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云南省大理州大理市下关一中2019-2020学年高二3月月考数学(理科)试题
云南 高二 月考 2020-09-16 79次

一、单选题添加题型下试题

3. 在区间eqId7f992f44b6c64819a9969b5b02a7691a内任取一个实数eqId70a27b6ddf6b478285353abb3b1f3741,使得关于eqIda9cd3f94eb8045438f75e9daccfa7200的方程eqIdf245a65d9e634af393b508415109e6a9有实数根的概率为(   )
A.eqId5f51ce9cc7fe4412baeb871cceb26665B.eqIdaf22e0e393474044907f7074dad72e76C.eqId5bdf412098cc4156b5e8fd514ebc7818D.eqIddda48cced83d424b89b7d8f8c62b1056
4. 已知两条不重合的直线eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7两个不重合的平面eqIdc13953f2514e4c8f9c8aaaf5241c33aceqId4eb56f42ca674f2f9c9101b548763159,则下列说法正确的为(   )
A.若eqId6cbd007ab49741748d41c4c7bdb977b5eqId9d7f22bed5c04d77b14ee0c3798463a5,则eqId06e21fc5b78e4677894e3646e79d8294
B.若eqId9d7f22bed5c04d77b14ee0c3798463a5eqIdb80cc2a953e34e32a62a2211f223c20a,则eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7为异面直线
C.若eqId342a1e9f4d8d444abd2df388b0e45f01eqId342a1e9f4d8d444abd2df388b0e45f01,则eqId6cbd007ab49741748d41c4c7bdb977b5
D.若eqId9d7f22bed5c04d77b14ee0c3798463a5eqIda9a5839d890f48c8880f78c33f0dc412eqId1b64978a1bbd40d58cb8eadb0e26b000eqIdd02fd5ff61524385a556673ea1b32106,则eqIdd80209f32d0945f7a14a286b64d35d96
7. 下列各函数中,最小值为2的是(   )
A.eqId51276aee3bcd41a58d3490b344bcc3afB.eqId7e055f35045d47569c99c30435d64ad7eqIdcd417b810d7840698ef8d00a3f9ef251
C.eqIded4b778e798c47809c8654f5e8b32d98D.eqIda3bf38a210c949338289b19bc697f423
8. “方程eqId72df3e0a00804475b199d32f6ef47706表示的曲线为椭圆”是“eqId94f91533d03242d6a24e0c8a0ec1a57b”的(   )
A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件
12. “斐波那契数列”由十三世纪意大利数学家列昂纳多·斐波那契发现,因为斐波那契以兔子繁殖为例子而引入,故又称该数列为“兔子数列”.斐波那契数列eqId054d5a7de5684002909fe944c86227c2满足eqId72539aa2204e4df69d266776d4beb8c7eqId5137d80943104d9b8dd1e6c22b890cfbeqId2b4592de6a4d4a37a8c6ed51deb7e5beeqId9277a91d918447219d400b2439c236caeqIdc73ad4de0ec14cba91db08ec61124907),记其前n项和为eqIddb5481de79c946c0a760143297d5eade.设命题eqId007e027d114d44f6a5f6a8b73a42c627,命题eqId4b0ae7b758164179b554584181467a8f,则下列命题为真命题的是(   )
A.eqIdc89abe1e4d584e16b3718409cb609213B.eqIded54e492a26d44e98134ecde924bfafcC.eqId6c47ec8dee564c10806839b4ddd1831dD.eqId17573da6b6de4537a990dcbf5da9cb45

二、填空题添加题型下试题

13. 若直线eqId51684fa1f95349ad8cc83ece5312e343和直线eqId0a26ef400c214cf29433cc1815eeb6d3互相垂直,则eqId70a27b6ddf6b478285353abb3b1f3741的值为______.
14. 已知eqIdbe3ed928bf5d492ebf14cde4ad8377eb,点eqIdbedf755e0fdb4d078d6859360706b163为抛物线eqId83dc0203c12f4337b54424dad7ab77e9上一动点,点eqIdbedf755e0fdb4d078d6859360706b163到直线eqId8e222b35ffdc4871a6a47ee7ddc18b42的距离是eqId096e32e1d18145d199ccbacb5a9a85fe,则eqId900b3fe7f98a41c4b3fc5528bb629e07的最小值为______.

三、解答题添加题型下试题

17. 已知函数eqId9862b8d68f4f49e39512d94b420285c1eqId0c10827df4214807ac8d1bda56ba2323eqId8ccf61601cf049d8a2100ee27d5b2419eqIdbad20911b86a4e65bc17526c7832f5aa)的部分图象如图所示.eqIdab136d331b204b01929464aaac1094c9eqIdf2a9c79f858c4e5280786f9c59fb6b0ceqIdf56abc916e344e8a87f37217e7d33248.
说明: figure
(1)求eqId4837c94ef0ff4dcf9b1dda4df363275a的解析式;
(2)将eqId9b37d03e47a347fc8fab9f814ba5fac4的图象先向右平移eqIdb47bf79338b1478a89eac53d16970cdf个单位,再将图象上的所有点横坐标变为原来的eqId49b7b111d23b44a9990c2312dc3b7ed9倍(纵坐标不变),所得到的图象对应的函数为eqId1942541e3e0c43ac97fcf12200fe70a2,求eqId1942541e3e0c43ac97fcf12200fe70a2的单调增区间.
18. 已知公差不为零的等差数列eqId93e38ecd74a24cb59da79181b95bfd3a满足eqIdafef604a391c44a0ac8931a973fb3925,且eqId0509add794484602a2c710f41d9ddddceqIdde5836d9a77e4e648c784e42488f7df8eqIda478bdeace294e2791d57250fe09a482成等比数列.
(1)求数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
(2)若eqId66c6122c1da343ffb93867f76080c389,且数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqIdf458db68122849abb588feb2e682d9ac项和为eqId92ed363a54bd4a8a93df9463bb3af1f5,求证:eqIdbdcaa575afc54e6fb4022fbec992608d.
19. 如图,已知扇形的圆心角∠AOBeqId022e530e1dd6453ab54467745e9df0a8,半径为eqId03859367a9b64a56ab90e31a0cec909a,若点CeqId1609e6778d084a1d9bb2bf4111fcf29a上的一动点(不与点AB重合).
说明: figure
(1)若弦eqId8a479f65fd284c23b465ba61efd77b85,求eqIde9e20ea2b5e0416483dfd1b21da92040的长;
(2)求四边形OACB面积的最大值.
20. 如图,在四面体eqId5ce7a06ae7a34393b92b5277978ac014中,eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175分别是线段eqId8a76bbe21fb549e3a9c2038d58c7a3d8eqId1b51efe7c2fa42748ac5a6be262e2fa4的中点,eqId1fddc1cfb97f4195aa8c978fcfd86b47eqId20f9d77213414330ae1ed557b86e3345eqId3557ebb69f5c43f89d827cd9014cc294eqIdddc7561d16e14d459a1e3584c42a8cad.
说明: figure
(1)证明:平面eqId675f4cf7703d4f989f327b7093a96684平面eqId0f24c9c77eb648e4aade772aaae0eca7
(2)求二面角eqId4c2586d8a60a45b983dc180bd17df3cd的余弦值.
21. 互联网正在改变着人们的生活方式,在日常消费中手机支付正逐渐取代现金支付成为人们首选的支付方式. 某学生在暑期社会活动中针对人们生活中的支付方式进行了调查研究. 采用调查问卷的方式对100名18岁以上的成年人进行了研究,发现共有60人以手机支付作为自己的首选支付方式,在这60人中,45岁以下的占eqId5f51ce9cc7fe4412baeb871cceb26665,在仍以现金作为首选支付方式的人中,45岁及以上的有30人.
(1)从以现金作为首选支付方式的40人中,任意选取3人,求这3人至少有1人的年龄低于45岁的概率;
(2)某商家为了鼓励人们使用手机支付,做出以下促销活动:凡是用手机支付的消费者,商品一律打八折. 已知某商品原价50元,以上述调查的支付方式的频率作为消费者购买该商品的支付方式的概率,设销售每件商品的消费者的支付方式都是相互独立的,求销售10件该商品的销售额的数学期望.
22. 已知椭圆eqId211c15b061ee47039dccbca908ea32b4的左、右焦点分别为eqId5f04473e64c141bcbe9b0a8af27f4aa8,弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3过点eqId0aa72756ed0c4c7a89f26aa94f43e47deqId59297415787c4fe698150fe68c3757d4的周长为eqId401586f7a7f248b7904a4cfeaa2ed2f0,椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的离心率为eqId2adca431bfc349e8bacc11042adc7cc4
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)若eqId99923718d1f743f2a5eb4f65896fd00a,求eqId59297415787c4fe698150fe68c3757d4的面积.