全一卷
1.设集合
,
,则
( )
![](http://static.xuejinqu.com/qimg/c0e/c0e37832879195211d96aec0c4e3ce02.png)
![](http://static.xuejinqu.com/qimg/1d3/1d36877ed51d35acafcb7f9fdcf2ee10.png)
![](http://static.xuejinqu.com/qimg/005/0050025e157fb4845d1b996985b7d710.png)
A.![]() | B.![]() | C.![]() | D.![]() |
2.某中学初中部共有110名教师,高中部共有150名教师,其性别比例如图所示,则该校女教师的人数为( )
![](https://img./dksih/QBM/2015/6/24/1572141016981504/1572141022371840/STEM/0784cd7f3c4f4b78ab9f0a1f11fc075b.png?resizew=302)
![](https://img./dksih/QBM/2015/6/24/1572141016981504/1572141022371840/STEM/0784cd7f3c4f4b78ab9f0a1f11fc075b.png?resizew=302)
A.167 | B.137 | C.123 | D.93 |
3.已知抛物线
的准线经过点
,则抛物线焦点坐标为
![](http://static.xuejinqu.com/qimg/61e/61e1fb55fbf8aac67fc7e52b435cce08.png)
![](http://static.xuejinqu.com/qimg/410/4105c48caba47935f28f72bb568293e9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
4.设
,则![](https:///quesimg/Upload/formula/ba34acf46158507f38e2271e3cd6fc9f.png)
![](https:///quesimg/Upload/formula/9ab37348e23ddefc98eef94f3cb2e231.png)
![](https:///quesimg/Upload/formula/ba34acf46158507f38e2271e3cd6fc9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
5.一个几何体的三视图如图所示,则该几何体的表面积为
![](https://img./dksih/QBM/editorImg/2023/10/7/d043faac-24c9-46dc-b177-db921a72d2c3.png?resizew=139)
A.![]() | B.![]() | C.![]() | D.![]() |
6.“
”是“
”的( )
![](https:///quesimg/Upload/formula/099baa4be0d87781c053cf59fe301ec9.png)
![](https:///quesimg/Upload/formula/ad99f286d557b3c400af3f220c7cfdbc.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充分必要条件 | D.既不充分也不必要条件 |
7.根据右边框图,当输入
为6时,输出的
()
![](//static.xuejinqu.com/qimg/210/210caaa7ac787b1d5594b4ccdd61a5aa.png)
![](http://static.xuejinqu.com/qimg/da2/da265e00cbf55e43498c18027a4b6e6e.png)
![](http://static.xuejinqu.com/qimg/e49/e493228c0afa988f815b143b1ddbc711.png)
![](http://static.xuejinqu.com/qimg/210/210caaa7ac787b1d5594b4ccdd61a5aa.png)
A.![]() | B.![]() | C.![]() | D.![]() |
8.对任意向量
,下列关系式中不恒成立的是
![](https:///quesimg/Upload/formula/c69613bda5b1face9751a8c13ae757ed.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
9.设
,则![](//static.xuejinqu.com/qimg/7d7/7d7ea35b75424b6b7f43ba114d63da35.png)
![](http://static.xuejinqu.com/qimg/abc/abc8f0e973e7916685c38ced3f586f2f.png)
![](http://static.xuejinqu.com/qimg/7d7/7d7ea35b75424b6b7f43ba114d63da35.png)
A.既是奇函数又是减函数 | B.既是奇函数又是增函数 |
C.是有零点的减函数 | D.是没有零点的奇函数 |
10.设
,若
,
,
,则下列关系式中正确的是
![](https:///quesimg/Upload/formula/3b17178d6ddc54592bf396563abecb24.png)
![](https:///quesimg/Upload/formula/2c6f3f534f21507e62dabcac5d406e88.png)
![](https:///quesimg/Upload/formula/aab374ac71c2fa12520694c5374cab5d.png)
![](https:///quesimg/Upload/formula/1f01a19dcd920df4b47fc4e24a66d7ed.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
11.某企业生产甲乙两种产品均需用A,B两种原料,已知生产1吨每种产品需原料及每天原料的可用限额如表所示,如果生产1吨甲、乙产品可获利润分别为3万元、4万元,则该企业每天可获得最大利润为()
![](//static.xuejinqu.com/qimg/02d/02d6db0b20d968af313ab0ea0bfbac12.png)
![](http://static.xuejinqu.com/qimg/02d/02d6db0b20d968af313ab0ea0bfbac12.png)
A.12万元 | B.16万元 | C.17万元 | D.18万元 |
12.设复数
,若
,则
的概率为( )
![](http://static.xuejinqu.com/qimg/a88/a883b9798736cb093008fa9023f26998.png)
![](http://static.xuejinqu.com/qimg/09c/09c11a33c01a79ae51c659d44c557999.png)
![](http://static.xuejinqu.com/qimg/9c3/9c3307f3cb18c367a5190af44e7eb6be.png)
A.![]() | B.![]() | C.![]() | D.![]() |
13.中位数为1010的一组数构成等差数列,其末项为 2015,则该数列的首项为__________ .
14.如图,某港口一天6时到18时的水深变化曲线近似满足函数y=3sin(
x+Φ)+k,据此函数可知,这段时间水深(单位:m)的最大值为____________.
![](https:///quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://img./dksih/QBM/editorImg/2023/8/17/1e81e220-3a10-4037-a598-f140c1b87e9a.png?resizew=273)
15.函数
在其极值点处的切线方程为____________ .
![](http://static.xuejinqu.com/qimg/169/1698ac676806861f1d67762099303358.png)
16.观察下列等式:
![](//static.xuejinqu.com/qimg/be8/be86d5181ec687216511681a93fa8b31.png)
据此规律,第
个等式可写为 ________.
![](http://static.xuejinqu.com/qimg/be8/be86d5181ec687216511681a93fa8b31.png)
据此规律,第
![](http://static.xuejinqu.com/qimg/9d8/9d892cfe6b2befe830ece30c103411c6.png)
17.
的内角
,
,
所对的边分别为
,
,
.向量
与
平行.
(Ⅰ)求
;
(Ⅱ)若
,
求
的面积.
![](https:///quesimg/Upload/formula/a84f69b4f8a9f2aae6f2fef17aa86995.png)
![](https:///quesimg/Upload/formula/0e2868b617c871e18c928c9a573bc8c7.png)
![](https:///quesimg/Upload/formula/49de2536004d4f0819e781fffca41a2a.png)
![](https:///quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https:///quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https:///quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https:///quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https:///quesimg/Upload/formula/6944379c49afaee22d84eb0060cdc328.png)
![](https:///quesimg/Upload/formula/f1723750667a365cb4ee3db227816044.png)
(Ⅰ)求
![](https:///quesimg/Upload/formula/0e2868b617c871e18c928c9a573bc8c7.png)
(Ⅱ)若
![](https:///quesimg/Upload/formula/783d6adfa8fb1352679c5185258d842a.png)
![](https:///quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https:///quesimg/Upload/formula/a84f69b4f8a9f2aae6f2fef17aa86995.png)
18.如图1,在直角梯形
中,![](//static.xuejinqu.com/qimg/e5f/e5f91bd3e3a9d2adc73d4a0ec2f42e3e.png)
,
是
的中点,
是
与
的交点,将
沿
折起到图2中
的位置,得到四棱锥
.
![](//static.xuejinqu.com/qimg/47c/47ce2a1143a2ce46aa44a1b62b03393a.png)
(Ⅰ)证明:
平面
;
(Ⅱ)当平面
平面
时,四棱锥
的体积为
,求
的值.
![](http://static.xuejinqu.com/qimg/84b/84b504d8c4c6b929d73e85789cc64078.png)
![](http://static.xuejinqu.com/qimg/e5f/e5f91bd3e3a9d2adc73d4a0ec2f42e3e.png)
![](http://static.xuejinqu.com/qimg/01f/01f3e55626a2e9bed6260628a7d6ebcd.png)
![](http://static.xuejinqu.com/qimg/235/23523c1f2bc71600e5ea2ad68fb5c403.png)
![](http://static.xuejinqu.com/qimg/4b3/4b3c1b3dc24c5986d0934fb86861be61.png)
![](http://static.xuejinqu.com/qimg/3a6/3a69470786d39bfc6512d9786ab5d9eb.png)
![](http://static.xuejinqu.com/qimg/747/74787b4807677fda6b8e4970b2888797.png)
![](http://static.xuejinqu.com/qimg/1ef/1ef33e70ed38498351ba8217287719d9.png)
![](http://static.xuejinqu.com/qimg/ca4/ca40fb92357a9ecc32242e71dfc3e182.png)
![](http://static.xuejinqu.com/qimg/1ef/1ef33e70ed38498351ba8217287719d9.png)
![](http://static.xuejinqu.com/qimg/5af/5af927740bde1e340381c88442e32390.png)
![](http://static.xuejinqu.com/qimg/155/155c7370fef677b060f550f31be749ef.png)
![](http://static.xuejinqu.com/qimg/47c/47ce2a1143a2ce46aa44a1b62b03393a.png)
(Ⅰ)证明:
![](http://static.xuejinqu.com/qimg/574/574c72c49b333dab20e85f79a81b51b8.png)
![](http://static.xuejinqu.com/qimg/913/913e19bfc820fdb6100dd62f4ab6318f.png)
(Ⅱ)当平面
![](http://static.xuejinqu.com/qimg/05c/05c977e5df2f93c8f746fd107e5de5f5.png)
![](http://static.xuejinqu.com/qimg/a25/a25b892ae886bb366909ec8dabd3f3be.png)
![](http://static.xuejinqu.com/qimg/155/155c7370fef677b060f550f31be749ef.png)
![](http://static.xuejinqu.com/qimg/735/7352fa8e6940609bd0e6b27baa8262c8.png)
![](http://static.xuejinqu.com/qimg/f5b/f5b715285b5e574c3962e74784fa9198.png)
19.随机抽取往年的一个年份,对西安市该年4月份的天气情况进行统计,结果如下:
(1)在今年4月份任取一天,估计西安市在该天不下雨的概率;
(2)西安市某学校拟从今年4月份的一个晴天开始举行连续两天的运动会,估计运动会期间不下雨的概率.
日期 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
天气 | 晴 | 雨 | 阴 | 阴 | 阴 | 雨 | 阴 | 晴 | 晴 | 晴 | 阴 | 晴 | 晴 | 晴 | 晴 |
日期 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
天气 | 晴 | 阴 | 雨 | 阴 | 阴 | 晴 | 阴 | 晴 | 晴 | 晴 | 阴 | 晴 | 晴 | 晴 | 雨 |
(1)在今年4月份任取一天,估计西安市在该天不下雨的概率;
(2)西安市某学校拟从今年4月份的一个晴天开始举行连续两天的运动会,估计运动会期间不下雨的概率.
20.如图,椭圆
经过点
,且离心率为
.
(I)求椭圆
的方程;
(II)经过点
,且斜率为
的直线与椭圆
交于不同两点
(均异于点
),
问:直线
与
的斜率之和是否为定值?若是,求出此定值;若否,说明理由.
![](https://img./dksih/QBM/editorImg/2023/4/17/0b3b7ac8-a21c-4aeb-b814-18c06a41b7be.png?resizew=173)
![](https:///quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https:///quesimg/Upload/formula/a6cffa52177f31cd10c42d00f69d4da1.png)
![](https:///quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(I)求椭圆
![](https:///quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(II)经过点
![](https:///quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https:///quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https:///quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https:///quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https:///quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
问:直线
![](https:///quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https:///quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://img./dksih/QBM/editorImg/2023/4/17/0b3b7ac8-a21c-4aeb-b814-18c06a41b7be.png?resizew=173)
21.设![](//static.xuejinqu.com/qimg/fb1/fb199de2ad1d7670a9bab77ddcc8cbbf.png)
(Ⅰ)求
;
(Ⅱ)证明:
在
内有且仅有一个零点(记为
),且
.
![](http://static.xuejinqu.com/qimg/fb1/fb199de2ad1d7670a9bab77ddcc8cbbf.png)
(Ⅰ)求
![](http://static.xuejinqu.com/qimg/e73/e73527f2f6d13d179500115f48e4e484.png)
(Ⅱ)证明:
![](http://static.xuejinqu.com/qimg/ee9/ee954046f250429355a67e03edf91b94.png)
![](http://static.xuejinqu.com/qimg/dc2/dc28985c04451520f00559203956c558.png)
![](http://static.xuejinqu.com/qimg/280/2800270f5cfd9276d9a473e4c03cb21c.png)
![](http://static.xuejinqu.com/qimg/8be/8be3ee3464f810292f4bd9aef90eb6db.png)
22.选修4-1:几何证明选讲
如图,
切
于点
,直线
交
于
两点,
垂足为
.
![](//static.xuejinqu.com/qimg/b67/b675e731d06168a8a4b5e9405779debb.png)
(Ⅰ)证明:![](//static.xuejinqu.com/qimg/1a6/1a6ac12f5407766100b5430854c76093.png)
(Ⅱ)若
,求
的直径.
如图,
![](http://static.xuejinqu.com/qimg/ef4/ef48d5225c41bc83e1fe326feacfa973.png)
![](http://static.xuejinqu.com/qimg/e28/e283e1f33808bcc6355ed3998ddb4177.png)
![](http://static.xuejinqu.com/qimg/7f4/7f4ba58e204b9831a2d04610deeb3622.png)
![](http://static.xuejinqu.com/qimg/d06/d066166df1ea2124a41d28e4b545b276.png)
![](http://static.xuejinqu.com/qimg/e28/e283e1f33808bcc6355ed3998ddb4177.png)
![](http://static.xuejinqu.com/qimg/6f3/6f3292fb1273fc0f4b0fd39c448c8357.png)
![](http://static.xuejinqu.com/qimg/634/63432c1860ebb498d2fcc56f372aae6a.png)
![](http://static.xuejinqu.com/qimg/d9f/d9fa9623df151ea3910896817b6e4bcb.png)
![](http://static.xuejinqu.com/qimg/b67/b675e731d06168a8a4b5e9405779debb.png)
(Ⅰ)证明:
![](http://static.xuejinqu.com/qimg/1a6/1a6ac12f5407766100b5430854c76093.png)
(Ⅱ)若
![](http://static.xuejinqu.com/qimg/8e9/8e94dd28ec6d409e72da4e5a3be11364.png)
![](http://static.xuejinqu.com/qimg/b22/b223edd3fec6169cc32de505bf88732d.png)
23.选修4-4:坐标系与参数方程
在直角坐标系
中,直线
的参数方程为
(
为参数).以原点为极点,
轴正半轴为极
轴建立极坐标系,
的极坐标方程为
.
(Ⅰ)写出
的直角坐标方程;
(Ⅱ)
为直线
上一动点,当
到圆心
的距离最小时,求
的直角坐标.
在直角坐标系
![](http://static.xuejinqu.com/qimg/8ff/8ff38d29a21f7832576cea75fc19a5fe.png)
![](http://static.xuejinqu.com/qimg/c4f/c4fbb49b23dba44a44f6ccbb846d9803.png)
![](http://static.xuejinqu.com/qimg/459/4598cb3b31104933b81f6ed790f849e1.png)
![](http://static.xuejinqu.com/qimg/c59/c5943327a7ad7c360da732e769acc000.png)
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
轴建立极坐标系,
![](http://static.xuejinqu.com/qimg/2ff/2ffcd2447bb8d0b821676b7ca85e2fc9.png)
![](http://static.xuejinqu.com/qimg/38b/38bc296cebf33b2f84eb7f92b004c585.png)
(Ⅰ)写出
![](http://static.xuejinqu.com/qimg/2ff/2ffcd2447bb8d0b821676b7ca85e2fc9.png)
(Ⅱ)
![](http://static.xuejinqu.com/qimg/4a4/4a4c4c651742957d49a9cc6ba6e28fd3.png)
![](http://static.xuejinqu.com/qimg/c4f/c4fbb49b23dba44a44f6ccbb846d9803.png)
![](http://static.xuejinqu.com/qimg/4a4/4a4c4c651742957d49a9cc6ba6e28fd3.png)
![](http://static.xuejinqu.com/qimg/0ac/0ac311f2889f0d3b77e75aa14f322e82.png)
![](http://static.xuejinqu.com/qimg/4a4/4a4c4c651742957d49a9cc6ba6e28fd3.png)
24.已知关于
的不等式
的解集为![](//static.xuejinqu.com/qimg/5c9/5c9a2d97687f4f5d421dc76cfacdf190.png)
(1)求实数
的值;
(2)求
的最大值.
![](http://static.xuejinqu.com/qimg/4cb/4cbd80f9610b2bfad04f39d54bf7eb64.png)
![](http://static.xuejinqu.com/qimg/223/223b7329ce949b3803031c75654d80e2.png)
![](http://static.xuejinqu.com/qimg/5c9/5c9a2d97687f4f5d421dc76cfacdf190.png)
(1)求实数
![](http://static.xuejinqu.com/qimg/988/988318a70f200324d3a5029fbe00711e.png)
(2)求
![](http://static.xuejinqu.com/qimg/084/084616a9e09da6e0a2d526d7438ce588.png)