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 |
3.二项式
的展开式中
项的系数为
,则![](//static.xuejinqu.com/qimg/e65/e65a4d42f4173a1fd9e36d06559a8810.png)
![](http://static.xuejinqu.com/qimg/34d/34d322e7b176383e7ab9f5b3db1c5a97.png)
![](http://static.xuejinqu.com/qimg/38e/38e12495a9803e0983433d5d3ad74e4f.png)
![](http://static.xuejinqu.com/qimg/926/92684e59a59d4aa60052c68057e5eacc.png)
![](http://static.xuejinqu.com/qimg/e65/e65a4d42f4173a1fd9e36d06559a8810.png)
A.4 | B.5 | C.6 | D.7 |
4.一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.![]() |
5.“
”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 |
6.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.![]() |
7.根据右边的图,当输入
为
时,输出的
()
![](//static.xuejinqu.com/qimg/c98/c98ca8eee25f3d502612aa6021d0920e.png)
![](http://static.xuejinqu.com/qimg/da2/da265e00cbf55e43498c18027a4b6e6e.png)
![](http://static.xuejinqu.com/qimg/b98/b9823a96ed85f72a4b3ffbeb75c664bb.png)
![](http://static.xuejinqu.com/qimg/e49/e493228c0afa988f815b143b1ddbc711.png)
![](http://static.xuejinqu.com/qimg/c98/c98ca8eee25f3d502612aa6021d0920e.png)
A.28 | B.10 | C.4 | D.2 |
8.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.![]() |
9.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 |
10.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.![]() |
11.对二次函数
(
为非零整数),四位同学分别给出下列结论,其中有且仅有一个结
论是错误的,则错误的结论是( )
![](http://static.xuejinqu.com/qimg/10a/10a6cca0db30a8d9610a0de5f44a4bba.png)
![](http://static.xuejinqu.com/qimg/f7e/f7ebe3f1509f13bb46fb292fc2a3f596.png)
论是错误的,则错误的结论是( )
A.![]() ![]() | B.1是![]() |
C.3是![]() | D.点![]() ![]() |
12.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)
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.若抛物线
的准线经过双曲线
的一个焦点,则![](//static.xuejinqu.com/qimg/ae4/ae4b0b7766525d381b69be8e8158462b.png)
____ .
![](http://static.xuejinqu.com/qimg/61e/61e1fb55fbf8aac67fc7e52b435cce08.png)
![](http://static.xuejinqu.com/qimg/a78/a78abc7baac4d458ce645929cb63b6f3.png)
![](http://static.xuejinqu.com/qimg/ae4/ae4b0b7766525d381b69be8e8158462b.png)
15.设曲线
在点(0,1)处的切线与曲线
上点
处的切线垂直,则
的坐标为_____ .
![](http://static.xuejinqu.com/qimg/5a9/5a9e82071c7ea8404daf726942bc595d.png)
![](http://static.xuejinqu.com/qimg/d63/d63acb1e18d7b62412fd7ba2fee532d8.png)
![](http://static.xuejinqu.com/qimg/d26/d263896ae815d30257aa5ed6ddcba538.png)
![](http://static.xuejinqu.com/qimg/d26/d263896ae815d30257aa5ed6ddcba538.png)
16.如图,一横截面为等腰梯形的水渠,因泥沙沉积,导致水渠截面边界呈抛物线型(图中虚线表示),则原始的最大流量与当前最大流量的比值为 .![](//static.xuejinqu.com/qimg/a60/a605a9f344d4f9201602f209c8d5fc31.png)
![](http://static.xuejinqu.com/qimg/a60/a605a9f344d4f9201602f209c8d5fc31.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
,在直角梯形
中,
,
,
,
,
是
的中点,
是
与
的交点.将
沿
折起到
的位置,如图
.
![](//static.xuejinqu.com/qimg/d85/d8535c56e1eb7f6f9f8a4bf804591d64.png)
(Ⅰ)证明:
平面
;
(Ⅱ)若平面
平面
,求平面
与平面
夹角的余弦值.
![](http://static.xuejinqu.com/qimg/97e/97e788e326fae381e0bef6543e6725be.png)
![](http://static.xuejinqu.com/qimg/7b8/7b8de148e768015d3f298fc8c6a1889a.png)
![](http://static.xuejinqu.com/qimg/03c/03c9d40011ce6566aaf640021cb0b091.png)
![](http://static.xuejinqu.com/qimg/274/2747704495a015e6f8aaee2688eb0547.png)
![](http://static.xuejinqu.com/qimg/015/015403030fd8c77745f4be3eb6a9c642.png)
![](http://static.xuejinqu.com/qimg/04e/04eeb5a258fd9b36390f53cf03b14f94.png)
![](http://static.xuejinqu.com/qimg/235/23523c1f2bc71600e5ea2ad68fb5c403.png)
![](http://static.xuejinqu.com/qimg/153/153c787522ed20fb2d280477964f2707.png)
![](http://static.xuejinqu.com/qimg/3a6/3a69470786d39bfc6512d9786ab5d9eb.png)
![](http://static.xuejinqu.com/qimg/8fd/8fd1c5788f688f4d81b6c67230b4d6e3.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/b67/b67374e2c136273ed8da7f46f83069cf.png)
![](http://static.xuejinqu.com/qimg/d85/d8535c56e1eb7f6f9f8a4bf804591d64.png)
(Ⅰ)证明:
![](http://static.xuejinqu.com/qimg/48a/48a1a838b97caf434004ff871c83acee.png)
![](http://static.xuejinqu.com/qimg/fd1/fd17411687f99c761c864af673a229eb.png)
(Ⅱ)若平面
![](http://static.xuejinqu.com/qimg/05c/05c977e5df2f93c8f746fd107e5de5f5.png)
![](http://static.xuejinqu.com/qimg/240/240b493b0176a0432b888b3813350a1f.png)
![](http://static.xuejinqu.com/qimg/f8e/f8eeb395ab83bafce50b8d55ac298d06.png)
![](http://static.xuejinqu.com/qimg/80c/80cddd78991db7158f08e186dd6516e9.png)
19.设某校新、老校区之间开车单程所需时间为
,
只与道路畅通状况有关,对其容量为
的样本进行统计,结果如图:
(1)求
的分布列与数学期望
;
(2)刘教授驾车从老校区出发,前往新校区做一个50分钟的讲座,结束后立即返回老校区,求刘教授从离开老校区到返回老校区共用时间不超过120分钟的概率.
![](http://static.xuejinqu.com/qimg/fc6/fc6a68c7d0e39eea689f765ecc181798.png)
![](http://static.xuejinqu.com/qimg/fc6/fc6a68c7d0e39eea689f765ecc181798.png)
![](http://static.xuejinqu.com/qimg/5db/5dbd5db1e52e896ec0f4de5c312b3101.png)
![]() | 25 | 30 | 35 | 40 |
频数(次) | 20 | 30 | 40 | 10 |
(1)求
![](http://static.xuejinqu.com/qimg/fc6/fc6a68c7d0e39eea689f765ecc181798.png)
![](http://static.xuejinqu.com/qimg/bcf/bcfcae9b36fe19627224b08a5ba250c6.png)
(2)刘教授驾车从老校区出发,前往新校区做一个50分钟的讲座,结束后立即返回老校区,求刘教授从离开老校区到返回老校区共用时间不超过120分钟的概率.
20.已知椭圆![](//static.xuejinqu.com/qimg/bbf/bbf54684a982529a2d845d15e00ef00e.png)
(
)的半焦距为
,原点
到经过两点
,
的直线的距离为
.
(Ⅰ)求椭圆
的离心率;
(Ⅱ)如图,
是圆![](//static.xuejinqu.com/qimg/fcb/fcb770b7dbb76a299c9b9a3a0343b8e3.png)
的一条直径,若椭圆
经过
,
两点,求椭圆
的方程.
![](//static.xuejinqu.com/qimg/9bb/9bb3b1fb69fd6f3074c26e8384f968c5.png)
![](http://static.xuejinqu.com/qimg/bbf/bbf54684a982529a2d845d15e00ef00e.png)
![](http://static.xuejinqu.com/qimg/033/03383ee5a02958f47d0ec6ae0e75b956.png)
![](http://static.xuejinqu.com/qimg/805/805e31c3dadfeb762a8decddd598cef4.png)
![](http://static.xuejinqu.com/qimg/13b/13b65aca5584d6d8be9dcf7f42d84833.png)
![](http://static.xuejinqu.com/qimg/3a6/3a69470786d39bfc6512d9786ab5d9eb.png)
![](http://static.xuejinqu.com/qimg/290/290defe51578063033c61ab0852bc97b.png)
![](http://static.xuejinqu.com/qimg/0b9/0b98a836de43a29ba6e07d17209dbbaf.png)
![](http://static.xuejinqu.com/qimg/fc8/fc800bc6fb6da9a8f95fc4e02a7d9c35.png)
(Ⅰ)求椭圆
![](http://static.xuejinqu.com/qimg/235/23523c1f2bc71600e5ea2ad68fb5c403.png)
(Ⅱ)如图,
![](http://static.xuejinqu.com/qimg/637/637ce537f513fd734ce903b5c29085b1.png)
![](http://static.xuejinqu.com/qimg/fcb/fcb770b7dbb76a299c9b9a3a0343b8e3.png)
![](http://static.xuejinqu.com/qimg/d39/d39b54b599aa9d67c3ac43104429f0a3.png)
![](http://static.xuejinqu.com/qimg/235/23523c1f2bc71600e5ea2ad68fb5c403.png)
![](http://static.xuejinqu.com/qimg/192/1925ea47fbab6fa1f0a10e0e0aaaa3ed.png)
![](http://static.xuejinqu.com/qimg/1d7/1d7e8e7e18ba05c445bcc19dae1e9118.png)
![](http://static.xuejinqu.com/qimg/235/23523c1f2bc71600e5ea2ad68fb5c403.png)
![](http://static.xuejinqu.com/qimg/9bb/9bb3b1fb69fd6f3074c26e8384f968c5.png)
21.设
是等比数列
,
,
,
,
的各项和,其中
,
,
.
(Ⅰ)证明:函数
在
内有且仅有一个零点(记为
),且
;
(Ⅱ)设有一个与上述等比数列的首项、末项、项数分别相同的等差数列,其各项和为
,比较![](https:///quesimg/Upload/formula/8a8fee24d72a91f2156da24c3da74fb5.png)
与
的大小,并加以证明.
![](https:///quesimg/Upload/formula/8a8fee24d72a91f2156da24c3da74fb5.png)
![](https:///quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https:///quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https:///quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https:///quesimg/Upload/formula/2537b72c74ac9482d538480c7af1fc40.png)
![](https:///quesimg/Upload/formula/4e26f2235031a8d214d82a5e405db676.png)
![](https:///quesimg/Upload/formula/4f7fde71807463dbdfd8fce1655a5a9f.png)
![](https:///quesimg/Upload/formula/b4e0a78970d3a16704c80584773d8170.png)
![](https:///quesimg/Upload/formula/ece1cabeedc0da3de06bd8b7753cdf52.png)
(Ⅰ)证明:函数
![](https:///quesimg/Upload/formula/f2a0c1f7ff56ac025f75377db81da179.png)
![](https:///quesimg/Upload/formula/d1f4c4985f8a820372f1349f21f8dc31.png)
![](https:///quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https:///quesimg/Upload/formula/581fa6a48a154d3f6c63e2503d5e57b0.png)
(Ⅱ)设有一个与上述等比数列的首项、末项、项数分别相同的等差数列,其各项和为
![](https:///quesimg/Upload/formula/4ee81f297cfac6ef59ebe37ce43c8374.png)
![](https:///quesimg/Upload/formula/8a8fee24d72a91f2156da24c3da74fb5.png)
与
![](https:///quesimg/Upload/formula/4ee81f297cfac6ef59ebe37ce43c8374.png)
22.(本小题满分10分)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/661/661643b672276416c6e2a111b964a539.png)
(Ⅰ)证明:
;
(Ⅱ)若
,
,求
的直径.
如图,
![](http://static.xuejinqu.com/qimg/e81/e81253e2ddefb659d7d4e0fac01e1cfb.png)
![](http://static.xuejinqu.com/qimg/827/8272ce59629c444fa254bd6edb770ee9.png)
![](http://static.xuejinqu.com/qimg/822/822331bce458a26bc8a96bf3d248b5fb.png)
![](http://static.xuejinqu.com/qimg/f79/f799566ec86f7d7b77eee2b4ca2f2f52.png)
![](http://static.xuejinqu.com/qimg/827/8272ce59629c444fa254bd6edb770ee9.png)
![](http://static.xuejinqu.com/qimg/fb5/fb5e31d214652cc41341562ebef6f9b8.png)
![](http://static.xuejinqu.com/qimg/4d1/4d1602a25edbf3ffae9026c4d41163c6.png)
![](http://static.xuejinqu.com/qimg/de9/de990bc70e181979e7f7320cd5b64067.png)
![](http://static.xuejinqu.com/qimg/f0a/f0a9794add918e5857db9388bf33e6b1.png)
![](http://static.xuejinqu.com/qimg/661/661643b672276416c6e2a111b964a539.png)
(Ⅰ)证明:
![](http://static.xuejinqu.com/qimg/9d1/9d10ca9ea6fcb82beda4d59002bd62e4.png)
(Ⅱ)若
![](http://static.xuejinqu.com/qimg/f54/f54158649fc67c476138179cbe4abbbf.png)
![](http://static.xuejinqu.com/qimg/cac/cac889630e35164fd1ba3f622c89c966.png)
![](http://static.xuejinqu.com/qimg/827/8272ce59629c444fa254bd6edb770ee9.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)