1 . 已知抛物线与双曲线
交于点T,两条曲线的公切线分别与抛物线、双曲线切于点P,Q.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5261a9730779339dc71818b9b6eff7.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5261a9730779339dc71818b9b6eff7.png)
A.理科男生多于文科女生 | B.文科女生多于文科男生 |
C.理科女生多于文科男生 | D.理科女生多于理科男生 |
3 . 为了了解高中学生课后自主学习数学时间(分钟/每天)和他们的数学成绩(
分)的关系,某实验小组做了调查,得到一些数据(表一).
表一
编号 | 1 | 2 | 3 | 4 | 5 |
学习时间 | 30 | 40 | 50 | 60 | 70 |
数学成绩 | 65 | 78 | 85 | 99 | 108 |
(1)请根据所给数据求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b343156cc2f05b714fd01aa61fb117d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea46c2c1af278afe8f7fb0bcc1ac2a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
(2)基于上述调查,某校提倡学生周末在校自主学习.经过一学期的实施后,抽样调查了220位学生.按照是否参与周未在校自主学习以及成绩是否有进步统计,得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
表二
没有进步 | 有进步 | 合计 | |
参与周末在校自主学习 | 35 | 130 | 165 |
未参与周末不在校自主学习 | 25 | 30 | 55 |
合计 | 60 | 160 | 220 |
附:,
,
.
0.10 | 0.05 | 0.010 | 0.005 | 0.001 | |
2.706 | 3.841 | 6.635 | 7.879 | 10.828 |
4 . 浙江省高考实行“七选三”选科模式,赋予了学生充分的自由选择权.甲、乙、丙三所学校分别有75%,60%,50%的学生选了物理,这三所学校的学生数之比为,现从这三所学校中随机选取一个学生,则这个学生选了物理的概率为
5 . 已知是定义域为
的函数
的导函数,
,
,
,
,则下列说法正确的是( )
A.![]() |
B.![]() ![]() ![]() |
C.存在![]() ![]() |
D.若![]() ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.![]() |
D.![]() |
7 . 已知等差数列中,
,公差为
,
,记
为数列
的前n项和,则下列说法正确的是( )
A.![]() |
B.![]() |
C.若![]() ![]() |
D.若![]() ![]() |
8 . 杭州第19届亚运会火炬9月14日在浙江台州传递,火炬传递路线以“和合台州活力城市”为主题,全长8公里.从和合公园出发,途经台州市图书馆、文化馆、体育中心等地标建筑.假设某段线路由甲、乙等6人传递,每人传递一棒,且甲不从乙手中接棒,乙不从甲手中接棒,则不同的传递方案共有( )
A.288种 | B.360种 | C.480种 | D.504种 |
9 . 机器人甲、乙分别在两个不透明的箱子中取球,甲先
箱子中取2个或3个小球放入
箱子,然后乙再从
箱子中取2个或3个小球放回
箱子,这样称为一个回合.已知甲从
箱子中取2个小球的概率为
,取3个小球的概率为
;乙从
箱子中取2个小球的概率为
,取3个小球的概率为
.现
两个箱子各有除颜色外其它都相同的6个小球,其中
箱子中有3个红球,3个白球;
箱子中有2个红球,4个白球.
(1)求第一个回合甲从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)求第一个回合后
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)两个回合后,用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342692a3b8e153aeb34f6445ec4aa9ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1325c6fe42a9e5c04520d8a9bb6821b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |