2023·新疆·模拟预测
1 . 如图,已知四棱锥
的底面ABCD为菱形,平面
平面ABCD,
,E为CD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/d9d90a46-b925-41f5-aef5-befb78fbbfcf.png?resizew=197)
(1)求证:
;
(2)若
,
,求平面PBC与平面PAE所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/d9d90a46-b925-41f5-aef5-befb78fbbfcf.png?resizew=197)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0180a58a753fced571fc00f0bee8ff0d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305cd5bd8f8a00aff4e9d9639a72622a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
您最近一年使用:0次
名校
2 . 如图,在四棱锥
中,
平面
,
,点
在棱
上,
,点
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/ef057583-3c3d-4deb-861e-6fa94b9455a0.png?resizew=170)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4374d3e92030b750cbbfeb41a332783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38a41b0f5e53b5566be42e5eb6ddb97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8676b624f105072a3185911b25c912dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/ef057583-3c3d-4deb-861e-6fa94b9455a0.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5536a3521cd3ea67a2c6b9a82cb60f4.png)
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2023-03-18更新
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415次组卷
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3卷引用:新疆阿勒泰地区2023届高三素养调研第一次模拟考试数学(理)试题(问卷)
解题方法
3 . 如图,在三棱柱
中,
平面
,
,
是
的中点,点
在棱
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/97072327-f4e9-4f54-b457-6bc6354b04a0.png?resizew=124)
(1)证明:
;
(2)若
,
,直线
与平面
所成的角为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/97072327-f4e9-4f54-b457-6bc6354b04a0.png?resizew=124)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb1e5ce42bcb37db532a66e6626d3d2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754119b17f3aa613526cec6c4fcb3f7d.png)
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2023-03-30更新
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3卷引用:新疆乌鲁木齐地区2023届高三二模数学(理)试题
4 . 如图甲所示的正方形
中,
,
,
,对角线
分别交
,
于点
,
,将正方形
沿
,
折叠使得
与
重合,构成如图乙所示的三棱柱
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/31/295ec9ad-baae-4ff4-9aeb-f906dc167109.png?resizew=315)
(1)若点
在棱
上,且
,证明:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c27162b93f88ff58afc18e06db4f80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eaba7d7d6f2f3d6d4a2fe85d3c427f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c237384c7ab460efcba2881b3b2d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf32cea2153f11f772f53be7df8eea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f422723c3267cad031751b9413cc6c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c27162b93f88ff58afc18e06db4f80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef67f23370e418c1e920699cacd6f21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/31/295ec9ad-baae-4ff4-9aeb-f906dc167109.png?resizew=315)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4f1fcdce96fea5c891d85bffa2a625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982d01f052709b72afeaf1015fc7acc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1de7da3ab92e70f135ea628a691167.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1de7da3ab92e70f135ea628a691167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1253885737cd104e24ddd2d4c96e4c86.png)
您最近一年使用:0次
2023-03-30更新
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4卷引用:新疆新和县实验中学2023届高三素养调研第一次模拟考试数学(理)试题
新疆新和县实验中学2023届高三素养调研第一次模拟考试数学(理)试题新疆柯坪县柯坪湖州国庆中学2022-2023学年高二下学期5月期中考试数学试题甘肃省2023届高三第一次高考诊断理科数学试题(已下线)重难点突破06 立体几何解答题最全归纳总结(九大题型)-1
5 . 在
中,
分别为
的中点,
,如图①,以
为折痕将
折起,使点A到达点
的位置,如图②.
(1)证明:
;
(2)若
平面
,求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a204736186742e998dd00acff244a3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/22/24978418-52bc-4570-ad0f-3fad43683187.png?resizew=351)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b05b2c4d1a2d7ccacd254f9f60ddd5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f1bb063892dfd8f301d327e2f68feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
您最近一年使用:0次
解题方法
6 . 如图,在直四棱柱
中,
,
,
为等边三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/3e2c6177-e025-46a9-b194-7b0f4cf6725f.png?resizew=152)
(1)证明:
;
(2)设侧棱
,点E在
上,当
的面积最小时,求AE与平面
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9536a2be7b84612f45cc875a00c5a5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a8f0043b21adab7e005fa4229b30e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/3e2c6177-e025-46a9-b194-7b0f4cf6725f.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6776b56bf28b48479d64bc135ec25264.png)
(2)设侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4893fbcb191420e06a239e63493626f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1167959ebbc724159e6181759b58658b.png)
您最近一年使用:0次
7 . 如图,在三棱柱
中,
平面
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/0a4ce981-6585-438e-8002-0cb5b6c4f51f.png?resizew=157)
(1)求证:
;
(2)求直线
与平面
所成角大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a55e453aa746c3239fa9d96a90ef55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/0a4ce981-6585-438e-8002-0cb5b6c4f51f.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4424c3527868ba1897b9246a6c8830b3.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
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2022-12-01更新
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516次组卷
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2卷引用:新疆于田县第一高级中学2023届高三第一次模拟数学试题
名校
8 . 如图,在四棱锥
中,
平面
,
,
,且
,
,
是
的中点,点
在
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/20/61c3c9aa-1227-42a2-9dc9-c45d6f4b4ce7.png?resizew=199)
(1)证明:
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a923784f083b7f4777891afe06b44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8459bfe1dd87957f217ffcd0d10f6f92.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/20/61c3c9aa-1227-42a2-9dc9-c45d6f4b4ce7.png?resizew=199)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f44f2b2f82a9126223138972850aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74011b64ff147ac2f10c36a11ac1b34d.png)
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2023-02-15更新
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741次组卷
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3卷引用:新疆乌鲁木齐地区2023届高三第一次质量监测数学(理)试题
名校
解题方法
9 . 已知椭圆C的中心在原点,焦点在x轴上,长轴长为4,且点
椭圆C上.
(1)求椭圆C的方程;
(2)设P是椭圆C长轴上的一个动点,过P作方向向量
的直线l交椭圆C于A、B两点,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
(1)求椭圆C的方程;
(2)设P是椭圆C长轴上的一个动点,过P作方向向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a471747cb60fece40c983bb72a6bad2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a430c41f782c5c12f68a49c5d0cb1ee2.png)
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2022-11-07更新
|
676次组卷
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6卷引用:新疆于田县第一高级中学2023届高三第一次模拟数学试题
新疆于田县第一高级中学2023届高三第一次模拟数学试题山西省晋城一中教育集团南岭爱物学校2022-2023学年高二上学期第三次月考数学试题湖南省长沙市明达中学2022-2023学年高三上学期12月月考数学试题(已下线)【题型分类归纳】2022-2023学年高二数学同步讲与练(空间向量与立体几何、直线与圆、圆锥曲线、数列)黑龙江省哈尔滨师范大学附属中学2022-2023学年高二下学期期末考试数学试题(已下线)第五篇 向量与几何 专题7 共轭直径微点1 共轭直径(一)
名校
解题方法
10 . 已知椭圆
的离心率为
,过焦点且与长轴垂直的直线被椭圆截得的弦长为
.
(1)求椭圆C的方程;
(2)设不过点
的直线l与C相交于A,B两点,直线TA,TB分别与x轴交于M,N两点,且
.求证直线l的斜率是定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求椭圆C的方程;
(2)设不过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05bdd8eb683395ada6a7d339c3929640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c9b4a7cc9dc8afd7b55b1c04266f44.png)
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2022-04-15更新
|
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