解题方法
1 . 设函数
是定义在
上的奇函数,且
.
(1)确定函数
的解析式;
(2)试判断函数
的单调性,并用定义法证明.
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c8d98ee11235b9ff6c47a5ab20b99c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad19d9b057bd7b2207dabe260e7bde86.png)
(1)确定函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708c2db9a8d2aea57809191a0a283382.png)
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2 . 求证:
(1)若
,且
,则
.
(2)若
,则
.(并讨论等号成立的条件)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e271b6e63206285461a7552d11efd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4477891a0849eed531ba60d9a2549582.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a655d6935ae3f646e17ff72bc213e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b20f398d8772984301018f832966b14.png)
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名校
解题方法
3 . 已知椭圆
的左、右顶点分别为
,且
,离心率为
为坐标原点.
(1)求椭圆
的方程;
(2)设
是椭圆
上不同于
的一点,直线
与直线
分别交于点
.证明:以线段
为直径的圆过椭圆的右焦点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17474927c574e224a2f6f5deb9457f8b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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4 . 如图,在四棱锥
中,
底面
,底面
是直角梯形,
,
,
,
是
的中点.
平面
;
(2)若二面角
的余弦值为
,求线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd3c2e2199cd4565c05b949bc21fc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5102c216393e133fa25dba98cd78535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
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2023-05-08更新
|
269次组卷
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2卷引用:甘肃省金昌市永昌县第一高级中学2022-2023学年高二下学期期中数学试题
名校
5 . 如图,在四棱锥
中,底面ABCD为正方形,侧面PAD是正三角形,侧面
底面ABCD,M是PD的中点.
(1)求证:
平面PCD;
(2)求平面BPD与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/15/efc9268a-8376-4dcb-8bd5-e226e5137906.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
(2)求平面BPD与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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2023-09-14更新
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10卷引用:甘肃省金昌市永昌县第一高级中学2023-2024学年高三上学期期中数学试题
甘肃省金昌市永昌县第一高级中学2023-2024学年高三上学期期中数学试题广东省江门市广雅中学2023-2024学年高二上学期期中数学A卷试题辽宁省朝阳市2023-2024学年高三上学期9月联考数学试题黑龙江省哈尔滨市第一二二中学校2023-2024学年高三上学期10月月考数学试题河北省高碑店市崇德实验中学2024届高三上学期10月月考数学试题河北省沧州市东光县等三县2024届高三上学期11月联考数学试题安徽省皖中名校联盟2024届高三上学期第四次联考数学试题广东省东莞市东莞外国语学校2024届高三上学期第四次月考数学试题辽宁省沈阳市新民市第一高级中学2023-2024学年高二上学期10月月考数学试题河北省保定市高碑店市崇德实验中学2024届高三上学期期末数学试题
名校
解题方法
6 . 如图,在棱长为2的正方体
中,E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/5/9f947787-0ea7-4fda-9269-1fb67ec5da78.png?resizew=171)
(1)求证:
平面
;
(2)求点C到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/5/9f947787-0ea7-4fda-9269-1fb67ec5da78.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd597851c0db4e4de4769e10e09383b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(2)求点C到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
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2023-05-02更新
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265次组卷
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2卷引用:甘肃省白银市会宁县会宁县第四中学2022-2023学年高二下学期期中数学试题
7 . 如图,在四棱锥
中,四边形
为矩形,
,
为正三角形,平面
平面
,E,F分别是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/9cf13ef0-7042-4cb8-983a-951cde6d746f.png?resizew=169)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc28e69c1ba0aac981256887f7dfa94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cbf03524f866cc66d019a01e7c4284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e05d8681a679bd31922e62480f69d55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0d0023d6ffebd1c9f0a42e6d6c2951.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/9cf13ef0-7042-4cb8-983a-951cde6d746f.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2246c0e92e8cc344f636ea8f8f9037e6.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4cba9d2412e4a28f8740bddd5738d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
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2023-09-05更新
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3卷引用:甘肃省武威市天祝一中、民勤一中、古浪一中2022-2023学年高二下学期期中数学试题
甘肃省武威市天祝一中、民勤一中、古浪一中2022-2023学年高二下学期期中数学试题湖北省恩施州巴东县第三高级中学2022-2023学年高二下学期第二次月考(3月)数学试题(已下线)通关练03 用空间向量解决距离、夹角问题10考点精练(58题) - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
8 . 直线
的方程为
.
(1)证明:直线
恒经过第一象限;
(2)若直线
一定经过第二象限,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5078c72c678f6e3e779622ea5960531a.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-09-02更新
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382次组卷
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2卷引用:甘肃省兰州市教育局第四片区联考2023-2024学年高二上学期期中考试数学试题
名校
9 . 如图,已知三角形
是等腰三角形,
,
,C,D分别为
,
的中点,将
沿CD折到△PCD的位置如图2,且
,取线段PB的中点为E.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/28/7d23d6bc-cfd6-4bd1-98e3-e51faf0595f6.png?resizew=297)
(1)求证:
平面PAD;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d7c0126e753ca02dbab9c41829d31e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99b994835978bf95118d74885133a94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da4da3fe00569551b54fd3c9ee28864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad895b1c422b40c35be89c8bef22e834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca15691dfea154b932004966f2fbca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94e59ad6695d077e3f31d330d5734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364d6c88726d8c3bb8ed297057332bac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/28/7d23d6bc-cfd6-4bd1-98e3-e51faf0595f6.png?resizew=297)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b98d08cb05a894f940009f56c74d83c.png)
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2023-04-26更新
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478次组卷
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2卷引用:甘肃省张掖市第一中学2022-2023学年高二下学期期中数学试题
10 . 已知函数
是定义在
上的函数,且
的图象经过
点.
(1)求
的表达式;
(2)用单调性定义证明函数
在
上为增函数;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab4d7524cdebd7ba7c68793cea6f9c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85be68bcfee53e08e9a14508b4a92527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用单调性定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85be68bcfee53e08e9a14508b4a92527.png)
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