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| 共计 28 道试题
填空题 | 一般(0.65) | 2022·贵州贵阳·(文)
1 . 如图,正方体eqId588284d93dc5489295f8f224f8e30d13的棱长为1,eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175分别是棱eqIdea82c30b37894b1bb742dee61200db07eqId8f39d706a505485987ccbb3f6177d72d的中点,过直线eqId1a0830891ff846de8422ea80714ecab4的平面分别与棱eqIdfe9cbfb067114ce8857e621d77cb5febeqIde4682078ddd9488281e376503edb4f95交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6.设eqIdd106695882344873b5c7633e9a26ed53eqId363b1adc1f524ba6a08e2cd7da586a7a,给出以下四个结论:①平面eqId87c167579d474033ab13c18e27ebf870平面eqIdccc64d3cf9f347bfa9a613f5c0d16c58;②当且仅当eqId3842beeb117f4a0c8210f663dbb3467b时,四边形eqIdb76b2e6d4ffa4859a0fa4e5a3de2e10c的面积最小;③四边形eqIdb76b2e6d4ffa4859a0fa4e5a3de2e10c的周长eqId45c2a97d6a2e413da14b9aa0c4b277b5eqId363b1adc1f524ba6a08e2cd7da586a7a是单调函数;④四棱锥eqIdaf73465861604255a06740d0769cb2cf的体积eqIdb6448e3bef2146ff9a0fab6a9ae0e737eqId363b1adc1f524ba6a08e2cd7da586a7a上先减后增.其中正确命题的序号是__________
说明: figure
单选题 | 较易(0.85) | 2021·浙江高二学业考试
2 . 如图,已知长方体eqId588284d93dc5489295f8f224f8e30d13,点E是棱eqId8f39d706a505485987ccbb3f6177d72d的中点,eqId491f1b02bc6a42bd9bcf11e596c84b80平面eqId9e721937484f4141acfc9fae7eb69f5d,则(   )
说明: figure
A.eqIdb746a5ba20344f189daa85b6f599b21cB.eqIdc623186b5571424ca1005a659dc4d7bd
C.eqId13e77217030a4748a0dadaa9769a9e60D.eqIdfdaba5164d80496a99a60e9dee7cd8a2
3 . 如图,在矩形eqId5ce7a06ae7a34393b92b5277978ac014中,eqId309bf7da6b2748ebb01e016772c0e680eqId9156aefc65c340b09db9cdfb143515a8,点eqId93cbffaa5ae045d6ac45d1e979991c3aeqId8a76bbe21fb549e3a9c2038d58c7a3d8的中点,将△eqId9f4208fa07f24bc69ce1bf42c811eec2沿eqId1dcb20a9ce8d4076af5dd64f7066c6d6翻折到△eqId92aa0bd224794c3c824038daa2b8cf30的位置,在翻折过程中,eqId432a72d3ff97432981c0f850dfeb0e96不在平面eqIdda27baf162634ddaab4c30f70ed6eb60内时,记二面角eqId87f5d8bc99054df8979ad6ca1b2fc2de的平面角为eqIdc13953f2514e4c8f9c8aaaf5241c33ac,则当eqIdc13953f2514e4c8f9c8aaaf5241c33ac最大时,eqIdb8dffd3595704fd791dd6b613ceaea07的值为______
说明: figure
4 . 阿基米德在他的著作《论圆和圆柱》中,证明了数学史上著名的圆柱容球定理:圆柱的内切球(与圆柱的两底面及侧面都相切的球)的体积与圆柱的体积之比等于它们的表面积之比.可证明该定理推广到圆锥容球也正确,即圆锥的内切球(与圆锥的底面及侧面都相切的球)的体积与圆锥体积之比等于它们的表面积之比,则该比值的最大值为________
5 . 已知eqId64b9b599fdb6481e9f8d9a94c102300b为等边三角形,eqIde78cce043a6c43329b55788351ff3484底面eqId89fbdcb029be4482b52165366491c70f,三棱锥eqId12175c05cfe240a0b8270ee03df1962f外接球的表面积为eqId7681784440c04c469bb134c3ea9fb53a,则三棱锥eqId12175c05cfe240a0b8270ee03df1962f体积的最大值是___________
单选题 | 困难(0.15) | 2021·全国高一专题练习
6 . 如图,已知在eqId64b9b599fdb6481e9f8d9a94c102300b中,eqIdef86e589850c4f148553de360aecc839为线段eqId0627be51821d4be7b3e024a354815d64上一点,沿eqId8a76bbe21fb549e3a9c2038d58c7a3d8eqId16396ab536cf462399ed2cefb9763997翻转至eqIdceab42cf19f54519b9f561d0c3809af5,若点eqId3c4ef2fb042d4b55b89d310b674f9e06在平面eqIdd128ff4f83ef4c12aad8920a558a97b7内的射影eqId8846d653e4404636a88754285c8bcb32恰好落在线段eqIdcf2da96900c948a1b3ce7cbfd420c080上,则二面角eqId02dfaa2d79984a6e93f3bd0bda7a3046的正切的最大值为(   )
说明: figure
A.eqIdbf4d8b310ca74c22a7eb63a406f4674aB.1C.eqId317ed84d205b4156847380f7e9f38b08D.eqIda2a0ce3781fa4c26b624f5966b7dee44
知识点:
单选题 | 容易(0.94) | 2021·陕西高一期末
解题方法
7 . 在空间直角坐标系中,已知A(1,0,6),B(7,2,6),C(x,4,3),若|AC|=5,则|BC|=(   )
A.5B.6C.7D.8
填空题 | 困难(0.15) | 2020·浙江温州市·高二期中
解题方法
8 . 如图,在四棱锥eqIddd5f333edd7c4a01b271754239943f8d中,底面eqId5ce7a06ae7a34393b92b5277978ac014是矩形,侧面eqId91dd62cb25ac4356a22d3e5abc34e478底面eqId5ce7a06ae7a34393b92b5277978ac014eqIdead78591f6944789b224097f5e9043b2是边长为eqIdc052ddfbd4524f67a79e0e77c2e5656a的等边三角形,点eqIdfcf606636c8549158e75f6db78c50096分别为侧棱eqId979629ae4ef845a184c5713921374792上的动点,记eqId50c0ff1a3ecb4745af0daa75eb850aa9,则eqId08191f2c12324f94b4ddfe2f324a71cf的最小值的取值范围是_________.
说明: figure
单选题 | 较难(0.4) | 2021·山东高三专题练习
9 . 如图所示,在三棱锥eqId12175c05cfe240a0b8270ee03df1962f中,eqId7ab23840900042c382a7cb7ba0888e78平面eqIdcb27f122349b42bd98ee6c48d59860dceqId4be2d5539d3d4c4a9ea26f92f69454d3eqId4e8257da281b4cec829bbde61b36de99,且eqId93cbffaa5ae045d6ac45d1e979991c3aeqIdc32e6ca0b0dd422d9331c3034c0b82e3的中点,eqIdad283ea569f04a6f98f0eec22a44f89feqId63db14a5b4334f3ea583c8fb12b0d175,当eqIdcf2da96900c948a1b3ce7cbfd420c080变化时,则三棱锥eqId67bc74255278492dbe43f34d7aa0c414体积的最大值是(   )
说明: figure
A.eqIdd1ebfa5c81a04d18900d19595d070677B.eqId317ed84d205b4156847380f7e9f38b08C.eqIde040834dfbee4ba4aa293a5c01e4d034D.eqId7c6baff39f9d4da3bb9b86ba60839e35
填空题 | 一般(0.65) | 2020·全国高二课时练习
10 . 已知四棱柱eqId588284d93dc5489295f8f224f8e30d13的底面是边长为2的正方形,侧棱与底面垂直.若点eqId19a4eb16029e4550a14f2afe4741a3c3到平面eqIdbe5e960371b8444faec6b8942bbc6d34的距离为eqId55a5d70ff2fd49ceab8e7f2ed0ebf7e1,则直线eqId6e9e3153fca343779f77e9d76e94d641与平面eqIdbe5e960371b8444faec6b8942bbc6d34所成角的余弦值为______.
更新:2020/08/13组卷:168
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