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广东省深圳市深圳外国语学校2019届高三第二学期第一次热身考试数学(文科)试题
适用年级:高三 试卷类型:一模 试题总数:23 浏览次数:345 上传日期:2019-06-12
1 . 已知集合eqIda16b24d3ff914c3eaf5714d7b64fa81beqIdb140d84657fd46c6963ba00ebf6daea6,则eqId170a03e31a0e4656b66452088e998e61(   ).
A.eqId5fa49633f79b4e55beb70da3295396c1B.eqId5c9d95bbee854c17a3f21ea974773751C.eqId79868eb4843549d88ebd8b14b385c956D.eqIdd36eb18e667f4088ad4a0ac3718e02bb
更新:2019/06/12难度:0.85题型:单选题组卷:425
2 . 已知复数eqId2cd9e2fe3d6540df9399dbefe49ada54是一元二次方程eqIda0c82513c9e3420585ee91dd6ae60a95的一个根,则eqId22ad563438bc4e1084cdf582fd08deef的值为(  )
A.1B.eqId65021072e3ee4edc934739d219c8c5e2C.0D.2
更新:2017/06/17难度:0.65题型:单选题组卷:415
3 . 为考察某种药物对治疗一种疾病的效果,在四个不同的实验室取相同的个体进行动物试验,根据四个实验室得到的列联表画出如下四个等高条形图,最能体现该药物对治疗该种疾病有效果的条形图是(  )
A.figureB.figure
C.figureD.figure
更新:2020/05/24难度:0.4题型:单选题组卷:396
4 . 3名同学各自在周六、周日两天中任选一天参加公益活动,则周六、周日都有同学参加公益活动的概率为(   ).
A.eqIde41289c7307b48bd893a195b321d250fB.eqId4f92ee88ff2f45b69f40d29e22c9da36C.eqIddb6b28cbd8a14caa9cf1146f6f7916c0D.eqIddda48cced83d424b89b7d8f8c62b1056
更新:2019/06/12难度:0.85题型:单选题组卷:337
5 . 已知椭圆eqId15bfbddeee0143e08c809ecf76ffb129的离心率为eqIdf304702bf4d04282970e845827d5a8f8,椭圆上一点eqIdd7be5abad1e34f6db17a56660de8d54f到两焦点距离之和为12,则椭圆的短轴长为__________.
更新:2020/04/05难度:0.85题型:填空题组卷:463
6 . 《孙子算经》中有道算术题:“今有百鹿入城,家取一鹿不尽,又三家共一鹿适尽,问城中家几何?”意思是有100头鹿,每户分1头还有剩余;每3户再分1头,正好分完,问共有多少户人家?设计框图如图,则输出的值是(   ).
figure
A.74B.75C.76D.77
更新:2017/04/04难度:0.94题型:单选题组卷:239
7 . 直线eqId417e80f1349244878d01fe90e0891f5f与平行四边形ABCD中的两边AB、AD分别交于E、F,且交其对角线AC于K,若eqId398cae65bb0e419ca09be71a1eb5046deqId3656b9a16d974cae802e4dc5c6153d85eqIda2780923b6204317b9029752df0aeddc(λ∈R),则λ=(  )
A.2B.eqId2411e237a6024ba5812575d3840e3781C.3D.5
更新:2018/03/28难度:0.65题型:单选题组卷:401
8 . 一个几何体的三视图如图所示(其中正视图的弧线为四分之一圆周),则该几何体的表面积为(  )
figure
A.72+6πB.72+4π
C.48+6πD.48+4π
更新:2019/06/12难度:0.65题型:单选题组卷:369
9 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项eqId9e63860db82e43b287e268e995e2d03a,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqIdf458db68122849abb588feb2e682d9ac项和为eqId46039ddb9f9f4d3586c0df7deb2ff686,若这两个数列的公共项顺次构成一个新数列eqId74ef5fe5183946caaee41d8974816a20,则满足eqIde9ba392811f54bacaec73a3328195639eqId3a4208e0040c42ed8b09de2cae9d562e的最大整数值为(   )
A.335B.336C.337D.338
更新:2017/05/09难度:0.65题型:单选题组卷:624
10 . 已知函数eqIdf0c0763ab97043e19b1caeaa01398ad6,若eqId75edd6ff38f44f73b1a72ae1266165fe在区间eqIdba1ca9eb59d6401b92b38554fac7abd1内有零点,则eqIdf15782a6b93b49aeb4285c6f304dbe29的取值范围是eqId28fe7ea2cdd940a3890be5a8f24864c9 eqId1dff27163d4a47f3a3201b3b8d5ae407
A.eqId0a24e9418ac149c7b791a38b646ca933B.eqIdc5aa08bb7648429ca9241da5449b3fa2
C.eqId17ac220d458a46dfbcb3c40efa1d4b3aD.eqIde68a4c23a1174722898cf5591697149b
更新:2017/05/18难度:0.65题型:单选题组卷:560
11 . 已知点eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3eqId0cd8063abf2b458f80091bc51b75a904均在球eqId2efda802d5534f6d92d9f8af7aaec28b上,eqId78ec6c00ef4340599e76ec72982e0142eqId1a4ee4d443234c40969626092de88c44,若三棱锥eqIda05cf829680e460f9f2ab31071f44695体积的最大值为eqId5f1c5a00ac3e4eb4a8e4afc97d7e78bf,则球eqId2efda802d5534f6d92d9f8af7aaec28b的表面积为(   ).
A.eqId5dcc3f21683f4fb6884a864497a95032B.eqIde835a5f3bdf34b269917bf97d468b3ccC.eqIdfceb10da8b63490dae4fdc016cf362d8D.eqId9ef62b7be5804093921c6279fa677899
更新:2019/12/25难度:0.65题型:单选题组卷:1136
12 . 已知定义在eqId3abaaedd36204e2cacb3fa4073cf99f5上的函数eqId9b37d03e47a347fc8fab9f814ba5fac4满足条件eqIdba47bb1b5fe1447393bfcb5b55a4bfbb,且函数eqIde8d0530ca0d74167a40c50f6d4cb3dc5是偶函数,当eqIde591e963307c4ebba24434528f150ad5时, eqIdd9f4f933027e41fe9aaf8dab2e355e82eqIdbd50864fb5d34cc3acfffd0e3752de6d),当eqId85a36d981c2e400487f2591d615e1d82时, eqId4837c94ef0ff4dcf9b1dda4df363275a的最小值为3,则a的值等于(   )
A.eqIde431dd7c6f9b45ce902a6bff721ae006B.eC.2D.1
更新:2017/06/09难度:0.65题型:单选题组卷:645
13 . 已知实数eqId8e15963708e9415da25069fea5906e24eqId072d7d6b911b42bc89207e72515ebf5f满足eqId6c74f7218aa84808b5d539ae7793ec0c,则eqIda1e9e2b0762f40d4812bedb68cc52f01的最大值是__________
更新:2019/06/12难度:0.65题型:填空题组卷:417
14 . 函数eqId24f583a355b8473ab7f8966ef4ae83c5为奇函数,则实数eqId783c5f01aa1e49b29f88c27d2eca4354__________
更新:2019/06/12难度:0.65题型:填空题组卷:692
15 . 已知双曲线eqId4fcfc672eb974b0b89d13bf0b90677d3的左、右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,过eqIdde963a24921f4ee7a991bf9d4f43a42e且与eqId8e15963708e9415da25069fea5906e24轴垂直的直线eqId417e80f1349244878d01fe90e0891f5f与双曲线的两条渐近线分别交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,eqId429880e36e5b4d81b0a4928d94ae8d5beqIdae20175e487048188efb951d40505268,动点eqId6963133c5a594c13a03d65a3baba484c在双曲线上,则eqId2716e9877d5f4709b295d1ec09fd84c1的最小值为__________.
更新:2019/06/12难度:0.65题型:填空题组卷:376
16 . 已知函数eqId32bf70f29ed649978bb2d28f7869f51b,数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqId5e6e7316bc6240dca1351421916d00a3,则数列eqId93e38ecd74a24cb59da79181b95bfd3a的前40项之和eqId0a7d8109c4d240aea4f788f0782b821d__________.
更新:2019/06/12难度:0.65题型:填空题组卷:329
17 . 已知eqId64b9b599fdb6481e9f8d9a94c102300beqIdcd0d74a708fa43f2bbec04996016045d,角eqId10bbe48f886a4fa78fdf8c1fd064f9b4的对边分别为eqId0ce93bfa1f6a4a23b3258410dd19847a
(1)若eqId0ce93bfa1f6a4a23b3258410dd19847a依次成等差数列,且公差为2,求eqIdad7cefefaba947e1a168bca491c4fca1的值;
(2)若eqId64b9b599fdb6481e9f8d9a94c102300b的外接圆面积为eqId7a1ead8f5cfa47f1b68f0ca61cd1599a,求eqId64b9b599fdb6481e9f8d9a94c102300b周长的最大值.
更新:2019/06/12难度:0.65题型:解答题组卷:1422
18 . 在四棱柱eqId588284d93dc5489295f8f224f8e30d13中,四边形eqId5ce7a06ae7a34393b92b5277978ac014是平行四边形,eqId9ddaee158ef5417d9f78bfa0f17bd117平面eqId5ce7a06ae7a34393b92b5277978ac014eqId0e67152dca434884938a186e656be4c5eqIdca20ea0b15ae4dc29bb20ef4b0f335ddeqId93cbffaa5ae045d6ac45d1e979991c3aeqId31581e8b21734ef88d2a14232de7e7a6中点.
figure
(1)求证:平面eqId81dac8f6b9e94a8c814fe471937c55e6平面eqIdba050c415ebc4dfaa3b3fcc19e35819d
(2)求多面体eqId234a6cb6a55849b78ceba76955bdc046的体积.
更新:2017/05/17难度:0.65题型:解答题组卷:548
19 . 我们国家正处于老龄化社会中,老有所依也是政府的民生工程.某市共有户籍人口400万,其中老人(年龄60岁及以上)人数约有66万,为了了解老人们的健康状况,政府从老人中随机抽取600人并委托医疗机构免费为他们进行健康评估,健康状况共分为不能自理、不健康尚能自理、基本健康、健康四个等级,并以80岁为界限分成两个群体进行统计,样本分布被制作成如下图表:
figure
(1)若采用分层抽样的方法再从样本中的不能自理的老人中抽取16人进一步了解他们的生活状况,则两个群体中各应抽取多少人?
(2)估算该市80岁及以上长者占全市户籍人口的百分比;
(3)政府计划为80岁及以上长者或生活不能自理的老人每人购买1000元/年的医疗保险,为其余老人每人购买600元/年的医疗保险,不可重复享受,试估计政府执行此计划的年度预算.
更新:2018/02/12难度:0.85题型:解答题组卷:281
20 . 已知eqIdcc614bd3390c4d028df189b234dcc351是抛物线eqIdd050af449075401299cc78c647d310e8上的一点,以点eqIdcc614bd3390c4d028df189b234dcc351和点eqIddf1e8ceba67a4f138f6b51f7ff813645为直径两端点的圆eqId19a4eb16029e4550a14f2afe4741a3c3交直线eqId5db4a4f976ba42089c0439595abeb40beqId71891062a8724584af9a2c4c77cd566e两点,直线eqId417e80f1349244878d01fe90e0891f5feqId99a3187c2b8f4bcc9703c74c3b72f1f3平行,且直线eqId417e80f1349244878d01fe90e0891f5f交抛物线于eqIdfcf606636c8549158e75f6db78c50096两点.
figure
(1)求线段eqId996e2048847f41d5a5fe0e2282909254的长;
(2)若eqId74f2bcfd48d94cde9699429ada748168,且直线eqId4ea1af672e334fb1a6a3ab675d494e72与圆eqId19a4eb16029e4550a14f2afe4741a3c3相交所得弦长与eqIdcfb81a24d4b34902a7997513d17fdc96相等,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
更新:2020/02/06难度:0.4题型:解答题组卷:766
21 . 已知函数eqId0afa76a233fe4ed79b9400b7b87ecdc0,曲线eqId9b37d03e47a347fc8fab9f814ba5fac4在点eqId1a862b050261403da2620145236a0572处的切线与直线eqId7921a304b3094405b788a0db6bde4d22垂直(其中eqIdf035b8f27d4645bb9f6a66f4a3f51918为自然对数的底数).
(I)求eqId4837c94ef0ff4dcf9b1dda4df363275a的解析式及单调递减区间;
(II)是否存在常数eqId4d2187284c5d4de29906363f7d21f60f,使得对于定义域内的任意eqId57be5baa4e9a43dbb2eb78791ab82343恒成立?若存在,求出eqId4d2187284c5d4de29906363f7d21f60f的值;若不存在,请说明理由.
更新:2016/10/12难度:0.15题型:解答题组卷:1058
22 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqId49b0155afe9946fb89315ecc9ab05a8eeqId32454977564e4ee18da36bd51156c509为参数).在以坐标原点为极点,eqId8e15963708e9415da25069fea5906e24轴正半轴为极轴的极坐标系中,圆eqIddd65124f5e9f4ddebf8cf3606a06b1ee的圆心为eqId3a63d00111554b9e8b896929779a293d
(1)说明eqIdcfc8599bedfb4ab4944abf141f348a9a是哪一种曲线,并将eqIdcfc8599bedfb4ab4944abf141f348a9a的方程化为极坐标方程;
(2)过原点且与直线eqIdf4a2e3d5aaa1402c9645b412377412cf (eqId32454977564e4ee18da36bd51156c509为参数,eqId2b2e91d596a3481384bbc3975f4ddeb3)平行的直线eqId32ece98e0955476591d5f4a55111a471eqId3a63d00111554b9e8b896929779a293d的交点为eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6,且eqIdfc3868feb54f47bdb0bdfa544d74a268的面积为2,求eqIdc13953f2514e4c8f9c8aaaf5241c33ac的值.
更新:2019/06/12难度:0.65题型:解答题组卷:485
23 . eqId2329690b06914dec8e1f91752f58467b
(1)画出eqId4837c94ef0ff4dcf9b1dda4df363275a的图象,并由图象写出eqId6037963c390547f4b194ba806a9eff55的解集;
(2)若存在eqIdc9f6e33170ea48a797d73c1ca20d4e65使不等式eqId6869ddeb0f4d4e61aa673aad57543474成立,求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
更新:2019/06/12难度:0.85题型:解答题组卷:273