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黑龙江省勃利县高级中学2019-2020学年高一下学期期末考试数学试题
黑龙江 高一 期末 2020-09-16 25次

一、单选题添加题型下试题

1. 下列选项中正确的是(   )
A.若eqId7e8ba780aaf645a184f7d70865886992,则eqId142fb6f8712a4e04a73b56741b7207aaB.若eqId142fb6f8712a4e04a73b56741b7207aaeqId57f20bfa2b1944708e8f837148e64f67,则eqId9bf2b9850c194baf89f947cc964f9a14
C.若eqId142fb6f8712a4e04a73b56741b7207aa,则eqIdba2e5ba6cb1249f2ad42ba5d138805e5D.若eqId3d835b170e3445c99c7fee987a3502b2,则eqId142fb6f8712a4e04a73b56741b7207aa
3. 设△ABC的内角ABC所对的边分别为abc,若2sinAcosB=sinC,则△ABC的形状为(   )
A.直角三角形B.等腰三角形
C.等腰直角三角形D.正三角形
4. 我国古代的天文学和数学著作《周髀算经》中记载:一年有二十四个节气,每个节气晷(gui)长损益相同(晷是按照日影测定时刻的仪器,晷长即为所测量影子的长).二十四个节气及晷长变化如图所示,相邻两个晷长的变化量相同,周而复始.若冬至晷长一丈四尺五寸,夏至晷长二尺五寸(一丈等于十尺,一尺等于十寸),则夏至之后的第三个节气(立秋)晷长是(   )
说明: figure
A.五寸B.二尺五寸C.五尺五寸D.四尺五寸
同步
7. 在eqIde6adbece3e764446a36462e961a80626ABC中,eqId081ffd50ec3949b296eaa333727485cf.则说明: figure的取值范围是()
A.(0,eqIdd3e88ecbd2db456396e01302a43b93d9]B.[eqIdd3e88ecbd2db456396e01302a43b93d9eqId7a1ead8f5cfa47f1b68f0ca61cd1599aC.(0,eqId87a9bbb6dd564186905f2064b8c22182]D.[eqId87a9bbb6dd564186905f2064b8c22182eqId7a1ead8f5cfa47f1b68f0ca61cd1599a
8. 在eqId64b9b599fdb6481e9f8d9a94c102300b中,eqId0c6ed9972e50496d9678d45f1e25b7eeeqIdba00dd4af19048d7a97e6f1a3882db2beqId4a9c640fe881474a939fb391b4022236,则eqId0718d54f504146f5a96d17cb9f0dcbbf(   )
A.eqId316faba8ed4043c885bfff0de4699d52B.eqId37ca714db275473ca38bbef6b1885ce8C.eqIdfc5a13d488f9498bbecc6fd388b6b967D.eqId7bcd573cee334383ad72cc4b179fcfb3
9. 已知等差数列eqId054d5a7de5684002909fe944c86227c2中,eqIddb5481de79c946c0a760143297d5eade是它的前eqIdf458db68122849abb588feb2e682d9ac项和,若eqId79690a658d4b4e4ea5418b466ae2ed3f,且eqId987dd3dfaf6e4876b8d038599a480e55,则当eqIddb5481de79c946c0a760143297d5eade取最大值时的eqIdf458db68122849abb588feb2e682d9ac值为(   )
A.8B.9C.16D.17
10. 已知等比数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和为eqIddb5481de79c946c0a760143297d5eade,且eqIde1b7986c24c24e0a8626272036ff38a6eqIddc088f297d20483582b4fbe935392b68,则eqIdf4e66c28d90849708c1075e027e82432(   )
A.16B.19C.20D.25
11. 若直线x+ym=0与曲线y=2﹣eqId72c0e5e346074ab9a5ffadedd91e3aa7没有公共点,则实数m所的取值范围是(   )
A.eqId13aade7f9830472b81f9314fc47601a5B.eqId28b5fa1d31b04283a527442a700487c1
C.eqIdff0c8443626e4d40b245d57c142d9d56D.eqId012e1d02eab148a5bdad6bc0c461d64d
典型
12. 唐代诗人李颀的诗《古从军行》开头两句说:“白日登山望烽火,黄昏饮马傍交河.”诗中隐含着一个有趣的数学问题一“将军饮马”问题,即将军在观望烽火之后从山脚下某处出发,先到河边饮马后再回军营,怎样走才能使总路程最短?在平面直角坐标系中,设军营所在区域为eqIdca6dcb39d4cd496c823a7a548198e209,若将军从点eqId79fdaa2ba7ec4f7ebfa76ae225ac0671处出发,河岸线所在直线方程为eqId048cd6998b6a4cc492eddf5aed091787,并假定将军只要到达军营所在区域即回到军营,则“将军饮马”的最短总路程为(   ).
A.eqId5d04f8a500ff47769300856360b7f29aB.eqId780532c2d72742409731cd475a30ac1aC.eqId81df204c88464d80854ddc1ebe158911D.eqId999ea08a1da146f39bf99bdeba9f3d9f

二、填空题添加题型下试题

16. 经过点P(2,1)作直线l分别交x轴、y轴的正半轴于AB两点,当△AOB面积最小时,直线l的方程为_____.

三、解答题添加题型下试题

18. 如图,在△eqId89fbdcb029be4482b52165366491c70f中,eqIdaeaeda2ee48844ce86f5b52f08326ca4eqId0cd8063abf2b458f80091bc51b75a904eqId0627be51821d4be7b3e024a354815d64中点,eqIddad31040fd02475ea52d192682cf59c6.记锐角eqId72d77b2732ae4fe487fb8bb246a9c30a.且满足eqId0151e13c46514bf3aa046e4b0a7a681a
说明: figure
(1)求eqIdb8dffd3595704fd791dd6b613ceaea07
(2)求eqId0627be51821d4be7b3e024a354815d64边上高的值.
20. 已知圆C:(x+2)2+y2=5,直线lmxy+1+2m=0,mR.
(1)判断直线与圆的位置关系,并说明理由;
(2)若直线eqId417e80f1349244878d01fe90e0891f5f与圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqId11ac1550e51640518ac966047848b311两点,求弦AB的中点M的轨迹方程.
21. 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eadeeqId032284ef281340a78dbf643944ff8cd4eqIdafc685ac2e4242b096b4c42dc1b907a5.数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足eqId46d68f4e66cf4136891c86d837a74e34eqIdc5ef5d4d2b7b453a801a28439cdf885a.
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)是否存在正实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c,使得eqIdeeb4ca98872f4e6d91cea28f43fc0b63是等比数列?并说明理由.