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1 . 已知圆柱的高为1,它的两个底面的圆周在直径为2的同一个球的球面上,则该圆柱的表面积为___________ .
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2 .
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2575794cc895207a3a33156aaf2f87.png)
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3 . 设
为复数,则下列命题正确的有_______ .(将全部正确的序号填在横线上)
①若
,则
②若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7977d7239c13e044382d3bdc9ab015.png)
③若
,则
④若
,则
或![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afae33365a8ae1103215ce5c15f0bd4.png)
⑤若
且
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be94c746ea0cb4834e5295672e229a4.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d30afe512997398cb2512d0462fdde7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37415281fdd270f4c12d700a30ee41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e29a3e6d968622d192af63ae2f1fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7977d7239c13e044382d3bdc9ab015.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e37c64fc12b438809bc6d723f359cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063fc82b8f5c123f1fbf572ce4cdf062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fb4f555f276487d6b5161432a267ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2695835f92683ba5df97d630362d9323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afae33365a8ae1103215ce5c15f0bd4.png)
⑤若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045c77d48c87794550c6a29e170d066d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbabf40571217de096d5974d11a3d0f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5262541a2107c9874b8d84945b9a8523.png)
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4 . 已知在数列
中,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.png)
________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a76fc5c4b88789bdcdd0825765bc4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa37e5661af68b263a3ed9030d4e9003.png)
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5 . 数列
中,
,则
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/144143bd6c8e422822745c16b86a2ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11075f2c574b6c59b97fb3038000e38.png)
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6 . 已知平面向量
,则向量
在
方向上的投影向量为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cd262cc3aa3bf4adf989edc3d92d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd8bbf47b69bbd7a6263b041290d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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解题方法
7 . 已知向量
,
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61df6db5f13202396a800df639732c9b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e139e7cec9ef14acedae556ebcd9fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0601da78869330b870d420dbebc674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2558ead24d56fb372fef95c10fddd3fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61df6db5f13202396a800df639732c9b.png)
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8 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322eccf22cb768d778b515bd208b8c08.png)
_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322eccf22cb768d778b515bd208b8c08.png)
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9 . 中国南北朝时期数学家、天文学家祖冲之、祖暅父子总结了魏晋时期著名数学家刘徽的有关工作.提出“幂势既同,则积不容异”“幂”是截面积,“势”是几何体的高,详细点说就是,界于两个平行平面之间的两个几何体,被任一平行于这两个平面的平面所截,如果两个截面的面积相等,则这两个几何体的体积相等,上述原理在中国被称为祖暅原理.一个上底面边长为2,下底面边长为4,高为
的正六棱台与一个不规则几何体满足“幂势既同”,则该不规则几何体的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
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10 . 如图,四边形
的斜二测画法直观图为等腰梯形
,已知
,
,则四边形
的周长为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7139f32092256a2e816d826d501be98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed006dde05c1f51a6098a8dc6ef3445e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6748d75e3e77945922d14e4a23fed67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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