充值 服务号
首页>试卷详情页
湖南省江西省普通高中名校联考2020届高三下学期信息卷(压轴卷一)数学(理)试题
适用年级:高三 试卷类型:其他 试题总数:23 浏览次数:66 上传日期:2020-08-02
1 . 已知复数eqIdfba453356b3c4183af78dc0e96c1d935的实部为3,其中eqIdb6e15e51d29a47a7aff44f98b1aafaee为虚数单位,则复数eqId2cd9e2fe3d6540df9399dbefe49ada54的虚部为(   )
A.eqIdfca343da1efc413487359c1551da9dbeB.eqId0ca9d0040a6a4ec3a0b286a55f3ed8d2C.eqId37705e1ef6a84bbdbe88433e75932cdfD.eqIdb6e15e51d29a47a7aff44f98b1aafaee
更新:2020/08/02难度:0.85题型:单选题组卷:166
2 . 已知集合eqId22b4ffa6906d44d0bd4c6782130d695a,集合eqId850be4ed73d948d693d421b6a6314060,则eqId30b0de3389244ed8839e3cb9aa12452d(    )
A.eqId8f3e391dadb242df97990cbcc233f499B.eqIdd9500da2b21447fd97407f47a048bffeC.eqIdf65c9c85c8224adab5cef5958804effdD.eqIdbe424e9b131746b2987ce0b5fee232c4
更新:2020/08/02难度:0.94题型:单选题组卷:268
3 . 已知函数eqIdc9a023831e56430582702703b05e927c的图象如图所示,则函数eqId5eee282dd2cd493a8a2c9c6b76ed6d40的图象可能(   )
figure
A.figureB.figureC.figureD.figure
更新:2020/08/02难度:0.85题型:单选题组卷:301
4 . 设eqIdf229620ac968402d8a3213797242f7d3是夹角为eqIdf1c3337151994ec4b99354c9d54f311c的单位向量,则eqIdfacea5167f3f4b99acbc8f7fbe1a95f6(   )
A.6B.eqId8dc47626058d4291b61c2d73fc1b59f1C.eqIdd1f30dbc126c4c019fb6297ec9249e7fD.7
更新:2020/08/02难度:0.85题型:单选题组卷:199
5 . 已知直线eqIde032e8738ad44165884501dc69b703d8与双曲线eqIdca9bbb19cd4b49ae8f45dbf75ce5374c的一条渐近线交于点eqIdbedf755e0fdb4d078d6859360706b163,双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的左,右焦点分别为eqId5f04473e64c141bcbe9b0a8af27f4aa8,且eqId0f31cd5e7af14ab48e534df87194d259,则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的渐近线方程为(   )
A.eqId3acfc397dd134acea8dc4cab964114efB.eqId50ba8293e66f4311adb087446975eddd
C.eqIdd21c3371586548509aaf59367b994852D.eqId3acfc397dd134acea8dc4cab964114efeqIdad2d7ed4e3f14bb681cd22b0655f74de
更新:2020/08/02难度:0.65题型:单选题组卷:299
6 . 已知eqId64b9b599fdb6481e9f8d9a94c102300b的三边长分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1,面积为eqId1b7d8b87b50e4cfdbf89d48980209a52,且eqIdcf3310efc6114b3d9051641d0c168947eqIdda43591caa9542f780355a1d58dae3c1,则eqIdd6f5d4de976a4571966cc2607e67e6d6的最大值为(   )
A.eqIda2a0ce3781fa4c26b624f5966b7dee44B.2C.3D.eqId65021072e3ee4edc934739d219c8c5e2
更新:2020/08/02难度:0.65题型:单选题组卷:86
7 . 根据下列算法语句, 当输入x为60时, 输出y的值为()
figure
A.25B.30C.31D.61
更新:2020/08/02难度:0.94题型:单选题组卷:777
8 . 算盘是中国传统的计算工具,其形长方,周为木框,内贯直柱,俗称“档”,档中横以梁,梁上两珠,每珠作数五,梁下五珠,每珠作数一.算珠梁上部分叫上珠,梁下部分叫下珠.例如:在十位档拨上一颗上珠和一颗下珠,个位档拨上一颗上珠,则表示数字65.若在个、十、百、千位档中随机选择一档拨一颗上珠,再随机选择两个档位各拨一颗下珠,则所拨数字大于200的概率为(   ).
figure
A.eqIdf033d892d71d42c8ad7eeae3d48dab97B.eqId767acf51abfd4d97a757561d1a882151C.eqId5f51ce9cc7fe4412baeb871cceb26665D.eqIddda48cced83d424b89b7d8f8c62b1056
更新:2020/08/02难度:0.65题型:单选题组卷:337
9 . 在正方体eqId588284d93dc5489295f8f224f8e30d13中,eqId93cbffaa5ae045d6ac45d1e979991c3a为棱eqId8f39d706a505485987ccbb3f6177d72d上一点且eqId07a1867de39e41f681525077e5413223,则异面直线eqId7fd836b3d4ac4d398fb8e461e090364ceqId30ace6b4ce264294a0534221c1b01e26所成角的余弦值为(   )
A.eqId19f87263e6e548369ef0c3ac1a4e2bdeB.eqIdc9e111290d53484cb6f01a14b78882c9C.eqId4069b54524774876a166ece59e6f794fD.eqId578d1360d960420f9728a4fd96957578
更新:2020/08/02难度:0.65题型:单选题组卷:139
10 . 已知函数eqIda8ce3cfeb6b845eaa6aa16e0710f85a5的一个零点是eqId20a8afcf566e45fc930c7d265367b3a6,则当eqIdf15782a6b93b49aeb4285c6f304dbe29取最小值时,函数eqId6f13759e937144069819aed2ae5a1057的一个单调递减区间是eqIdd996f15bd38249f7b7e35e6afefa8c0b  eqId8fbdf36fcfa44dddb74ad17d601f601d
A.eqId652210d3fc1c40a79398a0b4461c3e35eqIdf0dae54f346f4257af9e42d056de5bfdB.eqIda8827d8cf8094ef486a61eacfe8cc9c2eqId9d1256e2390b4cf68a5e75bc1ee3185fC.eqId7dd38f36adc84576b28a19fd93e05693eqId4a4f4c41f7f54910be17cafc9cc7d692D.eqIdafb6fd26bfca49b6880d5a6b3a2ba011eqIdf72829b38e9c4bffa4230c38dae0144e
更新:2020/08/02难度:0.65题型:单选题组卷:140
11 . 已知函数eqIdaae81be6d5c547a2a1113908a88f7890关于点eqIdfd05a3972e464d19984a469738998272对称,若对任意的eqIdee46bf92924d41c787e6fa1de661c2b0eqId77cf386290b142a39d8809f35b175ff6恒成立,则实数k的取值范围为(    )
A.eqId1363f9d6a6554ac0b7dd67900f813ab2B.eqId6a2f3f4d829c49ea80a2943b156dd1ebC.eqId876f0667f9d2407cbd471ccfcd72b049D.eqId20604849d87442e1817267d1781cfb44
更新:2020/08/02难度:0.65题型:单选题组卷:105
12 . 设椭圆eqId6b03804caa7e43d3ba17750b201331f6的左,右顶点为eqId86a53ca115cf4ef68e6573695b8206c6是椭圆上不同于eqIdeb53cb7cb0274f7d8f111c60f824c243的一点,设直线eqIdeef92dab467e4df7b4ab71ad17f2a53b的斜率分别为eqId79df476224874da48567d2482d95e8aa,则当eqIdb295ad35c2544fc7831e5ed7677f8f28取得最小值时,椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的离心率为( )
A.eqIde1490df2d2c84688942d45fd01c90a85B.eqId5f816d038c584dc7a249120298677ef3C.eqId170361f2c13a48679439924a405d8282D.eqIdcf32b3b919f04cc18988c622e750e9f1
更新:2020/08/02难度:0.4题型:单选题组卷:1097
13 . 已知直线eqId42ae91481be34d42b8bf3da945cfefa5与曲线eqId8f005c6110c343339b20c978a7528219eqId5596cae6676e4c60b70945893002ece1处的切线平行,则实数eqId4d2187284c5d4de29906363f7d21f60f的值为_______.
更新:2020/08/02难度:0.94题型:填空题组卷:151
14 . 已知实数xy满足条件eqId2c229fe354a848e696ae7f2e8e59f783,则eqId53579c942ece48a291596c18ca15f13a的最大值为________.
更新:2020/08/02难度:0.85题型:填空题组卷:16
15 . 已知函数eqId0711acc9c5a74d1683ec3df6633e8492eqId2ae988b00be3499786a3510849d92ff2上有两个不同的零点,则实数eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围是______.
更新:2020/08/02难度:0.65题型:填空题组卷:201
16 . 集合eqId539c9d23bb474f57bc548378502af888eqIde8076e2a19a94e3b942f3c00fa2af5e7,若eqIdc7e17aac3f664408a20c2c2cbb4f5426是平面上正八边形的顶点所构成的集合,则下列说法正确的为________
figure
eqId70a27b6ddf6b478285353abb3b1f3741的值可以为2;
eqId70a27b6ddf6b478285353abb3b1f3741的值可以为eqId65021072e3ee4edc934739d219c8c5e2
eqId70a27b6ddf6b478285353abb3b1f3741的值可以为eqIda6e2eb76c057467d9f7b524fb3d102cb
更新:2020/08/02难度:0.4题型:填空题组卷:290
17 . 已知数列eqId054d5a7de5684002909fe944c86227c2的前n项和为eqIddb5481de79c946c0a760143297d5eadeeqId77b3f6b9955e499dbdab033a38779496eqId77cf8281e243482eb987c8a7bf0ee862.
(1)求数列eqId054d5a7de5684002909fe944c86227c2的通项公式;
(2)若eqId26cd98cdd2824482bc8fe307ae32bd82,求数列eqId69fa66742e6b480eb0e55f574b8b7749的前n项和为eqId92ed363a54bd4a8a93df9463bb3af1f5.
更新:2020/08/02难度:0.65题型:解答题组卷:124
18 . 某地区在一次考试后,从全体考生中随机抽取44名,获取他们本次考试的数学成绩(x)和物理成绩(y),绘制成如图散点图:
figure
根据散点图可以看出yx之间有线性相关关系,但图中有两个异常点AB.经调查得知,A考生由于重感冒导致物理考试发挥失常,B考生因故未能参加物理考试.为了使分析结果更科学准确,剔除这两组数据后,对剩下的数据作处理,得到一些统计的值:eqId72b8944f9bb6422b8cf52193fae72c71eqId69d1dae710024bdf9191754807f10707eqId5997a154450f4984a69efe7dd26b40f3其中xiyi分别表示这42名同学的数学成绩、物理成绩,i=1,2,…,42,yx的相关系数r=0.82.
(1)若不剔除AB两名考生的数据,用44组数据作回归分析,设此时yx的相关系数为r0.试判断r0r的大小关系,并说明理由;
(2)求y关于x的线性回归方程(系数精确到0.01),并估计如果B考生加了这次物理考试(已知B考生的数学成绩为125分),物理成绩是多少?(精确到个位);
(3)从概率统计规律看,本次考试该地区的物理成绩ξ服从正态分布eqId995155952a92435790e9f7f7527f4f49,以剔除后的物理成绩作为样本,用样本平均数eqId73ec7781ec9145c88a6838fd00515ac7作为μ的估计值,用样本方差s2作为σ2的估计值.试求该地区5000名考生中,物理成绩位于区间(62.8,85.2)的人数Z的数学期望.
附:①回归方程eqId2ccf81b3e72e4134ba41817cbb82de6a中:eqId5307bf1e93fc46ca946d016c78677a06
②若eqId8c9017335d61491cb88e3f189c18c5ac,则eqIdb044c85258c74fe5b9e0cee6a21cc572
eqId4461990ef1844b4480f52670bfac18cd11.2
更新:2020/08/02难度:0.65题型:解答题组卷:248
19 . 已知抛物线eqId57b7756abc2649419bbcc75e0aecaad9,过抛物线焦点eqId63db14a5b4334f3ea583c8fb12b0d175的直线eqId417e80f1349244878d01fe90e0891f5f分别交抛物线eqId93cbffaa5ae045d6ac45d1e979991c3a和圆eqId6ed6772f9c6e4ef3ad7267b84336f60c于点eqIda8868741942141b8b33361d8e9b03a5b(自上而下).
(1)求证:eqId232cfcba69514390bafa5565a4bf6f4f为定值;
(2)若eqId34a238c56f5e4a1a8ed26a020a783a73eqId7c49ad29518f4d3db9e3c2cdc48dfacceqIdc2f9e83707664f4f9f3c96228f91e00a成等差数列,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
更新:2020/08/02难度:0.65题型:解答题组卷:80
20 . 如图①:在平行四边形eqId5ce7a06ae7a34393b92b5277978ac014中,eqIde86156e38560430c93f2d953c4e80b2c,eqIded42dcfef6df434abaecbc3fc6323fa0,将eqId39726fa171f74d35ae623009d5bf7637沿对角线eqId1b51efe7c2fa42748ac5a6be262e2fa4折起,使eqIdeecb96c84ba340069d573f6c1caefbbb,连结eqIda8a864b9fabf4fb7a377d5f4450895ce,得到如图②所示三棱锥eqId97af93bc48424679a970c09ac8f447cd.
figurefigure
(1)证明:eqIda36d795513d54a13a53061be6e0f72d0平面eqIdd128ff4f83ef4c12aad8920a558a97b7
(2)若eqIddd7fc8bbe932453a85c6eb3aa59cf5a5,二面角eqId5c3c454878944e92afce8af56043fb69的平面角的正切值为eqId807b61b62f09462994e31cf497210538,求直线eqId1b51efe7c2fa42748ac5a6be262e2fa4与平面eqIdd128ff4f83ef4c12aad8920a558a97b7所成角的正弦值.
更新:2020/08/02难度:0.65题型:解答题组卷:383
21 . 已知函数eqId6b8d6ee678f74117937b469a792a5c5d.
(1)当eqIdcafc0fcddbbe41f2a19b236340c0e82b时,求eqId4837c94ef0ff4dcf9b1dda4df363275a的最小值;
(2)若eqIdc877dcb3970a41cc9fbf60b96b052eb6时,eqId11ca756a74ec4b4b9f7c6a23c3b7dfa7,求实数a的取值范围.
更新:2020/08/02难度:0.4题型:解答题组卷:239
22 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqId1d6daeecc2b743c4b7dc94815eea9e89,(eqIdf9db0aee08264a238b9741675591065e为参数),以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqId8e15963708e9415da25069fea5906e24轴的非负半轴为极轴的极坐标系中,曲线eqId3a63d00111554b9e8b896929779a293d的极坐标方程为eqId021a4a8c65af4ceb86356440feb4f9b2,点eqIdbedf755e0fdb4d078d6859360706b163在曲线eqIdcfc8599bedfb4ab4944abf141f348a9a上,点eqId75a143b898e14ccdb032561fba9da811在曲线eqId3a63d00111554b9e8b896929779a293d上.
(1)求曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的一般方程和曲线eqId3a63d00111554b9e8b896929779a293d的直角坐标方程;
(2)求eqIdb30a7f74215a45849f88704ca844a445的最大值.
更新:2020/08/02难度:0.85题型:解答题组卷:59
23 . 已知函数eqIdede6688db71f45e5af0f423e2352fa0a.
(1)若eqIde052bbcb4ee04c788e97e80679050379,求不等式eqIdb7ab9ec4e9844158af9b01ee2169167d的解集;
(2)设函数eqId4837c94ef0ff4dcf9b1dda4df363275a的图象与x轴围成的封闭区域为eqIdc126eb5e474f44328981eb16a7eeb595,证明:当eqId5c67bde74ba042b1a2b4695b6b4d5473时,eqIdc126eb5e474f44328981eb16a7eeb595的面积大于eqIdf2d7d3bff5e542e38bb1b31d9d2fac91.
更新:2020/08/02难度:0.65题型:解答题组卷:99