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山东省实验中学等四校2019届高三联合考试理科数学试题-

适用年级:高三试卷类型:高考模拟试题总数:23浏览次数:86上传日期:2019/6/12
一、单选题
1 . 已知集合eqIddc9df5749c1e452e96e1eca3ae59c600,集合eqId342c441d7de24c9c91a952997be4adac,则eqId43332ee5d620449ca02db9f897200abb(  )
A.eqId74c19d26c3b84210b9fae81202490390B.eqId4b62e75539a74974a263d9d1da9bbbb1C.eqId6544ba9f80b94782a3bc3b7a2d772761D.eqIdad3cb384415a46a5a2db95f26ba25b52
难度系数:0.94使用:215次题型:单选题更新:2019/6/12
2 . 已知复数eqId2cd9e2fe3d6540df9399dbefe49ada54满足eqId8bcb6d61dd3f482ab72ed44be4ce0434eqIdcef329895f614248b69712b61bfa9883是虚数单位),则eqIdb99107e2becb4c6a83d81135996881b3=(  )
A.eqId8e11c74453ef4676bb48871ff0e38ba4B.eqId90ac5e5338b6416bbf424ec059f1cfd7C.eqId11ed6e5095a54d75a211b434777dbc21D.eqId3750d9b5892d4f7e838cc6aa36d53d9c
难度系数:0.94使用:114次题型:单选题更新:2019/6/12
3 . 已知等差数列eqId93e38ecd74a24cb59da79181b95bfd3a的公差不为零,eqIddb5481de79c946c0a760143297d5eade为其前eqId6a64a6458938477ea9222d722f9cca2f项和,eqId627ee8fb1e6845169fcbdefcb41342e4,且eqIde13b6923fda942988d83235a6d1ef37beqId342d29d0c2514c4e8e8dea0a7200a1eceqId0be5c7f76d2a49719fc20b93d8c8aef3构成等比数列,则eqId13d80a5db51c4bf49fcf6a45afd7010e(  )
A.15B.-15C.30D.25
难度系数:0.94使用:236次题型:单选题更新:2019/6/12
4 . 已知正实数eqId70a27b6ddf6b478285353abb3b1f3741eqIde3ff50261b3b48789d45dd3876c7571beqIde35f447365484e7f891dc56884132698满足eqId7802aecb2843433083227fa55bef3c68,则(  )
A.eqId604bd8a4f63149b88c5b8afde46ed88eB.eqIdecc707aba3694439a35b0982eba4741bC.eqId65af10f1205847b3b6aa2d6df7b3536eD.eqIdec2c77c882354615b183d621604f562f
难度系数:0.94使用:171次题型:单选题更新:2019/6/12
5 . 已知实数eqIdc12aac8c2448479687a40735b3572a23eqId072d7d6b911b42bc89207e72515ebf5f满足约束条件eqIdcdb9f187339d4ba1b90a61cb1ecd06e6,则目标函数eqId98095914d0a644e29bbd187cb2e42a29的最小值为
A.eqId4c0fea3781d84454a9f933aab6fe70bcB.eqId9e7446ae83ae4aa580a362ecb09f7dc8
C.eqIdca7f979b4aed44608faf40debecd18b1D.eqIdfcc58431683b452ca65d1d9977a280bd
难度系数:0.94使用:207次题型:单选题更新:2019/6/12
6 . 某三棱锥的三视图如图所示,则此三棱锥的外接球表面积是(  )
figure
A.eqId2f11b34abcec44a181fe4fb5715941e7B.eqIdcec062e8553849e4870aa69f974c376fC.eqIda0eae706b1064e7886e43192ccba3263D.eqIdddfed4b8139f4fc7859bdb659ef104f6
难度系数:0.85使用:99次题型:单选题更新:2019/6/12
7 . 给甲、乙、丙、丁四人安排泥工、木工、油漆三项工作,每项工作至少一人,每人做且仅做一项工作,甲不能安排木工工作,则不同的安排方法共有(  )
A.12种B.18种C.24种D.64种
难度系数:0.85使用:191次题型:单选题更新:2019/6/12
8 . 如图eqIddd05921f809848a9a7ee5d77470a77a9中,eqId1f61ec1bf49d4e58a8c7fa5a63baf9b2eqIdc5bc9649f4574c2fb31060635e0d351feqIdfdf3c3092e204ed0ba3d11c407d3d200平分线交△ABC的外接圆于点eqId0cd8063abf2b458f80091bc51b75a904,设eqId45d494563eba421eb099c46c5ad6a893eqIdd6e6af60d1604ebba9f0be559eeb334b,则向量eqId903460518278481dbf02a2e0eb0da6d1(  )
figure
A.eqIdfc0b4fd046874028babe6e135efeff08B.eqIdcd86d63ede3a455395798d9600016be4C.eqIdac85bcbbb23443d084c07fea9f49f5c8D.eqId7714bb0e259e40d39088014dca46b61e
难度系数:0.65使用:94次题型:单选题更新:2019/6/12
9 . 在eqId992fe44057cf4492895193f3f5398449中,eqId70a27b6ddf6b478285353abb3b1f3741eqIde3ff50261b3b48789d45dd3876c7571beqIde35f447365484e7f891dc56884132698分别为角eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的对边,若eqId992fe44057cf4492895193f3f5398449的面为eqId1b7d8b87b50e4cfdbf89d48980209a52,且eqId09c72f1978904eec90dcd940f3ffeaff,则eqId9e3a80af95c543fea4d7287a0b0f3d42(  )
A.1B.eqIdffa9f6ff180f47d685d2393e2336411dC.eqIdaeda45c70853411387ff9847fdcc2fffD.eqIda999caba669f4097bbfffaa1234b41c1
难度系数:0.65使用:264次题型:单选题更新:2019/6/12
10 . 下图中的图案是我国古代建筑中的一种装饰图案,形若铜钱,寓意富贵吉祥.在圆内随机取一点,则该点取自阴影区域内(阴影部分由四条四分之一圆弧围成)的概率是(  )
A.B.C.D.
难度系数:0.85使用:228次题型:单选题更新:2018/2/13
11 . 已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIde9b1737ca0154a95ad75cc03d12cccb4eqIda11e829c4716456ba41062c5766cd252的左、右焦点分别为eqIdadf5adeb3ae644dc89c819829df0a901eqId0cfe24caa0fc44de8e0fcd142d6c1377eqId2381423d4cd146cab95f55527681a766为椭圆上异于长轴端点的一点,eqIded9fea236074493598d5b4d086e0e616的内心为eqIdfe4f3387154b4adabbb52781c511ad2e,直线eqId7c64b61819b34524a9a10236667fc7b7eqIdc12aac8c2448479687a40735b3572a23轴于点eqId93cbffaa5ae045d6ac45d1e979991c3a,若eqIdad7ce5a89b1e41f695cf9889a7186765,则椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的离心率是(  )
A.eqIdffa9f6ff180f47d685d2393e2336411dB.eqIddb6b28cbd8a14caa9cf1146f6f7916c0C.eqIdcf32b3b919f04cc18988c622e750e9f1D.eqIda8012d5322b240128851ebf3cd086e12
难度系数:0.85使用:83次题型:单选题更新:2019/6/12
12 . 已知函数eqId6e368b541f0b4c2694efb471b2944544,当eqIdabc83049630440938d390c2194c0c9d9时,方程eqId964f3e1961fb47ceaa82f8a334e81cea有4个不相等的实数根,则eqId70a27b6ddf6b478285353abb3b1f3741的取值范围是(  )
A.eqId197dc900fb034a33a8d4d54c1004cd0eB.eqId96e41017eda143599b24fe0d213faf41
C.eqIda0fde40d55c14dee9f38cbc011b1e50eD.eqId079b4273289e463c9c6d0c7cd480be8e
难度系数:0.65使用:157次题型:单选题更新:2019/6/12
二、填空题
13 . 观察下列式子,eqId896e81a376404151987c5e0fb6038faceqIdbdb08ee87073466eb8fa473c97849b41eqId0410fb26e5754e6c8eea55baac74bdaf,……,根据上述规律,第eqIdf458db68122849abb588feb2e682d9ac个不等式应该为__________.
难度系数:0.65使用:124次题型:填空题更新:2019/6/12
14 . 若eqId238b9bde1c0c4de282815f14c3f36ccb,则eqIdf672d868ccbe482f9256f8d5af39d8ec_________.
难度系数:0.85使用:201次题型:填空题更新:2019/6/12
15 . “圆材埋壁”是我国古代数学著作《九章算术》中的一个问题:“今有圆材,埋在壁中,不知大小.以锯锯之,深一寸,锯道长一尺.问径几何.”用现在的数学语言表述是:“如图所示,一圆柱形埋在墙壁中,eqId70cba2a76eaa49eea339ec577dc06abe尺,eqId0cd8063abf2b458f80091bc51b75a904eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点,eqId46cc74314850457e97bf4fb436aabf13eqId94762cd8cda44ee2a95b3bbc7a097fa2寸,则圆柱底面的直径长是_________寸”.(注:l尺=10寸)figure
难度系数:0.85使用:54次题型:填空题更新:2019/6/12
16 . 如图所示,边长为1的正三角形eqId8b26d5b4d5b448f0a91a35e9988d4472中,点eqId2381423d4cd146cab95f55527681a766eqId8eea7f6267fb49d9bce12b8ba079a43e分别在线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIdcf2da96900c948a1b3ce7cbfd420c080上,将eqId98d5e62410c741349f61e9620844ae39沿线段eqId996e2048847f41d5a5fe0e2282909254进行翻折,得到右图所示的图形,翻折后的点eqIdcc614bd3390c4d028df189b234dcc351在线段eqIde84e0278d905475dbdfd36c2a4101592上,则线段eqId70cd1808ec2941c8b922af637375e79b的最小值为_______.figure
难度系数:0.65使用:45次题型:填空题更新:2019/6/12
三、解答题
17 . 已知数列eqId93e38ecd74a24cb59da79181b95bfd3a的前n项和eqIddb5481de79c946c0a760143297d5eade满足eqIdb0cae05fb8cb4a50acc7693315675c83,且eqIdaebe3dd7d7eb458d91d8b31a52b1f0e6
(1)求数列的通项公式eqIdef9cef8e6d054d8dac46b8cde14953ad
(2)记eqIdc513116c161b4eb7aa426153063106dceqId92ed363a54bd4a8a93df9463bb3af1f5eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqId6a64a6458938477ea9222d722f9cca2f项和,求使eqId9df23744c9d04873be86ff76064021e8成立的eqId6a64a6458938477ea9222d722f9cca2f的最小值.
难度系数:0.65使用:464次题型:解答题更新:2019/1/21
18 . 如图在直角eqId992fe44057cf4492895193f3f5398449中,eqId8754ce8cf7f34f04abb9a0c041f57f5c为直角,eqId87cf970383b54b239c06d723503a5e2feqId93cbffaa5ae045d6ac45d1e979991c3aeqIdd5b10b2a13f148b78e0d5a1b820538fd分别为eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIdcf2da96900c948a1b3ce7cbfd420c080的中点,将eqIdfa027fe8a1a444ae84312f40da7c630b沿eqIdbf3c8333111643ec975d03c2e117f870折起,使点eqIdcc614bd3390c4d028df189b234dcc351到达点eqId0cd8063abf2b458f80091bc51b75a904的位置,连接eqId1b51efe7c2fa42748ac5a6be262e2fa4eqIdccfc85989cfa418badd1721049a70165eqId2381423d4cd146cab95f55527681a766eqIdccfc85989cfa418badd1721049a70165的中点.
(Ⅰ)证明:eqId5376ec542ea546cfb535d51b85a8abceeqId9e37c9c7db6b49c183010c0394cc18e4
(Ⅱ)若eqId11e77fc4ac65443881d0759ef0ce4225,求二面角eqIddb3f38412b214c2d85ecc87e2be5cfad的余弦值.figure
难度系数:0.65使用:178次题型:解答题更新:2019/6/12
19 . 随着科技的发展,网络已逐渐融入了人们的生活.网购是非常方便的购物方式,为了了解网购在我市的普及情况,某调查机构进行了有关网购的调查问卷,并从参与调查的市民中随机抽取了男女各100人进行分析,从而得到表(单位:人)
 
经常网购
偶尔或不用网购
合计
男性
50
 
100
女性
70
 
100
合计
 
 
 
 
(Ⅰ)完成上表,并根据以上数据判断能否在犯错误的概率不超过0.01的前提下认为我市市民网购与性别有关?
(Ⅱ)①现从所抽取的女市民中利用分层抽样的方法抽取10人,再从这10人中随机选取3人赠送优惠券,求选取的3人中至少有2人经常网购的概率;
②将频率视为概率,从我市所有参与调查的市民中随机抽取10人赠送礼品,记其中经常网购的人数为eqIdb649f6e8a2ce413e9fc9368dc1d4d047,求随机变量eqIdb649f6e8a2ce413e9fc9368dc1d4d047的数学期望和方差.
参考公式:eqId365b199f0c4f4386b1f6fe06bcbfcd19
eqIdb4f9d00ed8c045f4ab749e648db42d16
0.15
0.10
0.05
0.025
0.010
0.005
0.001
eqId32496a190cfa4aba85cd36f9f0c0b5c3
2.072
2.706
3.841
5.024
6.635
7.879
10.828
 
难度系数:0.85使用:236次题型:解答题更新:2019/6/12
20 . 抛物线eqId19a4eb16029e4550a14f2afe4741a3c3eqId9af484fcc7704c1c8280ffcc20c0f4e7,直线eqId417e80f1349244878d01fe90e0891f5f的斜率为2.
(Ⅰ)若eqId417e80f1349244878d01fe90e0891f5feqId19a4eb16029e4550a14f2afe4741a3c3相切,求直线eqId417e80f1349244878d01fe90e0891f5f的方程;
(Ⅱ)若eqId417e80f1349244878d01fe90e0891f5feqId19a4eb16029e4550a14f2afe4741a3c3相交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c,线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中垂线交eqId19a4eb16029e4550a14f2afe4741a3c3eqIdd7be5abad1e34f6db17a56660de8d54feqIdca9308a4ebd84ed8a28d8a519a8dbb39,求eqIdd09796b583cd470aa3844f38232a961d的取值范围.
难度系数:0.65使用:50次题型:解答题更新:2019/6/12
21 . 已知函数eqId6258035681c645d09116d17e751d5821eqId909d08b2b3fb413b8e78dbe1f8bd458d
(Ⅰ)当eqId2d569479cd1c43c1af15895792b64db6时,证明eqIdb1f8a7d6c6a24cf3a208c37f4f240629
(Ⅱ)已知点eqIdc010e0af33f4438e91b60d267d0e7a20,点eqId0b201196b46042eca44f00330030937b,设函数eqIdfeec4f10fb99489f868d7cd2df47a88b,当eqId5311747bbee940a2a4fe9d36b6252f5e时,试判断eqId97e0bb1d0e0f40f884e25f90ab6598aa的零点个数.
难度系数:0.4使用:107次题型:解答题更新:2019/6/12
22 . 在平面直角坐标系eqIdf6795042a6be4af49cb950f48e99a5ea中,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqIdbc9d125649074506bda8c3f0610f096aeqId32454977564e4ee18da36bd51156c509为参数),曲线eqId19a4eb16029e4550a14f2afe4741a3c3的极坐标方程为eqId82da5c743ebc4e0caadb9f8a85421600
(Ⅰ)求直线eqId417e80f1349244878d01fe90e0891f5f的普通方程及曲线eqId19a4eb16029e4550a14f2afe4741a3c3的直角坐标方程;
(Ⅱ)设点eqId29eb9af361ed4d3a8c2f4163b9f08581,直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c,求eqIdae22eaf7b47b478793001e89765f2402的值.
难度系数:0.65使用:322次题型:解答题更新:2019/6/12
23 . 已知函数eqId08dcb33dd1724b2ebab2a00680efeb26
(Ⅰ)解关于eqIdc12aac8c2448479687a40735b3572a23的不等式eqIdf35ba38eecb04601b9bd15355cfb6600
(Ⅱ)若eqIded02d391cbe140a9805f405c2c55b428恒成立,求实数eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围.
难度系数:0.65使用:186次题型:解答题更新:2019/6/12
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