1 . 已知椭圆
的左、右焦点分别为
,
,离心率为
,点
,且
为等腰直角三角形.
(1)求椭圆
的标准方程;
(2)设点
为
上的一个动点,求
面积的最大值;
(3)若直线
与
交于
两点,且
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20a7cb8494b71121a4d176f923d4318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50667ce76318b23b69ac6b8e16dc80d0.png)
(3)若直线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c27ca17526003f779a0b68993a26180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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5卷引用:河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题
河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题河南省部分重点高中2023-2024学年高二下学期5月质量检测数学试题(已下线)湖南省岳阳市第一中学等多校2023-2024学年高二下学期5月月考数学试题山西省临汾市部分学校2023-2024学年高二下学期5月质量检测数学试题(已下线)模型6 非对称结构和齐次化处理问题模型
解题方法
2 . 已知椭圆C
的左、右焦点分别为
,过点P(2,1)的直线l与C交于A,B两点,当直线l过
时,直线l的斜率为
,且
的周长为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706e6c63b376e3a7cf45a2b475c4f0b4.png)
(1)求C的方程;
(2)若过点A且斜率为
的直线交C于另外一点D,证明:直线BD恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b68bed5f53ce98a19785d81b7ca2336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47cfe4e08c06bde245e58aa22485044c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706e6c63b376e3a7cf45a2b475c4f0b4.png)
(1)求C的方程;
(2)若过点A且斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
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3 . 已知椭圆
的左、右焦点分别为
,
,过点
的动直线l交E于A,B两点,且点A在x轴上方,直线
与E交于另一点C,直线
与E于另一点D.
(1)求
的面积最大值;
(2)证明:直线CD过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff1455a4045eb93f482c0751840aea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
(2)证明:直线CD过定点.
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3卷引用:云南省昆明市第一中学2024届高三第十次考前适应性训练数学试卷
名校
解题方法
4 . 如图,在多面体
中,平面
与平面
均为矩形且相互平行,
,设
.
平面
;
(2)若多面体
的体积为
:
(i)求
;
(ii)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff64de03b0302dbc12f2fc207b70d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/336e0a8f5fbc1c44a02adab5a1fffb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc99203b785fbdbd399bb03c7556fbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(2)若多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(ii)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffee8b7eff437080a0936d837ceabe95.png)
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2卷引用:重庆市乌江新高考协作体2023-2024学年高二下学期第二阶段性学业质量联合调研抽测(5月)数学试题
名校
5 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)已知
有两个极值点.
(ⅰ)求
的取值范围;
(ⅱ)若
的极小值小于
,求
的极大值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e589b525104e0f2f599ed6ecf27701fd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a691a1db38dabca5af44a4c6817d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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5卷引用:河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题
河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题河南省名校2023-2024学年高二下学期5月质量检测数学试题河南省部分重点高中2023-2024学年高二下学期5月质量检测数学试题山西省临汾市部分学校2023-2024学年高二下学期5月质量检测数学试题(已下线)专题08 导数的运算、几何意义及极值最值常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)
名校
解题方法
6 . 在
中,
.
为边
上一点,
为边
上一点,
交
于
.
(1)若
,求
;
(2)若
,求
和
的面积之差.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb9a326aece050cf5e9f4713176bb1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b210112e06c09e01255f901f22417500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abf471da32c43bc2e56679a2038cac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c444af7a40000c15940578f9826ef99.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b0216fb4161cda4be672d5224cedfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fbd6b9f85c086ac95562fe45e8d969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f483a71f250bac98cb05d67dccad14.png)
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名校
解题方法
7 . 已知数列
的前
项和为
,若存在常数
,使得
对任意
都成立,则称数列
具有性质
.
(1)若数列
为等差数列,且
,求证:数列
具有性质
;
(2)设数列
的各项均为正数,且
具有性质
.
①若数列
是公比为
的等比数列,且
,求
的值;
②求
的最小值.
![](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/fc983f1bad03411ae64d84ff7bdf2551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a548095fa134cb2b52721af225cbbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193a0efaa1aa835eb3e061bb25dad4dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7470297de40027847c5c73fc5d1719c.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
①若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4338dd5d6ac02dbb9d5069eb98f436d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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4卷引用:江西省临川第二中学2023-2024学年高二下学期6月月考数学试题
江西省临川第二中学2023-2024学年高二下学期6月月考数学试题河南师范大学附属中学2024届高三下学期最后一卷数学试题江苏省泰州市2024届高三下学期四模数学试题(已下线)高二下期末考前押题卷01--高二期末考点大串讲(人教B版2019选择性必修)
8 . 已知椭圆
的离心率为
,A,
分别为椭圆的左顶点和上顶点,
为左焦点,且
的面积为
.
(1)求椭圆
的标准方程:
(2)设椭圆
的右顶点为
、
是椭圆
上不与顶点重合的动点.
①若点
,点
在椭圆
上且位于
轴下方,设
和
的面积分别为
,
,若
,求点
的坐标;
②若直线
与直线
交于点
,直线
交
轴于点
,如下图,求证:
为定值,并求出此定值(其中
、
分别为直线
和直线
的斜率).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
①若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04147e15b00989da8277da4422f8b443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96645a3530e72d5d733d2c72147d340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6374212b29c4f8cf33650465d2f508f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21577004a2cd71f8001fb4639d39b0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827fa7cf443d9be9b56226d50fafd53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32117168271970dcfa7595338a3c662f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350e954f629c1901a5cec03558319e46.png)
您最近一年使用:0次
解题方法
9 . 已知抛物线C:
与椭圆E:
的一个交点为
,且E的离心率
.
(1)求抛物线C和椭圆E的方程;
(2)过点A作两条互相垂直的直线AP,AQ,与C的另一交点分别为P,Q,求证:直线PQ过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c9bebea391a1f9956dfcca98d9d1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dab74e16403e8131f9f5b2a74f3a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求抛物线C和椭圆E的方程;
(2)过点A作两条互相垂直的直线AP,AQ,与C的另一交点分别为P,Q,求证:直线PQ过定点.
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名校
10 . 函数
.
(1)求
的单调区间;
(2)若
只有一个解,则当
时,求使
成立的最大整数k.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61edbe77befb7e5354100d04b603d9c1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f2c3547f47ce4f1ddcd38dc180175d.png)
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