2024高三上·全国·专题练习
解题方法
1 . 如图
,已知椭圆
的方程为
和椭圆
,其中
分别是椭圆
的左右顶点.
恰好为椭圆
的两个焦点,椭圆
和椭圆
有相同的离心率,求椭圆
的方程;
(2)如图
,若椭圆
的方程为
.
是椭圆
上一点,射线
分别交椭圆
于
,连接
(
均在
轴上方).求证:
斜率之积
为定值,求出这个定值;
(3)在(2)的条件下,若
,且两条平行线的斜率为
,求正数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3082b0f763a3f9a73d1c3e5e448f74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaebaf8ceed245eba896f36d8ff14b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1470a8fcbdd2fa9badb34e498d14de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b11b45b1ae99a58e5aac679974dabcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82875c5fd5f92475e5def5fb14207fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6398cc77bc5e5a65168505985fcbc36b.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec853fb315a3c7ce3699bc4ca0d74f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d17816617696dc58a42cacaa454e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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真题
解题方法
2 . 设向量
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de90ebc599dee1d3dec0733f0ddf83bc.png)
A.“![]() ![]() | B.“![]() ![]() |
C.“![]() ![]() | D.“![]() ![]() |
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3 . 如图,在直三棱柱
中,
,
,
,
.
时,求证:
平面
;
(2)设二面角
的大小为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42da806a6bd2472459f6c4ad1dab7b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b360c98bd3fd209525fd8fece4246590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306681bd5aaa51e9c63ab3002e23dec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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解题方法
4 . 已知
,
,
分别是
三内角
,
,
的对边,则“
”是“
为直角三角形”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35069268e62dbff379b4555d3f7d6016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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5卷引用:解三角形-综合测试卷B卷
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5 . 命题“
,
”的否定为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8645952ea14b25443f411d39bdec641e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6af0ef4759a6e20e172e843a165669d2.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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6 . 波斯诗人奥马尔·海亚姆于十一世纪发现了一元三次方程
的几何求解方法.在直角坐标系
中,P,Q两点在x轴上,以
为直径的圆与抛物线C:
交于点
,
.已知
是方程
的一个解,则点P的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19db0a8b4c9108e50d1d1de215220139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071d4c1556de22088445f191a80b8a25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776bee64c15a10647a81af32c6c1082b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a032228f52b919700de88ab7a806840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b80ba68333c85361226405acf33d56.png)
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7 . 已知
或
.
(1)若
是
的充分条件,求实数
的取值范围;
(2)若
是
的必要不充分条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558723a72857184db7c8ba0d2c2fa840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87492cf46ac0260bef61414c8035134.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e26b38e357c7d985656ba7bb3c794a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 . 已知集合
.
(1)若
,求实数
的值;
(2)若命题
为真命题,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f19ed48c4b65f777695d5d25031f22.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed961de27af72b7d11887ccfb6f15071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c712af17f519beff6c8fe6ba648e6d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . 如图,四棱锥
内,
平面
,四边形
为正方形,
,
.过
的直线
交平面
于正方形
内的点
,且满足平面
平面
.
的轨迹长度;
(2)当点
到面
的距离为
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd051fedb6691e2183e658f1fe487ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392469b357b12b998528499929366c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03203dd5ac79dd8c6707e4340773359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6ebfed81c159368d135f211b9860f01.png)
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10 . 命题:“
”的否定是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70fe5d366e868de7f6c9c7175e28a095.png)
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