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2018年上海市曹杨第二中学高考三模数学试题

适用年级:高三试卷类型:三模试题总数:20浏览次数:24上传日期:2020/2/15
1 . 已知集合eqId01a86482f08041989c7ebde0c6e1a0f5,集合eqIdda9a36f2fbe14665ad88c8f332699135,若eqId4ba4d0833b3746cdac653347b9d6e75d,则实数eqIdd33c7c1015944e2b81de4ff8695de842_____________.
难度:0.94组卷:80题型:填空题更新:2020/2/16
2 . 计算:eqId9c4e4c75c8a34695bcd80f62b2cd5c79_______.
难度:0.65组卷:9题型:填空题更新:2020/2/15
3 . 若复数eqId336ffeee83a0451db09c989a58ad37a3i表示虚数单位),则eqIdc4f6339df5e94be1af1552f2b014e86b_______.
难度:0.94组卷:60题型:填空题更新:2020/2/15
4 . 不等式eqId3e5012f458c845aa8933683ad060403c的解集是_______.
难度:0.65组卷:27题型:填空题更新:2020/2/15
5 . 函数eqId704e7311f2084de18353501c7896b17f的反函数eqId764f06454c2f4a1c9e0a6588867b49b3_______.
难度:0.85组卷:14题型:填空题更新:2020/2/15
6 . 已知两个球的表面积之比为1:2,则这两个球的体积之比为_______.
难度:0.65组卷:19题型:填空题更新:2020/2/15
7 . 已知棱形eqId5ce7a06ae7a34393b92b5277978ac014,若eqIdba354e0410cc4730bd1d91cf2681405eeqId32e7610d932c4d13b03ee0952f7577d3,则向量eqId042fbfb868334efa9e60cd2cc4d81b29eqId25b9116216b546ea90c6bf9ae3a388fa上的投影为_______.
难度:0.85组卷:21题型:填空题更新:2020/2/15
8 . 二项式eqId249c012fadc143619ae0e89826cb9b6e展开式中,其中的常数项是第_______项.
难度:0.85组卷:44题型:填空题更新:2020/2/15
9 . 有红、黄、蓝三种颜色的旗帜各3面,在每种颜色的3面旗帜上分别标上号码1,2和3,现任取出3面,它们的颜色与号码均不相同的概率是_______________.
难度:0.65组卷:134题型:填空题更新:2020/3/6
10 . 在直角坐标平面,已知定点eqId59f3e657ba424c82b32e35381d6ceb6ceqId157d7184d5384a01b149eb7ac3660091和动点eqIda911a2ff25c240098d9cef36c7ec7ef1满足eqIdba78802c3cfa4c959353705af18fa4cf,则点eqIdd099264fa3c546ef9b84fac7361c04bd构成的区域面积为_______.
难度:0.65组卷:32题型:填空题更新:2020/2/15
11 . 设两曲线eqIdfb4791752d78428cb7be530343c7be14eqId06e16c85e7d64df6a9102565f73dc5bf的交点为ABO是坐标原点,若eqIdea6a4f47fd004664960342c742567b6a是锐角三角形,则实数a的取值范围是_______.
难度:0.4组卷:52题型:填空题更新:2020/2/15
12 . 已知直角坐标平面上两条直线方程分别为eqId98e6ff42551b4040aa08741dab08ddf4eqIda1c5e9beb1b14b289d3c16c2ada36cee,那么“eqId116d027b9a7d45b6a911382908aabf8a”是“两直线eqId65aea8add6684b2fb1e575c82b5c7a70eqIdff568bda2bab48588c733e25c8c1645c平行”的(   )
A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分又不必要条件
难度:0.65组卷:24题型:单选题更新:2020/2/15
13 . 若一个正三棱柱的正视图如图所示,则其侧视图的面积等于
figure
A.eqIda515a9acf7de48c193122a37ba80e98fB.2
C.eqIdbf89e7ceea86412e8f88c3e4092fd370D.6
难度:0.85组卷:444题型:单选题更新:2020/2/15
14 . 动点eqIdbedf755e0fdb4d078d6859360706b163在抛物线eqId5abf27ae9ea34c7da642a1918df9ed91上移动,若eqIdbedf755e0fdb4d078d6859360706b163与点eqId602fce42eabe4a14bbbae60e0d03c53a连线的中点为eqId2381423d4cd146cab95f55527681a766,则动点eqId2381423d4cd146cab95f55527681a766的轨迹方程为
A.eqId03cb1073f3bb414da69d32569033723fB.eqId66cd489b379e4b2ab81aa2534cf17985C.eqId4b163dc468a241ba99d4adfa668ecb97D.eqIdceb001d3e02548fabbc73d5913cc77f5
难度:0.85组卷:648题型:单选题更新:2020/2/15
15 . 设函数eqId9b37d03e47a347fc8fab9f814ba5fac4eqId1942541e3e0c43ac97fcf12200fe70a2的定义域、值域均为R,以下四个命题:①若eqId9b37d03e47a347fc8fab9f814ba5fac4eqId1942541e3e0c43ac97fcf12200fe70a2都是奇函数,则eqId0e64e16847aa499f885d6e8e738ca973是偶函数;②若eqId9b37d03e47a347fc8fab9f814ba5fac4eqId1942541e3e0c43ac97fcf12200fe70a2都是R上递减函数,则eqId0e64e16847aa499f885d6e8e738ca973R上递减函数;③若eqId0e64e16847aa499f885d6e8e738ca973是周期函数,则eqId9b37d03e47a347fc8fab9f814ba5fac4eqId1942541e3e0c43ac97fcf12200fe70a2都是周期函数;④若eqId0e64e16847aa499f885d6e8e738ca973存在反函数,则eqId9b37d03e47a347fc8fab9f814ba5fac4eqId1942541e3e0c43ac97fcf12200fe70a2都存在反函数其中真命题的个数是(   )
A.0B.1C.2D.3
难度:0.4组卷:69题型:单选题更新:2020/2/15
16 . 如图,在四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,已知eqIde78cce043a6c43329b55788351ff3484平面eqId5ce7a06ae7a34393b92b5277978ac014,且四边形eqId5ce7a06ae7a34393b92b5277978ac014为直角梯形,eqIdc041cd09016145d3b2e53d6763eec5f8eqIdb4abdf10a8e344eba797f68589e7519deqIdfe737ff044dd42c1bba7c0bd71ecb93b.
figure
(1)求四棱锥eqIdac097205e9cb41279269aadcac3fb6f1的体积;
(2)若点Q为线段BP的中点,求直线eqIdac8c1b8c4014477991ea15f7e7acca35与平面eqId108f58c83c8840259eb56b45bfabc384所成角的大小(用反三角函数值表示).
难度:0.65组卷:29题型:解答题更新:2020/2/15
17 . 已知定义在eqId97c3408239c149fd860d0950fecd159d上的函数eqId6f13759e937144069819aed2ae5a1057是奇函数,且当eqIdcd417b810d7840698ef8d00a3f9ef251时,eqId4e1c65494a5e45ae839e7cffba0bfabc.
(1)求eqId6f13759e937144069819aed2ae5a1057在区间eqId97c3408239c149fd860d0950fecd159d上的解析式;
(2)当实数m为何值时,关于x的方程eqId545dcb49cb9e44cba01c47a4b6d5b100eqId97c3408239c149fd860d0950fecd159d有解.
难度:0.65组卷:18题型:解答题更新:2020/2/15
18 . 如图,AB是海岸线OMON上两个码头,海中小岛有码头Q到海岸线OMON的距离分别为eqId189fa43b9deb44f6bdf63bffdf678b5eeqId7a4fc6dbb4f74b7694347866d1dd58e5,测得eqIda41d8838332f4b488663d36314b204a7eqId85a1195cd59d4b089034ec975776cf40,以点O为坐标原点,射线OMx轴的正半轴,建立如图所示的直角坐标系,一艘游轮以eqId61ca2c7de59541fbaa33c22058f4f650小时的平均速度在水上旅游线AB航行(将航线AB看作直线,码头Q在第一象限,航线BB经过点Q).
figure
(1)问游轮自码头A沿eqId3719fcad464c419291c2d254d26e10f2方向开往码头B共需多少分钟?
(2)海中有一处景点P(设点PeqId2272a344734c4fb088737b84294f7219平面内,eqId13b5f80dbdc042879b6df31eec9244ca,且eqId1094822679e6400f86cc91a0ebe27015),游轮无法靠近,求游轮在水上旅游线AB航行时离景点P最近的点C的坐标.
难度:0.65组卷:28题型:解答题更新:2020/2/15
19 . 已知直线eqIdbd7573e1dfa74982ae46a8861bdd1f50是双曲线eqId7b8e652de9704bd0bfb0b450970ebc1e的一条渐近线,点eqId5bc716730e624f1a9a3a94c680184c39在双曲线C上,设坐标原点为O.
(1)求双曲线C的方程;
(2)若过点eqId574a197886e84358b460d8394a0bbcd5的直线l与双曲线C交于RS两点,若eqId6ae46bd37fc14b0595d3ba8e22d90c3c,求直线l的方程;
(3)设eqId00c68161f1344675b54541877ce01e0c在双曲线上,且直线AMy轴相交于点P,点M关于y轴对称的点为N,直线ANy轴相交于点Q,问:在x轴上是否存在定点T,使得eqId832faa70c95549e2b67c9bc71dbe1b45?若存在,求出点T的坐标;若不存在,说明理由.
难度:0.4组卷:59题型:解答题更新:2020/2/15
20 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式为eqIdaee6c04958604a0eaaedcd5fc7fed48b,其中eqId3155695fcb1f4876aa7c22385c0dd5cceqId5c8f4a8b9d374601808646fd16319c1b.
(1)若eqId93e38ecd74a24cb59da79181b95bfd3a是正项数列,求eqId75fdb198d83447e59e31c1f4923cc3bc的取值范围;
(2)若eqIdbfa925487012443d833b7e530a6c8381,数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63满足eqIdae6c0d5e37e9407aacec49af54520c5e,且对任意eqId471db9c28eea48a0864755cb639d0f9b,均有eqId0ecdc455308d4b2a8f9afcb3860e7d8c,写出所有满足条件的eqId75fdb198d83447e59e31c1f4923cc3bc的值;
(3)若eqId11e3137f9e00469fa12bb7e11254a7b8,数列eqId74ef5fe5183946caaee41d8974816a20满足eqId7a14439824d24614b3e38594da5426df,其前n项和为eqIddb5481de79c946c0a760143297d5eade,且使eqId6b55cf8b1fbc4cfea6be149dbe8ad9b9ij至少4组,eqIde0b0a69153d74086acac0f2b28878deceqIdc36de5c6d722440e9911d9802c4068f8、……、eqIddb5481de79c946c0a760143297d5eade中至少有5个连续项的值相等,其它项的值均不相等,求eqIdd4bf9298f0db4fb5afb67e0d739f3074eqId75fdb198d83447e59e31c1f4923cc3bc满足的充要条件并加以证明.
难度:0.15组卷:58题型:解答题更新:2020/2/15
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