中,eqIde78cce043a6c43329b55788351ff3484底面eqId89fbdcb029be4482b52165366491c70feqIdeecb96c84ba340069d573f6c1caefbbbeqId22c42ea54d614056ac7901b1de2c41db,点eqId0cd8063abf2b458f80091bc51b75a904为线段eqIdcf2da96900c948a1b3ce7cbfd420c080的中点,点eqId93cbffaa5ae045d6ac45d1e979991c3a为线段eqIda4133d812272499891a1f8813d5747f8上一点.
说明: figure
(1)求证:平面eqIde3f1e1baea654cbf8b97c994b94f3f6e平面eqId1bf8da710ed845aaadfe28ce37f184f2.
(2)当eqIda0b826143be84f39822399489e12ec84平面eqId076f835a1f2c428898c79204bd1d52fd时,求三棱锥eqIdbc4ee36eb33b44249b77b80bebf978a4的体积.
22. 2020年开始,山东推行全新的高考制度,新高考不再分文理科,采用“3+3”模式,其中语文、数学、外语三科为必考科目,满分各150分,另外考生还需要依据想考取的高校及专业要求,结合自己的兴趣爱好等因素,在思想政治、历史、地理、物理、化学、生物6门科目中自选3门参加考试(6选3),每科满分100分,2020年初受疫情影响,全国各地推迟开学,开展线上教学.为了了解高一学生的选科意向,某学校对学生所选科目进行线上检测,下面是100名学生的物理、化学、生物三科总分成绩,以组距20分成7组:[160,180),[180,200),[200,220),[220,240),[240,260),[260,280),[280,300],画出频率分布直方图如图所示.
说明: figure
(1)求频率分布直方图中a的值;
(2)由频率分布直方图;
i)求物理、化学、生物三科总分成绩的中位数;
ii)估计这100名学生的物理、化学、生物三科总分成绩的平均数(同一组中的数据用该组区间的中点值作代表);
(3)为了进一步了解选科情况,由频率分布直方图,在物理、化学、生物三科总分成绩在[220,240)和[260,280)的两组中,用分层随机抽样的方法抽取7名学生,再从这7名学生中随机抽取2名学生进行问卷调查,求抽取的这2名学生来自不同组的概率.