1 . 设命题
:实数
满足
,其中
,命题
:实数
满足
.
(1)若
,且
和
都是真命题,求实数
的取值范围;
(2)若
是
的充分不必要条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50ec8e309669099d4ab475049b5ed36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f06cfe0871caa39a020a4e09a497c5c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 如图,一个酒杯的内壁的轴截面是抛物线的一部分,杯口宽
,杯深
,称为抛物线酒杯. 在杯内放入一个小的玻璃球,要使球触及酒杯底部,则玻璃球的半径的最大值为_____________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4de7cb50f975c3d9c82d1e71ccf8020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fb986e1a656aac2f6982351c4324ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72026e70f45cea6a7c49881592e73a02.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/a5f11f9e-4462-4209-a262-891a86ec9c00.png?resizew=241)
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名校
解题方法
3 . 已知抛物线
:
的焦点坐标为
,过点
的直线与抛物线相交于
,
两点,点
在抛物线上.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/fac92d87784b7fc23108b108a2ec413d.png)
A.![]() |
B.当![]() ![]() |
C.![]() |
D.若![]() ![]() ![]() |
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4 . 已知抛物线
(
)的准线为l,过抛物线上一点B向x轴作垂线,垂足恰好为抛物线C的焦点F,且
.
(1)求抛物线C的方程;
(2)设l与x轴的交点为A,过x轴上的一个定点
的直线m与抛物线C交于D,E两点.记直线
,
的斜率分别为
,若
,求直线m的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a4b3bddd48155c1e3eec7a8aea61588.png)
(1)求抛物线C的方程;
(2)设l与x轴的交点为A,过x轴上的一个定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7021efec959ee7f8c0405599e119b5.png)
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5 . 如图,在平面直角坐标系
中,抛物线C:
(
)与圆O的一个交点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/9/b568a608-559b-431b-9fc2-3fdd574b5c36.png?resizew=147)
(1)求抛物线C及圆O的方程;
(2)设直线l与圆O相切于点R,与抛物线C交于A,R两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20624370f8310a2da2f4e99f8f5a770.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/9/b568a608-559b-431b-9fc2-3fdd574b5c36.png?resizew=147)
(1)求抛物线C及圆O的方程;
(2)设直线l与圆O相切于点R,与抛物线C交于A,R两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b7fdcd237d89fd82b977ed60655ed2.png)
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6 . 已知椭圆
的焦点为
,点
在椭圆上且
,则点
到
轴的距离为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f642cc82f9cb94f68265b4ec78f8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cbe65ea2e3819776927f7378d35505.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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7 . 已知椭圆
的左右焦点分别为
,
,点B为短轴的一个端点,则
的周长为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b747db7eaf469c6d1607e4b0d028299f.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/47444b5fbc4252516d54263062e47c81.png)
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解题方法
8 . 如图,在长方体
中,E是
的中点,点F是AD上一点,
,
,
,动点P在上底面
上,且满足三棱锥
的体积等于1,则直线CP与
所成角的余弦值的最大值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cee0f36dc452e58086832c0152b641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90da0522dd9378bab25de2f560aec563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
您最近一年使用:0次
2024-02-04更新
|
487次组卷
|
5卷引用:黑龙江省哈尔滨市第一中学校2023-2024学年高二上学期期末考试数学试卷
黑龙江省哈尔滨市第一中学校2023-2024学年高二上学期期末考试数学试卷(已下线)第3章 空间向量及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)专题02 求空间角及空间向量的应用(三大类型)(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点8 空间范围与最值问题综合训练(已下线)高二 模块3 专题1 第4套 小题进阶提升练(苏教版)
名校
解题方法
9 . 已知点A,B分别为椭圆E:(
)的左、右顶点,点
,直线BP交E于点Q,
,且
是等腰直角三角形.
(1)求椭圆E的方程;
(2)设过点P的动直线l与E相交于M,N两点,当坐标原点O位于以MN为直径的圆外时,求直线l斜率的取值范围.
您最近一年使用:0次
10 . 已知椭圆
与双曲线
有相同的焦点为
,椭圆
的离心率为
,双曲线
的离心率为
,点
为椭圆
与双曲线
的交点,且
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8210484dd6815b5bebc7b22f1389cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62166e3ab8b16f12c27082d437fdbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d7f9f941778a83e4c38f872cc5ad1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800a29fd0142a45e478ceb501a1ed142.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次