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江苏省常州市第一中学2019-2020年高二上学期期中数学试题
适用年级:高二 试卷类型:期中 试题总数:22 浏览次数:66 上传日期:2020-04-04
1 . 已知命题p:∃x∈R,使tanx=1,其中正确的是(  )
A.¬p:∀x∈R,使tanx≠1B.¬p:∃x∉R,使tanx≠1
C.¬p:∀x∉R,使tanx≠1D.¬p:∃x∈R,使tanx≠1
更新:2020/05/30难度:0.85题型:单选题组卷:63
2 . 椭圆eqId59bc86495cca4c85b0931154bfa16016的左右焦点为eqIdf63bd695cded4f1aad8f6594e65cc44e,一直线过F1交椭圆于AB两点,△ABF2的周长为( )
A.32B.16C.8D.4
更新:2020/04/04难度:0.94题型:单选题组卷:775
3 . 已知数列eqId054d5a7de5684002909fe944c86227c2满足eqIdc392506c5d084f30bb06b947867fa24f,且eqId2eab301538d74849ade5448fcbca81f1成等比数列,则数列eqId054d5a7de5684002909fe944c86227c2的通项公式为(    )
A.eqId68738b1827174995971ad0b1ae61b4dbB.eqId13c00c475b134ba4bad70d46f3fe905eC.eqIdc96b26a18c7a4b6389cbeb5e1c5aaf2cD.eqId7c0deee61d894c25a14b237d0a13cbb8
更新:2020/04/04难度:0.85题型:单选题组卷:832
4 . 不等式eqId3697f6db1959403193824578eecf1af7的解集为R,则a的取值范围为(   )
A.eqId96b0ae9748c445cf94e1c659423c46b5B.eqId31471f4532aa4305a3aa0201791cefb6C.eqIdc229e990ee1a481db198959f47c0c677D.eqId96b1aedb27c44f15ad6eaf58414cea0d
更新:2020/04/04难度:0.94题型:单选题组卷:178
5 . 已知条件peqId7cbd022739e1417c91112e6ded5a0a2e;条件qeqId830fca6b53d146c490c2b95d9e98e5ff,若qp的充分不必要条件,则实数m的取值范围是(   )
A.eqIdd96fc10bdd764b45925272a311dd746fB.eqIdc91c2d7f032146deb56bc1b851a70ddd
C.eqId9519a44c8442409ca793c00e3c968d34D.eqIddf53afc736b84c5ba06450e73b972115
更新:2020/04/04难度:0.65题型:单选题组卷:23
6 . 设eqId5f04473e64c141bcbe9b0a8af27f4aa8是双曲线eqIdd1b75aad05e94c42af9b6d0580b302ba的两个焦点,eqIdbedf755e0fdb4d078d6859360706b163是双曲线上的一点,且eqId6d2f5e95452f432c9a7ec49f5de8731b,则eqId4cd2c77f45b74c709061330d26be4e39的面积等于(    )
A.eqId03859367a9b64a56ab90e31a0cec909aB.eqIdaba042ed0e954a03b435e391ca6a552e
C.24D.48
更新:2020/04/13难度:0.65题型:单选题组卷:269
7 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和为eqId5f7c64b55c1e4664a54776c9ea9b2b0f,且eqId93e38ecd74a24cb59da79181b95bfd3a既不是等差数列也不是等比数列,则k的值为(   )
A.0B.1C.2D.eqIdc14e31598ba946ecb74ef3970711d186
更新:2020/04/04难度:0.65题型:单选题组卷:21
8 . 已知点eqIdc4f74c92876a42958f07b07acbd924c9eqIdbccc312a5c924131b96f332405964d60是椭圆eqId8884cb65a4764caeb55f4ce3b8fcaf43的左右焦点,点P是该椭圆上的一个动点,那么eqId85bfba65d1c04a10afa96c9a3242383e的最小值为(   )
A.0B.1C.2D.eqId2644c4fd7d684e75ae5ed93cb3581244
更新:2020/04/04难度:0.85题型:单选题组卷:5
9 . 设等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和为eqIddb5481de79c946c0a760143297d5eade,若eqIdbb1fba07f88342f2987257bf13fee30ceqId78dd70e756f14d1bbffa8223e2ae5eda,则eqId70caa757fdf6418b92c46142cbec7f0feqIdc9dc79e3fdab4b79a3ef8885322e2d5aeqId8046b4e659174093853841a40cbf146c,…, eqId2491e4b6fa494bc3a40f9a7a4e875278中的最大是(   )
A.eqId8046b4e659174093853841a40cbf146cB.eqId2d15da7045534a0fbb7ea70a748864d3C.eqId2813b6e9de6c44f897bf5ed2acbf8bb8D.eqId56e3bd2ef9fa4a2ba90cf811cfe1fa3a
更新:2020/04/04难度:0.65题型:单选题组卷:157
10 . 设椭圆eqIdd448b721bc2f41f8bed63e9521739ce3的左右焦点分别为eqIdc4f74c92876a42958f07b07acbd924c9eqIdbccc312a5c924131b96f332405964d60,焦距为eqId3c880ae4e9054c509a18f0df84afc7fa,点eqId199ba68fc16d47f2b9adf9c3a7dc8b7d在椭圆的内部,点P是椭圆上的动点,且eqIdf8b4f837d0f445d4a3331710d2578be2恒成立,则椭圆的离心率的取值范围为(   )
A.eqIdcc4c64688625488bbd4ea4c0742ca5eaB.eqId235b684d7647447688d606db52f2e218C.eqId65f21579814e494b8a006949f2c9777aD.eqId716f4dafb0c34123b4bf3cb96fbd35ce
更新:2020/04/04难度:0.4题型:单选题组卷:27
11 . 已知方程eqId0a1206664ff74f0abb9be76383082b31表示的曲线C,则下列判断正确的是(   )
A.当eqId497d29e603dd4eff89a2fbc29a105300时,曲线C表示椭圆;
B.当eqId4387eb54b57f4f8f841d34eca43d286deqIdb8142f7566554fe2a6119dcac2aa8289时,曲线C表示双曲线;
C.若曲线C表示焦点在x轴上的椭圆,则eqIdf6f61728568c425e85c5f648823f0ec7
D.若曲线C表示焦点在y轴上的双曲线,则eqId4387eb54b57f4f8f841d34eca43d286d
更新:2020/04/04难度:0.65题型:多选题组卷:74
12 . 已知等比数列eqId93e38ecd74a24cb59da79181b95bfd3a的公比为q,前n项和eqId95b8c8174b054abe8d11e9a5299312b1,设eqIdd330cf9c3da942ebae1222a3f40a973b,记eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前n项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,则下列判断正确的是(   )
A.若eqIdf1d502b240bc43a581ef8425cb95f991,则eqId11fb74e3918d4b4c90e8851e7a53b89aB.若eqIdfba8f48803dc41e59d7e43199f81de7b,则eqId2ac386fb9d564dd48378cd00547f1db6
C.若eqId4c308c0d5e9c4dd292e9dfbe5b996738,则eqId2ac386fb9d564dd48378cd00547f1db6D.若eqIde52ed85ac98f4ab89363ad6fba87b7f9,则eqId2ac386fb9d564dd48378cd00547f1db6
更新:2020/04/04难度:0.15题型:多选题组卷:13
13 . 点P到图形C上每一个点的距离的最小值称为点P到图形C的距离,那么平面内到定圆C的距离与到定点eqIdcc614bd3390c4d028df189b234dcc351的距离相等的点的轨迹可能是(   )
A.圆B.直线C.椭圆D.双曲线的一支
更新:2020/04/04难度:0.65题型:多选题组卷:8
14 . 直线eqIdb887d3ed1d1c47edbc220e113246642e为双曲线eqIda3dc8ed52c4a473694b8116e30ac1b7c的一条渐近线,则eqIdaea992e70d4943e49e893817eb885ed7的值为__________
更新:2020/04/10难度:0.85题型:填空题组卷:415
15 . 已知实数4,m,9构成一个等比数列,则圆锥曲线eqIde9eea6a0b120494e9d0134635e7922a5的离心率为________.
更新:2020/04/04难度:0.65题型:填空题组卷:6
16 . 已知正数xy满足eqIdc60939f5e3b8405cbcf5ccf0c869527e,则eqIdbd07d13ae13b482dae07ace4ed8a0aac的最小值为________.
更新:2020/04/04难度:0.65题型:填空题组卷:29
17 . 已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和为eqIddb5481de79c946c0a760143297d5eade,公差为d,且eqIddc915f990b1d47438fb2794894c7b773eqIdfd784c7b198c46b997d1a5432264d4cb,其中eqIdcb76cddb8be94be18e0b5bfd4d806a3f为常数且eqId91e620c61948404a9c98ad3a2caa729a等比数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的首项为1,公比为eqIdafc1517f15f3415db1f7734f22351fd7,前n项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,若存在正整数m,使得eqId11abe0cd8ff54f5cbf915b13c9e4fe87,则eqId5512abdadb95474a84550c0bb477fd32________.
更新:2020/04/04难度:0.4题型:填空题组卷:42
18 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,设椭圆eqId15bfbddeee0143e08c809ecf76ffb129的左右两个焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,过右焦点eqIdde963a24921f4ee7a991bf9d4f43a42e且与eqId8e15963708e9415da25069fea5906e24轴垂直的直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3相交,其中一个交点为eqIda5c2bc0cbcba46a0b4cbb9db169710b4.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)若椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的一个顶点为eqId56e2f95406f74dcc9e31c9ad37561288,直线eqId078a55bed08847b4b2fa537fd90d14d4交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3于另一点eqId517584fed25c413ba8b7bb33ffa2d5c6,求eqIdceaedb2d99b64e1ca3ad0e0a8ff72b2f的面积.
更新:2020/04/04难度:0.65题型:解答题组卷:531
19 . 设数列eqId93e38ecd74a24cb59da79181b95bfd3a的各项均为正数,eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和eqIdbb7edba16153460281b657f002c49539eqIdc73ad4de0ec14cba91db08ec61124907
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)设数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63eqIdbef5b582d2b048de9ca8fbe82639d00aeqId01a5e18204a9418d8c2e96845f5efd5deqId92e21db2171e4c96b87d96826d7e827f),eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前n项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,若eqIdc08da7b408d44d0da03bec58b9557346对于eqIdc73ad4de0ec14cba91db08ec61124907恒成立,求λ的范围.
更新:2020/04/04难度:0.65题型:解答题组卷:31
20 . 如图,有一块边长为1(eqIdef715f02e03c4a6cab652b54c69ae711)的正方形区域eqId5ce7a06ae7a34393b92b5277978ac014,在点eqIdcc614bd3390c4d028df189b234dcc351处装有一个可转动的小摄像头,其能够捕捉到图象的角eqIdf31475fa3f0848f494384b992f22225c始终为45°(其中点eqIdd7be5abad1e34f6db17a56660de8d54feqId75a143b898e14ccdb032561fba9da811分别在边eqId0627be51821d4be7b3e024a354815d64eqId34c6b6e427744abfb88dc90b8c7c2111上),设eqId8f35e8dd1f494ced801b84dbd6205ee0,记eqId77ff490a2b71444fb112392d61fd9fb5.
figure
(1)用eqId32454977564e4ee18da36bd51156c509表示eqId4ea1af672e334fb1a6a3ab675d494e72的长度,并研究eqIdc8df1f608cb842a5b1549cd556a9c41a的周长eqId417e80f1349244878d01fe90e0891f5f是否为定值?
(2)问摄像头能捕捉到正方形eqId5ce7a06ae7a34393b92b5277978ac014内部区域的面积eqId1b7d8b87b50e4cfdbf89d48980209a52至多为多少?
更新:2020/04/04难度:0.65题型:解答题组卷:99
21 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的首项为1,eqIddb5481de79c946c0a760143297d5eade为数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和,eqIdb9d517f5ce124ffc81f98f4281a89b5c,其中eqIdcf86a3efea6a4f738de6634cd0fe6ad3eqIdc73ad4de0ec14cba91db08ec61124907
(1)若eqIda51bc1cf7fa94123910b97c3006fa605eqIda6dc2d911eaf472a99bf5094df04d636eqId8e365030656747899efaf03c639793c3成等差数列,求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)设双曲线eqId07b1d67362304750895236ed6c08d3f7的离心率为eqIdbab091d5cb4149ca9f0d64ea39129f06,且eqId28bd705e96be4f4a9664e974db1c2bbb,判断并证明:eqIde1b5ac32b8f94aa692ea1edc6b64315aeqIdfe958d7147f6433ca5fc65f3cf12b5bf的大小关系.
更新:2020/04/04难度:0.4题型:解答题组卷:20
22 . 平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,椭圆CeqIdd448b721bc2f41f8bed63e9521739ce3eqIde9c1eda3dc0c4304868ea148d833743f)左,右焦点分别为eqIdc4f74c92876a42958f07b07acbd924c9eqIdbccc312a5c924131b96f332405964d60,且椭圆的长轴长为eqId7bcd573cee334383ad72cc4b179fcfb3,右准线方程为eqIdf9fbcb1bc1f24d9ea3b3cc940257490f.
(1)求椭圆C的方程;
(2)设直线l过椭圆C的右焦点eqIdbccc312a5c924131b96f332405964d60,且与椭圆相交与AB(与左右顶点不重合)
(i)椭圆的右顶点为M,设eqIde1636eca174740a0b0bd266927becc8f的斜率为eqId491d4bd0c5ab4ab2b4ff3a8a1b248dd9eqIdb63ccadd9d1348f7a45824d5e1c38891的斜率为eqId39b176e9ba044d5bbef577f34e5730d3,求eqIdf4e14963d04c4361ae81cd883df54f49的值;
(ii)若椭圆上存在一点D满足eqIda93e2078c45f4c1c9103a1853a07dd30,求直线l的方程.
更新:2020/04/04难度:0.15题型:解答题组卷:33