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2016届上海市高境第一中学高三下学期5月热身(理)数学试题
适用年级:高三 试卷类型:其他 试题总数:23 浏览次数:72 上传日期:2020-02-14
1 . 若线性方程组的增广矩阵为eqId47375da9ea594891be094afb537faad9,则该线性方程组的解是______.
更新:2020/02/14难度:0.85题型:填空题组卷:20
2 . 的展开式中的系数是         . (用数字作答)
更新:2020/02/14难度:0.65题型:填空题组卷:600
3 . 若双曲线eqId0ec52df422324ebbb42aaa4b6d2d81bb的一条渐近线方程为eqId880bc3db696f4c2980e83e3353b48e7e,则a= ________________
更新:2020/02/14难度:0.94题型:填空题组卷:524
4 . eqId98b3ba35d8ae406daaa8e113d7909054_________.
更新:2020/02/14难度:0.85题型:填空题组卷:46
5 . 若直线eqId417e80f1349244878d01fe90e0891f5f过点eqId4c33bf068751457396f330d902841106,且与圆eqId7a74452793a34aa0816c74e93747ed60相切,则直线eqId417e80f1349244878d01fe90e0891f5f的方程是________.
更新:2020/02/14难度:0.94题型:填空题组卷:169
6 . 函数eqId4d223455cc414223afb0776ce865aa82的最小正周期是____
更新:2020/02/15难度:0.65题型:填空题组卷:576
7 . 一支田径队有男运动员48人,女运动员36人,若用分层抽样的方法从该队的全体运动员中抽取一个容量为21的样本,则抽取男运动员的人数为____________
更新:2020/03/14难度:0.65题型:填空题组卷:1106
8 . 若行列式eqId6c4013a7490d4901a2cb54dc3d4f808e,则eqId70c52126b23a4d5388d832c32cc794a4________.
更新:2020/02/14难度:0.85题型:填空题组卷:15
9 . 如图,测量河对岸的塔高AB时,可以选与塔底B在同一水平面内的两个测点CD.测得eqIda3faf60a23a34ff78a3b93e642054b75eqIdd94e55c09674438ea34e2fc7cc25ba09eqId22b1566fa80141f88a66bfa34219e5c3米,并在点C测得塔顶A的仰角为eqIdb9383ae687874bf9a7a4a81aefe24376,则塔高eqIdd716dcfa0ae240a7b8da0ced1c7b2b54________米.figure
更新:2020/02/14难度:0.65题型:填空题组卷:105
10 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,圆eqId19a4eb16029e4550a14f2afe4741a3c3的参数方程为eqId1983c42a2cd248338e2650087b9fff9beqIdf9db0aee08264a238b9741675591065e为参数),以原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqId8e15963708e9415da25069fea5906e24轴正半轴为极轴建立极坐标系,若直线eqId417e80f1349244878d01fe90e0891f5f上两点eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c的极坐标分别为eqId3b7f4c18de994306a1b8c772ed314b2feqId8a5f93513bc643f89ae51156e988fb25,则直线eqId417e80f1349244878d01fe90e0891f5f与圆eqId19a4eb16029e4550a14f2afe4741a3c3的位置关系是____________
更新:2020/02/14难度:0.85题型:填空题组卷:53
11 . 圆柱形容器内部盛有高度为8cm的水,若放入三个相同的球(球的半径与圆柱的底面半径相同)后,水恰好淹没最上面的球(如图所示),则球的半径是           cm.figure
更新:2020/02/14难度:0.65题型:填空题组卷:791
12 . 设幂函数eqId482e08ef86c144d4ad6596033b65b5dd,若数列eqId054d5a7de5684002909fe944c86227c2满足:eqIdeef16360a5f14fd9b3aaba18a79162a3,且eqId0fa387098ef24eb399a4bc98dc99d46beqId82d4a42b3490469f8647891a282edde9则数列的通项eqId38e7aab9632e418f8d07479b236353ec________.
更新:2020/02/14难度:0.65题型:填空题组卷:52
13 . 函数y=eqId14e0e21fc2ca4ee1bdf2d49851820ce4的图象与函数y=2sinπx(-2≤x≤4)的图象所有交点的横坐标之和等于            .
更新:2020/02/14难度:0.4题型:填空题组卷:425
14 . 直角坐标平面上,有个非零向量,且,各向量的横坐标和纵坐标均为非负实数,若(常数),则的最小值为        
更新:2020/02/14难度:0.4题型:填空题组卷:1032
15 . 下列函数中既是奇函数,又在区间eqIdc1e1551e600844748738c6200bfc5c44上是增函数的为()
A.eqId0cc175df74834003ba36497fbc3af089B.eqId21418c9e87ef4f30af18655eb0f1785aC.eqIdd11dea1fbcf149828dd62a16f2537678D.eqIdad317b2f220a4d1d8363655bbb0dc56c
更新:2020/06/08难度:0.85题型:单选题组卷:296
16 . 执行如图所示的程序框图,输出的eqId1b7d8b87b50e4cfdbf89d48980209a52的值为(  )
figure
A.eqId37705e1ef6a84bbdbe88433e75932cdfB.eqIdfca343da1efc413487359c1551da9dbe
C.eqId30c998d35a344d80a18e14a8c8f2d14fD.eqIda86879ae304449a4a6e6461c485a1f13
更新:2020/02/14难度:0.65题型:单选题组卷:813
17 . 已知随机变量eqIdc688382b53d04eb9aca74b12c3b14d16的分布律如下:
eqId8e15963708e9415da25069fea5906e24
eqIda86879ae304449a4a6e6461c485a1f13
eqId37705e1ef6a84bbdbe88433e75932cdf
eqIdc052ddfbd4524f67a79e0e77c2e5656a
eqId1720e1de6b5c4ea987a1654472ad184c
eqId70a27b6ddf6b478285353abb3b1f3741
eqIdaea992e70d4943e49e893817eb885ed7
eqIdad7cefefaba947e1a168bca491c4fca1
 
其中eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1成等差数列,若eqIdc688382b53d04eb9aca74b12c3b14d16的均值eqId34d707b256584a60a01348fed009f50a,则eqIdc688382b53d04eb9aca74b12c3b14d16的方差eqIda98daac0a4014583a6a50d328d63e987等于(   )
A.eqId836db6d106e440cd9e5ec0272122b7bbB.eqIda8012d5322b240128851ebf3cd086e12C.eqId5b7fb20e420642068fbd5be267156d14D.eqId5b9776561eae4f2c9c8ebc74647da317
更新:2020/02/14难度:0.85题型:单选题组卷:302
18 . 已知点eqId74f1e72a666f410b90e8e18148c12c1a.若曲线eqId92869ac114124367b45f631d030ed6bd上存在eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3两点,使eqId64b9b599fdb6481e9f8d9a94c102300b为正三角形,则称eqId92869ac114124367b45f631d030ed6bdeqIdbf31c16f10784d76851cf83e57c2eeed型曲线.给定下列三条曲线:
eqId8b8f9e1364654791b2f568fbdf1fe73c
eqId101663766cf142f0a7159370acf20ec3
eqId79194cfabb77419ba3196c44b5f3f759
其中eqIdbf31c16f10784d76851cf83e57c2eeed型曲线的个数是
A.eqIda86879ae304449a4a6e6461c485a1f13B.eqId37705e1ef6a84bbdbe88433e75932cdf
C.eqIdc052ddfbd4524f67a79e0e77c2e5656aD.eqId8898c1dc81824f3098bbeae74e8f11fd
更新:2020/02/14难度:0.4题型:单选题组卷:698
19 . 已知关于eqId8e15963708e9415da25069fea5906e24的不等式eqId333a7163aea74919b64f9535e73a3e99解集为eqId7162192b280e4a7bbb333f3c01c82d2f.
(1)求实数eqId3a4208e0040c42ed8b09de2cae9d562e的值;
(2)若复数eqId93c321ce543744a9b0e54df7d421ef58eqId6612d2fb00d64c44854262e39c12cd41,且eqId93dd08ebcedc4488a9ea5ba69f893dd7为纯虚数,求eqIdfdf226b6dece4a3c9118f7e7bf9290db的值.
更新:2020/02/14难度:0.65题型:解答题组卷:85
20 . 如图所示,直四棱柱eqId588284d93dc5489295f8f224f8e30d13的侧棱eqIdea82c30b37894b1bb742dee61200db07长为eqId70a27b6ddf6b478285353abb3b1f3741,底面eqId5ce7a06ae7a34393b92b5277978ac014是边长eqId8a8d6e47623c45e9be9dd7da221e526beqId34057530424b4e289e5919c5dc60455f的矩形,eqId93cbffaa5ae045d6ac45d1e979991c3aeqId3549028b0a264a919e61d7f350198187的中点,
figure
(1)求证:eqId23854a2bf1824013ac76521ecea384f5平面eqIdc97f045463594160af5f8eed0e81619b
(2)求异面直线eqId1b51efe7c2fa42748ac5a6be262e2fa4eqId13992fb40f4c45c29adf8b5a786e497c所成的角的大小(结果用反三角函数表示).
更新:2020/02/14难度:0.65题型:解答题组卷:36
21 . 设eqId9d619b7d07094a57af8eae0074eedfa4eqId7f2ce998595d4290bdb4b6d8b80d2217为奇函数.
(1)求实数eqId70a27b6ddf6b478285353abb3b1f3741的值;
(2)设eqIdd7df49c4310341bebab721998d5e0276,若不等式eqId2a6d6155c5884d2fae984c3096f41d68在区间eqIdd44e9012bf4c49b496fc1913ff30f552上恒成立,求实数eqId4d2187284c5d4de29906363f7d21f60f的取值范围.
更新:2020/02/14难度:0.4题型:解答题组卷:68
22 . 已知数列eqIddda09b6ac34b42f5996ad5a6d4bca970.如果数列eqId542f6c90b11a46d4ba892f473458009b满足eqId6d838747e8074dab993ebc2c7cd076a9eqIdabe2ee6e54084a2b83eaafef703cc789 ,其中eqId7f361257cd8f439eb09a80bb297405da,则称eqIda6e202873b10451d97ccb33f6744588ceqId174d58136ce34b5089892e7bb0dd4004的“衍生数列”.
(Ⅰ)若数列eqId0cd42fe2e52d4853b051156809dd0906的“衍生数列”是eqIda414743197c84ab38f45a3d25ab13995,求eqId0f09a759943b4797b47375be661e5126
(Ⅱ)若eqIdf458db68122849abb588feb2e682d9ac为偶数,且eqId174d58136ce34b5089892e7bb0dd4004的“衍生数列”是eqIda6e202873b10451d97ccb33f6744588c,证明:eqIda6e202873b10451d97ccb33f6744588c的“衍生数列”是eqId174d58136ce34b5089892e7bb0dd4004
(Ⅲ)若eqIdf458db68122849abb588feb2e682d9ac为奇数,且eqId174d58136ce34b5089892e7bb0dd4004的“衍生数列”是eqIda6e202873b10451d97ccb33f6744588ceqIda6e202873b10451d97ccb33f6744588c的“衍生数列”是eqIdcd8b006a766b441896481934ce8624da,….依次将数列eqId174d58136ce34b5089892e7bb0dd4004eqIda6e202873b10451d97ccb33f6744588ceqIdcd8b006a766b441896481934ce8624da,…的第eqId4dd1a1e7776746c8b457f96c912636f4项取出,构成数列eqIdfb42fc30c01645908777614710f860cd .证明:eqIdbc37ee444c50421b95d936ab1825a1b5是等差数列.
更新:2020/02/14难度:0.15题型:解答题组卷:952
23 . 如图,椭圆eqIddfa565848b7146759e2bcf25195efb3deqId8e15963708e9415da25069fea5906e24轴被曲线eqId22a1ab6bae924dfd92bebaa1791079d0截得的线段长等于C1的长半轴长.
figure
(1)求实数b的值;
(2)设C2eqId072d7d6b911b42bc89207e72515ebf5f轴的交点为M,过坐标原点O的直线eqId417e80f1349244878d01fe90e0891f5f与C2相交于点A、B,直线MA、MB分别与C1交于点D、
A.
①证明:eqId8616974171b8432485795edae57f46ef
②记△MAB,△MDE的面积分别是eqId5c41ed11ac604e0595a4df2aec9eb70aeqIdfc503046517b4d43a225f07a9608377d,求eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的取值范围.
更新:2020/05/20难度:0.15题型:解答题组卷:1026