解题方法
1 . 甲,乙,丙,丁四人相互做传球训练.每人控制球时都等可能将球传给其他三人.
(1)若先由甲控制球,记
次传球后球在甲手中的概率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e786c8ea893bfce791ca9c50eb51f9.png)
①求
的值;
②求
与
的关系,并求
;
(2)若丁临时有其他任务,甲,乙,丙继续训练.当甲控制球时,传给乙的概率为
,传给丙的概率为
;当乙控制球时,传给甲和丙的概率均为
;当丙控制球时,传给甲的概率为
,传给乙的概率为
.若先由甲控制球,经过3次传球后,乙控制球的次数为
,求
的分布列与期望
.
(1)若先由甲控制球,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e786c8ea893bfce791ca9c50eb51f9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7807638578edd712265463a7a5eab0.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(2)若丁临时有其他任务,甲,乙,丙继续训练.当甲控制球时,传给乙的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
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2 . 袋中有4个红球,
个黄球,
个绿球.所有球除颜色不同外,形状,大小,质量完全一样.现从中任取两个球,若取出的两个球都是红球的概率为
,记取出的红球数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d419c30ff40e9b368a3f151f639dac8f.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d419c30ff40e9b368a3f151f639dac8f.png)
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解题方法
3 . 若二项式
的展开式中,
的系数是80,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9752a8550ea456ac96754ba2c6b5cf.png)
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e190853d062125bd2df01b67bb64bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9752a8550ea456ac96754ba2c6b5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1677f099445a17d5b4a95e45adb43829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d6839b3487a9dea2b5b5a5e3ac34b9.png)
A.2 | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知
分别为椭圆
的左顶点和左焦点,直线
与椭圆交于
两点,若直线
交线段
于
,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8348c89c6f13053325f4e1c62e29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b9af8dcc33088cedc3fbefaab69970.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
5 . 已知函数
.
(1)当
时,求函数
的极值;
(2)求函数
的单调区间;
(3)当
时,若
在
时恒成立,求整数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a884c696e802c2962004fdf519482b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1749eb0942146be0ef6c0b39a33d8b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
6 . 已知函数
.
(1)求函数
的单调区间;
(2)若
恒成立,求实数
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff7978e698b20c3b12f2e9d3a00c47b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6卷引用:湖北省部分省级示范高中2023-2024学年高二下学期4月期中测试数学试题
湖北省部分省级示范高中2023-2024学年高二下学期4月期中测试数学试题2024届海南省省直辖县级行政单位琼海市高考模拟预测数学试题安徽省马鞍山市第二中学2023-2024学年高二下学期5月月考数学试题江苏省海安市实验中学等四校联考2023-2024学年高二下学期5月检测数学试题(已下线)第12题 分类讨论法讨论函数的单调性(高二期末每日一题)(已下线)专题09 导数与零点、不等式综合常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)
7 . 已知
,则
的大小关系正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b9b0319b04ffaed294f767ba89ae69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 任取一个正整数,若是奇数,就将该数乘3再加上1;若是偶数,就将该数除以2.反复进行上述两种运算,经过有限次步骤后,必进入循环圈
.这就是数学史上著名的“冰雹猜想”.比如取正整数
,根据上述运算法则得出
.递推关系如下:数列
满足
,若
,则
所有可能的取值集合是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a16f78ce0dab1ac8fa6abbd70f2b008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94174f37421d296a192b2df66c05f875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f51525b08db1b2b919c22b726c6aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9adb21335215c1ff3a870a1bad32c7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42aab89e67736c81f63af477d8990dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 从5名男生和4名女生中选出4人去参加2项创新大赛,每项至少有1人参加,且男生甲与女生乙参加同一项目,则不同的安排种数为( )
A.84 | B.126 | C.42 | D.63 |
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10 . 已知各项都不相等的等差数列
的前六项和为60,且
为
和
的等比中项.
(1)求数列
的通项公式及前n项和
;
(2)若数列
满足
,且
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc29ee719feeedfbc8c529cf11348abf.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9b4f764dcedeee11023817f5880b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4995fa0403e013d888c0935ebfe15024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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