1 . 有下列命题:
①抛物线
的准线方程为
;
②已知直线过两点
,
,则此直线的斜率是
;
③若方程
表示双曲线,则实数
的取值范围是
.
其中正确命题的序号为________ (把正确的答案都填上).
①抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db63cef6d8bbb08137d71c6f7b6e741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
②已知直线过两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedad6bb70631b944c69f8f0b02b35d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47153fdd73c0661fa460130082e30929.png)
③若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc5494f7d24f95a721555b85c84e8a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127aacea765b09f5110b3176493f0dd2.png)
其中正确命题的序号为
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2 . 已知点A为抛物线
上一点(点A在第一象限),点F为抛物线的焦点,准线为l,线段AF的中垂线交准线l于点D,交x轴于点E(D、E在AF的两侧),四边形
为菱形,若点P、Q分别在边DA、EA上,
,
,若
则
的最小值为______ ,
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08c14e87a2bcf7090eab2fea73667d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1074ae4cfaa6c7ab2eabe04bf97513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe7112901e241c4db02f538795d1b79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8b5ad14031c353573710741dc68549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bdbdec26c6aa6565eef79515056a036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ef5824baf830ec04377a49df11513c.png)
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名校
解题方法
3 . 如图,已知正方体
的棱长为2,M,N分别为
,
的中点.有下列结论:
在平面
上的正投影图为等腰三角形;
②直线
平面
;
③在棱BC上存在一点E,使得平面
平面
;
④若F为棱AB的中点,且三棱锥
的各顶点均在同一求面上,则该球的体积为
.
其中正确结论的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5697ef048e910e7b85ed6bac01056362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b808a8facf9af30cd8a083010a7b850d.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a40d8806b86572352ed08aa2b7f89f7.png)
③在棱BC上存在一点E,使得平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcadc521b53fabecc10ed30fe8d96c2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee5a94f9063a71581f409e47ebaf602.png)
④若F为棱AB的中点,且三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b5d7a90614288e46bebdb611e9bd23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefdcd39676298f214654051fc51ba92.png)
其中正确结论的个数是( )
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
2022-07-12更新
|
3214次组卷
|
12卷引用:天津市新四区示范校2022-2023学年高一下学期期末联考数学试题
天津市新四区示范校2022-2023学年高一下学期期末联考数学试题四川省成都市2023届高三上学期摸底考试文科数学试题四川省成都市2023届高三摸底测试理科数学试题安徽省宣城中学2023届高三原创模拟金卷(一)数学试题第一章 空间向量与立体几何单元测试(巅峰版)(已下线)第04讲 空间直线、平面的垂直 (讲)-1(已下线)考向25空间几何体的结构、三视图和直观图(重点)山西省运城市景胜中学2022-2023学年高二上学期9月月考数学(A)试题(已下线)考向26空间几何体的表面积与体积(重点)-2河南省南阳市第八中学校2022-2023学年高二上学期第一次线上考试(月考)数学试题广东省珠海市斗门区第一中学2022-2023学年高二上学期期中数学试题河南省周口市周口恒大中学2023-2024学年高二下学期5月月考数学试题
名校
4 . 2021年6月17日,神舟十二号载人飞船顺利升空并于6.5小时后与天和核心舱成功对接,这是中国航天史上的又一里程碑,我校南苍穹同学既是航天迷,又热爱数学,于是他为正在参加期末检测的你们编就了这道题目,如图,是神舟十二号飞船推进舱及其推进器的简化示意图,半径相等的圆
与圆柱
底面相切于
四点,且圆
与
与
与
与
分别外切,线段
为圆柱
的母线.点
为线段
中点,点
在线段
上,且
.已知圆柱
,底面半径为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/3/78e25f34-db50-45eb-82da-472097cfab1d.png?resizew=153)
![](https://img.xkw.com/dksih/QBM/2021/6/29/2753530368434176/2754982265675776/STEM/095b1cdbb79d4b85b5e8d416ecefceb9.png?resizew=257)
(1)求证:
平面
;
(2)线段
上是否存在一点
,使得
平面
若存在,请求出
的长,若不存在,请说明理由;
(3)求二面角
的余弦值;
(4)如图,是飞船推进舱与即将对接的天和核心舱的相对位置的简化示意图.天和核心舱为底面半径为2的圆柱
,它与飞船推进舱共轴,即
共线.核心舱体两侧伸展出太阳翼,其中三角形
为以
为斜边的等腰直角三角形,四边形
为矩形.已知推进舱与核心舱的距离为4,即
,且
,
.在对接过程中,核心舱相对于推进舱可能会相对作出逆时针旋转的运动,请你求出在舱体相对距离保持不变的情况下,在舱体相对旋转过程中,直线
与平面
所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedae9bc8fe49c3c98914f89a0670158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1ac49b4139636fb1809fe970b23a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46336351200396508fcc05fef6a26625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba671abb53449fe1012b8f5e017f5c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e430821d59f79d5aa0fc9934e240603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1ac49b4139636fb1809fe970b23a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf3e262887cd9bfad78cad43b979b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c4c2157cf374ebe6352715ef100471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47d2403519f528c80887ad7045b630c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b993fdfc49cb68be99ff1f04f71388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e980772d05dd94fafd77f69c20e6e882.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/3/78e25f34-db50-45eb-82da-472097cfab1d.png?resizew=153)
![](https://img.xkw.com/dksih/QBM/2021/6/29/2753530368434176/2754982265675776/STEM/095b1cdbb79d4b85b5e8d416ecefceb9.png?resizew=257)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaf581b4f42a25087f7eee23a7d66b6.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de7ea432599108b34a0ccaa0f2c75e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b131bc54bb464a496e79ada0c6a7cabd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f3fd3258a508a38c7616464cfb86e4.png)
(4)如图,是飞船推进舱与即将对接的天和核心舱的相对位置的简化示意图.天和核心舱为底面半径为2的圆柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3711953485a76de370a04756009a644a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeaf090a8dc4e381e3001c24473a0ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e046095eefc95b26511f64d1cb3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cce6cac0fdd4b1a434af8bcaec8fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134c3d2c318a33a82da4134dd17fa57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbf49977b753e293bdf415fccd91abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23be45176cc25e19752dc551147b02eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d2a5b65d9119ddd8649164ecde37ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134c3d2c318a33a82da4134dd17fa57e.png)
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