11-12高二上·福建莆田·单元测试
解题方法
1 . 如图,圆柱
内有一个三棱柱
,三棱柱的底面为圆柱底面的内接三角形,且
是圆
直径.
(Ⅰ)证明:平面
平面
;
(Ⅱ)设
,在圆柱
内随机选取一点,记该点取自于三棱柱
内的概率为
.
(i)当点
在圆周上运动时,求
的最大值;
(ii)记平面
与平面
所成的角为
,当
取最大值时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5629041fdcb10ce365d799f59b463189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(Ⅰ)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3b89eddba301a7dcd65950ad4b6643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5629041fdcb10ce365d799f59b463189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(i)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(ii)记平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/739c629772c553e9a2329d5d71173736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9f6421745313307418e4c375279c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
![](https://img.xkw.com/dksih/QBM/2011/11/24/1570360762925056/1570360768397312/STEM/c56b127e-029a-4259-aa4f-4dcc231dfdf4.png?resizew=174)
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11-12高二上·福建莆田·单元测试
2 . 如图,在三棱柱ABC﹣A1B1C1中,已知BC=1,BB1=2,AB
,∠BCC1=90°,AB⊥侧面BB1C1C,E为CC1的中点
(1)求证:EA⊥EB1
(2)求二面角A﹣EB1﹣A1的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae65bdb69940a67a18d56ff02060b22.png)
(1)求证:EA⊥EB1
(2)求二面角A﹣EB1﹣A1的大小.
![](https://img.xkw.com/dksih/QBM/2011/11/24/1570360762925056/1570360768356352/STEM/0769afa2c1884767b56634151919dd86.png?resizew=225)
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11-12高二上·福建莆田·单元测试
3 . 在如图的多面体中,
⊥平面
,
,
,
,
,
,
,
是
的中点.
(1) 求证:
平面
;
(2) 求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4a6b8ef3e79b4482388c3391d8b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29f27c9a3af7044faf147bdaeb3fe81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4ffb68a9ca3bf66788363bc89dab45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bd9e8b54864ca44115d24a5aeeb83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70801d43498c8ae772b960f0353131f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1496042c1d721cffd25053e997a9a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6922690417492dea5c60acd5f031efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(1) 求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c96bc9a285172c48e4726ee6492670ef.png)
(2) 求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://img.xkw.com/dksih/QBM/2011/11/24/1570360762925056/1570360768315392/STEM/523f888003c24903ac9b2760a2c20095.png?resizew=252)
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11-12高二上·福建莆田·单元测试
解题方法
4 . 将一颗骰子先后抛掷两次,记下其向上的点数,试问:
(1)“点数之和为6”与“点数之和为8”的概率是否一样大?从中你能发现什么样的一般规律?(直接写出结论,不必证明)
(2)求至少出现一次5点或6点的概率.
(1)“点数之和为6”与“点数之和为8”的概率是否一样大?从中你能发现什么样的一般规律?(直接写出结论,不必证明)
(2)求至少出现一次5点或6点的概率.
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