1 . 正
的边长为2,
是
边上的高,
分别是
和
的中点(如图(1)).现将
沿翻折成直二面角
(如图(2)).在图(2)中:
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/38d5e306d13a477299f990dc0fee2ceb.png)
(1)求证:
平面
;
(2)在线段
上是否存在一点
,使
?证明你的结论;
(3)求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/0675c286c3cb438585ac2f9b67d0f800.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/07963e3dadb447d091501a49411fcf5e.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/7b499e7a04ba4d38b028550cb36e7705.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/0a245c041053483991cc472b42383a4d.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/18e4dd3ed4eb4c42aaff38c98423364a.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/dea62cbfc42c4007b7b7345555c57fb1.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/0675c286c3cb438585ac2f9b67d0f800.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/020534bd75fc4cce8b883c621cc13737.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/38d5e306d13a477299f990dc0fee2ceb.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/2fdddf16856c44ba9406a7429bce8253.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/74b51661ce834a34bdaf2cd3ae564b9a.png)
(2)在线段
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/dea62cbfc42c4007b7b7345555c57fb1.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/2f4bdc4497ad463db02811a5ab8a9006.png)
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/9a9d1970ab34459ca176ba3f47098898.png)
(3)求二面角
![](https://img.xkw.com/dksih/QBM/2016/5/10/1572629506252800/1572629511708672/STEM/4ce62353534943dd80241cd138613f57.png)
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解题方法
2 . 如图,在正四棱柱
中,
M是棱
上任意一点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ec2ef125fa3aa6c0adda3f8b884a5a.png)
(2)若M是棱
的中点,求异面直线AM与BC 所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ab779ed6b44029d03c8a62ae928210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6dcf3710241e0a5081f5f285384d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ec2ef125fa3aa6c0adda3f8b884a5a.png)
(2)若M是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
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3 . 如图,在四棱锥
中,
平面ABCD,四边形ABCD为正方形,
,F,E分别是PB,PC的中点.
;
(2)求平面ADEF与平面PCD的夹角.
![](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/828d70017e2681ddc069b7a856796c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5acad7a0811d29ce09125359f43ca75.png)
(2)求平面ADEF与平面PCD的夹角.
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名校
解题方法
4 . 已知椭圆
的离心率为
,椭圆上的点到焦点的距离的最大值为3.
(1)求椭圆C的标准方程;
(2)设A,B两点为椭圆C的左、右顶点,点P(异于左、右顶点)为椭圆C上一动点,直线PA,PB的斜率分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆C的标准方程;
(2)设A,B两点为椭圆C的左、右顶点,点P(异于左、右顶点)为椭圆C上一动点,直线PA,PB的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
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2024-06-15更新
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名校
解题方法
5 . 已知函数
在点
处的切线方程为
.
(1)求函数
的解析式;
(2)证明:在
上,恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad589c45e13d45aa6f52f6a18dae2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
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7日内更新
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2卷引用:青海省海东市第二中学2023-2024学年高二下学期第一次月考数学试题
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6 . 如图,在四棱锥
中,底面
是边长为2的正方形,
,
,
为等边三角形,
为
的中点.
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66cef506a91c5e28723f6f19895c27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409b28f7cb97726646e79709ad25190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c7a937699f989b685f285041434000.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
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2024-06-12更新
|
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名校
解题方法
7 . 已知函数
.
(1)若
恰有两个极值点,求实数
的取值范围;
(2)若
的两个极值点分别为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125c0225ea4ef140fd3236739a9aa024.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ced2ceab6d52a14af4d477a9ff09823.png)
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2024-04-01更新
|
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4卷引用:青海省海东市第一中学2023-2024学年高二下学期第一次月考数学试题
青海省海东市第一中学2023-2024学年高二下学期第一次月考数学试题甘肃省武威市天祝第一中学、民勤县第一中学2023-2024学年高二下学期第一次月考数学试题吉林省珲春市第一高级中学、图们市第二高级中学2023-2024学年高二上学期期末考试数学试题(已下线)专题07 函数的极值和最值的应用8种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
8 . 如图,在直三棱柱
中,
,
,
,
,点
是棱
的中点.
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122ca7141c43c15c783968f5f0dbc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cb62f4c1e0e023619922eb8a509c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
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2卷引用:青海省海东市第一中学2023-2024学年高二上学期第一次月考数学试题
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9 . 如图,在四棱锥
中,
平面
,四边形
为菱形,
为棱
上一点.
为棱
的中点,平面
平面
,求证:
;
(2)若
,求直线
与平面
所成角的正弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c659d2ab07b9b66ed9a60cb604dd9aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48abba67b697688749cf92b8c7205161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9915bc06e82813cec0d8854bb28ac2f9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dbd79f684c0cc68e1f9becc3f3591b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
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2023-07-08更新
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2卷引用:青海省海东市第二中学2023-2024学年高二上学期入学考试数学试题
10 . 如图,在底面为矩形的四棱锥P-ABCD中,
底面ABCD.
(1)证明:平面
平面PBC.
(2)若AB=3,AD=5,E为侧棱PB上一点,且BE=2PE,若CE与底面ABCD所成的角大于60°,求PA的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/11/30c19161-bc42-4fa6-91f3-5c75a01422a0.png?resizew=153)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
(2)若AB=3,AD=5,E为侧棱PB上一点,且BE=2PE,若CE与底面ABCD所成的角大于60°,求PA的取值范围.
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