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河南省新乡市第二中学2019-2020学年高三上学期第四次月考数学(理)试题
适用年级:高三 试卷类型:月考 试题总数:22 浏览次数:60 上传日期:2020-05-23
更新:2020/05/23难度:0.85题型:单选题组卷:379
2 . 若直线eqIdb1b2ff3316ce43feaaca2ba31c9b869c与圆eqIdd427dd2f0f634c99a2abe4a57044452e相交所得弦长为eqId5d04f8a500ff47769300856360b7f29a,则eqIdd33c7c1015944e2b81de4ff8695de842(   )
A.1B.2C.eqIdcd9b24a6a6e5426ab775be20461174e3D.3
更新:2020/05/23难度:0.85题型:单选题组卷:596
3 . 抛物线eqId8f87ffbd43a04eb8bafe0f3d1c2702a1的准线方程是eqId0d53f8a482854e2bba881bf7412e5a3a,则实数eqId783c5f01aa1e49b29f88c27d2eca4354(   )
A.eqId6c134c414a5e4643849c88caa4d6a5f0B.eqIddda48cced83d424b89b7d8f8c62b1056C.eqIdca7f979b4aed44608faf40debecd18b1D.eqIde72c898310bf4fb1a72beeaf8a335d66
更新:2020/05/23难度:0.85题型:单选题组卷:234
4 . 已知eqId6a49d6a75a274fad89d146bd685326e8eqId37d1a37c2b8441fba2309a1b0f0d8845pq的(   )
A.充分而不必要条件B.必要而不充分条件
C.充分必要条件D.既不充分也不必要条件
更新:2020/05/23难度:0.85题型:单选题组卷:178
5 . 一个圆锥的底面和一个半球底面完全重合,如果圆锥的表面积与半球的表面积相等,那么这个圆锥轴截面底角的大小是(   )
A.eqIdef27c2db0d3d4d34b1f7a17fdadda355B.eqId44f15ecc6b094edf8e97a6208a254053C.eqIdd6a4ffb2ff824cc69667031a754ada5cD.eqIdb9383ae687874bf9a7a4a81aefe24376
更新:2020/05/23难度:0.85题型:单选题组卷:202
6 . 已知F是双曲线eqId6ad074cfa73749d39264d50c7a29780fk为常数)的一个焦点,则点F到双曲线C的一条渐近线的距离为(   )
A.2kB.4kC.4D.2
更新:2020/05/23难度:0.85题型:单选题组卷:148
7 . 关于函数eqId40c6dcee4f054141b0d850f5ee8eb03b在区间eqId5c76bbf7f1514fd8b112defc7d7b38fb的单调性,下列叙述正确的是(   )
A.单调递增B.单调递减C.先递减后递增D.先递增后递减
更新:2020/05/23难度:0.85题型:单选题组卷:284
8 . 在棱长为a的正方体eqId588284d93dc5489295f8f224f8e30d13中,EFM分别是ABADeqIdea82c30b37894b1bb742dee61200db07的中点,又PQ分别在线段eqId31581e8b21734ef88d2a14232de7e7a6eqId9773922f56d549e18e0f97d076771cb7上,且eqIdbbab1754fe4a42e1b70bcbaf6478b123,设平面eqIdaf832b7838284837bcab96c8ea614e87平面eqId27e2b3cffb3f4d7b84287f74f004ce1c,则下列结论中不成立的是(   )
figure
A.eqIdaf987d25f3d14859b02c68327fa3cc18平面eqIdccc64d3cf9f347bfa9a613f5c0d16c58B.eqId1b43866a15c9453eba593b62db04cfd7
C.当eqId279c5501beef468b9ece619a87e2d176时,平面eqIdec01ad6ef3b44679aa709551515f74a7D.当m变化时,直线l的位置不变
更新:2020/05/23难度:0.65题型:单选题组卷:271
9 . 已知抛物线eqId294af0137a7a4b2f873817ba8fbafb44F为抛物线的焦点且MN为过焦点的弦,若eqIdb2e85bc4859a418db2a91bece1c9d47beqIdde4573f2429c4a4c9f681eea255460f1,则eqId9d077b0e8046474baac2bfb36c94af2b的面积为(   )
A.eqId2644c4fd7d684e75ae5ed93cb3581244B.eqId09e05062a16b4f488a1f9b4f661d0c75C.eqId03859367a9b64a56ab90e31a0cec909aD.eqIda153c848bd2847b4a61b1487a5a5079b
更新:2020/05/23难度:0.65题型:单选题组卷:232
10 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,内角ABC所对的边分别为abc,且eqId99da8581a0014e0eafcb41ea8bda57db.若eqIda08ce385279d41c789695fb651b17890eqId64b9b599fdb6481e9f8d9a94c102300b的面积为eqId92fb54e2a5d64707833e6bdf41097979,则eqIdcc3f0f44c2de4b19a948f212a5c85301(   )
A.5B.eqId2644c4fd7d684e75ae5ed93cb3581244C.4D.16
更新:2020/05/30难度:0.65题型:单选题组卷:848
11 . 存在点eqId20ed9c34348a4ba3872faa567169c153在椭圆eqId15bfbddeee0143e08c809ecf76ffb129上,且点M在第一象限,使得过点M且与椭圆在此点的切线eqIdb0d72122ba914d84a86aeb8508cbe51a垂直的直线经过点eqId73bd213c3ab54c3d993213815ac7a2f6,则椭圆离心率的取值范围是(   )
A.eqId70e6c3520a51468489b383b5919ec8b7B.eqIde7495324ec2446c0adcdfd21afd2beb6C.eqId68686bc4de3144e9a06433a6156d3cb2D.eqIddc03fb53633f4b31b3de2539c87d7dad
更新:2020/05/23难度:0.65题型:单选题组卷:0
12 . 已知正三棱锥eqId97af93bc48424679a970c09ac8f447cd的所有顶点都在球eqId2efda802d5534f6d92d9f8af7aaec28b的球面上,其底面边长为4,eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175eqId92869ac114124367b45f631d030ed6bd分别为侧棱eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIdcf2da96900c948a1b3ce7cbfd420c080eqIdbf4db7d066034b139ff80a09ab139d45的中点.若eqId2efda802d5534f6d92d9f8af7aaec28b在三棱锥eqId97af93bc48424679a970c09ac8f447cd内,且三棱锥eqId97af93bc48424679a970c09ac8f447cd的体积是三棱锥eqId5054cac39fe6489ea40200b9274caf2d体积的4倍,则此外接球的体积与三棱锥eqId31400eec3c3c4e3eb8a1e70d309eb115体积的比值为(   )
A.eqId91b497baccfb423b846c231ec31a172bB.eqId72c7db9127184b709e33ecffe967a86cC.eqId139ee5dbf44a4dbc8ee868550b97c9f6D.eqId4ba8d1fea210430383b94fb6b9224ee4
更新:2020/05/23难度:0.4题型:单选题组卷:207
13 . 若双曲线eqId0f14428848fa4e8cbdaccdcb9711090d的两条渐近线斜率分别为eqIdd4bf9298f0db4fb5afb67e0d739f3074eqId75fdb198d83447e59e31c1f4923cc3bc,若eqIdc1937f398b974ad1b83bd4d9ea9c9532,则该双曲线的离心率为________.
更新:2020/05/23难度:0.85题型:填空题组卷:239
14 . 已知在等差数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqIdca1ae6b26e374c4db4775f8b7ef631b2eqIdbb5a8fde0cd44d75a6ce0aea350cea1d,前n项和为eqIddb5481de79c946c0a760143297d5eade,则eqIda53c861ef26c46368a29295614721567________.
更新:2020/05/23难度:0.85题型:填空题组卷:553
15 . 已知抛物线eqIdf91aad2290ad408799ceac6f8a03ae91的焦点和椭圆eqIdc5ecf5c8a6a64d7492c7a2876523baed的右焦点重合,直线过抛物线的焦点eqId63db14a5b4334f3ea583c8fb12b0d175与抛物线交于eqIdbedf755e0fdb4d078d6859360706b163eqId75a143b898e14ccdb032561fba9da811两点和椭圆交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,eqId2381423d4cd146cab95f55527681a766为抛物线准线上一动点,满足eqId0babcecaa000426f8194e5e7519eb901eqId974854d4b9e24e0aac568895b329ad9a,当eqId04c35937f36b432d92235f094013b289面积最大时,直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3的方程为______.
更新:2020/05/23难度:0.4题型:填空题组卷:130
16 . 已知三棱锥eqId12175c05cfe240a0b8270ee03df1962feqId829c3b65802b41feb4db730b8af793c5eqId64b9b599fdb6481e9f8d9a94c102300b是边长为4的正三角形,eqId0cd8063abf2b458f80091bc51b75a904eqId93cbffaa5ae045d6ac45d1e979991c3a分别是eqId6f782d71f5a7422aa78bd8204949ce26eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点,eqId63db14a5b4334f3ea583c8fb12b0d175为棱eqId0627be51821d4be7b3e024a354815d64上一动点(点eqId19a4eb16029e4550a14f2afe4741a3c3除外),eqId7d84495a10204c67a2d2dd93f9d0fc1f,若异面直线eqIdcf2da96900c948a1b3ce7cbfd420c080eqIdf6f5c737ab8c49e08d2129bee38fdfe0所成的角为eqIdf9db0aee08264a238b9741675591065e,且eqIdd0f2ca48c27d48cdb5891155a24e29a1,则eqIdfc27ac3260d04b38bd818634d4401fe5______.
更新:2020/05/23难度:0.4题型:填空题组卷:150
17 . 在数列eqId93e38ecd74a24cb59da79181b95bfd3a和等比数列eqId5e64dd99b8164af5a9d8a78f16208f07中,eqId3fdd9265022344acb9ce2be3ca387ba3eqId175ba2764e9c4c419547792f94c11e6feqIdb5914b09aacf4ad39332f3e2998ebf5c.
(1)求数列eqId5e64dd99b8164af5a9d8a78f16208f07eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)若eqId358929fcc3464f3d88bb0e4d77a0968a,求数列eqIdb691f3cef6cd413c89f181dc2426e8ce的前n项和eqIddb5481de79c946c0a760143297d5eade.
更新:2020/05/23难度:0.65题型:解答题组卷:572
18 . 如图,在四棱锥eqIddd5f333edd7c4a01b271754239943f8d中,平面eqId1696ce98d8ce40588bd2be63a1ef4872平面ABCDeqIdb26044745dc940609a90050b627ea710eqIdc2ee86d63c0f4025a28b8205723e0321,底面ABCD是边长为2的菱形,点EF分别为棱DCBC的中点,点G是棱SC靠近点C的四等分点.
figure
求证:(1)直线eqId4b81563e05a84c29a3d87224094fb792平面EFG
(2)直线eqIde2a08563fb0140d3b16360de6f7d6c7a平面SDB.
更新:2020/05/23难度:0.65题型:解答题组卷:277
19 . 设抛物线eqId7e148e9b5def4bf1af4353dbf1ccc544过点eqIde8f301038a7a49f184dd08c555ba29bb.
(1)求抛物线C的方程;
(2)F是抛物线C的焦点,过焦点的直线与抛物线交于AB两点,若eqId1eb1c7350dcd46f19225a5083cb8ef17,求eqId66ba99fc247f4e37bbfea682679b3146的值.
更新:2020/05/23难度:0.65题型:解答题组卷:194
20 . 已知在四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,eqIde78cce043a6c43329b55788351ff3484平面ABCDeqIda0af5876813c412e81346f492ae6c7c6,在四边形ABCD中,eqId4b15129480ae41128d094331d3781be5eqId785a1c870ceb45ae936e4f703ba50e70eqId41dd4d30e43847c1b31da0790872de8fEPB的中点,连接DEFDE的中点,连接AF.
figure
(1)求证:eqId8eaed44fd3de4bd299d032a58b787098
(2)求点D到平面AEC的距离.
更新:2020/05/23难度:0.65题型:解答题组卷:211
21 . 已知函数eqId3ce9bb009ba84ec29656ae7fed3ad146.
(1)求eqId6f13759e937144069819aed2ae5a1057的单调区间;
(2)讨论eqId811ef3e4409640679f444cc0f704ab30零点的个数.
更新:2020/05/23难度:0.65题型:解答题组卷:443
22 . 已知椭圆eqIdf8ef9ec340b848fc8802eec4cf1a8b89eqIdf18b5700afd748c9af08fbce0977010b的离心率为eqId767acf51abfd4d97a757561d1a882151,直线eqId417e80f1349244878d01fe90e0891f5feqId4a4dbef515464d88a39f688f1c9bc458与以原点为圆心,以椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的短半轴长为半径的圆相切.eqIdcc614bd3390c4d028df189b234dcc351为左顶点,过点eqId90085281db004c739f2f6436ec2669fa的直线交椭圆eqIdf8ef9ec340b848fc8802eec4cf1a8b89eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3两点,直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIdcf2da96900c948a1b3ce7cbfd420c080分别交直线eqIdd59777a92d8f4da290823fc3dc6b5c26eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点.
figure
(1)求椭圆eqIdf8ef9ec340b848fc8802eec4cf1a8b89的方程;
(2)以线段eqId996e2048847f41d5a5fe0e2282909254为直径的圆是否过定点?若是,写出所有定点的坐标;若不是,请说明理由.
更新:2020/05/23难度:0.4题型:解答题组卷:130