名校
解题方法
1 . 比较下列各组中
与
的大小,并给出证明.
(1)
与
,其中
;
(2)
与
;
(3)
与
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b5bc4aacc85a270b2cf47c59ab0f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c512ead5eebabcf7d2ca3b49dfd17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87d7a77ae297d0dc81fa9c688161e59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec5d773175d989de798f1be8f7f5269.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099d808c6cbd400af31ec2d5282fe37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1212b363731f4c79a60d807810ee0e.png)
您最近一年使用:0次
2 . 在平面直角坐标系
中,已知点A,B在抛物线
:
上,抛物线C在A,B处的切线分别为
,
,且
,
交于点P.
(1)若点
,求
的长;
(2)从下面①②中选取一个作为条件,证明另外一个成立.
①直线AB过抛物线C的焦点;②点P在抛物线C的准线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec3fdb2722c0bcac5303546e87152a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)从下面①②中选取一个作为条件,证明另外一个成立.
①直线AB过抛物线C的焦点;②点P在抛物线C的准线上.
您最近一年使用:0次
3 . (1)已知集合
,
.证明:
的充要条件是
;
(2)模仿上述命题,写出一个不同于(1)的命题,判断命题的真假并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc51f46147795c15d5a6bbe3991d10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006107f3f86781dd22d5b8d07eabc3af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd731967bb86ddf18e9e473daa96041a.png)
(2)模仿上述命题,写出一个不同于(1)的命题,判断命题的真假并说明理由.
您最近一年使用:0次
解题方法
4 . 如图,在四棱锥
(图一)和三棱锥
(图二)中,四边形
为正方形,
平面
,
≌
,将四棱锥
和三棱锥
重新组合成一个新的几何体(图三),且面
和面
完全重合,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/484436c0-9d40-48c2-a9e9-8517e1310270.png?resizew=480)
(1)证明:
平面
;
(2)求四棱锥
的体积与组合后的几何体的体积比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9deb96336e49627dff7bfaf36623b941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6358776bf61b2f84d329c310ac9b96be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900e90179062ff6cb33f58d361aedf5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217d37ca5469a57cb7417a2ac0d58efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9deb96336e49627dff7bfaf36623b941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c133b31ab3c50dc87d80879bbb0633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed4f6bd8368c262808d798dd3747f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48901f9b0ee1e3c2b766bf908f4da30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307d88c54b47edca0308cea049965732.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/484436c0-9d40-48c2-a9e9-8517e1310270.png?resizew=480)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9111c8e64fc183a777dbe0e82c9202cd.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
您最近一年使用:0次
5 . 角
可以看成
与
的和,也可以看成
与
的和.同理,角
可以看成
与
的差,也可以看成
与
的差,利用正弦的和差去证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6802fa592c03ef7c4a8c03f3e8932f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dd0c52aca1675c17b9a019aa7901e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6802fa592c03ef7c4a8c03f3e8932f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dd0c52aca1675c17b9a019aa7901e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab72a320d3f7f844d18a62bd49d22f3.png)
您最近一年使用:0次
名校
6 . 对于给定集合
,若集合
中任意两个不同元素之和仍是集合
中的元素,则称集合
是“封闭集合”.设
为实常数且
,集合
,证明:集合
为“封闭集合”的充要条件是:存在整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3ac83c571110d41a396d12d8eea1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01addf1c0dae299be04495dec2a3c733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a141495f9abd68126822a2ae920aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd44d872abf0e0480c139e86d9bb5c1.png)
您最近一年使用:0次
7 . 某公司出产了一款美观实用的筷子笼,如图,是由与圆柱底面成一定角度的截面截圆柱所得.如果从截面的最底端到最高端部分还原圆柱,如下图所示,AB,
分别为圆柱
底面直径,
,
为圆柱的母线,
,过
的平面
截圆柱且与底面所在平面交于直线
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/e8c50ced-4ea3-475f-92fa-a78be6572be7.png?resizew=511)
(1)证明:
;
(2)若底面有一动点M从A点出发在圆O上运动,过动点M的母线与截面
交于点N,设
,
,其中
.
①求
与
的函数关系;
②将圆柱
侧面沿母线
剪开并展平,请在所给的展开图中画出平面
截圆柱侧面的截痕,并建立适当的平面直角坐标系直接 写出其解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3671adea94a33848afff9b2edb6a902e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae781496bb5bc79b67abced9aa3cd0c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/e8c50ced-4ea3-475f-92fa-a78be6572be7.png?resizew=511)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa812513cb17ffa7901d1f5e3fb25c5.png)
(2)若底面有一动点M从A点出发在圆O上运动,过动点M的母线与截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d685845e1baa7e66d2502eebfcbb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4914d142641c85ea5454b1eb05ac4204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d7581e52d1fa9eb225928fabd57fe9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②将圆柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
8 . 已知中心为坐标原点,焦点在坐标轴上的椭圆
经过点
,
.
(1)求
的方程;
(2)已知点
,直线
与
交于
两点,且直线
的斜率之和为
,证明:点
在一条定抛物线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94718313450e8a66d1fd47728891375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c59b8c8470f9eb1d2686f5287991b59.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b671cdde6baf9ab577330696ca8ff121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4d9dc481eb068489c6fb35d47aadac.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/342ba1917a6b854ad111a3e6f5514934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808426112792e9a80a06f611b60827a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5445b4183917494ad8aa1731073dd1d5.png)
您最近一年使用:0次
2022-12-20更新
|
697次组卷
|
5卷引用:专题9-2 圆锥曲线(解答题)-2
2022高一·全国·专题练习
9 . 已知直线l,m,a,b,l⊥a,l⊥b,m⊥a,m⊥b,且a,b是异面直线,求证:l∥m.
您最近一年使用:0次
名校
解题方法
10 . 对于实数构成的集合
.若对任意
都有
(其中“
”表示普通的乘法运算),则称集合
对“
”是封闭的.
(1)已知集合
,判断
是否属于集合
;
(2)在(1)的条件下,若
,证明
的充要条件是
;
(3)若集合
对“
”都是封闭的,试判断
是否对“
”封闭,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8af42f2ec410ad1b28be69d3415ed10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9f1ff137e76626b7b608cef7c36349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50dae68b646f975a8a0c6bed67d028ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57ed82958abb00776e75987aa62d723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ecef225b27b5857d2d76fbe5b34982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff58fdfe14af9fb8aa0e0cf0d60853a.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a3375139541ed61929fa658f16bb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
您最近一年使用:0次