名校
解题方法
1 . 如图,在正方体
中,点E,F分别是棱
,
的中点.
(1)求证:
平面
;
(2)求异面直线
与AF所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/27/48ce9f4e-f66e-4c29-a6ed-c42e509f560e.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4a94e889d2869ea84082575fae52ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d365ce9f4bacc4d4bb15dbdb5306a5.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
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2卷引用:江西省萍乡市2022-2023学年高一下学期期末考试数学试题
名校
2 . 在棱长为2的正方体中,
为棱
上的动点(含端点),则下列说法正确的是( )
A.存在点![]() ![]() ![]() |
B.对于任意点![]() ![]() ![]() |
C.异面直线![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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解题方法
3 . 如图,
为圆锥的顶点,
是圆锥底面的圆心,
是底面的内接正三角形,
是
的重心.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/27/bd9a1f8b-1cf5-4129-afe5-f46de2ee6401.png?resizew=204)
(1)求证:
∥平面
;
(2)若
,
,求圆锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08c39e44b50d0cac4a10106f8d09339.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/27/bd9a1f8b-1cf5-4129-afe5-f46de2ee6401.png?resizew=204)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93767331e9bac06a564973a9f4fc663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9344303efb0541eb449d782ad2b488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
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解题方法
4 . 如图,在三棱锥
中,
,点D,M分别为AC,PB的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/28/41844a0a-3d7d-4ab6-b0cf-7826649f5e4b.png?resizew=149)
(1)证明:
//平面BDF;
(2)若平面
//平面BDF,其中
平面
,
,证明:AN是AM在平面PAC上的投影.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8459bfe1dd87957f217ffcd0d10f6f92.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/28/41844a0a-3d7d-4ab6-b0cf-7826649f5e4b.png?resizew=149)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc986df251862fc30dbc7717d644ebde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69c81371d95d5651999011237b8251b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828247a3338571cb0d4ba2a5bf88929c.png)
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名校
5 . 已知
,
是两条不同的直线,
是一个平面,则下列命题是真命题的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() ![]() |
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名校
6 . 如图,正方体
的棱长为1,E为
的中点,下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
A.![]() ![]() |
B.直线![]() ![]() |
C.在直线![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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江西省宜春市宜丰中学2023-2024学年高二下学期6月月考数学试题辽宁省朝阳市育英高级中学2021-2022学年高二上学期期末数学试题湖北省襄阳市第五中学2023-2024学年高一下学期5月月考数学试题(已下线)第1套 全真模拟卷 (基础)【高一期末复习全真模拟】
名校
解题方法
7 . 如图,
中,
,
是正方形,平面
平面
,若
、
分别是
、
的中点.
(1)求证:
∥平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6321a96e7f0768394f6932a121adc84e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5352d28609d1b3d09a0a29d023d1bb72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/20/30978d16-29fa-47c0-9501-0b4b46c22b8a.png?resizew=131)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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名校
解题方法
8 . 如图,在多面体
中,已知
,
,
,平面
平面
,四边形
是正方形,则点
到平面
的距离是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657d5471e57b894c3833bb3f43ff38ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a1ce226f636a38dcb980164d69e46a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a41e1be0d39b6666edcf4f2d5fe7729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/653ddc9c58281c1cc096de7c15ed0749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bc51695e51aa8cd2f97d220c8f5340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bc51695e51aa8cd2f97d220c8f5340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719103f93166bab4828257608e641a9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/20/1d8233f1-01f2-4108-b616-35a0747baee0.png?resizew=164)
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2卷引用:江西省丰城拖船中学2023-2024学年高二上学期开学测试数学试题
9 . 如图,在正六棱锥
中,
为底面中心,
,
.
(1)若
,
分别是棱
,
的中点,证明:
平面
;
(2)若该正六棱锥的顶点都在球
的表面上,求球
的表面积和体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7858d6cc36eeb5a39dc631f7e5ac1394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f1750bc092092927d2d73b0b79fde0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9466d03bc916a9169eaf39863d59fceb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/9f657da7-ebe7-4db4-beaa-09608eb29508.png?resizew=186)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
(2)若该正六棱锥的顶点都在球
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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10 . 如图,三棱柱
中,侧面
为矩形,
且
,
为
的中点,
.
(1)证明:
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377762229df8daa3e5263ef2d9954bca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/865133c5-85f4-4be4-8597-7b0f38bac7f2.png?resizew=183)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89006cac018a9875f65ed7bd429c61bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
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2023-07-09更新
|
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