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北京市陈经纶中学2019-2020学年第一学期高二数学期中试题

适用年级:高二试卷类型:期中试题总数:20浏览次数:0上传日期:2020/3/26
1 . 命题“eqIddfd22fbc6b264ba0b9a64ba634999fc0eqId25be94deaecd40c1a350de9a86026174”的否定是(   )
A.eqIdb940e6eb1cb4452eb06eb321b9356056eqId6fe9956deaff42d69ddb7a1fea480af1B.eqIddfd22fbc6b264ba0b9a64ba634999fc0eqId81788c8d3e6c447c81dddee3bf26824f
C.eqIddfd22fbc6b264ba0b9a64ba634999fc0eqId22585802f2fa4546b38f40d1048e72b3D.eqIdb940e6eb1cb4452eb06eb321b9356056eqId5ee6f2a0cc524550a7171de323e53ed3
难度:0.94组卷:0题型:单选题更新:2020/3/26
2 . .设eqId14a8c8d180cd4ff9b7e5b47b43dc421b是不同的直线,figure是不同的平面,下列四个命题中,正确的是()
A.若eqIdb1db77aa8c324c6cb64a53fa2aaf4273,则eqIdef85d86427e94afea43f7f4727f6ad4dB.若eqId307bce42230d4b1d90b5cced5444728deqIdef85d86427e94afea43f7f4727f6ad4d
C.若eqId61c6564dc3744fbbb8c684366ca6a25aeqId97c60367cc4a49818568a8267440d8aeD.若eqId81cc8a994acd4b8f914f4dcb425d3f11eqId490b8b24ec574d05af18c0dd91820e02
难度:0.94组卷:865题型:单选题更新:2020/3/26
3 . 阅读下列各式,其中正确的是(   )
A.eqIdd3d8f5dc8306458db69bee30a02bfe0fB.eqId1b0247d7880a412883c0d093dc3703ffeqId9571681b7f574f5da47428bc3ba778e6
C.eqId28fa8ad284014f52bc2667617d3592d9D.eqIdb6931793dab74a9d8117d87822e0a940
难度:0.85组卷:0题型:单选题更新:2020/3/26
4 . 在各项都是正数的等比数列eqId93e38ecd74a24cb59da79181b95bfd3a中,若eqId90171c734cb448d989e3c49d55b37f4eeqId9f2a788d2a3143e5a88f7214ef4b5d24eqIde21167e5af3f4bfcb19164fa7e5284e9成等差数列,则eqId5a8242f69ddd4276a04fb0763d91bd14的值为(   )
A.9B.6C.3D.1
难度:0.85组卷:0题型:单选题更新:2020/3/26
5 . 数列eqId5e5086929bc04a68a227cd2743e40c58中,eqId8c20b2ec512c4e6cb31c367665f3e1da,则数列eqId5e5086929bc04a68a227cd2743e40c58前12项和等于()
A.76B.78C.80D.82
难度:0.4组卷:1891题型:单选题更新:2020/3/26
6 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade,则“eqId93e38ecd74a24cb59da79181b95bfd3a为常数列”是“eqId49fe0669de4f42d6a3c499fd703c62b9eqId61cc1c9d7cc048b1b04f0155e1e9c638”的(   )
A.充分不必要条件B.必要不充分条件C.充分必要条件D.既不充分也不必要条件
难度:0.85组卷:0题型:单选题更新:2020/3/26
7 . 已知四边形eqId5ce7a06ae7a34393b92b5277978ac014为矩形,eqIde78cce043a6c43329b55788351ff3484平面eqId5ce7a06ae7a34393b92b5277978ac014,连接eqIdcf2da96900c948a1b3ce7cbfd420c080eqId1b51efe7c2fa42748ac5a6be262e2fa4eqIde9b50933e347462ea824ccc9bf51fc93eqIda4133d812272499891a1f8813d5747f8eqIdd293923b221045898dcc5442f88aa67a,则下列各组向量中,数量积不为零的是(     )
A.eqId3f3a6f6f8c644ef9adffeb16ef350513eqId694be1b220f546a5abf828ac9937ce5dB.eqId39e1708f441549cc8284fb937bd4187aeqId3c84f958a76c488ca1b86ebcf394e232C.eqIde4dea0e15be942e885ca6a3b19e889fbeqId3719fcad464c419291c2d254d26e10f2D.eqId9c743066eeae432ba57e4ba776b42ecaeqId562958597771473895309c568c43467a
难度:0.94组卷:22题型:单选题更新:2020/3/26
8 . 椭圆eqId89a4466d2e4f4e948af19613bf71c85a的左,右顶点分别是eqIdeb53cb7cb0274f7d8f111c60f824c243,左,右焦点分别是eqId5f04473e64c141bcbe9b0a8af27f4aa8,若eqId417c52d027cc4982bbd2bc4a5987ee77成等比数列,则此椭圆的离心率为
A.eqIde41289c7307b48bd893a195b321d250fB.eqId5222c2ea3b544c58bafb590c9238c493C.eqId767acf51abfd4d97a757561d1a882151D.eqId32e593f38beb404dbead779752d399c2
难度:0.85组卷:1454题型:单选题更新:2020/3/29
9 . 正方形eqId5ce7a06ae7a34393b92b5277978ac014边长为1,点eqId93cbffaa5ae045d6ac45d1e979991c3a在正方形eqId5ce7a06ae7a34393b92b5277978ac014外,且eqId22f24fb278ba4b8d9035798700f27bb1,则eqId2d002e9cd33a446dac7b848e4586da04的最大值是(   )
A.2B.eqIdaa636217281449809574f5fb60028f05C.3D.4
难度:0.85组卷:0题型:单选题更新:2020/3/26
10 . 已知两平行平面eqIdc13953f2514e4c8f9c8aaaf5241c33aceqId4eb56f42ca674f2f9c9101b548763159间距离为4,直线eqIdaa33c49fa88a4b15a965e8aee889285c,点eqIdd0a738ffa01240b19c7917bd6a97bb13,则平面eqIdc13953f2514e4c8f9c8aaaf5241c33ac内到点eqIdcc614bd3390c4d028df189b234dcc351的距离为5,且到直线eqId70a27b6ddf6b478285353abb3b1f3741的距离为eqId5d04f8a500ff47769300856360b7f29a的点的轨迹是(   )
A.一组平行线B.两段线段C.两端圆弧D.四个点
难度:0.85组卷:0题型:单选题更新:2020/3/26
11 . 命题“若eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7都是偶数,则eqId4d6d40a0a9ab4d5d89ef5ee949c9456a是偶数”的否命题是__________,该否命题的真假性是__________.(填“真”或“假”)
难度:0.85组卷:0题型:填空题更新:2020/3/26
12 . 在正四面体O-ABC中,eqId359ddeef4d1841749425efc215cda1f2DBC的中点,EAD的中点,则eqId6f89a77c97c84f0a88d519f8c03be5df______________(用eqIde10c5a5cf98c45cabe279aa2c051ab12表示).
难度:0.4组卷:1819题型:填空题更新:2020/3/26
13 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade,且满足eqId4a44404f4d9548f0b70addb5bb0c0168,则通项eqId38e7aab9632e418f8d07479b236353ec__________.
难度:0.85组卷:0题型:填空题更新:2020/3/26
14 . 如图,在长方体eqId588284d93dc5489295f8f224f8e30d13中,设eqId4f3a160f8cc2486db8160a0d6fee22baeqIdb60bb1649c8b41cb935771acc097167e,则eqId7eab43cbde184960993378eef003d4e6__________,eqId0d8b4fe54f084ad0a77f965935dcbbb2__________.figure
难度:0.85组卷:0题型:填空题更新:2020/3/26
15 . 数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIdce257bad7cb447d781207e9c8190e847eqId6c2146ec6df54fc9af9b2aef04489c8b,则eqId38e7aab9632e418f8d07479b236353ec__________,数列eqId83c7283f85694238910b73221c8b8a18中最大项的值为________.
难度:0.65组卷:100题型:填空题更新:2020/3/26
16 . 已知曲线eqId19a4eb16029e4550a14f2afe4741a3c3的方程eqIde707707efcce411e9e95c801987ca0c8,给出下列eqIdddd35c5d043e4ebeac32a99367053c68个结论:
①曲线eqId19a4eb16029e4550a14f2afe4741a3c3是以点eqId4c1d443af674451aa43ffa4f754e6b03eqId54d26c3b27524287934469736797c36b为焦点的椭圆的一部分;
②曲线eqId19a4eb16029e4550a14f2afe4741a3c3关于eqId8e15963708e9415da25069fea5906e24轴、eqId072d7d6b911b42bc89207e72515ebf5f轴、坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b对称;
③若点eqIda733cd9df1394d929d03733bfeda55f8在曲线eqId19a4eb16029e4550a14f2afe4741a3c3上,则eqId54c6f8f452644bbcab90cc703e838208eqId9e9fa19272c84cdcb5a7baa124edb7c7
④曲线eqId19a4eb16029e4550a14f2afe4741a3c3围成的图形的面积是eqId26f1d01cdbbc4f73909a617af5e3e6a2
其中,所有正确结论的序号是__________
难度:0.4组卷:456题型:填空题更新:2020/3/26
17 . 已知等比数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdddd35c5d043e4ebeac32a99367053c68项和eqId2df935d9d0134a9e9c50da381e2e320b,且eqId8948735949d8496b8dd16af5b3d86c98成等差数列.
(Ⅰ)求eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(Ⅱ)设eqIdeeb4ca98872f4e6d91cea28f43fc0b63是首项为eqIdc052ddfbd4524f67a79e0e77c2e5656a,公差为eqId8433a30867ac48f8b3d8940499e2ee8b的等差数列,其前eqIdf458db68122849abb588feb2e682d9ac项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,求满足eqIda94e99b02a5c4ca29ef4a05ee80dde1a的最大正整数eqIdf458db68122849abb588feb2e682d9ac
难度:0.65组卷:695题型:解答题更新:2020/3/26
18 . 已知椭圆E的中心在坐标原点O,两个焦点分别为A(﹣1,0),B(1,0),一个顶点为H(2,0).
(1)求椭圆E的标准方程;
(2)对于x轴上的点P(t,0),椭圆E上存在点M,使得MP⊥MH,求实数t的取值范围.
难度:0.65组卷:77题型:解答题更新:2020/3/26
19 . 四棱锥eqIddd5f333edd7c4a01b271754239943f8d中,eqIdade7975ad42c46d4b9aada13bc22c654平面eqId5ce7a06ae7a34393b92b5277978ac014,底面四边形eqId5ce7a06ae7a34393b92b5277978ac014为直角梯形,eqId397c03e525444a989afc6269369b5cdbeqId1acddecbe2a24d149cbad7e37b42bc75eqId631983261edb4c49a81fb7a7fc943d09eqId790707287e604e1a97e1484c1457c054.
figure
(Ⅰ)求证:平面eqId1696ce98d8ce40588bd2be63a1ef4872平面eqId911194e8bdd14e3a943a486588dc8285
(Ⅱ)求二面角eqIdf0265b51bb6542928884244dfee4aa1a的余弦值;
(Ⅲ)eqId2381423d4cd146cab95f55527681a766eqId17cf387aa11242af969dcfd73db2a4d5中点,在四边形eqId5ce7a06ae7a34393b92b5277978ac014所在的平面内是否存在一点eqId517584fed25c413ba8b7bb33ffa2d5c6,使得eqIdefbe4303bc964cb1bc3a76d308ba961d平面eqId11a1b1d16a2e412784a39dba2b832898,若存在,求三角形eqIddb22c9f59e504a6eb95ad922507412ed的面积;若不存在,请说明理由.
难度:0.65组卷:0题型:解答题更新:2020/3/26
20 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade,且满足eqId35c5b2bf33b64f0a8cbeedc42717d803eqIdbce7c9fbfb41451cb656361fd7b48ad6,设eqId89b299df551f4e46b49413ed77fc65e2eqIdc73ad4de0ec14cba91db08ec61124907.
(Ⅰ)求证:数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63是等比数列;
(Ⅱ)若eqId89504540b7c44fc49d836798d0382095eqIdc73ad4de0ec14cba91db08ec61124907,求实数eqId70a27b6ddf6b478285353abb3b1f3741的最小值;
(Ⅲ)当eqId06cc9b4949ce4809a05ce82e20fa6282时,给出一个新数列eqIda5fe2f95aaf64969913b1e71a2160965,其中eqId4ed5523a2e7d4c11bd1361d2a0fad8f6,设这个新数列的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIdcd8b006a766b441896481934ce8624da,若eqIdcd8b006a766b441896481934ce8624da可以写成eqIddfa8c407d51f4755b02a7efe4960c1e4eqId32454977564e4ee18da36bd51156c509eqId34183d6823814508bb3a469860ca3c01eqIdd1676c2740214139bd95cdd3d448c3d0eqId3ae5584e22d94db98f02990ea85c2c0d)的形式,则称eqIdcd8b006a766b441896481934ce8624da为“指数型和”.问eqId558c17324d4f40c8b990a5f077e40f0c中的项是否存在“指数型和”,若存在,求出所有“指数型和”;若不存在,请说明理由.
难度:0.15组卷:0题型:解答题更新:2020/3/26
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