解题方法
1 . 已知双曲线
的虚轴长为
,点
在
上.设直线
与
交于A,B两点(异于点P),直线AP与BP的斜率之积为
.
(1)求
的方程;
(2)证明:直线
的斜率存在,且直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90acecacaab778257a1a1e903b2028a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2卷引用:2024届青海省海南藏族自治州高考二模数学(理科)试卷
解题方法
2 . 如图,在三棱柱
中,
,四边形
为菱形,
.
;
(2)已知平面
平面
,
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9332278351ab92e03e984e9279dd06a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43732729894297552d9210f41a634769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870cee007535b979d35bc7feab75616.png)
(2)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b65798afbc7efaed6d65d0719c3c391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34f6658a6fa46b1597f382a3455ad04.png)
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3卷引用:2024届青海省西宁市大通县高考四模数学(文)试卷
解题方法
3 . 已知质数
,且曲线
在点
处的切线方程为
.
(1)求m的值;
(2)证明:对一切
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e2da4647a9925ccc924b0f9f3b40ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8eb06f527d4201b93636710c62d461.png)
(1)求m的值;
(2)证明:对一切
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92222bd1bfa79c6082eea07ced5a98ef.png)
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2024-05-14更新
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2卷引用:青海省部分学校2023-2024学年高三下学期联考模拟预测理科数学试题
名校
4 . 如图,在四棱锥
中,四边形
是正方形,
,M为侧棱PD上的点,
平面
.
.
(2)若
,求二面角
的大小.
(3)在(2)的前提下,在侧棱PC上是否存在一点N,使得
平面
?若存在,求出
的值;若不存在,请说明理由.
![](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/267172a953126e44e36ab085165543ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2d2fbc26a7be008f550b5828f615fe.png)
(3)在(2)的前提下,在侧棱PC上是否存在一点N,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f214481e6b23307a37940f6dd0313d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d7478de8e7971491d38e784529aff5.png)
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4卷引用:2024届青海省西宁市大通县高考四模数学(理)试卷
名校
5 . 如图,在三棱锥
中,平面
平
.
.
(2)若
为
的中点,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88685c5cd2d13a8d51c80e98012b32ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c8a9af7f6fd91de42d30da0b327524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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2024-05-08更新
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6卷引用:2024届青海省海南藏族自治州高考二模数学(理科)试卷
2024届青海省海南藏族自治州高考二模数学(理科)试卷甘肃省白银市2023-2024学年高二下学期5月期中考试数学试题2024届广东省江门市新会华侨中学等校高考二模数学试题浙江省东阳市外国语学校2023-2024学年高二下学期5月月考数学试题(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)(已下线)专题01 空间向量与立体几何解答题必考题型(6类题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(江苏专用)
名校
解题方法
6 . 已知函数
.
(1)求不等式
的解集;
(2)若函数
的最小值为
,且正数
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4aac5487f0cd46559e938ff98a5cfc.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04bbcc3eb28e550b30e7ba6eaa09fe8f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d86be2de99fbf7f99cd54ab399146b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a3cfe361051dc5e9a3a36b2818db0.png)
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4卷引用:青海省西宁市大通县2024届高三第二次模拟考试数学(文)试题
解题方法
7 . 已知函数
.
(1)若
,求
的极值;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9e829dbc3f88ba7e1209dd46573f63.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9910a0b00ee436bd41b4133501fd678c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788cc2823597b34fdd8bf55165ca4ca1.png)
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解题方法
8 . 如图,在三棱锥
中,
平面
,
、
分别为
、
的中点,且
,
,
.
平面
.
(2)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bae7599ad243c12d94325ad917f0a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80de8656637bb7102f8111c172add996.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
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9 . 记等差数列
的前
项和为
,
是正项等比数列,且
.
(1)求
和
的通项公式;
(2)证明
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738639bed93112168095c6e96df7c350.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae99a02a5fda4c6138f273f3e612ac48.png)
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名校
10 . 如图,在三棱锥
中,
平面PAB,E,F分别为BC,PC的中点,且
,
,
.
平面
.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bae7599ad243c12d94325ad917f0a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80de8656637bb7102f8111c172add996.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f726924c16c769a012d7a111f81e44e7.png)
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3卷引用:青海省部分学校2023-2024学年高三下学期联考模拟预测理科数学试题